Control of fuel cell Hybrid electric vehicle ( PDFDrive )

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<p>PED-project | 8th semester</p><p>Group P842 |Deadline: May 26rd 2010</p><p>Institute of Energy Tecnology</p><p>Pontoppidanstræde 101</p><p>DK - 9220 Aalborg</p><p>Control of fuel cell</p><p>Hybrid electric vehicle</p><p>I</p><p>Title: Control of Fuel Cell Hybrid Electric Vehicle</p><p>Semester: Power Electronics and Drive, 8. semester</p><p>Semester theme: Control in Converter-Fed AC Drives</p><p>Project period: 01.02.2010 to 26.05.2010</p><p>ECTS: 26</p><p>Supervisor: Torben Matzen</p><p>Project group: 842</p><p>__________________________</p><p>Fornella Luca</p><p>__________________________</p><p>Lanni Daniele</p><p>Number printed: 2</p><p>Numbers of pages: 160</p><p>Appendices: 8</p><p>By signing this document each member of the project group certify that</p><p>everybody have participated equal with work, and be jointly and severally liable</p><p>for the contents of the report.</p><p>SYNOPSIS:</p><p>The project treats how to control a PMSM</p><p>motor. It treats how we can implement this</p><p>motor on a vehicle. This is done mostly by</p><p>simulating different types of control</p><p>through the simulator of Matlab.</p><p>Furthermore we study a real case of open</p><p>loop implementation control. The control</p><p>of PMSM motors is made by a DSP.</p><p>II</p><p>Preface</p><p>This report documents a semester project completed by the student in group P101-842 at the 8th</p><p>semester of the PED education at the university of Aalborg.</p><p>This project concerns the modelling and the analysis of power system for the control of a PMSM</p><p>motor. The system consist of a electric machines the PMSM motor and an electronic power system</p><p>the inverter, and an electronic control system, the dsp, the sensor and the encoder.</p><p>Parallel with the project there have been given courses regarding power electronic and motor</p><p>control. The theory learned in these course have been put to use in the project</p><p>The report begins with a presentation of the main characteristics of a vehicle. Thereafter the main</p><p>report will be separated into three parts containing a part for study the component of hybrid vehicle</p><p>a part of modelling, and a part regarding the practical realization of the open loop control.</p><p>Material which has relevance for the project but does not belog inside the report is accompanied</p><p>either in paper format in the appendix of the report or on the appended CD. The CD contains</p><p>Simulink models, a PDF version of the reportand the data sheets used in the project.</p><p>At last the project group would like to thank to own supervisor and all the personnel at the</p><p>laboratories and workshop for their help for the realization of the project.</p><p>Group P101-842, May 2010</p><p>III</p><p>Contents</p><p>1 Problem Analysis and Project Approach……………………………………………… 1</p><p>1.1 Initial Problem…………………………………………………………………… 2</p><p>1.2 Problem Analysis………………………………………………………………… 3</p><p>1.2.1 Propulsion Engines Choice………………………………………………………. 3</p><p>1.2.2 Inverter Operating………………………………………………………………... 5</p><p>1.2.3 Recharge Battery Pack…………………………………………………………… 7</p><p>1.2.4 Ultra-Capacitor Use……………………………………………………………… 9</p><p>1.2.5 DSP Tasks……………………………………………………………………….. 10</p><p>1.3 Problem Formulation……………………………………………………………. 12</p><p>1.4 Project Strategy…………………………………………………………………... 13</p><p>2 Estimation HEV Traction System Drive………………………………………………. 15</p><p>2.1 Physical Relations for the HEV………………………………………………….. 16</p><p>2.1.1 Free Body Diagram………………………………………………………………. 16</p><p>2.2 Design Features…………………………………………………………………... 22</p><p>2.3 Propulsion Electrical Motors Choice…………………………………………….. 22</p><p>2.4 Estimation HEV Performance…………………………………………………… 24</p><p>2.5 HEV Motion Model Implementation……………………………………………. 26</p><p>2.6 Primary and Secondary Energy Sources Estimation……………………………. 29</p><p>2.6.1 Fuel Cell………………………………………………………………………….. 29</p><p>2.6.2 Battery……………………………………………………………………………. 31</p><p>2.6.3 Ultra-Capacitors…………………………………………………………………. 33</p><p>3 Drive Design, Control and Measurements for HEV………………………………… 35</p><p>3.1 General Operation for HEV Drive………………………………………………. 36</p><p>3.2 PEM Fuel Cell……………………………………………………………………. 40</p><p>3.3 Electric Schematic and Architecture for HEV…………………………………… 49</p><p>3.4 Operation for each Control and Measurement Device………………………….. 51</p><p>3.4.1 Digital Signal Processor…………………………………………………………. 51</p><p>3.4.1.1 DSP Common Structure………………………………………………... 52</p><p>3.4.1.2 Texas Instruments TMS320F28335 Peripherals………………………. 53</p><p>3.4.2 Encoder…………………………………………………………………………… 57</p><p>3.4.2.1 General Features………………………………………………………... 57</p><p>3.4.2.2 Encoder Structure………………………………………………………. 57</p><p>3.4.2.3 Incremental Encoder……………………………………………………. 60</p><p>3.4.2.4 Absolute Encoder………………………………………………………. 63</p><p>3.4.3 Voltage and Current Hall Effect Probe…………………………………………... 66</p><p>3.4.3.1 General Features………………………………………………………... 66</p><p>3.4.3.2 Current Probes………………………………………………………….. 68</p><p>3.4.3.3 Voltage Probes………………………………………………………….. 69</p><p>4 PMSM Modeling………………………………………………………………………… 70</p><p>4.1 PMSM Design Features………………………………………………………….. 71</p><p>4.2 IPMSM Electromechanical Model………………………………………………. 75</p><p>4.2.1 3-Phase Dynamic Model (abc fixed reference frame)…………………………… 75</p><p>4.2.1.1 State Form Model………………………………………………………. 77</p><p>4.2.1.2 Electromagnetic Torque Calculation…………………………………… 78</p><p>4.2.2 α-β Reference Frame Model……………………………………………………... 80</p><p>4.2.2.1 Clarke Transformation (abc → α-β transformation)…………………… 80</p><p>4.2.3 d-q Reference Frame Model……………………………………………………… 82</p><p>IV</p><p>4.2.3.1 Park Transformation (α-β → d-q transformation)…………………….. 82</p><p>4.3 Relation Synchronous Inductances-Stator Field Inductances- Phase Inductances. 86</p><p>4.4 IPMSM Equivalent Electric Circuit……………………………………………… 87</p><p>4.5 IPMSM Operating Conditions…………………………………………………… 88</p><p>5 IPMSM Control Strategy………………………………………………………………. 91</p><p>5.1 IPMSM Operating Domain Control…………………………………………….. 92</p><p>5.2 IPMSM Control Strategy Optimizations……………………………………….. 99</p><p>5.2.1 Maximum Torque per Ampere (MTPA)…………………………………………. 100</p><p>5.2.2 Field Weakening Control (FWC)………………………………………………… 104</p><p>5.2.3 Maximum Torque per Voltage (MTPV)………………………………………… 110</p><p>5.3 IPMSM Control Trajectory……………………………………………………… 112</p><p>5.4 IPMSM Demagnetization Limits………………………………………………… 116</p><p>6 IPMSM Control System Development………………………………………………… 120</p><p>6.1 Implementation of the IPMSM Mathematical Model……………………………. 121</p><p>6.1.1 IPM Motor Rated Values and Parameters……………………………………….. 124</p><p>6.1.2 IPM Motor Nominal Tests……………………………………………………….. 125</p><p>6.1.3 SVPWM-VSI…………………………………………………………………… 127</p><p>6.2 IPMSM Control System Realization…………………………………………… 127</p><p>6.2.1 Decoupling d-q Axis……………………………………………………………. 128</p><p>6.1.2 Current Loop Design……………………………………………………………. 130</p><p>6.2.2.1 Current PI Controllers Design………………………………………… 131</p><p>6.2.3 Torque Control………………………………………………………………….. 133</p><p>6.2.3.1 Non-Optimized Torque Control………………………………………. 134</p><p>6.2.3.2 MTPA Control…………………………………………………………. 136</p><p>6.2.4 Speed Loop Control and Design………………………………………………… 139</p><p>6.2.4.1 FWC Strategy …………………………………………………………. 140</p><p>7 IPMSM Drive System Realization …………………………………………………… 144</p><p>7.1 Instrumentation and Configuration System…………………………………….. 145</p><p>7.2 PWM Generation………………………………………………………………… 147</p><p>7.3 Currents Measurement…………………………………………………………… 149</p><p>7.4 Encoder Measurement…………………………………………………………… 151</p><p>7.5 IPMSM Open Loop Control……………………………………………………… 152</p><p>8 Conclusion…………………………..…………………………………………………… 157</p><p>8.1 The project put into perspective …………..…………………………………….. 158</p><p>Bibliography…………………………………………………………………………………… 159</p><p>Appendix</p><p>Data sheet for LEM LA 100 p/ SP 13</p><p>Data sheet for Encoder Waycon A36</p><p>V</p><p>Introduction</p><p>The objectives of this 8th semester PED project are in accordance with the study programme:</p><p>• To gain understanding for design and digital implementation of control algorithms of a</p><p>transmission system containing an PMSM-motor.</p><p>• To be able to use power electronics in connection with electrical actuators</p><p>device</p><p>on the DC Bus without damage it. Besides is necessary to have the possibility to invert the current flow</p><p>when the HEV is starting-up, to support the PEM FC. For these reasons the DC/DC Buck-Boost Converter</p><p>must work necessarily for two quadrant (V,I and V-I). Otherwise discussed for the DC/DC Step-up</p><p>Converter, the switching frequency for T1 and T2 could be different in according with the different recharge</p><p>status in the V,I operating region, so obtaining always the maximum power from the DC Bus and minimizing</p><p>the losses (MPPT Algorithm).</p><p>The PMSM Control is realized with an Inverter. The Inverter will work like a Rectifier when the HEV needs to</p><p>recharge the Battery pack from the Grid. Indeed the PMSM used has six terminals to change the</p><p>connections when the charging is required.</p><p>50</p><p>Figure 3.20 – Basic Electric Circuit for HEV Drive System</p><p>51</p><p>3.4 Operation for each Control and Measurement Device</p><p>In the HEV Control System there are a lot of devices whose operation and characteristics are very important</p><p>to better understand the behavior of the Electrical Drive aboard. In the following analysis will be treated</p><p>the general issues for each measuring and control component, their advantages and functionality,</p><p>evaluating every type of problem occurred for these applications.</p><p>3.4.1 Digital Signal Processor</p><p>The Digital Signal Processor (term literally means "digital signal processor”, the acronym DSP) is a</p><p>microprocessor optimized to run in mode extremely efficient a sequences of instructions (such as sums,</p><p>multiplications and translations) of digital signals. The DSP uses a set of techniques, technologies,</p><p>algorithms that can process a continuous signal after it has been sampled, that is the operation that</p><p>convert an analog signal in a digital signal.</p><p>The origin of the DSP back to the sixties and seventies when the first digital computers became available.</p><p>Today in fact there are processors software (applications) that allow you to analyze and modify various</p><p>types of signals by mathematical functions (most used the FFT - Fast Fourier transformer). Used in various</p><p>fields of science for the following purposes: image enhancement, speech recognition and generation, data</p><p>compression, motor control, and in the industry in general. The applications are numerous since almost all</p><p>analog signals are converted to digital.</p><p>The first monolithic DSP launched in the market in 1978 was the Intel 2920 with Alu without multiplier and</p><p>Harvard architecture VLIW (Very Long Instruction Word) 24-bit EPROM stored at 192 locations, an area of</p><p>RAM of 40 words from 25 bit and ADC and DAC interfaces on board. Their speed was 2.5 MIPS at the time a</p><p>high speed.</p><p>DSP are classified in function of the length, 16, 24, 32, 64 bit and the type of data fixed or floating point,</p><p>that are able to process.</p><p>Each DSP is therefore suitable for specific applications: for example, DSP 16-bit fixed-point are used for</p><p>packaging of voice signals and find their main field of application in telephony (fixed and mobile), while the</p><p>DSP 32 -bit floating point, having a much more dynamic, are mainly used in image processing and three-</p><p>dimensional graphics.</p><p>THE DSP are characterized by performance indices: MIPS If we are considering fixed point, MFLOP if we are</p><p>considering floating point DSP.</p><p>52</p><p>Figure 3.21 – Main Features of DSP TMS320 Family [Texas Instrument]</p><p>3.4.1.1 DSP Common Structure</p><p>A typical DSP Structure (Figure 3.22) is composed by:</p><p>• One or more arithmetic logic unit (ALU) which have the task to perform simple mathematical</p><p>operations such as sums and products;</p><p>• A memory where is stored program code to be executed;</p><p>• A memory where is stored data;</p><p>• An external memory when the application needed;</p><p>• Devices that allow interactions with external interfaces;</p><p>• One or more bus that allow the communication between ALUs, memories and peripherals.</p><p>Figure 3.22 – General DSP Structure [Texas Instrument]</p><p>The internal structure of elaboration in the DSP is Harvard. This type of structure has as main characteristic</p><p>to use two types of separate memories, one for storing program code, and the other used to store data,</p><p>like is possible to see from the Figure 3.23.</p><p>53</p><p>Figure 3.23 – Harvard DSP Internal Structure [Wikipedia 2010]</p><p>3.4.1.2 Texas Instruments TMS320F28335 Peripherals</p><p>The type of DSP that it has been chosen for the Project is Texas Instrument TMS320F28335. All the</p><p>following peripheral descriptions have like reference the Texas Instrument TMS320F28335 Datasheet.</p><p>C28x CPU</p><p>The F2833x/F2823x (C28x+FPU) family is a member of the TMS320C2000™ digital signal controller (DSC)</p><p>platform. The C28x+FPU based controllers have the same 32-bit fixed-point architecture as TI's existing</p><p>C28x DSCs , but also include a single-precision (32-bit) IEEE 754 floating-point unit (FPU). It is average</p><p>efficient C/C++ engine, enabling users to develop their system control software in a high-level language. It</p><p>also enables math algorithms to be developed using C/C++. The device is as efficient at DSP math tasks as it</p><p>is at system control tasks that typically are handled by microcontroller devices. This efficiency removes the</p><p>need for a second processor in many systems. The 32 x 32-bit MAC 64-bit processing capabilities enable the</p><p>controller to handle higher numerical resolution problems efficiently. Add to this the fast interrupt</p><p>response with automatic context save of critical registers, resulting in a device that is capable of servicing</p><p>many asynchronous events with minimal latency. The device has an 8-level-deep protected pipeline with</p><p>pipelined memory accesses. This pipelining enables it to execute at high speeds without resorting to</p><p>expensive high-speed memories. Special branch-look-ahead hardware minimizes the latency for conditional</p><p>discontinuities. Special store conditional operations further improve performance.</p><p>Memory Bus (Harvard Bus Architecture)</p><p>As with many DSC type devices, multiple busses are used to move data between the memories and</p><p>peripherals and the CPU. The C28x memory bus architecture contains a program read bus, data read bus</p><p>and data write bus. The program read bus consists of 22 address lines and 32 data lines. The data read and</p><p>write busses consist of 32 address lines and 32 data lines each. The 32-bit-wide data busses enable single</p><p>cycle 32-bit operations. The multiple bus architecture, commonly termed Harvard Bus, enables the C28x to</p><p>54</p><p>fetch an instruction, read a data value and write a data value in a single cycle. All peripherals and memories</p><p>attached to the memory bus will prioritize memory accesses. Generally, the priority of memory bus</p><p>accesses can be summarized as follows:</p><p>Highest:</p><p>Data Writes (Simultaneous data and program writes cannot occur on the memory bus.)</p><p>Program Writes (Simultaneous data and program writes cannot occur on the memory bus.)</p><p>Data Reads Program (Simultaneous program reads and fetches cannot occur on the Reads memory bus.)</p><p>Lowest:</p><p>Fetches (Simultaneous program reads and fetches cannot occur on the memory bus.)</p><p>Peripheral Bus</p><p>To enable migration of peripherals between various Texas Instruments (TI) DSC family of devices, the</p><p>2833x/2823x devices adopt a peripheral bus standard for peripheral interconnect. The peripheral bus</p><p>bridge multiplexes the various busses that make up the processor Memory Bus into a single bus consisting</p><p>of 16 address lines and 16 or 32 data lines and associated control signals. Three versions of the peripheral</p><p>bus are supported. One version supports only 16-bit accesses (called peripheral frame 2).</p><p>Another version supports both 16- and 32-bit accesses (called peripheral frame 1). The third version</p><p>supports DMA access and both 16- and 32-bit accesses (called peripheral frame 3).</p><p>The main features are:</p><p>• High-Performance Static CMOS</p><p>Technology</p><p>– Up to 150 MHz (6.67-ns Cycle Time)</p><p>– 1.9-V/1.8 -V Core, 3.3-V I/O Design</p><p>• High-Performance 32-Bit CPU (TMS320C28x)</p><p>– IEEE-754 Single-Precision Floating-Point Unit (FPU) (F2833x only)</p><p>– Code-Efficient (in C/C++ and Assembly)</p><p>– Harvard Bus Architecture</p><p>– Fast Interrupt Response and Processing</p><p>• On-Chip Memory</p><p>– F28335/F28235: 256K x 16 Flash, 34K x 16 SARAM</p><p>• Enhanced Control Peripherals</p><p>55</p><p>– Up to 18 PWM Outputs</p><p>– Up to 2 Quadrature Encoder Interfaces</p><p>• 12-Bit ADC, 16 Channels</p><p>– 80-ns Conversion Rate</p><p>• Temperature Options:</p><p>– A: –40°C to 85°C (PGF, ZHH, ZJZ)</p><p>56</p><p>Figure 3.24 – Functional Block Diagram of the DSP TMS320F28335 [Texas Instrument]</p><p>57</p><p>3.4.2 Encoder</p><p>3.4.2.1 General Features</p><p>An encoder is essentially a linear or angular position transducer of electromechanical type, able to provide</p><p>as a value output an electrical signal, analog or in digital form. Depending that the position is determined</p><p>using an angular measurement system (through shaft coupling device) or linearly measurement system (for</p><p>example in a bar or through appropriate optical coupling gear rack /line) we refer to linear or rotary</p><p>encoder.</p><p>The encoder is a device that transforms a mechanical movement in a size of different nature that is always</p><p>a voltage or a current depending by the output interface integrated into the encoder itself. We define the</p><p>ENCODING such the transformation of mechanical motion which implements the rotation of encoder in</p><p>digital or analog values.</p><p>The encoding process is of discrete type (quantized) that is the encoder shaft position is detected in</p><p>discrete steps defined by the encoder resolution. Depending on the types of encoders, they can have</p><p>resolutions from minimum of 1 pulse/rev up to 360,000 pulses/rev. The encoder resolution defines</p><p>therefore the maximum achievable precision on the measure of angle turn. The world of the encoder is</p><p>generally divided into two broad type:</p><p>• Incremental Encoder</p><p>• Absolute Encoder (single-turn / multi-turn, programmable)</p><p>The operating principle upon which every family work is the same, but the position information is showed</p><p>to the user in two different ways. In the case of incremental encoder there is an pulse sequence rectangular</p><p>or sine wave) that represents the transition from a position to another immediately adjacent in according</p><p>to the encoder resolution. In the case of absolute encoders the output is a string of bits, which represented</p><p>in uniquely mode the position of encoder, in addition, this position is held (memory) also if encoder turn</p><p>off, this is the main feature between the two types of encoders.</p><p>3.4.2.2 Encoder Structure</p><p>The physical system that implements the mechanical-electrical conversion is made up of by the following</p><p>components:</p><p>• LED emitter</p><p>• Disk + collimator (also called reticle)</p><p>• Receiver system</p><p>58</p><p>• Signal Conditioning</p><p>• Output Interface</p><p>In the case of rotary encoders, the method typically used for generate pulses is modulating in correct mode</p><p>a beam of light emitted by a diode LED (typically in GaAsAl) detect the modulated light through a device</p><p>photosensitive, which may be a photodiode or a phototransistor. To modulate the light synchronously with</p><p>the movement of the encoder shaft using a disc of plastic, metal or glass on which are recorded one or</p><p>more concentric circular crowns by different techniques described below, divided each in a number of</p><p>areas of alternating light and dark together, see for example Figure 3.25 which shows a possible example</p><p>of incremental disk of 15 pulse/turn.</p><p>The modulated light from the disk, in case of high resolutions, is still filtered through a collimator placed</p><p>close to the receiving system to give the system a better quality of the light signal to be transduced.</p><p>Figure 3.25 – Example of Incremental Encoder [Omron]</p><p>The light generated by the diode emitter is then interrupted by the holes that are created on disk surface,</p><p>filtered by the collimator and finally detect by the receiving system that implementing optical-electrical</p><p>conversion. Because the light, that generate by the LED has an emission stationary in time, is modulated by</p><p>the rotation of the disk, and the receiver get light pulses with frequency equal to:</p><p>= = >�?.@�4A.2</p><p>B�</p><p>��. E. F. � (3.10)</p><p>The (3.10) is basic relationship that allows estimation the maximum frequency of signals output from a</p><p>generic encoder in function of the number of turns, expressed per minute. The receiving system, depending</p><p>on the encoder resolution, is defined two different type:</p><p>59</p><p>• Single receiver</p><p>• Double- receiver or differential</p><p>The technique of reading with double receiver, also called differential reading, using two receivers channel</p><p>allows for benefits in terms of stability of the output signal and frequency response, substantially better</p><p>than the single receiver. This technique also is good because get a greater immunity of the output signal to</p><p>variations in supply voltage, making this technique ideal in electrically hostile systems (for example in the</p><p>case of the position of engines). It has also increased robustness of the reading system to variation of</p><p>parameters caused by temperature and aging of optoelectronic components.</p><p>The signals detected by the receiving system (differential or single type) can be send immediately to the</p><p>output stage or square and send to the interface output. In the first case we call of sinusoidal output</p><p>encoder in second case, we call of square wave output. The rectangular wave signal is obtain by using a</p><p>squaring circuit known classically triggers Schmitt, capable of providing immunity to signal by mechanical</p><p>disturbances, vibration, undesirable shaft encoder superimposed on normal move rotary detected and</p><p>transduced by encoder. The rectangular signal generated in output has always duty cycle of 50%, this for</p><p>ensure maximum immunity to interference on the signals produced from the encoder.</p><p>The encoder disk can be constructed using materials of following type:</p><p>• Plastic</p><p>• Glass</p><p>• Metal</p><p>The disk in plastic has the following characteristics:</p><p>• Unbreakable (resistant to mechanical stress such as shock and vibration);</p><p>• operating temperature medium / high;</p><p>• Resolutions medium / low;</p><p>• Low cost.</p><p>The disk glass instead has the following properties:</p><p>• Delicate, not suitable in mechanically hostile environments;</p><p>• Suitable for high temperature;</p><p>• High resolution;</p><p>• High cost.</p><p>60</p><p>Finally, the metal disk is used for low resolutions, and generally less than 100 pulse turn and have low cost.</p><p>The choice of using the different type of disc are determinate by two factors:</p><p>• disc size and its resolution;</p><p>• precision photo etching process.</p><p>In the case of the plastic disk is deposited the emulsion and is exposed to UV polymerizing the regions of</p><p>interest, this is essentially similar to a normal photographic development. In the case of glass disks, start by</p><p>a plate of glass on which is create a uniform layer of metal (e.g. chromium), by metal deposition. After</p><p>create the holes in the disk by evaporation of metal or by electrograph (there is essentially a selective</p><p>removal process similar to that used in the manufacture of integrated circuit).</p><p>The process on glass disks allows to have a holes with a minimum width of 2 μm against 10 μm obtained by</p><p>the photographic process on plastic disk, also in the case of glass disks the holes have a better definition</p><p>(straight lines) for this reason this is the only process adopting for create disk for high resolution.</p><p>Than for increasing resolution, is possible choice two different paths: working with the same holes width</p><p>and increasing the diameter of the disc</p><p>and then the final size of the encoder, or reduce the width of the</p><p>holes, passing, if necessary, from plastic disk to glass disk.</p><p>The choice of type of material of the disk, must be made also in function of the work condition, indeed a</p><p>glass disk requiring greater care and less stress of a plastic disk.</p><p>This considerations leads to the conclusion that the choice of a type of encoder rather than another should</p><p>not be made solely considering the resolution, but also considering some boundary conditions of specific</p><p>application and the environment Electrical / Mechanical in which the encoder will be operating.</p><p>3.4.2.3 Incremental Encoder</p><p>The family of incremental encoders is most present on the market. When the encoder shaft is rotated by an</p><p>angle equal to:</p><p>G = HB�</p><p>I∙>�?.@�4A.2</p><p>�KLMNLL� (3.11)</p><p>The encoder generates on output an pulse (rectangular or sinusoidal) of voltage with variable amplitude,</p><p>depending by the model of encoder considered (in particularly by the type of electronic output).</p><p>61</p><p>To understand the origin of (3.11) consider for example the disk shown in Figure 3.25, from this can be</p><p>seen as for obtain a resolution of 15 pulses per turn is necessary have 30 have divisions (between light and</p><p>dark holes) draw on surface of the disc, from what we understand the presence of the coefficient of 2 in</p><p>this denominator of (3.11). Because an incremental encoder is designed to detect an angular position or</p><p>rotational speed of a shaft, it is have on output an signal of rectangular pulses with frequency f expressed</p><p>by (3.10). This is called one-way encoder.</p><p>Having only one signal is not possible to discern the direction of rotation encoder, in fact whether it rotates</p><p>clockwise or counterclockwise at every elementary step the encoder generate a single pulse.</p><p>To determine the direction of motion requires two signals, with a phase shift between the two signals of</p><p>90°. In that case, going to read both signals simultaneously, it is easy to see if it's clockwise rotation</p><p>or counterclockwise. This is called a bi-directional encoder.</p><p>Figure 3.26 – Incremental Encoder Clock-wise Rotation [Omron]</p><p>Figure 3.27 – Incremental Encoder Anticlock-wise Rotation [Omron]</p><p>The incremental encoder, by its nature, detects the difference between two successive positions providing</p><p>a number of pulses equal to the increase occurred from the initial position to the final. It follows an</p><p>inherent inability to distinguish between absolute angular values, in other words to equal number of pulses</p><p>generated may correspond to different angular positions. To help the user is generate by encoder a</p><p>reference signal through which (through PLC) get a absolute information on the angle position. The signal in</p><p>question, is generated in addition to the two channels mentioned above, and is called synchronous</p><p>Channel Zero (CHZ). The zero signal has an impulse every complete turn, with three different mode:</p><p>62</p><p>• In sync with the channel (width 180 ° electrical);</p><p>• synchronized with the B channel (width 180 ° electrical);</p><p>• Synchronized with A & B (width 90 ° electrical).</p><p>The timing synchronization is shown in the Figure 3.28</p><p>Figure 3.28 – Output Signal for a Incremental Encoder, Clock Rotation [Omron]</p><p>The resolution of an incremental encoder can be easily increased by using the electronic multiplication</p><p>technique, which provides substantially multiplies x2 x4 the basic resolution. This system is based on the</p><p>use of rising or falling edge on one or both channels encoder output. Disadvantage is that the duty-cycle</p><p>signals in same case is different to 50%. Multiplication for x2 is obtained considering the rising edges and</p><p>falling edges of one of the two channel for each front and generating a pulse of fixed duration (about half</p><p>of the period of the maximum frequency that we want to create). Another way used to achieve 2x</p><p>multiplier is to perform by the XOR of two channels, so it has the form wave shown in Figure 3.29 in which,</p><p>as noted, the duty cycle is still 50%. In the case of multiply x4 you must generate a pulse for each rising and</p><p>falling edge present on both channels. The output signals generate with two techniques are visible in the</p><p>Figures 3.29 and 3.30.</p><p>63</p><p>Figure 3.29 - Electronics multiplication X2 of signal by XOR operation between two channels</p><p>[Omron]</p><p>Figure 3.30 - Electronics multiplication X4, duty cycle different to 50 % [Omron]</p><p>This technique makes insensible the encoder to the direction of rotary, and is necessary providing the</p><p>encoder of a signal for the direction of rotation.</p><p>3.4.2.4 Absolute Encoder</p><p>Regarding the optical system and electronics output is substantially similar to the incremental models, the</p><p>essential difference occurs in the disc design and in the mode with transmit the data. An absolute encoder</p><p>always remembers the location of the shaft whether that the encoder is supply or is turn off. Because,</p><p>instead of having on the disk a simple lattice at each channel has a number of holes arranged in mode to</p><p>provide in output a numeric, or analog code univocal in function of the position of the shaft. An example of</p><p>a disk is shown in Figure 3.31</p><p>64</p><p>Figure 3.31 - Example of disc for absolute encoder with implement of Gray Code at 4 bit</p><p>[Omron]</p><p>The arrangement of holes allows the formation of a numerical code whose value depends by the position of</p><p>the shaft. To assign to each angular position a unique numeric value there are different possibilities, but all</p><p>are based on the fact that the signals detected by the reading system can take only two levels "0" and "1".</p><p>For this reason is defines a coding system to the base 2 or binary, for which are possible only two digits 0</p><p>and 1 in particular. The first code that could be used is the natural binary code, this way to implement the</p><p>code on disk includes a number of problems when reading the code same. These problems are associated</p><p>with ambiguities that arise at the switching sides. It possible understands this noting that in the code</p><p>between two adjacent codes is possible that changes the state in more of one bit. Because the system</p><p>cannot adapt To avoid this situations use other types of codes that, for their nature, provide in the passage</p><p>between adjacent codes, to change the status of only a single bit. This will eliminate ambiguities of reading</p><p>making the system more stable. One of these types of codes is the Gray code, Gray excess 3, Gray</p><p>truncated in the center, that can be used as an alternative to the binary and BCD respectively. If instead it</p><p>requires that the output of encoder is in binary code within the encoder implements a Gray-Binary</p><p>conversion giving to the user two different systems of data acquisition:</p><p>• by signal STROBE</p><p>• by signal LATCH</p><p>The STROBE is generated from the encoder whenever it have a valid data output. The LATCH instead is</p><p>given by the user and causes the freezing of output data encoder, when given the command and waited a</p><p>sufficient time to do stabilize the output data is possible reading the output.</p><p>In the market there are two type of absolute encoders:</p><p>65</p><p>•Single turn</p><p>• Multi-turn</p><p>The single-turn absolute encoders are composed of a single disk, said main disk, which contain all the</p><p>information needed to develop the code for the resolution desired.</p><p>The encoders multi-turn are instead made by a disk called main disk and a series of disks, usually smaller of</p><p>the main, called satellites. For each turn of the main disk, the satellites moving of a fraction of angle in</p><p>relation to the type of multiply desired.</p><p>There are different techniques of assembly, the most common for encoder with protruding shaft are:</p><p>• Servo mounting (hole service side on the shaft).</p><p>• Mounting</p><p>clamps (allows the orientation of the encoder).</p><p>• Servo mounting clamps (combination of the two previous modes).</p><p>• Square flange.</p><p>• REO flange 444.</p><p>• hybrid systems</p><p>In the case of hollow shaft encoders (blind or through) there are the following options:</p><p>• Grains of fixing.</p><p>• Collar mounting.</p><p>• Clamp the spindle.</p><p>In the case of encoder with protruding shaft does not have specific instructions if not use a flexible</p><p>coupling, to better withstand high pulses stress on the shaft of the encoder, and in the case should be</p><p>offset thermal expansion of materials (important in the case of glass disks) or is required a coupling</p><p>between shaft of different diameters. In any case the system should not be a rigid system. In the case of</p><p>encoder with hollow shaft, the situation is different and presents more problems.</p><p>Hollow shaft encoder are characterized by the game, always present, between the shaft on that want to</p><p>detect the position and the hallow shaft of encoder. This game causes an eccentricity between these two</p><p>entities generating mechanical vibrations that are transmitted to the reading system and in particular to</p><p>66</p><p>the encoder disk, causing a increased jitter superimposed on the output signals (minimization by adopting</p><p>the technique differential reading).</p><p>3.4.3 Voltage and Current Hall Effect Probe</p><p>3.4.3.1 General Features</p><p>In physics, the Hall effect is the formation of a potential difference (Hall potential) on opposite sides of the</p><p>electrical conductor due to a magnetic field perpendicular to the electric current flowing in it. In the Figure</p><p>3.32 are shown the basic operating principles for the Hall Effect Probe.</p><p>Figure 3.32 - Basic operating principles for the Hall Effect Probe [Wikipedia 2010]</p><p>The Hall element is formed by a strip of conductive material, usually a metal conductor or a semiconductor.</p><p>Fitness is used a strip because we consider only two dimensions, the thickness is negligible respect the</p><p>other two. In this material is made to run a current by applying a voltage across it. In conductors, electrons</p><p>move from negative to positive pole. We use a magnet creates a magnetic field directed from north to</p><p>south pole of the magnet. The Hall element is immersed in this magnetic field.</p><p>The conduction electrons that move, and therefore have a velocity, are affected by the magnetic field:</p><p>upon them the Lorentz force act:</p><p>O = PQORSTO (3.12)</p><p>67</p><p>where:</p><p>q is the electron charge equal to -1.6 · 10-19 C, v is the velocity of the electron and B is the magnetic field.</p><p>Using the vector product F, I B form a right-handed triad between them, or using the right-hand rule (place</p><p>the thumb, index and middle fingers all orthogonal to each other) the thumb indicates the direction of the</p><p>force, the index the direction of the velocity from positive to negative voltage source, and with the average</p><p>the magnetic field direction, that is direct from north pole to south pole of the magnet. Keep in mind that</p><p>the electron charge is negative (q = 1.6x10-19-C) and then the product v x B changes sign. We will indicate</p><p>that electrons do not go from positive to negative voltage source, but on the contrary, for include already</p><p>the minus sign on the direction of speed and using the absolute value of electronic charge.</p><p>For how willing the voltage and the magnet, in Figure 3.32 A, the electrons undergo a Lorentz force</p><p>directed upwards. Is possible check this fact going to measure the voltage difference that exists between</p><p>the areas above and below the Hall element. As indicated with red and blue zones, the electrons forced to</p><p>move upwards creates a thickening of negative charges, and for maintaining the neutrality of Hall element,</p><p>the bottom formed a group of positive charges. The potential difference measured between the top and</p><p>bottom is called Hall voltage.</p><p>the Figures 3.32 A, B, and C and D is possible to see the trend of the force at which the electrons are subject</p><p>to changing directions of tension voltage and magnetic field.</p><p>After a fairly long time, when all the variations become negligible, there is a balance of forces between the</p><p>longitudinal electric field, the force that creates the tension of Hall, and the Lorentz force. Meaning:</p><p>P�TO = PQUTTTTORSTO (3.13)</p><p>where:</p><p>q is the electron charge, E It is the absolute value of longitudinal electric field, B is the absolute value of</p><p>magnetic field and vd is the velocity of electrons, called drift velocity.</p><p>In the fields take the absolute value because they have opposite directions. Since the Hall voltage is V = Ed,</p><p>we find E and then find the speed of electric charges. Knowing the physical size of the conductor and the</p><p>68</p><p>value of electric current, we can determine the number of electrical charges through a section of Hall</p><p>element. Indeed:</p><p>� = A</p><p>VW��</p><p>(3.14)</p><p>where:</p><p>n is the number of charges, A is the area element of Hall and I is the current density, called the Hall current.</p><p>Between the current flowing in the Hall element and Hall voltage measured, there is a certain connection.</p><p>This allows you to create precision resistors. The Hall effect is also used in the current probes, such as</p><p>current clamps: these particular instruments can measure the electric current flowing in a wire without the</p><p>need to put the measuring instrument in series, that is without shutting down and stop the circuit. Hall</p><p>probes, instead, are used to measure the magnetic field strength.</p><p>3.4.3.2 Current Probes (Open loop and Closed Loop Transducers)</p><p>Open Loop Transducer</p><p>The magnetic flux created by the primary current Ip is concentrated in a magnetic circuit and measured in</p><p>the airgap through the probe Hall effect. The output of the probe is sent to a conditioning circuit to provide</p><p>out the exact value of the primary current Ip (Figure 3.33).</p><p>.</p><p>Figure 3.33 – Current Probe with Open Loop Transducer [University of Cassino]</p><p>69</p><p>Closed Loop Transducer</p><p>The magnetic flux created by the primary current Ip is balanced an additional flow producted by a current</p><p>generated by a secondary circuit, that circulates in a second winding. The circuit secondary is driven by Hall</p><p>effect sensor and vary the current up to undo the effect of two fields (Figure 3.34).</p><p>Figure 3.34 – Current Probe with Closed Loop Transducer [University of Cassino]</p><p>3.4.3.3 Voltage Probes</p><p>Closed Loop Transducer</p><p>The voltage probes measure circuit has a very small current limited by series resistance on which we must</p><p>perform the measure and send it to the primary coil. At this point, the principle of is identical to that of</p><p>current transducers already discussed.</p><p>Figure 3.35 – Voltage Probe with Closed Loop Transducer [University of Cassino]</p><p>70</p><p>Chapter 4</p><p>PMSM Modeling</p><p>Contents:</p><p>4.1 PMSM Design Features</p><p>4.2 IPMSM Electromechanical Model</p><p>4.2.1 3-Phase Dynamic Model (abc fixed reference frame)</p><p>4.2.1.1 State Form Model</p><p>4.2.1.2 Electromagnetic Torque Calculation</p><p>4.2.2 α-β Reference Frame Model</p><p>4.2.2.1 Clarke Transformation (abc → α-β transformation)</p><p>4.2.3 d-q Reference Frame Model</p><p>4.2.3.1 Park Transformation (α-β → d-q transformation)</p><p>4.3 Relation Synchronous Inductances-Stator Field Inductances-</p><p>Phase Inductances</p><p>4.4 IPMSM Equivalent Electric Circuit</p><p>4.5 IPMSM Operating Conditions</p><p>This Chapter will take in examination the necessary mathematical handling to</p><p>achieve the PMSM model, analyzing the behaviors of the electrical variables</p><p>into the Motor. Besides will be considered the equivalent electric circuits of the</p><p>Machine and how to pass from a 3-phase circuit to an equivalent 2-phase</p><p>system.</p><p>71</p><p>4.1 PMSM Design Features</p><p>The Permanent Magnet Synchronous Motors (or AC Brushless Motors), are more commonly used in</p><p>industrial applications when good dynamic requirements and optimal steady-state precisions are</p><p>demanded, primarily for low-medium Electric Power Drive (0,1÷60 kW). For these reasons their utilization is</p><p>essentially for high cost electrical drives, whose great performances justify the considerable expense (due</p><p>for the presence of high quality Permanent Magnets on the rotor shaft).</p><p>In this type of electric machine the stator and the rotor have a cylindrical shape, are made of laminate</p><p>ferromagnetic material and separated by airgap. On the rotor are placed the Permanent Magnets that</p><p>generate a constant Magnetic Field, whose function substituting the rotor windings typically used for an</p><p>Induction Motor. Indeed the great available Energy Density (BH)MAX (high Magnetic Remanent Flux Density</p><p>Br and the Coercive Force Hc values) makes the PM, in particular the rare earth materials like Samarium-</p><p>Cobalt (SmCo) and Neodymium-Iron-Boron (NdFeB), very suitable to be used for this task (Figure 4.1).</p><p>Figure 4.1 – Demagnetization curves for the main PM materials [Mehrdad Yimin Ali 2010]</p><p>The stator windings are 3-phase, each one with a phase displacement of 120° and with a pair of terminals</p><p>indicated respectively with aa’, bb’ and cc’ (Figure 4.2). Supplying the stator windings with an external 3-</p><p>phase source will generate a rotating magnetic field, which will interact with the magnetic field created by</p><p>PM (starting rotating) on the Rotor. This interaction between the Stator Current Vector (exactly the</p><p>imaginary component of the vector) and the rotating magnetic field produced by the PM generate the</p><p>Torque necessary for the motion of the rotor. The electromechanical conversion uses the Lorentz Force</p><p>(F=B*i*l) to get motion, because the forces will work on the stator conductors (fixed part of the machine),</p><p>but for the mentioned principle the rotor will be consequently put in rotation. A schematic representation</p><p>of a PMSM with two poles is shown in Figure 4.2.</p><p>72</p><p>Figure 4.2 – Schematic representation of a PMSM, with Airgap Flux Density produced by PM (a)</p><p>and by Phase-a Stator Winding (b) [Wikipedia 2010]</p><p>The PMSM are manufactured with two basic configurations, depends how the PM are placed on the rotor,</p><p>because their position affects the behavior of the Brushless Motor. Indeed PM have a differential magnetic</p><p>permeability very similar that of the air, so determining a rotor Magnetic Isotropy (Magnetic Reluctance) if</p><p>the PM are mounted on the rotor surface (SPMSM or Surface Permanent Magnet Synchronous Motor) and</p><p>a rotor Magnetic Anisotropy if the PM are buried inside the Rotor (IPMSM or Interior Permanent Magnet</p><p>Synchronous Motor). In the Figure 4.3 is possible to observe the constructive differences between SPMSM</p><p>and IPMSM.</p><p>Figure 4.3 – Structures of SPMSM (a) and IPMSM (b) [Iqbal 2003]</p><p>73</p><p>The SPMSM, have the PM mounted on the rotor surface, so will need of a wider airgap to guarantee good</p><p>operating conditions. As the SPMSM are isotropic motors, will have the same Field Inductances according</p><p>the direct-axis (Lsd) and the quadrature-axis (Lsq), where the d-axis coincides with a rotor Nord Pole axis</p><p>while the q-axis is shifted of 90 electrical degrees anticlockwise (Figure 4.4). Besides these kind of PMSM</p><p>having a wide airgap, will propose a low Field Inductance value, making become the Stator Electrical Time</p><p>Constant very fast.</p><p>Figure 4.4 – Flux path according the rotor d-axis and q-axis for a SPMSM [Salvatore]</p><p>The IPMSM have a more robust mechanical structure than SPMSM, because the PM are buried and</p><p>protected inside the rotor and this makes them particularly suitable for high speed applications. Despite</p><p>these motors have an isotropic structure, the magnetic circuit must be considered anisotropic because the</p><p>PM have a magnetic permeability value similar to the air. For this theme the PM thickness will behave like</p><p>an airgap for the magnetic flux path along the d-axis, while the magnetic flux path along the q-axis will not</p><p>undergo significant variations because each magnet is covered by a polar shoe of soft iron with high</p><p>permeability.</p><p>Figure 4.5 – Flux path according the Rotor d-axis and q-axis for a IPMSM [Salvatore]</p><p>74</p><p>Since the PM have low permeability (higher reluctance than iron), the reluctance of the magnetic flux path</p><p>varies according to the rotor position. That is called Magnetic Saliency ζ and for IPMSM it will be so</p><p>responsible for the variation about d-axis and the q-axis Inductance (Lsq and Lsd) during the rotor rotation,</p><p>making have Lsq≠Lsd:</p><p>� � ������ (4.1)</p><p>This phenomenon will make different the effective magnetic flux length due to Lsd and Lsq, because the PM</p><p>will be involved and crossed in the magnetic flux path, like is possible to see in the Figure 4.6.</p><p>Figure 4.6 – d-axis and q-axis Inductances paths for a IPMSM [Jun Kang]</p><p>The Magnetic Saliency in IPMSM changes also the Electromagnetic Torque generation. Indeed, addition to</p><p>the torque produced for the interaction between PM flux (oriented towards rotor d-axis) and the</p><p>quadrature component of the Stator Current (called PM Torque), will be also present a Reluctance Torque</p><p>due to the Rotor Magnetic Saliency. The Reluctance Torque is proportional to the difference between the</p><p>Field Inductances according d-axis and q-axis (Lsd-Lsq), considering that the q-axis Inductance Lsq is greater</p><p>than d-axis inductance Lsd because the magnetic flux path according the q-axis has a low reluctance value</p><p>and so an high Inductance value (it passes only on the rotor steel) if compared with the d-axis magnetic flux</p><p>path.</p><p>For the HEV Drive has been choice the IPMSM because these type of Motors can work well in the Constant</p><p>Torque Region (nominal torque region) and also in the Constant Power Region (high speed region) through</p><p>proper weakening operation. Indeed IPMSM are ideal for a vehicle typical work cycle because can produce</p><p>high Torque value for low speed and using a right weakening operation less Torque for high speed range</p><p>values, but needs to an Control Algorithm to manage efficiently the passage from the Constant Torque</p><p>Region to Constant Power Region.</p><p>75</p><p>4.2 IPMSM Electromechanical Model</p><p>4.2.1 3-Phase Dynamic Model (abc fixed reference frame)</p><p>To comprehend how control the different operating conditions of a IPMSM must be found before his</p><p>Electromechanical Model, which gives fundamental information about the electrical variables behavior.</p><p>The following mathematical handling will take like reference the document [Petrella].</p><p>In a IPMSM the entire linked magnetic flux with the stator windings will be the sum between the magnetic</p><p>field created by the rotor PM and that created supplying the stator coils with a balanced and symmetrical</p><p>3-phase current system. So to find the Electromechanical Model should start to calculate the Voltage</p><p>expression (for each phase) due to the presence both magnetic fields:</p><p>��</p><p>�</p><p>�� �</p><p>��� + ������� �</p><p>��� + ������� �</p><p>��� + �����</p><p>�</p><p>(4.2)</p><p>Where in the (4.2) V=V(t), i=i(t) and λ= λ(t) and represent respectively the Voltage on the stator phase</p><p>winding, the current through stator phase winding and the concatenated total magnetic flux with a single</p><p>phase. Besides it’s supposed symmetry geometric for the electric motor, will have all the stator resistances</p><p>equal (Ra=Rb=Rc=RS).</p><p>The total linked magnetic flux for each phase (λa, λb and λc) considers also the PM magnetic flux, so</p><p>assuming linearity for the magnetic circuits and (still) geometric symmetry will have:</p><p>��� � ����� + ����� + ����� + ������ � ����� + ����� + ����� + ������ � ����� + ����� + ����� + ����</p><p>� (4.3)</p><p>Where in the (4.3) λaPM, λbPM and λcPM are the linked Magnetic Fluxes due to PM inside the Rotor, whose</p><p>values depend on the rotor position, which is the angle θr between the phase-a axis (fixed reference frame)</p><p>and the d-axis (rotating reference frame), like is possible to watch in the Figure 4.7.</p><p>76</p><p>Figure 4.7 – Fixed (abc) and Rotating (dq) Reference Frame Schematic for a IPMSM [Petrella]</p><p>So as said the linked PM magnetic fluxes for each phase will have the following expressions:</p><p>� ���� � ���� cos#$%&���� � ���� cos'$% ( 2* 3, -���� � ���� cos'$% + 2* 3, -� (4.4)</p><p>Ever in the (4.3) Laa, Lbb and Lcc are the Self-Inductances, through which is possible to treat for each winding</p><p>phase the linked magnetic flux due to the flowing current in itself. Because the equivalent magnetic circuit</p><p>is anisotropic, the Self-Inductances will change their values in function of the rotor position θr:</p><p>� ��� � �./ + �01 + �0� cos#22%&��� � �./ + �01 + �0� cos#22% + 2* 3, &��� � �./ + �01 + �0� cos#22% ( 2* 3, &� (4.5)</p><p>Where in the (4.5):</p><p>o Lσs is the leakage Inductance with which is possible to consider the leakage Magnetic Flux from</p><p>each winding (i.e. own Magnetic Flux part that doesn’t able to pass the airgap and achieve the</p><p>Rotor).</p><p>o Lm0 and Lma are respectively the constant component and the anisotropic component (function of</p><p>the rotor position θr) of the Field Inductance, which considers the Magnetic Flux that crosses the</p><p>airgap to close on the Rotor.</p><p>77</p><p>In the (4.3) there are also the Mutual Inductances Lab, Lba, Lbc, Lcb, Lac, Lca that consider the concatenated</p><p>magnetic flux by every coil due to the flowing current in the others windings (Mutual Magnetic Flux). Still</p><p>these Inductances will depend from the rotor position θr:</p><p>���� � ��� � �0� cos(22% − 2* 3, ) + 40��� = ��� = �0� cos(22% + 2* 3, ) + 40��� = ��� = �0� cos(22%) + 40</p><p>� (4.6)</p><p>In the (4.6) the Mm Inductance represents a fraction of the Field Inductance constant component Lm0</p><p>obtained considering the phase displacement between each magnetic axis (2π/3):</p><p>40 = �01 cos(2* 3, ) = − 56 �01 (4.7)</p><p>4.2.1.1 State Form Model</p><p>Resuming the windings Voltage equations (4.2) for each phase will be possible to write the mathematical</p><p>model for the machine in a matrix form:</p><p>�/��� = 7</p><p>/8����/��� + 9:�;<=</p><p>9> (4.8)</p><p>Where in the (4.8) appear the Vectors regarding Stator Voltages, Currents and concatenated Magnetic</p><p>Fluxes and where the superscript abc indicates the phase reference for these variables:</p><p>�/��� = ?������ @ ; 7</p><p>/8��� =</p><p>/ ?1 0 00 1 00 0 1@ ; �/��� = ?������ @ ;</p><p>�/��� = ?������ @ = 7�/(2$%)8����/��� + �/�����($%) (4.9)</p><p>From the (4.9) will be possible explicit the PM Magnetic Flux Vector like:</p><p>�/�����($%) = �/�� D cos($%)cos'$% − 2* 3, -cos'$% + 2* 3, -E (4.10)</p><p>Besides the Stator Field Inductance matrix [LS(2θr)] can be explicit like:</p><p>7�/(2$%)8��� = 7�/18��� + 7�/�(2$%)8��� (4.11)</p><p>7�/18��� =</p><p>FGG</p><p>GH�./ + �01 − 56 �01 − 56 �01− 56 �01 �./ + �01 − 56 �01− 56 �01 − 56 �01 �./ + �01IJJ</p><p>JK</p><p>(4.12)</p><p>78</p><p>7�/�(2$%)8��� = �0� FG</p><p>GH cos(2$%) cos(22% − 2* 3, ) cos(22% + 2* 3, )cos(22% − 2* 3, ) cos(22% + 2* 3, ) cos(2$%)cos(22% + 2* 3, ) cos(2$%) cos(22% − 2* 3, )IJ</p><p>JK (4.13)</p><p>Where in (4.12) is described the constant component matrix [LS0] of the Field Inductance matrix, while in</p><p>the (4.13) there is the anisotropic component matrix [LSa(2θr)] of the Field Inductance matrix.</p><p>Using the relation (4.9), (4.10) and (4.11) and substituting them in the (4.8) will be possible to write the</p><p>electric model of a IPMSM in a State Form, continuing still to work with phase variables in a fixed reference</p><p>frame (abc reference frame):</p><p>�/��� = 7</p><p>/8����/��� + 99> L7�/(2$%)8����/��� + �/�����($%)M</p><p>= 7</p><p>/8����/��� + 7�/(2$%)8��� 9N�;<=</p><p>9> + 97��(6OP)8;<=9> �/��� + 9:�QR;<=(OP)9></p><p>= 7</p><p>/8����/��� + 7�/(2$%)8��� 9N�;<=</p><p>9> + 97��(6OP)8;<=9> �/��� + 9:�QR;<=(OP)9OP ST0 (4.14)</p><p>The model in the (4.14) is not complete because treats only the electrical variables for IPMSM. Indeed the</p><p>(4.14) has four unknowns (the 3 Currents ��, �� and �� and the rotor mechanical speed T0 = T%/S) while</p><p>this mathematical model has only three equations. So to complete the IPMSM model will need add also the</p><p>D’Alambert equation about the mechanical balance, obtaining the complete IPMSM Electromechanical</p><p>model:</p><p>VW0 − VXY�9 = Z �[\�� (4.15)</p><p>Where in the (4.14)-(4.15) J is the total Inertia of the rotating masses, p is the number of pole pairs and Tload</p><p>is the Load Torque. Before using the (4.15) in the IPMSM model, must be obtained the expression regarding</p><p>Tem putting in relation it with the 3-phase stator currents system, so allowing to make solvable the</p><p>mathematical model.</p><p>4.2.1.2 Electromagnetic Torque Calculation</p><p>Are possible two methods to get the Electromagnetic Torque equation, namely one can be obtained by an</p><p>energy balance using Power and mechanical Speed and the other one can be obtained using the Magnetic</p><p>Energy. The following analysis will treat the second method, calculating the Electromagnetic Torque</p><p>starting from Magnetic Energy variations regarding a general case of n magnetically coupled circuits:</p><p>VW0 = �S �]��$^ _N`�Y/> (4.16)</p><p>79</p><p>Where Wc is the Magnetic Energy that can be expressed (ever for n magnetic circuits) like:</p><p>]� = �a �1 ��5Nb1 _Nc`Nd`⋯Nf`1 + �a �2 ��6Nc1 _Nb`Nd`⋯Nf`1 + ⋯ + �a �g−1 ��hi5Nfjb1 _Nb`Nc`⋯Nfjb`1 (4.17)</p><p>Particularized the (4.17) in the IPMSM 3-phase case and using before a summation to express the Magnetic</p><p>Energy Wc and then a matrix form, will have respectively the (4.18) and (4.19):</p><p>]� = 56 ∑ (∑ lmn(2$%)�m�n�n`� ) + ∑ �op4($%)�n`��m`� �n</p><p>(4.18)</p><p>]� = 56 �q7�(2$%)8� + �p4($%)�q (4.19)</p><p>Substituting the (4.19) in the (4.16) will be possible to find the Electromagnetic Torque expression in</p><p>function of the 3-phase stator currents system:</p><p>VW0 = S r56 �q 97�(6OP)89OP � + 9:QR(OP)9OP �qs (4.20)</p><p>In the (4.20) can be explicit the contributions due to the Torque created by the Anisotropy (Reluctance</p><p>Torque) (4.21) and that created by the Rotor Magnets (PM Torque) (4.22):</p><p>V%WX = −S�0� tuL��6 − 56 ��6 − 56 ��6 − ���� − ���� + 2����M sin(2$%)x +</p><p>√z6 {'��6 − ��6 − 2���� + 2���� + 2����- cos(2$%)|} (4.21)</p><p>V�� = S�/�� u− L�� − 56 �� − 56 ��M sin($%) + √z6 (�� − ��) cos($%)x (4.22)</p><p>VW0 = V�� + V%WX (4.23)</p><p>At this point it would be possible to write the complete IPMSM Electromechanical Model, with all the</p><p>electrical variables expressed in a phase fixed reference frame (abc reference frame):</p><p>��</p><p>�</p><p>�/��� = 7</p><p>/8����/��� + 7�/(2$%)8��� 9N�;<=</p><p>9> + 97��(6OP)8;<=9> �/��� + 9:�QR;<=(OP)9OP ST0V�� + V%WX − VXY�9 = Z �[\��T0 = 5~ �OP��</p><p>� (4.24)</p><p>The (4.24) Electromechanical IPMSM Model is a nonlinear dynamic mathematical model whose there are 4</p><p>scalar equations for 4 scalar unknowns ��, ��, �� and T0.</p><p>80</p><p>4.2.2 α-β Reference Frame Model</p><p>To realize and to implement the control for the IPMSM can be very useful analyze and modeling it with a</p><p>mathematic tool which allows to handle the model in another form. Indeed the IPMSM model obtained in</p><p>(4.24) shows a self-consistent mathematical model for each phase, but the existence of physical constraints</p><p>makes the three equations not independent from each other. For this reason can be used two</p><p>mathematical transformations, like Clarke Transformation (abc → α-β) and Park Transformation (α-β → d-</p><p>q), that allows to pass from an abc fixed reference frame to a d-q rotating reference frame, so reducing the</p><p>IPMSM Electromechanical model in a simpler mathematic form without any loss if information.</p><p>4.2.2.1 Clarke Transformation (abc → α-β reference frame transformation)</p><p>Using this mathematical transformation will be possible to pass from the 3-phase abc Stator reference</p><p>frame to a 2-phase αβ Stator reference frame. To have all the electrical variables in the (4.24) transformed</p><p>in the αβ reference frame the linear matrix Tαβγ must be used in the following transformation valid in a</p><p>general case with general variable x:</p><p>?������ @ = {V���| ?������ @ = 6z FGG</p><p>GH1 ( 56 ( 560 √z6 ( √z656 56 56 IJJ</p><p>JK ?������ @ (4.25)</p><p>The (4.25) expresses the general way to transform an abc system in a αβ system, without change the</p><p>physical reference for each variables. Besides the (4.25) expresses an zero sequence component ��, which</p><p>treatment can be neglected if the 3-phase system is considered symmetrical and balanced.</p><p>In the following Figure 4.8 is shown the schematic passage from abc to αβ reference frame for the electrical</p><p>variables into the IPMSM.</p><p>Figure 4.8 – Schematic abc → αβ Reference Frame Transformation for a IPMSM [Petrella]</p><p>81</p><p>Applying the general abc → αβ transformation for all the electrical variables in the IPMSM</p><p>Electromechanical model will have the transition from 3-phase reference to the Stator reference, so</p><p>allowing to write (4.14) in the αβ reference frame (4.27) according the (4.26) expressions:</p><p>�// = ?�����Y@ = {V��Y|�/��� ; �/ / = ������Y� = {V��Y|�/��� ; �// = ������Y� = {V��Y|�/���</p><p>�// = ������Y� = 7�/(2$%)8/�// + �/�� /($%) ; �/�� /($%) = �z6 �/�� ?cos($%)sin($%)0 @</p><p>7�/(2$%)8/ = 7�/18/ + 7�/�(2$%)8/</p><p>7�/18/ = D�./ + z6 �01 0 00 �./ + z6 �01 00 0 �./</p><p>E</p><p>7�/�(2$%)8/ = z6 �0� ?cos(2$%) sin(22%) 0sin(22%) − cos(22%) 00 0 0@ (4.26)</p><p>�// = 7</p><p>/8/�/ / + 9N��</p><p>9> 7�/(2$%)8/ + 97��(6OP)8�9> �/ / + 9:�QR�(OP)9OP ST0 (4.27)</p><p>To find the Electromagnetic Torque expression in the αβ reference frame and complete the IPMSM</p><p>Electromechanical model is sufficient apply the (4.26) relations for the Reluctance Torque V%WX in (4.21) and</p><p>for PM Torque V�� in (4.22):</p><p>V%WX = �� S�0�{'��6 − ��6- sin(2$%) + 2�������(2$%)| (4.28)</p><p>V�� = z6 S�/��{−�� sin($%) + �����($%)| (4.29)</p><p>Manipulating equation (4.28) and (4.29) in a way that links the Electromagnetic Torque with the linked</p><p>Magnetic Fluxes and the Currents with αβ reference frame, will have:</p><p>V%WX = − z6 S�� tz6 �0�{�� sin(2$%) − �����(2$%)|} + z6 S�� tz6 �0�{�� cos(2$%) + ����g(2$%)|} (4.30)</p><p>V�� = − z6 S��(�/�� sin($%)) + z6 S��(�/�� cos($%)) (4.31)</p><p>Using the (4.23), adding and subtracting the term S L�./ + z6 �01M ���� and finally applying the (4.26)</p><p>expression regarding the fluxes �//</p><p>will be possible reach the following Electromagnetic Torque equation in</p><p>the αβ reference frame:</p><p>VW0 = − z6 S�� tz6 �0�{�� sin(2$%) − �����(2$%)| + �/�� sin($%)}</p><p>+ 32 S�� �32 �0�{�� cos(2$%) + ����g(2$%)|+�/�� cos($%)�</p><p>82</p><p>� z</p><p>6 S'(���� � ����- (4.32)</p><p>Through the vector equation (4.27) and with the (4.32) will form the IPMSM Electromechanical model</p><p>wrote in the fixed αβ reference frame, getting the benefit of reducing the variables in the model and to</p><p>manipulate better the electrical equations to control and manage the Motor operating conditions.</p><p>��</p><p>�</p><p>�// � 7</p><p>/8/�// � 7�/#2$%&8/ 9N��</p><p>9> � �// 97��#6OP&8�</p><p>9> � 9:�QR�#OP&</p><p>9OP ST0</p><p>z</p><p>6 S'(���� � ����- ( VXY�9 � Z 9[\9></p><p>T0 � 5</p><p>~</p><p>9OP9></p><p>� (4.33)</p><p>4.2.3 d-q Reference Frame Model</p><p>The Clarke Transformation allows just to pass from a Stator abc reference frame to an αβ reference frame,</p><p>but always in a fixed Stator reference. To bring all the electrical variables in a rotating reference frame is</p><p>necessary to catch them and using the Park Transformation.</p><p>4.2.3.1 Park Transformation (α-β → d-q reference frame transformation)</p><p>This type of transformation is required when there is the intention to implement a IPMSM control with all</p><p>the electrical variables reported on the Rotor, evaluating the Rotor shaft position $%, namely the angular</p><p>displacement between the dq rotating reference frame (with an electrical speed T%) and the αβ fixed</p><p>reference frame. This way to implement the control is typically used for Synchronous Machines in which</p><p>Stator and Rotor Magnetic Field have the same</p><p>frequency.</p><p>Figure 4.9 – Schematic αβ → dq Reference Frame Transformation for a IPMSM [Petrella]</p><p>83</p><p>Considering ever a general case for a generic variable x and without the zero sequence component, will be</p><p>possible to make the Park Transformation for all the electrical variables in the (4.33) IPMSM model (except</p><p>for the magnetic flux generated by the PM because is already reported in the rotor reference frame) using</p><p>the following 2x2 transformation matrix Tdq:</p><p>u�9��x = {V9�| ������ = � cos($%) sin($%)− sin($%) cos($%)� ������ (4.34)</p><p>So using the (4.34) for all the (4.26) expressions will have αβ electrical equations like in the following (4.35)</p><p>dq electrical equations:</p><p>�/% = u�9�� x = {V9�|�// ; �/% = ��9��� = {V9�|�// ; �/% = ��9��� = {V9�|�//</p><p>�/% = ��9��� = 7�/8%�/% + �/��% ; �/��% = u�/��0 x 7�/8% = 7�/18% + 7�/�8%</p><p>7�/18% = 7�/18/ ; 7�/�8% = z6 �0� u1 00 −1x (4.35)</p><p>Where the r superscript indicates that all the variables are reported to the Rotor reference. Is very</p><p>important to note like now the PM effects on the Stator are not anymore a function of the Rotor position $%, but also The Field Inductances will be not anymore a $% function.</p><p>At this point the equivalent equation of the (4.8) can be written as:</p><p>�/% = 7</p><p>/8%�/% + 9:�P</p><p>9> (4.36)</p><p>Using the relation regarding �/%</p><p>in the (4.35) equations and knowing that all the electrical variables rotate</p><p>synchronous with the Rotor electrical Speed T%, will be obtainable the electrical equation of the (4.33)</p><p>IPMSM model in the dq rotating reference frame:</p><p>�/% = �/��[P> = 7�/8�/��[P> + �/����[P></p><p>⇒ 9L:�W��P�M9> = 7�/8 9N�9> ��[P> + �T%7�/8�/��[P> + �T%�/����[P> (4.37)</p><p>Evaluating the (4.36) with same phasor representation and still using the (4.37) just found:</p><p>�/��[P> = �7</p><p>/8�/ + 7�/8 ��/�� + �T%7�/8�/ + �T%�/��� ��[P></p><p>�/ = 7</p><p>/8�/ + 7�/8 9N�9> + �T%7�/8�/ + �T%�/�� (4.38) �/ = 7�/8�/ + �/�� (4.39)</p><p>84</p><p>The set of equations in (4.38) and (4.39) are described in a vector form with the phasors referred to a</p><p>system of rotating axes. These equations can be also represented separating the Real Part from the</p><p>Imaginary Part, so permitting to use two scalar equations instead only one vector equation for each one:</p><p>�/ = 7�/8�/ + �/�� ⇒ � �/ = �/9 + ��/� �/ = �/9 + ��/� � ⇒ ��/9 = �/9�/9 + �/���/� = �/��/� � (4.40)</p><p>Where in the (4.40) appear the d-axis Synchronous Inductance (�/9) and the q-axis Synchronous Inductance</p><p>(�/9). Substituting the (4.40) in the (4.38) will be possible to obtain the IPMSM electrical equations</p><p>according the d-axis and q-axis in a scalar form:</p><p>� �/9 =</p><p>/�/9 + �/9 9N��9> − T%�/��/��/� =</p><p>/�/� + �/� 9N��9> + T%(�/9�/9 + �/��)� (4.41)</p><p>A phasor representation regarding all the electrical variables in the (4.41) is shown in the Figure 4.10, while</p><p>in the Figure 4.11 is shown the structural transformation for a IPMSM in the dq reference frame.</p><p>Figure 4.10 – Rotating Phasors Representation of the Electrical Variables for a IPMSM</p><p>85</p><p>Figure 4.11 – Structural Transformation for a IPMSM in the dq reference frame [Petrella]</p><p>To complete definitely the IPMSM Electromechanical model in the d-q rotating reference frame misses the</p><p>transformation about the Electromagnetic Torque equation, which can be attained using an energetic</p><p>balance, starting from the Input Electric Power to the IPMSM and using the phasors handling (scalar</p><p>product between Voltage vector and Current Vector), with all the electrical variables already evaluated in</p><p>the rotating reference frame:</p><p>��/ = '�/9 + ��/�- = 6z L�� + ����cd� + �����d�M�/ = '�/9 + ��/�- = 6z L�� + ����cd� + �����d�M ⇒ pW � �/��/ � z6 '�/9�/9 + �/��/�-� (4.42)</p><p>Using now the (4.42) in the (4.41):</p><p>pW � z6 L</p><p>/�/96 + �/9�/9 9N��9> ( T%�/��/��/9 +</p><p>/�/�6 + �/��/� 9N��9> + T%�/9�/9�/� + T%�/���/�M (4.43)</p><p>In the (4.43) are circled in red the Joule Losses and circled in green the Energy Variations in the d-axis and</p><p>q-axis Inductances. All these terms don’t contribute to generate Electromagnetic Torque because don’t</p><p>able to be transformed in Mechanical Power for the Rotor shaft. Instead the other terms will contribute to</p><p>be transformed in Mechanical Power, so generating the Electromagnetic Torque. Using the following (4.44)</p><p>expressing the Mechanical Power, will be possible to get it:</p><p>�p0 � VW0T0T% � ST0 ⇒ VW0 � 32 ST0'(�/��/��/9 + �/9�/9�/� + �/���/�-T0 �</p><p>⇒ VW0 � z</p><p>6 S�/���/� � z</p><p>6 S'�/9 ( �/�-�/9�/� (4.44)</p><p>86</p><p>How already seen, the Electromagnetic Torque VW0 is composed by the PM Torque V��and by the</p><p>Reluctance Torque V%WX, so the (4.44) can be divided in the (4.45) and (4.46) equation:</p><p>V�� = z6 S�/���/� (4.45)</p><p>V%WX = z6 S'�/9 − �/�-�/9�/� (4.46)</p><p>The complete IPMSM Electromechanical model in the d-q rotating reference frame that describes the</p><p>motor behavior can be finally wrote. The following state form model will be taken in consideration to</p><p>implement the control of the PMSM in all the possible HEV working conditions:</p><p>��</p><p>�</p><p>�/9 =</p><p>/�/9 + �/9 9N��9> − ST0�/��/��/� =</p><p>/�/� + �/� 9N��9> + ST0(�/9�/9 + �/��)V�� + V%WX − VXY�9 = z6 S�/���/� + z6 S'�/9 − �/�-�/9�/� − VXY�9 = Z 9[\9></p><p>� (4.47)</p><p>In the (4.47) IPMSM dynamic model the unknowns will be �/9, �/� and T0, the forcing input to the system</p><p>will be �/9, �/�and VXY�9 and the constant parameters of the Motor will be J, p, �/��,</p><p>/, �/9 and �/�.</p><p>4.3 Relation Synchronous Inductances-Stator Field Inductances-Phase Inductances</p><p>Consideration about the 7�/8 matrix must be done. Indeed this term is called Stator Field Inductance matrix</p><p>and represents the equivalent matrix of the (4.11) equation in the d-q reference frame. This matrix will be</p><p>made by the Synchronous d-axis Inductance (�/9), by the Synchronous q-axis Inductance (�/�) and the</p><p>leakage Inductance �./ (neglectable), like is possible to comprehend from the (4.48) 7�/8 matrix listed</p><p>below:</p><p>7�/8 = ��/9 0 00 �/� 00 0 �./� (4.48)</p><p>�/9 and �/� consider the Stator Leakage Inductances �./ and the Field Inductances according d-axis (�09)</p><p>and q-axis (�0�): �/9 = �./ + �09</p><p>�/� = �./ + �0�</p><p>(4.49)</p><p>�09 = z6 (�01 + �0�)</p><p>�0� = z6 (�01 − �0�) (4.50)</p><p>Besides the constant component �01 and the anisotropic component �0� of the Field Inductances can be</p><p>expressed like:</p><p>87</p><p>�01 = 5z '�09 + �0�-</p><p>�0� = 5z '�09 − �0�- = 5z '�/9 − �/�- (4.51)</p><p>The expressions used from (4.48)÷(4.51) are very important because allow:</p><p>� To represent in detail the IPMSM equivalent electric circuit for the d-axis an q-axis.</p><p>� To calculate without any problem the Torque expression using the �/9 and �/� Inductances, so</p><p>modifying the (4.23)-(4.32)-(4.46) expressions.</p><p>� To pass from a 2-phase equivalent circuit to a 3-phase equivalent circuit (and vice-versa), very</p><p>useful when are only known the Synchronous d-axis and q-axis Inductances from the nominal</p><p>machine parameters.</p><p>4.4 IPMSM Equivalent Electric Circuit</p><p>From the electrical equations regarding �/9 and �/�in the (4.47) model can be reached an equivalent circuit</p><p>valid for a dynamic system, like is possible to observe respectively in the Figure 4.12.</p><p>Figure 4.12 – IPMSM Equivalent Electric Circuits according d-axis and q-axis</p><p>The IPMSM equivalent circuit is similar to BDC equivalent circuit because when there is the passage from</p><p>the Stator fixed reference frame to Rotating reference frame will add for the d-axis and q-axis Voltage</p><p>equations a Back-Electro-Motive Force terms (T%�/� and T%�/9 are called B-EMF), which value is</p><p>proportional to the Electrical Speed ST0 and determines the Voltage limit for the IPMSM, like in a BDC.</p><p>88</p><p>4.5 IPMSM Operating Conditions</p><p>In order to comprehend how drive the IPMSM, very important considerations can be made from the</p><p>IPMSM Electromechanical model in the (4.47):</p><p>1) Observing the (4.44) Electromagnetic Torque expression is easy to realize that for an Isotropic</p><p>PMSM will result �/9 = �/�, so the Tem will depend only from the Stator q-axis Current �/�. Instead</p><p>for an Anisotropic PMSM (�/9 ≠ �/�) will be present also the Reluctance Torque component</p><p>depending from the Stator d-axis and q-axis Currents �/9and �/�.</p><p>As the Magnetic Saliency ζ will depend from the Rotor constructive shape (how the PM are buried</p><p>in the Rotor), a IPMSM will have the Reluctance value along the d-axis bigger than the Reluctance</p><p>value along the q-axis, because on the d-axis Magnetic Flux path will meet the PM with a magnetic</p><p>permeability value very near to air magnetic permeability (Figure 4.13). For this reason will result �/� > �/9, so to obtain an useful contribution also for the Reluctance Torque in the (4.44) the d-</p><p>axis Stator Current �/9 must be negative while the q-axis Stator Current �/� must be positive.</p><p>Figure 4.13 – d-axis and q-axis Magnetic Flux Path for a IPMSM with 2 pole pairs</p><p>[Petrella]</p><p>2) Decomposing the Stator Current Vector �/ in the d-axis and q-axis component and evaluating the</p><p>displacement ε between �/ and the PM Magnetic Flux Vector �/�� (placed on the d-axis), will be</p><p>possible to evaluate the Maximum Electromagnetic Torque value in function of the ε angle (4.53),</p><p>using the (4.52) relations and substituting them in the (4.44):</p><p>�/9 = �/���(�)</p><p>�/� = �/sin(�) (4.52)</p><p>89</p><p>VW0 = z6 S�/���/sin(�) + z� S'�/9 − �/�-�/6sin(2�) (4.53)</p><p>As the (4.53) has '�/9 − �/�- < 0, to produce an useful Reluctance Torque �/9 must be negative</p><p>and this means that the displacement ε must be bigger than 90°, like shown in the Figure 4.14 (valid</p><p>for a constant amplitude of �/).</p><p>Figure 4.14 – Electromagnetic Torque trend for a IPMSM with ¡¢ = £¤¢¥</p><p>Besides the (4.53) depends from the square of the �/, namely if the �/ value will improve, the locus</p><p>points regarding the Maximum Electromagnetic Torque will move towards higher ε values (Figure</p><p>4.15), so optimizing the ratio Electromagnetic Torque/amplitude Stator Current.</p><p>Figure 4.15 – Points Locus describing the Maximum Tem/is ratio</p><p>90</p><p>3) The IPMSM Mechanical Speed can be adjusted modifying the frequency of the 3-phase Stator</p><p>Currents (or modifying the frequency of the 3-phase Stator Voltage), while the rotation sense can</p><p>be changed modifying the rotation sense of the 3-phase Stator Currents (for example imposing that</p><p>b-phase Current is ahead and the c-phase Current is behind if compared with the a-phase Current).</p><p>91</p><p>Chapter 5</p><p>IPMSM Control Strategy</p><p>Contents:</p><p>5.1 IPMSM Operating Domain Control</p><p>5.2 IPMSM Control Strategy Optimizations</p><p>5.2.1 Maximum Torque per Ampere (MTPA)</p><p>5.2.2 Field Weakening Control (FWC)</p><p>5.2.3 Maximum Torque per Voltage (MTPV)</p><p>5.3 IPMSM Control Trajectory</p><p>5.4 IPMSM Demagnetization Limits</p><p>This Chapter will treat all the possible IPMSM operating regions and how</p><p>realize the control strategy without overpassing the operative area. Besides</p><p>will be provided all the mathematical expressions capable to implement</p><p>different types of optimizations for the used control strategy, achieving at the</p><p>last the IPMSM control trajectory able to optimize the motor operating for the</p><p>entire speed range.</p><p>92</p><p>5.1 IPMSM Operating Domain Control</p><p>The IPMSM Control is strongly depending by the Motor plate data (like nominal Voltage, Current or Speed</p><p>and machine parameters) and by the Inverter used to drive it (like Voltage bus or maximum Current</p><p>through the switches). All these electrical requirements must be observed to comprehend which is the</p><p>maximum operative range (V-I) for the IPMSM and how to adapt these limits to the particular required</p><p>working conditions (T-ω), so choosing the best control strategy for a generic application. In this way the</p><p>IPMSM operating region will be bound with the specific requests of the electric drive.</p><p>To analyze the operating domain is important to start from the IPMSM Electromechanical Model in the</p><p>(4.47), but evaluating that equations during the steady-state, without depending by time:</p><p>� ��� = ����� −</p><p>���</p><p>��</p><p>��</p><p>= ����</p><p>+</p><p>������� +</p><p>�������� = ��� + ���� = �� 	������</p><p>+ �� 	���� − ��</p><p>������</p><p>� (5.1)</p><p>To simplify the mathematical handling is not wrong to assume the windings resistance �� very small, so</p><p>neglecting the related voltage drops, obtaining the (5.2) model:</p><p>� ��� = −</p><p>���</p><p>��</p><p>��</p><p>=</p><p>������� +</p><p>�������� = ��� + ���� = �� 	������</p><p>+ �� 	���� − ��</p><p>������</p><p>� (5.2)</p><p>In the (5.2), both Voltages and Currents must be contained in a range of nominal values. These restrictions</p><p>identify only a specific working region for the IPMSM, given by the simultaneously intersection between the</p><p>regions expressing the Voltage limits and the Current limits.</p><p>The Current Limit is identified from the maximum amplitude of the Stator Current Vector that the IPMSM</p><p>will able to conduct in nominal conditions during the steady-state:</p><p>�� = �����+��</p><p>� ≤ ��� (5.3)</p><p>Similarly, The Voltage Limit can be found ever considering that the maximum amplitude of the Stator</p><p>Voltage Vector</p><p>can’t overpass (ever during the steady-state) the nominal voltage value ��� regarding the</p><p>Inverter or the Machine:</p><p>�� = �����+��</p><p>� ≤ ��� = �� √� (5.4)</p><p>Using the expressions about ��� and ��</p><p>inside the (5.4) Voltage Limit expression, will be possible to obtain</p><p>the following equation:</p><p>93</p><p>��� ≥ ��−</p><p>���</p><p>��</p><p>�� + 	�</p><p>��#������ + ����$�</p><p>⇒ &'()*)+,)-'.) ≥ /��� + 0'12-'. 3� + /-'4-'.3� ��</p><p>� (5.5)</p><p>The expression (5.3) about the Current Limit expresses the mathematical relation for a circle with the</p><p>center in (0,0) and radius ���, so all the possible working points regarding the Current of a IPMSM must be</p><p>contained in that circle area.</p><p>The expression (5.5) about the Voltage Limit expresses the mathematical relation for an ellipse with the</p><p>following characteristics:</p><p>o center in → 5− ���� ���6 , 09</p><p>o radius on the q-axis (vertical axis) → :</p><p>= &'(*+,-'4</p><p>o radius on the d-axis (horizontal axis) → :� = &'(*+,-'.</p><p>Besides by rq and rd it’s easy to understand that, if the Mechanical Speed will increase, both the radius of</p><p>the ellipse will become smaller because the Voltage value is maintained always on the constant value ���.</p><p>To protect the machine from the PM Demagnetization is also important to do something for don’t allow to</p><p>the d-axis current to produce an opposite Magnetic Flux too big, weakening too much the PM Magnetic</p><p>Flux. In facts, there is a limit in the IPMSM indicating the Permanent Demagnetization and called km (this</p><p>value can be between 0 and 1):</p><p>������ ≥ −;����� ⇒ ��� ≥ − =,0'12-'. (5.6)</p><p>All the Inequalities regarding Currents, Voltages and PM Flux, respectively in the (5.3),(5.5) and (5.6), can be</p><p>represented at the same time on the same reference system (��� , ��</p><p>$ , determining the IPMSM operating</p><p>region according all the possible values of the machine. For example in the (5.5) the Voltage Limit for the</p><p>IPMSM will be respected if all the Voltage values provided to the Motor are maintained inside the Voltage</p><p>ellipse. Same thing happens in the (5.6), namely the Demagnetization Limit will not surpassed if the</p><p>operating conditions of the IPMSM will allow to work ever in the region on the right of that straight line</p><p>indicating the limit.</p><p>The Intersection between these three constraints will provide the possible steady-state operating domain</p><p>in which make working the IPMSM according the performance required to the IPMSM Electric Drive, like is</p><p>possible to see in the Figures 5.1 and 5.2.</p><p>94</p><p>Figure 5.1 – Operating Domains for a IPMSM regarding Current Limit (blue), Voltage Limit (red)</p><p>and Demagnetization Limit (orange)</p><p>Figure 5.2 – Nominal Operating Region for a IPMSM in the isd-isq system</p><p>Is very important to note that the center of the Voltage Limit (the ellipse) is not bound to stay inside the</p><p>Current Limit (the circle), because position depends only from the PM Magnetic Flux and from the d-axis</p><p>Inductance ���, but determines how obtain the trajectory that able to maximize the ratio Torque/Current.</p><p>95</p><p>For the moment in the following analysis the ellipse center will be considered always inside the circle (more</p><p>difficult case).</p><p>The neglected voltage drops on the stator resistance Rs can influence only the Voltage Limit. Such limits will</p><p>restrict the Operating Region for high Speed values, but only for high frequency the Motor Impedance</p><p>values will be bigger and will allow to consider still neglectable the voltage drops on Rs. How the Voltage</p><p>Limit changes shape in function of the speedup is shown in the Figure 5.3.</p><p>Figure 5.3 – Speedup and different Voltage Limits for a IPMSM</p><p>Finally the Electromagnetic Torque Characteristic can be found describing the contour line with constant</p><p>values of Tem in the isd-isq system. So obtaining the q-axis current ��</p><p>from the Electromagnetic Torque</p><p>expression in the (5.2) should have:</p><p>��</p><p>= >?,@)*A0'12B�-'.C-'4�D'.E (5.7)</p><p>Representing the (5.7) in the dq reference and evaluating the variation among different Torque values will</p><p>be possible to find many different Hyperboles, with the horizontal asymptote given by the (5.8) and the</p><p>vertical asymptote given by the (5.9):</p><p>��</p><p>= 0 (5.8)</p><p>��� = 0'12�-'.C-'4� (5.9)</p><p>96</p><p>Figure 5.4 – Graphic Representation for different Electromagnetic Torque trends in the isd-isq</p><p>system [Acampa]</p><p>Joining all the characteristics displayed in the Figure 5.3 and 5.4 regarding Current Limit, Voltage (Speed)</p><p>Limits and the points locus with constant values of Electromagnetic Torque, will be possible to note from</p><p>the following Figure 5.5 that for each Current amplitude value, the maximum achievable value about the</p><p>Torque characteristic is identified on the Hyperbole tangent to the Current Circle. This figure is referred for</p><p>a particular machine and uses A/p.u. for the currents value and p.u. for the torque and speed values.</p><p>Figure 5.5 – Representation of the IPMSM for different Electromagnetic Torque characteristics,</p><p>Current circles and an unique Voltage ellipse</p><p>97</p><p>For example if the Motor had a good design, will be possible to cross the Voltage ellipse at the nominal</p><p>voltage value (so at the nominal speed) with the Current circle at the maximum torque point, exactly in the</p><p>B point in Figure 5.5, so ensuring always the maximum torque value until the nominal speed. It’s easy to</p><p>comprehend that all the maximum Torque/Current ratios are placed on the same line where is placed the B</p><p>point, but this is true only until the nominal velocity.</p><p>Considering the case in which the speed ellipse center is contained in the Current circle, to comprehend</p><p>how the max working point T/I moves on the (��� , ��</p><p>$ system for speed bigger than nominal speed is</p><p>sufficient observing the Figure 5.6. Indeed putting in the graph all the variables in p.u., will be possible to</p><p>say that from the nominal speed and torque point in B, if the speed increases the working point regarding</p><p>the max T/I ratio will move initially on the Current circle until the P point, while the Electromagnetic Torque</p><p>Characteristics will be decrease. In the P point, namely when the Electromagnetic Torque Characteristic</p><p>with a such speed intersects the hyperbole corresponding at the Maximum Torque values, the working</p><p>point moves towards the internal part of the Current circle, using ever decreasing Electromagnetic Torque</p><p>Characteristics (red point). The mechanical limitations about the speed may determine the maximum</p><p>velocity for the IPMSM (ωEND) around the center of the ellipse (blue x point).</p><p>Figure 5.6 – Moving of the IPMSM working point for different Electromagnetic Torque</p><p>characteristics, Voltage ellipses and an unique Current circle (currents in A/p.u., while torque</p><p>and speed in p.u.)</p><p>98</p><p>In the low speed region, named Constant Torque Region, the machine will work always with the maximum</p><p>and nominal value of torque Temnom just until the nominal speed, called Base Speed ωB, because when</p><p>exceeding this speed value the back-emf on the stator windings could become too high to be tolerated by</p><p>the maximum voltage</p><p>In the world we live, the continued exploitation of oil resources has led to a sudden increase of level</p><p>of pollution, however creating a significant level of welfare. Now we unable to eliminate the</p><p>problem immediately and permanently, we need to limit more possible. We start considered which</p><p>is a major emitters pollutants: the car. This object that we all know and use every day. The first cars</p><p>were propelled by an electric motor but for practical reasons were converted to internal combustion</p><p>engine, that burns oil and its derivatives. This project wants study how use new technologies made</p><p>available science to find a substitute more ecological of the oil: electricity. We want more precise</p><p>make a car driven by electric motors, finding a rational and efficient way to integrate the various</p><p>components. In the project we have been made many simulations to understand the behaviour of the</p><p>PMSM motor, and was finally implemented a simple open loop control using a DSP.</p><p>Chapter 1</p><p>Problem Analysis and Project</p><p>Approach</p><p>Contents:</p><p>1.1 Initial Problem</p><p>1.2 Problem Analysis</p><p>1.2.1 Propulsion Engines Choice</p><p>1.2.2 Inverter Operating</p><p>1.2.3 Recharge Battery Pack</p><p>1.2.4 Ultra-Capacitor Use</p><p>1.2.5 DSP Tasks</p><p>1.3 Problem Formulation</p><p>1.4 Project Strategy</p><p>This Chapter contains information about the main problems to analyze for the</p><p>Project and some possible way to solve them. In order will be considered:</p><p>o How develop and realize the principal Purposes of the Project.</p><p>o How plan a complete Drive for an Hybrid Electric Vehicle.</p><p>o How deal and solve the primary problems met.</p><p>o Which generally approach is possible to use for the Project</p><p>2</p><p>1.1 Initial Problem</p><p>The necessity to use a different primary energy sources like hydrogen obliges to revamp all the Traction</p><p>System for the Vehicle. Indeed, using this type of source, the drive on the Vehicle changes completely if</p><p>compared with a classic Internal Combustion Engine Vehicle (ICEV).</p><p>In the Figure 1.1 illustrated below is shown the complete structure of the Drive taken as reference for the</p><p>Hybrid Electric Vehicle (HEV) into the Project. As possible to observe, the main energy source aboard is</p><p>provided by Fuel Cell (FC). From this point, the Drive for the Traction System becomes completely Electrical</p><p>with a mono-directional power flow introduced on the Bus Voltage, so will have an All-Electric Vehicle (EV).</p><p>Figure 1.1 – Schematic of a Fuel Cell Hybrid Electric Vehicle [Aalborg University]</p><p>The main Focus of the Project is to realize a Control for the Traction Motors and to evaluate the general</p><p>issues regarding an HEV. The Control Unit aboard the Vehicle and used in the Project will be represented by</p><p>a DSP Controller.</p><p>This type of configuration for the entire HEV drive is studied to increase the overall efficiency and</p><p>performance of an Hybrid Vehicle, so an HEV will have also problems as:</p><p>• Be able to recharge the Battery Pack aboard of the Vehicle, using the External Grid as Source and so</p><p>the Inverter like a Rectifier.</p><p>• Battery Pack must assist the Fuel Cell during the start-up of the Vehicle (approximately 6�10</p><p>minutes) and during short terms of energy requirements (to climb up-hill). Instead, for the rest of</p><p>3</p><p>the time in which the Vehicle is running, the Battery Pack must be recharged (controlled charge) by</p><p>the Fuel Cell.</p><p>• Ultra-Capacitors must be used to provide short terms peak of power (when the Vehicle requires</p><p>strong acceleration) or to capture and storage the braking energy.</p><p>• The contemporary Control of both Electrical Motors results very difficult during the turning of the</p><p>Vehicle and when the target is to realize an Anti-Slip Control.</p><p>The Initial Problem will be estimate, select, simulate and testing all the main electric traction devices</p><p>aboard, from the FC clamps until the Electric Motors (EM), excluding the Auxiliary Services for the Vehicle</p><p>(Light, Heater, etc.). Besides for a HEV it’s very important to comprehend how to make for put together</p><p>every device of the Drive and how manage and coordinate their operation, finding the best solution in</p><p>terms of type, min/max performance, quality, cost, weight and volume for each components aboard. For</p><p>these reasons the focus and the problems already described will be analyzed separately in the following</p><p>paragraph, while in the Problem Formulation paragraph will link these analysis regarding each problem to</p><p>reach a general setting for the Project.</p><p>1.2 Problem Analysis</p><p>To analyze all the problems is better to divide their handling into several sub-analyses. In the following</p><p>analyses will be dealt only the main aspects for each problem. A more detailed analysis for the most</p><p>important targets of the Project will be done in the next chapters.</p><p>1.2.1 Propulsion Electric Motor Choice</p><p>When is designing a Vehicle, as first important thing is required know the Nominal Power of the Vehicle and</p><p>which Types of Motors is possible to use for the entire Traction System. Done this, is easy then to calculate</p><p>the size of all the devices for the complete Drive and so the Final Performances for the Vehicle, like</p><p>Maximum Speed, Maximum Acceleration, Consumption and Autonomy (related with a specific Work Cycle),</p><p>Type of Car, etc.</p><p>The method just described can be used with a reverse logic, namely is possible also start with assigned</p><p>Performances for the Vehicle and then estimate and choose all the components for the Drive, including</p><p>Nominal Power and Types of Motors.</p><p>4</p><p>In this Project will be used the last approach, so will suppose assigned several Specific Performances for the</p><p>Hybrid Electric Vehicle (Velocity, Acceleration, Nominal Torque and Power, etc.) and will select every device</p><p>aboard in relation to this choice, including both Electric Motors. This means that if is projecting a rear-</p><p>wheel drive car as indicated in the Figure 1.1, each Propulsion Engine must have approximately a Nominal</p><p>Power equal to half Nominal Power of the HEV (not considering eventual kind of losses in the machines for</p><p>the moment).</p><p>As regards the Electric Motors Choice should be considered some kind of issues:</p><p>� Torque-Speed Characteristic</p><p>� Type</p><p>� Cost</p><p>� Advantages and Disadvantages about Control</p><p>� Efficiency</p><p>� Power Density</p><p>� Maintenance Problem</p><p>To choose exactly the Vehicle Motors is not necessary follow the order listed above because in this</p><p>particular case there are several considerations to do. Indeed each of these items can be more or less</p><p>important for the final choice about Traction Motors, depending of the HEV desired characteristics.</p><p>NOTE: The Electrical Drive for the HEV used in the Project (Figure 1.1) works implicitly with two AC-Motors,</p><p>but the following analysis treats still the possibility to use DC-Motors for the Traction System. In this way</p><p>will be possible to examine with more details the criteria about the Electric Motor choice. However an</p><p>eventual DC-Motors use will change only the Converter Type (in this case the Inverter will be substituted</p><p>with a DC/DC Converter).</p><p>For this specific application can be difficult to choose the correct Electric Motor to use, because a real HEV</p><p>can achieve approximately a Range Power of 30÷80 kW. This Range Power value gives the chance to apply a</p><p>Brushed DC Motor (BDC), an Induction Motor (IM), an AC Brushless Motor (PMSM) or a DC Brushless Motor</p><p>(BLDC). These four types of Electrical Motors have several Advantages and Disadvantages that must be</p><p>analyzed and compared to realize which is the best Electric Motor for the HEV. In the following table is</p><p>shown a comparison between these different solutions and pointed out in green there are the appreciated</p><p>skills for our Traction System (for Cost and Maintenance the reviews are qualitative):</p><p>insulation of the machine, so creating also problems regarding the temperature</p><p>inside the motor. So to not reduce the useful lifetime of the IPMSM, the idea is to inject a negative</p><p>component (opposite to the PM Magnetic Flux) of the d-axis Current ��� to obtain the Field Weakening, but</p><p>now working with fixed values of currents and voltages, so working in the Constant Power Region with a</p><p>lower value of Torque (ω>ωB). In the Figure 5.6 will happen that while the speed is increasing, the Voltage</p><p>ellipse will decrease the extension, moving the optimal working point from the maximum Torque/Current</p><p>ratio line. In this case the IPMSM Control Strategy will be completely revised or combined with other kind</p><p>of strategies</p><p>Figure 5.7 – Electromechanical Torque-Speed Characteristic for a IPMSM with Constant</p><p>Torque/Power Region Transition</p><p>99</p><p>5.2 IPMSM Control Strategy Optimizations</p><p>Before to choose the best Control Strategy capable to optimize the IPMSM behavior with the performances</p><p>demanded by the Electric Drive, is necessary evaluating if all the electrical values are achievable without</p><p>overshooting the nominal limits of the machine plus inverter, ensuring good operating conditions.</p><p>In relation with the previously analysis regarding the operating domains of a IPMSM, will be possible to</p><p>distinguish 4 different type of Control for this Motor. Each one of these Control Strategies is based on the</p><p>Rotor Flux Oriented Control (RFOC), namely in every instant the Rotor Position F� must be known, taking it</p><p>between the rotating magnetic d-axis and the stator fixed magnetic position according the α-axis (look</p><p>Figure 4.10). The possibilities are listed below:</p><p>1) Control with GHI = J. The IPMSM Control Algorithm becomes very simple because is sufficient for</p><p>the Implementation to process a command signal where will be present only the reference</p><p>regarding ��</p><p>. This simplification allows to make linearized the relationship Torque/Current, but</p><p>doesn’t use the Reluctance Torque and so doesn’t allow to optimize the Torque/Current ratio,</p><p>making lose an useful Electromagnetic Torque contribute for the IPMSM.</p><p>2) Control with ε>K L6 Constant. Such solution allows to control the Electromagnetic Torque</p><p>instantaneous value evaluating the angle ε between the PM Magnetic Flux ���� and the Stator</p><p>Current Vector �� and using all the electrical variables in the αβ reference frame. In this way is</p><p>possible to optimize the use of the Electromagnetic Torque, achieving a good compromise between</p><p>simple realization and discrete Torque/Current ratio.</p><p>3) Optimum Torque Control. Such strategy maximizes the T/I ratio, working until the Base Speed</p><p>always with the maximum Electromagnetic Torque that the IPMSM can provide. This Control</p><p>Algorithm so must optimize the Current Trajectory on the system (��� , ��</p><p>$ like in the Figure 5.6,</p><p>using the criterion Maximum Torque per Ampere (MPTA), namely following always the Trajectory</p><p>able to ensure the max T/I ratio.</p><p>4) Optimum Torque + Field Weakening Control. This Control Algorithm implements the same</p><p>mathematical expressions used for the MPTA, but just until the nominal speed (or Base Speed ωB).</p><p>Indeed over this point becomes impossible to follow the Trajectory capable to maximize the</p><p>Torque/Current ratio because is impossible to stay still in the Constant Torque Region. So from the</p><p>Base Speed must be applied the Field Weakening Control Strategy, implementing and calculating</p><p>new mathematical relations capable to create a signal command for the d-axis and q-axis Current</p><p>Regulators able to make working the IPMSM in the Constant Power Region. Besides using this</p><p>strategy is very important to be accurate about the nominal speed, because will be possible to</p><p>comprehend exactly when the IPMSM is starting the weakening, so avoiding wrong transitions from</p><p>a region to another one (is very important because the Control Algorithm changes completely).</p><p>100</p><p>The most suitable IPMSM Control Strategy to use for HEV Drive is the Optimum Torque + Field Weakening</p><p>Control, because it is able to provide high Torque value for low Speed and to extend the velocity control</p><p>range towards high mechanical speed values. The capacity to obtain high efficiency until the ωEND makes</p><p>this IPMSM Control Strategy particularly indicated for HEV. It’s obviously that using this strategy the</p><p>Algorithm and all the Control System complexity will increase considerably.</p><p>5.2.1 Maximum Torque per Ampere (MTPA)</p><p>As is necessary to find an Electromagnetic Torque expression capable to maximize the T/I ratio until the</p><p>nominal speed ωB, is possible to start from the (5.2) expressions, in particular from the expression</p><p>regarding the Electromagnetic Torque. So using the (5.3) in function of the q-axis current ��</p><p>, will be</p><p>possible to have:</p><p>��� = �� 	��������−���� + �� 	���� − ��</p><p>��������−���� (5.10)</p><p>Now calculating the maximum of the Electromagnetic Torque expression in the (5.10) in function of the</p><p>Stator d-axis current ��� and equaling it to zero, will be possible to obtain the maximum ��� mathematical</p><p>expression capable to maximize the T/I ratio, namely able to identify the right Current Trajectory on the</p><p>(��� , ��</p><p>$ system and at the same time optimizing the Electrical Drive Performances:</p><p>M���M��� = 32 	 PQ</p><p>QR���� 12 #−2���$</p><p>����−���� + ���� − ��</p><p>���� 12 #−2���$</p><p>����−���� + ���� − ��</p><p>�����−����</p><p>TU</p><p>UV = 0</p><p>⇒ 2���� − ��</p><p>�����+������� − ���� − ��</p><p>���� =0</p><p>⇒ ��� = 0'12W�-'4C-'.� − �0'12)BX�-'.C-'4�)D')</p><p>W�-'4C-'.� (5.11)</p><p>The relation in (5.11) is very important because allows to find the Current Trajectory to realize the</p><p>maximum Torque/Current ratio Algorithm. Indeed implementing the (5.11) and the inverse relation of the</p><p>(5.3) will be already possible to generate the correct references ���∗ and ��</p><p>∗ for the d-axis and q-axis</p><p>currents controllers(until the nominal speed) and to compare them with the real value ��� and ��</p><p>provided</p><p>by the IPMSM, typically approach used for Feed-back Control Scheme, like is shown in the Figure 5.8.</p><p>101</p><p>Figure 5.8 – Generic Current Control Scheme used for Feed-back Control</p><p>So fixed a such pair of currents ��� and ��</p><p>inside the Current circle (nominal limits) and implementing the</p><p>(5.11) and the (5.3) will obtain always the maximum Electromagnetic Torque value, but however the</p><p>IPMSM will present some applicative limits due to the maximum speed value regarding the MTPA. Indeed</p><p>for low mechanical speed whose verifies the condition ω<ωB, it’s easy to comprehend that, the admissible</p><p>locus points in the Current circle where the Torque is maximized can exist only until the values ����Z[ and ��</p><p>�Z[, like is understandable by the Figure 5.9.</p><p>Figure 5.9 – d-axis and q-axis Currents for the Maximum Torque Hyperbola with ω<ωB</p><p>����Z[ and ��</p><p>�Z[ represent the maximum current values that the Control Strategy is able to give on the</p><p>output only until the Base Speed ωB and can be extracted analytically comparing the (5.11) and the (5.3)</p><p>expressions and using the nominal value ��� inside them. The Electromagnetic Torque calculated with these</p><p>values will be equal to the nominal Electromagnetic Torque that the IPMSM will be able to support.</p><p>However will be possible to have the following current values in the (5.12) and (5.13) expressions:</p><p>����Z[ = 0'12W�-'4C-'.� − \] 0'12W�-'4C-'.�^� + D'()� (5.12)</p><p>102</p><p>��</p><p>�Z[ = ����� − ����Z[� (5.13)</p><p>All this MTPA theory is valid until ω<ωB,</p><p>because then for ω=ωB (Figure 5.10) the Voltage ellipse will restrict</p><p>crossing the Maximum Torque Hyperbole and the Nominal Current circle exactly in the ����Z[ and ��</p><p>�Z[</p><p>point. In this moment, physically in the machine will have that the contributions due to the b-emf will</p><p>increase, tending to overpass the Voltage Limit. In this case, for don’t damage the IPMSM, must be started</p><p>the Weakening Control Strategy, finding and calculating specific mathematical relations to apply with the</p><p>Control Algorithm the right Current Trajectory.</p><p>To achieve the value of the Base Speed ωB and be able to recognize when is the moment to pass from the</p><p>Constant Torque Region to the Constant Power Region is possible using the (5.5) with the equal sign and</p><p>putting in it the ����Z[ and ��</p><p>�Z[ values:</p><p>_` &'(*��0'12B-'.D'.,ab�)B-'4)D'4,ab) (5.14)</p><p>Figure 5.10 – d-axis and q-axis Currents for the Maximum Torque Hyperbola with ω=ωB</p><p>Instead, when the Mechanical Speed ω>ωB will happen the situation illustrated in Figure 5.11, namely the</p><p>IPMSM operative area will restrict, allowing to the MTPA Control Strategy to be applied just for the stretch</p><p>bordered by the Voltage Limit. In this situation the points locus in whose is possible to maximize the T/I</p><p>ratio can be followed until the new values ���c and ��</p><p>c. These two terms represent respectively the</p><p>transition values of the Stator d-axis and q-axis Current that will met when the IPMSM is passing from the</p><p>Constant Torque Region to Constant Power Region, so will depend necessarily from the speed. They can be</p><p>obtained using the (5.11) in the (5.5) with the equal sign:</p><p>103</p><p>���c = -'4)C�-'4-'.B�-'.)��-'4C-'.��-'4)B-'.)� ���� − \ �-'4)C�-'4-'.B�-'.)�)</p><p>W�-'4C-'.�)�-'4)B-'.)�) ����� + / d'(ef,3)C0'12)</p><p>-'4)B-'.) (5.15)</p><p>��</p><p>c = ����c� − 0'12�-'4C-'.� ���c (5.16)</p><p>Figure 5.11 – d-axis and q-axis Currents for the Maximum Torque Hyperbola with ghi>ω>ωB</p><p>When the IPMSM mechanical speed ωm reaches the End Transition Speed ωBt, like is possible to see by the</p><p>Figure 5.12, the points locus regarding the maximum torque characteristic will cross the Voltage ellipse only</p><p>in the origin of the axes, staying completely outside from the operative area. This means that is achieved</p><p>the MTPA Limit, i.e. will not be possible anymore to apply this Optimum Torque Control Strategy over the</p><p>End Transition Speed ωBt. This velocity value able to define the maximum applicability of the MTPA Control</p><p>Strategy can be calculated in a simple way using the (5.5) with the Stator d-axis and q-axis Current equal to</p><p>zero:</p><p>_c = &'(*0'12 (5.17)</p><p>It’s very important differentiate the meaning between</p><p>_ and</p><p>_c. The first mechanical speed indicates</p><p>the real velocity that the IPMSM can reach without overpassing the Nominal Limits regarding voltages and</p><p>currents and that must be taken like reference point to make the passage from MTPA to Field Weakening</p><p>Control Strategy, while the second mechanical speed represents just the maximum velocity after which the</p><p>104</p><p>MTPA Control Algorithm can’t apply anymore a Trajectory capable to maximize the T/I ratio because the</p><p>IPMSM operative area is changed.</p><p>Figure 5.12 – d-axis and q-axis Currents for the Maximum Torque Hyperbola with ω=ωBt</p><p>5.2.2 Field Weakening Control (FWC)</p><p>Analyzing the case when the IPMSM mechanical speed is included between</p><p>_ and</p><p>_c (Figure 5.13), will</p><p>be possible to see that the MTPA Control Strategy can be applied only until ���c and ��</p><p>c (values not</p><p>matching with the End Transition Speed</p><p>_c).</p><p>Despite the MTPA Control Strategy can be used until</p><p>_c, it’s really advisable to pass to the Field</p><p>Weakening Control (FWC) Strategy previously, from the Base Speed</p><p>_. In this way will be possible to</p><p>maintain ever the nominal operating conditions for the Motor, but above all will be optimized the</p><p>Electromagnetic Torque generation and at the same time will be allowed to expand the IPMSM Control</p><p>Domain.</p><p>Ever referring to the Figure 5.13 and treating the case ωB<ω<ωBt, to comprehend the different</p><p>performances in this range between MTPA and FWC is sufficient to observe that for the same speed value</p><p>the MTPA can provide only the #���c , ��</p><p>c$ pair, while the FWC allows to provide the #���j , ��</p><p>j$ pair,</p><p>namely the FWC is giving an higher Electromagnetic Torque value than MPTA, recovering a considerable</p><p>part. Indeed from the #���c, ��</p><p>c$ point, following the voltage limit stretch between the points locus for the</p><p>maximization of the torque and the current circle, will arrive to work on the #���j , ��</p><p>j$ point always in the</p><p>IPMSM operative area, but not maximizing anymore the T/I ratio. The ���j and ��</p><p>j will represent the</p><p>generic current values with which supply the Motor through the FWC Strategy.</p><p>105</p><p>So to not lose a good Torque contribute is very important start with the FWC exactly from the Base Speed</p><p>_ (Figure 5.10), because continuing with the MTPA should be possible to arrive just until</p><p>_c, while with</p><p>FWC will be possible to work until</p><p>klm (Figure 5.14).</p><p>Figure 5.13 – Torque Recovery Stretch for FWC than MTPA with ωB<ω<ωBt</p><p>Figure 5.14 – Different Regions Control for MTPA Control and FWC [Acampa]</p><p>106</p><p>The FWC allows to expand the IPMSM T-ω Domain Control, but is indispensable before to implement this</p><p>Control Strategy to calculate all the mathematical expressions capable to make move the working point</p><p>from /����Z[, ��</p><p>�Z[3 and Constant Torque Hyperbole to another generic ����j , ��</p><p>j� point. Moving the</p><p>operating point over the End Transition Speed</p><p>_c, although the locus points for the maximization of the</p><p>T/I ratio are completely outside of the IPMSM operative area, however will remain the possibility to follow</p><p>the voltage limit stretch because it is included in the current circle, so still staying in the IPMSM operative</p><p>area, like is possible to see in the Figure 5.15.</p><p>Figure 5.15 – d-axis and q-axis Currents for the FWC Strategy with ωEND>ω>ωBt</p><p>To impose into the FWC Strategy the correct reference signals ���j∗ and ��</p><p>j∗ for the d-axis and q-axis</p><p>Current Regulators, the mechanical speed</p><p>� must be known, like also the feedbacks about the real ���</p><p>and ��</p><p>values. So will be possible to determine the d-axis and q-axis current references calculating ���j and ��</p><p>j at the intersection between the voltage ellipse and the current circle (after</p><p>_), namely using the (5.3)</p><p>equation explicit in function of ��</p><p>j and substituting it in the (5.5) with the equal sign, will reach the</p><p>following equations to implement in the FWC Algorithm:</p><p>���j = -'40'12-'4)C-'.) − \ -'4)0'12)</p><p>�-'4)C-'.)�) − / d'(ef,3)C0'12)C-'4)D'()</p><p>-'4)C-'.) (5.18)</p><p>��</p><p>j = ����� − ���j� (5.19)</p><p>107</p><p>Calculating the (5.18)-(5.19) values with these equations and putting them in the (5.2) can be found the</p><p>Electromagnetic Torque reference value imposed by the FWC Algorithm. Comparing this value with the real</p><p>Electromagnetic Torque value given by the Motor will be possible to have the Torque error to implement at</p><p>least the current loop in the IPMSM Control Scheme.</p><p>The FWC analysis until this moment can allow to the IPMSM Electric Drive to work over the nominal speed</p><p>_, but reducing the Electromagnetic Torque when the speed increases</p><p>and ever respecting all the IPMSM</p><p>nominal constraints.</p><p>To know which is the FWC upper limit speed without overtaking the IPMSM nominal limits must be</p><p>analyzed the position of the voltage ellipse center in the (��� , ��</p><p>) axes, identified by the coordinates</p><p>(−���� ���⁄ , 0) already described (values easily reachable from the IPMSM plate data). Besides is very</p><p>important to have information about the voltage ellipse center because knowing where it is placed will be</p><p>possible comprehend how the IPMSM operating point will move in the (��� , ��</p><p>) axes, ever with the purpose</p><p>to maximize the Electromagnetic Torque in each working condition.</p><p>So the voltage ellipse center, like is possible to realize from the following cases, can assume 3 different</p><p>position in relation to the current circle position, partly changing the FWC behavior:</p><p>1) Voltage ellipse center outside from the Current circle: if the IPMSM parameters are such that the</p><p>ellipse center is not inside the current circle (Figure 5.16) will have the possibility to use the FWC</p><p>Strategy from the (����op, ��</p><p>�op) point until the point with the coordinate (−���, 0), namely will</p><p>be possible to apply the FWC until the situation whose the voltage ellipse becomes tangent to the</p><p>current circle. So for IPMSM with this property and that use this control strategy, the maximum</p><p>speed achievable without overpass the nominal limit of the electric machine is given precisely from</p><p>the speed value</p><p>klmq reached in the point (−���, 0), where obviously will provide an</p><p>Electromagnetic Torque value ideally equal to zero. Over this limit is impossible to guarantee the</p><p>right IPMSM operating conditions because is impossible to work into the IPMSM operative area.</p><p>108</p><p>Figure 5.16 – FWC Trajectory for a IPMSM with |−stuv wtx⁄ | > |−zt{| (From gh to g|}~�)</p><p>The maximum mechanical speed</p><p>klmq can be calculated using the d-axis radius definition and</p><p>particularizing it for the case whose the voltage ellipse becomes tangent to the current circle,</p><p>providing the following (5.20) expression:</p><p>� :� = &'(*+����-'.:� = |−���� ���⁄ | − |−���| ⇒�</p><p>klmq` d'(e����'12 �'.⁄ ��|��'(|��'. (5.20)</p><p>2) Voltage ellipse center placed on the Current circle: this case can be considered an extreme situation</p><p>of the case 1), because despite is a very rare possibility, may happen that the voltage limit center</p><p>could stay exactly on the current circle border (Figure 5.17). However for this eventuality the FWC</p><p>behavior will be the same of that analyzed in the case 1), with the only exception regarding the</p><p>maximum speed</p><p>klm. Indeed there isn’t a real theoretical limit about the speed value because</p><p>until the “ideal” velocity</p><p>klm� ></p><p>klmq (matching to the (−���, 0) point) the IPMSM will operate</p><p>always in the nominal operative area, as the voltage ellipse will shrink on itself still conserving the</p><p>right conditions for continue to apply the FWC Strategy.</p><p>109</p><p>Figure 5.17 – FWC Trajectory for a IPMSM with |−stuv wtx⁄ | = |−zt{| (From gh to g|}~L)</p><p>It’s easy to realize that in this particular case the maximum speed</p><p>klm� can’t be calculated</p><p>analytically and so it will have only mechanical limitations bound to the specific IPMSM used into</p><p>the electric drive. However it’s really advisable don’t use the FWC Strategy until the mechanical</p><p>speed limitations, but it’s better to work until a safe speed value</p><p>klm�� <</p><p>klm� to avoid</p><p>mechanical failures.</p><p>3) Voltage ellipse center inside the Current circle: in this situation the FWC behavior is exactly the</p><p>same already discussed for the cases 1) and 2), but just until the mechanical speed corresponding</p><p>to the P point (Figure 5.18). Indeed, being the voltage ellipse center contained in the current circle,</p><p>there are two different modalities regarding how to make the FWC from the P point.</p><p>Observing the Figure 5.18, the first possibility would be continue to move on the current circle</p><p>(orange path) like already discussed for the case 2), till arrive in the (−���, 0) point where the</p><p>voltage ellipse is tangent to the current circle. From this point, if the speed continues to increase</p><p>his value, the voltage ellipse will restrict on itself around the (−���� ���⁄ , 0) point and to keep the</p><p>nominal IPMSM operative area must be decreased (without other possibilities) the �� amplitude.</p><p>It’s fundamental to comprehend that in this way there isn’t any type of optimization for the</p><p>Electromagnetic Torque because in practice when is surpassed the (−���, 0) point the IPMSM will</p><p>not provide anymore an useful value of Torque. Besides, from the P point until the (−���, 0) point,</p><p>if the FWC works following this trajectory will lose an useful Torque contribute because will not</p><p>maximize the T/V ratio, like will be possible to do if is used the other path.</p><p>110</p><p>Figure 5.18 – FWC Trajectory for a IPMSM with |−stuv wtx⁄ | < |−zt{| (From gh to g|}~�)</p><p>The second possibility is almost totally used for this type of electrical drive. Indeed from the P point</p><p>if is followed the trajectory corresponding to the maximum T/V ratio (violet path) will be possible to</p><p>optimize the Electromagnetic Torque. The change of the trajectory from the P point will occur</p><p>exactly when the T/V maximization curve will cross the current circle, for such speed value ωP.</p><p>To calculate which is the exactly T/V maximization curve to use after the P point and to obtain the</p><p>best FWC Trajectory until the ωEND3 (also in this case theoretically infinite) can be understood</p><p>analyzing the IPMSM behavior when is applied the Maximum Torque per Voltage (MTPV) Control</p><p>Strategy.</p><p>5.2.3 Maximum Torque per Voltage (MTPV)</p><p>When the IPMSM is working for high speed value ω>ωP, to optimize the Electromagnetic Torque generation</p><p>when the voltage ellipse center is contained inside the current circle is necessary to use the MTPV</p><p>Algorithm, namely must be found the analytic expression that permits to maximize the T/V ratio with the</p><p>purpose to implement it in the Control Strategy.</p><p>The max T/V ratio expression can be obtained rewriting the (5.5) equation with the equal sign and using in</p><p>it the Magnetic Saliency ζ definition saw in the (4.1):</p><p>&'()*)+,) = #������ + ����$� + ��������</p><p>� (5.21)</p><p>111</p><p>To continue the mathematical handling is useful to define new variables (using �m and �� instead ��� and ��</p><p>) that allow also to use a reference frame centered in the max T/V ellipse:</p><p>��m = -'.D'.B0'12�-'. ⇒ ��� = ��m − 0'12-'.�� = ��</p><p>� (5.22)</p><p>Where �m and �� can be considered respectively like the d-axis and q-axis components of a dummy Stator</p><p>Current Vector �m� and with which is easy to define for it amplitude and phase:</p><p>� �m� = ��m�+���</p><p>〈�m�〉 = � = tanCq /D�D�3 ⇒ ��m = �m� cos ��� = �m� sin � �� (5.23)</p><p>Substituting the (5.22) and (5.23) equations inside the (5.21) expression will be possible to reach the �m�</p><p>value that will be used in the Electromagnetic Torque equation:</p><p>&'()*)+,) = ��m�+���������� = �m�������� ⇒ �m� = &'(*�-'.+, (5.24)</p><p>Now using the (5.24) in the (5.2) Electromagnetic Torque formula (with already incorporated the Magnetic</p><p>Saliency definition ζ from (4.1)) and exploiting the polar form expression for the (5.23) will have:</p><p>��� = �� &'(+,�-'. ����� sin � + #1 − �$ &'(*+,� cos � sin �� (5.25)</p><p>As the objective is that to maximize the T/V ratio needs to divide the (5.25) for the ���, make the</p><p>Electromagnetic</p><p>Torque derivative among the � angle (concerning the fictive displacement between the �m� vector and the d-axis) and equaling all to zero. In this way will be possible to have the maximization of</p><p>the T/V ratio with dummy variables:</p><p>M /��� ��6 3M� = 32 ���</p><p>����� ]���� cos � + #1 − �$ ���</p><p>�� #sin �� − cos ��$^ = 0</p><p>⇒ ���� cos � + #1 − �$ &'(*+,� #sin �� − cos ��$ = 0 (5.26)</p><p>Bringing back the (5.26) into the normal reference system (��� , ��</p><p>$ will be possible to achieve the MTPV</p><p>Trajectory to implement in the Control Algorithm that can ensure the maximum T/V ratio for certain speed</p><p>values:</p><p>���#1 − �$ ]/-'.D'.B0'12�-'. 3� − ��</p><p>�^ + ���� /-'.D'.B0'12�-'. 3 = 0 (5.27)</p><p>112</p><p>The T/V trajectory in (5.27) will describe an ellipse that will intersect the d-axis exactly in the voltage ellipse</p><p>center, while it will intersect the current circle in the P point (Figure 5.18) for a speed value corresponding</p><p>to ωP. It’s very important to note that T/V maximization curve used for the FWC Trajectory (after the P</p><p>point) doesn’t depend by a specific speed value, but only by the IPMSM parameters and by the current</p><p>values ��� and ��</p><p>. This means that there is only one max T/V curve depending from the voltage ellipse</p><p>center position.</p><p>To calculate the speed value ωP when there is the transition of the FWC Trajectory from the current circle</p><p>to the maximum T/V curve can be done considering during such speed value that the nominal current circle</p><p>(so ���value) will cross the voltage ellipse (corresponding to the speed ωP) and the max T/V curve exactly in</p><p>the P point. So for this reason using the (5.3) in the (5.27), will be possible to obtain a second degree</p><p>equation with ��� like variable wrote in function of the nominal stator current ���. Making this manipulation</p><p>and then some mathematical steps will have:</p><p>���#1 − �$ / q�) + 13 ���� + ��#qC�$0'12�) + 0'12� � ��� + #qC�$0'12)�)-'. + 0'12)�-'. − ���#1 − �$���� = 0 (5.28)</p><p>The (5.28) equation can be solved finding two solutions ���q and ����, but only one solution between them</p><p>will be appropriate to calculate the ωP expression (the solution able to ensure a negative ��� value).</p><p>Assuming ���q like possible right solution, now it’s easy to achieve the ωP speed exploiting the (5.5) and</p><p>particularizing it in the P point, so using the ���q current corresponding for that point:</p><p>&'()*)+1)-'.) = /���q + 0'12-'. 3� + /-'4-'.3� ����� − ���q�� ⇒</p><p>� = &'(</p><p>*-'.\�D'.�B�'12�'. �)B��'4�'.�)�D'()CD'.�)� (5.29)</p><p>5.3 IPMSM Control Trajectory</p><p>Evaluated all the IPMSM optimal control domains with the MTPA and MTPV strategies, ultimately is</p><p>necessary to comprehend how apply the FWC Strategy with a complete extension regarding all the IPMSM</p><p>speed range, from zero until the maximum velocity ωEND (considering a general case).</p><p>With MTPA and MTPV strategies have been possible to represent the locus points where the Torque</p><p>Hyperboles was tangent respectively with the Current Circles and Voltage Ellipses, so optimizing the Torque</p><p>in any IPMSM operating condition and ever respecting the nominal limits. Indeed the current circle and the</p><p>voltage ellipse define the IPMSM operative area and them will depend respectively from the nominal</p><p>current value capable to flow through the Inverter and from the nominal Bus DC voltage value on the</p><p>Converter DC side.</p><p>Other theoretical limitations regard the IPMSM operating quadrants, because if the electrical machine will</p><p>operate like a motor will work in the 2° quadrant (negative ��� and positive ��</p><p>), while if it will work during</p><p>113</p><p>the braking phase will need to operate in the 3° quadrant (negative ��� and negative ��</p><p>). However, as the</p><p>2° and 3° IPMSM regions are symmetric, it’s sufficient to examine the case when the machine is working</p><p>like a motor.</p><p>So considering the maximizations of T/I and T/V ratios already discussed, from the following Figure 5.19 is</p><p>possible to see that the IPMSM optimum operating range is confined inside the limits got from the OBPC</p><p>area, namely from the points bordered from the intersection between max T/I trajectory-current circle-</p><p>nominal voltage ellipse-max T/V trajectory.</p><p>Figure 5.19 – IPMSM Operating region in the (GHI,GH�) System</p><p>Analyzing each single segment of the region bordered by OBPC will be possible to establish:</p><p>� Line OB: represents the trajectory capable to maximize the T/I ratio (MTPA) for a speed range</p><p>between 0≤ω≤ωB, with a possible range of Electromagnetic Torque values that go from zero to the</p><p>maximum value Tem nom. Surpassed the Base Speed ωB, to maintain the operating conditions into the</p><p>IPMSM operative area must be changed trajectory.</p><p>� Line BP: overtaken the Base Speed ωB the IPMSM starts to operate with the FWC, engaging on the</p><p>current circle and so maintaining constant the amplitude of the Stator Current ��. In this way the</p><p>Electromagnetic Torque values will decrease because the FWC will reduce the ��</p><p>and will raise the ��� amplitude until the speed corresponding to the P point, making have a range speed ωB<ω≤ωP.</p><p>� Line PC: when the voltage ellipse center is out or exactly on the border of the current circle this</p><p>segment doesn’t exist. This means that only when the center is included in the current circle will be</p><p>possible to apply the maximization of the T/V ratio (MTPV) from the speed value corresponding to</p><p>114</p><p>ωP until a theoretical infinite value. In this stretch is ever kept the FWC Strategy, combining it with</p><p>the MTPV and making decreasing the Torque and the Current values until null values.</p><p>The Control Strategy has to select, in every operating condition (both transient and steady-state), the</p><p>optimum current pair (��� , ��</p><p>$ related with the torque and speed values required. Indeed if the IPMSM</p><p>Control Algorithm provides the right Trajectory (exactly like shown in the Figure 5.20) in the entire speed</p><p>range, will be generated on the BPC stretch the maximum Electromagnetic Torque considering the limits</p><p>due to the maximum current and voltage of the motor, so optimizing the FWC Strategy for the IPMSM in</p><p>each possible zone.</p><p>Figure 5.20 – IPMSM Control Trajectory and Optimal FWC Operating Point in the (GHI,GH�)</p><p>System</p><p>Over the nominal speed ωB, namely when is started the weakening, the working point Q during the steady-</p><p>state is represented by the intersection between the controlled torque hyperbola and the controlled speed</p><p>ellipse. This point can be achieved moving on the max T/V curve until the intersection with the torque</p><p>required and then engaging on it, up to arrive on the controlled speed ellipse in the Q point. Obviously that</p><p>the other intersection point Q’ cannot be used because will surpass the current limits.</p><p>It’s very important to comprehend, referring to the Figure 5.19, that without a correct FWC Algorithm, the</p><p>current regulators could demand, near the B point, a voltage value bigger than nominal value, making take</p><p>the voltage limitation. In this case will lose every kind of control about the current values and the IPMSM</p><p>behavior will be determined by the voltage limitation, with which will be set current values that will give a</p><p>smaller Electromagnetic Torque value, making decelerate the IPMSM.</p><p>115</p><p>Besides the nominal speed value ωB, calculable from the (5.14), depends only by the IPMSM parameters, so</p><p>eventual inaccuracies about their values will cause differences between the ωB value calculated with the</p><p>FWC Algorithm and the real speed value measured, namely making wrong the instant whose the weakening</p><p>must start. Indeed the PM Magnetic Flux ���� has a very strong dependence from the Temperature (like</p><p>also the Stator Resistance), while the Synchronous d-axis and q-axis Inductances ��� and ��</p><p>depend from</p><p>the Load variation (meanly ��</p><p>).</p><p>A Control Strategy based on the (5.14) expression risks to apply the FWC Algorithm in an imprecise way,</p><p>namely weakening before to achieve the nominal speed ωB means to apply for the IPMSM drive control the</p><p>(5.18) and (5.19) instead the (5.11) and (5.3) relations.</p><p>Figure 5.21 – IPMSM Anticipated Weakening in the (GHI,GH�) System</p><p>Observing the Figure 5.21 listed above, if there is an error between the estimated voltage ellipse and the</p><p>real voltage ellipse, the weakening will start in the P1 point, so renouncing unconsciously to the P1P2</p><p>stretch. In this way, as the FWC starts to operate in the P1, the Electromagnetic Torque will lose a part of</p><p>his value, i.e. losing a IPMSM dynamic performances part.</p><p>If will happen the opposite mistake, with the estimated voltage ellipse delayed among the real voltage</p><p>ellipse, the current regulator will saturate, making have a sudden Electromagnetic Torque hole because the</p><p>operating point will be imposed by the voltage limitations and not anymore by the current reference.</p><p>116</p><p>5.4 Demagnetization Limits</p><p>When is implemented a FWC Strategy, can assume great importance the IPMSM limits regarding the</p><p>Permanent Magnet Demagnetization. Indeed, for don’t damage the proper functioning of the PM, could be</p><p>necessary to keep some application limits for the Control Strategy.</p><p>The limits capable to avoid the PM Demagnetization depend by the IPMSM parameters value, so will be</p><p>possible 3 cases depending where is positioned the vertical line indicating the Demagnetization Limit km:</p><p>1) Demagnetization Limit completely on the left of the current circle: in this situation there isn’t any</p><p>type of intersection between the current circle and the demagnetization limit (Figure 5.22), so the</p><p>current circle radius ��� will be lower than the ��� value in the (5.6), making have the condition:</p><p>��� ≤ − =,0'12-'. (5.30)</p><p>When is verified the (5.30) are valid all the considerations taken until this moment, namely the</p><p>FWC Strategy will not have limits regarding the PM demagnetization. For example if is considered</p><p>the case with the voltage ellipse center outside the current circle, will be possible without any</p><p>problem to have speed range values between 0 and ωEND1, namely when the voltage ellipse will be</p><p>tangent to the current circle.</p><p>Figure 5.22 – Demagnetization Limit on the left of the Nominal Current Circle</p><p>2) Demagnetization Limit intersects the current circle: in this case is necessary redefining the IPMSM</p><p>operative area because the (5.30) condition is not satisfied anymore. Indeed, like is possible to see</p><p>from the Figure 5.23, the Demagnetization Limit will define a new IPMSM operative area for a such</p><p>speed value, named Limit Exchange Speed ωL, corresponding to the intersection in the same L</p><p>point between the demagnetization limit, the current circle and the voltage ellipse.</p><p>117</p><p>For speed values smaller than ωL will not be necessary to change the FWC Strategy because will be</p><p>possible always to apply the (5.18) and the (5.19) equations without go out from the IPMSM</p><p>operative area. Instead for speed values bigger than ωL, the area made by the intersection</p><p>between the voltage ellipse and the demagnetization limit (always in the current circle) will</p><p>provide the limit d-axis and q-axis current values ���� and ��</p><p>� that the FWC Strategy should apply.</p><p>To calculate these values is sufficient to use the (5.6) particularized for this case and then</p><p>substitute it in the (5.5) equation:</p><p>���� = − =,0'12-'. (5.31)</p><p>��</p><p>� = q-'4 �/ &'(*+ 3� − �����#1 − ;�$� (5.32)</p><p>Figure 5.23 – Demagnetization Limit Intersection with the Nominal Current Circle</p><p>The limit speed value ωL over which is not anymore possible to continue with the normal FWC</p><p>Strategy can be calculated exploiting that the current circle, the demagnetization limit and the</p><p>voltage ellipse cross the same L point. So substituting the (5.31) in the (5.3), getting the q-axis</p><p>current ��</p><p>� and putting all in the (5.5), will be possible to have the speed value ωL:</p><p>- = &'(</p><p>*\-'4)D'() B0'12)¡qC�=,B¢qC�'4)�'.)£=,)¤ (5.33)</p><p>The IPMSM mechanical speed can be still increase over</p><p>-. Indeed to maintain the IPMSM</p><p>operative area inside the nominal region will be possible to arrive until a speed value</p><p>-� in</p><p>118</p><p>whose the voltage ellipse is tangent to the demagnetization limit line. Over the</p><p>-� velocity is</p><p>impossible to work because there isn’t a common region where are satisfied at the same time the</p><p>current limit, the voltage limit and the demagnetization limit. So to calculate</p><p>-� is sufficient</p><p>substitute the ��� and ��</p><p>values in the (5.5) expression and find the maximum</p><p>-� speed that is</p><p>possible to reach with the FWC Strategy:</p><p>-�` d'(e�'12#��¥,$ (5.34)</p><p>3) Demagnetization Limit intersects the current circle and the max T/I curve: in this case the</p><p>demagnetization limit will intersect also the curve that able to maximize the T/I ratio, so making</p><p>change necessarily the FWC Algorithm. Like shown in the Figure 5.24, the demagnetization limit</p><p>line will cross the max T/I curve for the (����, ��</p><p>�) point (F) into the current circle area, so when</p><p>the torque is corresponding to that point will not be possible continue to move on the max T/I</p><p>curve because will be exceeded the IPMSM operative area, but in this case will have a good</p><p>optimization of the FWC Strategy if the Algorithm Trajectory will allow to move from such point on</p><p>the demagnetization limit until to arrive to cross the current circle in the (���D, ��</p><p>D) point. Such</p><p>point represents the transition from the maximization of the T/I ratio to the value capable to</p><p>protect by the PM demagnetization.</p><p>To find the ���� and ��</p><p>� expressions can be considered that ���� will coincide with the (5.31),</p><p>while ��</p><p>� can be found substituting the ���� in the (5.16):</p><p>���� = − =,0'12-'. (5.35)</p><p>��</p><p>� = ������ − 0'12�-'4C-'.� ���� (5.36)</p><p>Instead to find ���D and ��</p><p>D is sufficient to evaluate that ���D has the same expression of the (5.35),</p><p>while ��</p><p>D expression can be reached substituting the (5.35) in the (5.3):</p><p>���D = − =,0'12-'. (5.37)</p><p>��</p><p>D = �����−���D� (5.38)</p><p>119</p><p>Figure 5.24 – Demagnetization Limit Intersection with the Current Circle and Max T/I</p><p>Curve</p><p>So for low speed values, such to avoid the nominal voltage limit, will be followed the T/I</p><p>maximization curve till the F point, but then the machine will provide a torque following the</p><p>demagnetization limit line, until the (���D , ��</p><p>D) point. So for the Control Strategy will be</p><p>implemented the (5.11) and (5.3) till the F point (normal MTPA Strategy), but to move on the</p><p>demagnetization limit must be found the generic ���D* and ��</p><p>D* expressions that the FWC</p><p>Algorithm should impose like reference for the current regulators.</p><p>The ���D* value can be found from the (5.6) considering that the trajectory is moving on the</p><p>demagnetization limit line:</p><p>���D∗ = − =,0'12-'. (5.39)</p><p>The ��</p><p>D* value instead can be reached using the (5.2) Electromagnetic Torque equation</p><p>particularized for the generic point on the demagnetization limit center:</p><p>��</p><p>D∗ = >?,∗@)*0'12¥,�'4¦#��¥,$�'.�'.</p><p>(5.40)</p><p>120</p><p>Chapter 6</p><p>IPMSM Control System</p><p>Development</p><p>Contents:</p><p>6.1 Implementation of the IPMSM Mathematical Model</p><p>6.1.1 IPM Motor Rated Values and Parameters</p><p>6.1.2 IPM Motor Nominal Tests</p><p>6.1.3 SVPWM-VSI</p><p>6.2 IPMSM Control System Realization</p><p>6.2.1 Decoupling d-q Axis</p><p>6.2.2 Current Loop Design</p><p>6.2.2.1 Current PI Controllers Design</p><p>6.2.3 Torque Control</p><p>6.2.3.1 Non-Optimized Torque Control</p><p>6.2.3.2 MTPA Control</p><p>6.2.4 Speed Loop Control and Design</p><p>6.2.4.1 FWC Strategy</p><p>This Chapter will treat all the possible IPMSM operating regions and how</p><p>realize the control strategy without overpassing the operative area. Besides</p><p>will be provided all the mathematical expressions capable to implement</p><p>different types of optimizations for the used control strategy, achieving at the</p><p>last the IPMSM control trajectory able to optimize the motor operating for the</p><p>entire speed range.</p><p>121</p><p>6.1 Implementation of the IPMSM Mathematical Model</p><p>Before to realize the implementation in MATLAB/Simulink® about the complete IPMSM Electromechanical</p><p>model in the d-q rotating reference is necessary to take the non linear mathematical model wrote in the</p><p>(4.47) and transforming it in a way capable to explicit all the unknowns in function of a derivative form, like</p><p>is reported in the following (6.1):</p><p>��</p><p>�</p><p>�� ��� =</p><p>���� +</p><p>�� ������ − ���</p><p>�����</p><p>��� =</p><p>���� +</p><p>�� ������ + ����</p><p>����� + �����</p><p>��� + ��� − � !"� = #$ �������� + #$ �%</p><p>�� −</p><p>��&������ − � !"� = ' �()��</p><p>⇒</p><p>��</p><p>�</p><p>��</p><p>������ = − +�,�� ��� + -(),��,�� ��� + .��,�������� = − -(),��,�� ��� − +�,�� ��� + .��/-()0�12,��</p><p>�()�� = 34-50�12���6%,��/,��&������7/89:;�</p><p><</p><p>== (6.1)</p><p>In the (6.1) form will be possible to implement the IPMSM mathematical model, namely will be possible to</p><p>realize a Control Algorithm with the inputs represented by the d-axis and q-axis stator voltage ��� and ���</p><p>and by the load torque � !"�, while the outputs by the variables ���, ��� and �� (unknowns). So knowing all</p><p>the IPMSM parameters, it’s feasible to develop a control system where making a feedback about the</p><p>IPMSM model variables and comparing them with the corresponding references imposed on the input, will</p><p>allow to supply the machine with the appropriate values of 3-phase stator voltages for achieve the desired</p><p>performances.</p><p>The IPMSM model, according the (6.1) equations, can be implemented in MATLAB/Simulink® following the</p><p>schemes shown in the Figures 6.1, 6.2 and 6.3 regarding respectively the d-axis equation, the q-axis</p><p>equation and the electromagnetic torque equation.</p><p>Figure 6.1 – MATLAB/Simulink implementation for the IPMSM d-axis equation</p><p>122</p><p>Figure 6.2 – MATLAB/Simulink implementation for the IPMSM q-axis equation</p><p>Figure 6.3 – MATLAB/Simulink implementation for the IPMSM torque equation</p><p>As the IPMSM model is written in the d-q rotating reference frame, is better to use before the machine</p><p>inputs ��� and ��� two blocks able to transform the 3-phase stator voltages imposed by the Voltage Source</p><p>Inverter (VSI) in the d-q stator voltages. Such blocks (Figure 6.4 and 6.5) will implement internally the Clarke</p><p>transformation with which is possible to pass from a 3-phase fixed system to αβ fixed reference frame,</p><p>while the sequential Park transformation is necessary to pass from a αβ fixed reference frame to dq</p><p>rotating reference frame. The mathematical expressions that allow to implement these processing have</p><p>already been treated respectively in the (4.25) and (4.34) and are valid in a general case for all the electrical</p><p>variables.</p><p>123</p><p>Figure 6.4 – MATLAB/Simulink implementation for the Clarke transformation (3phase→αβ)</p><p>Figure 6.5 – MATLAB/Simulink implementation for the Park transformation (αβ→dq)</p><p>The Algorithm Control will be realized with all the electrical variables in the d-q rotating reference frame</p><p>because is very suitable. Indeed will be preferred to implement a type of control based on the 2-phase</p><p>electrical variables than 3-phase because will reduce the difficult about the IPMSM mathematical model</p><p>(from 4 equations to 3 equations) without any loss of information, so simplifying also the controllers</p><p>design. Besides, as the IPMSM Control Algorithm needs to know exactly the rotor position to apply always</p><p>the maximum torque (because needs to know which is the rotor angle >� between the stator current vector</p><p>and the d-axis in the rotating reference frame), is very convenient to use the electrical variables in the rotor</p><p>reference frame dq instead in the fixed stator reference frame αβ.</p><p>Ordering the MATLAB/Simulink schemes in many subsystems and putting together them will be possible to</p><p>represent the IPMSM complete model like shown in the Figure 6.6, respecting exactly the same inputs,</p><p>outputs and parameters displayed in the set of equations (6.1).</p><p>124</p><p>Figure 6.6 – MATLAB/Simulink implementation for the complete IPMSM Electromechanical</p><p>model</p><p>6.1.1 IPM Motor Rated Values and Parameters</p><p>To test and verify the validity of the IPMSM model in MATLAB/Simulink must be used the parameters</p><p>regarding a real IPM Motor. So to verify the correct implementation will be choice a 3-phase IPM Motor</p><p>(Yaskawa Electric Corporation) with the following features:</p><p>Output Power P 200 W</p><p>Rated Current I 2 A</p><p>Bus DC Voltage VDC 100 V</p><p>Pole Pairs p 4</p><p>Stator Resistance</p><p>� 2.5 Ω</p><p>Stator d-axis Inductance</p><p>�� 8.3 mH</p><p>Stator q-axis Inductance</p><p>�� 8.6 mH</p><p>PM Flux ���� 0.046 Wb</p><p>Inertia J 0.8*10</p><p>-3</p><p>kg*m</p><p>2</p><p>Rated Torque ��� 0.64 N*m</p><p>Rated Speed �� 3000 rpm</p><p>Table I – IPM Motor nominal values (Yaskawa Electric Corporation)</p><p>125</p><p>Must be done just a clarification about the Rated Current I, which represents the rms current value that is</p><p>possible to impose on the IPMSM Stator windings without overpassing the nominal operating conditions.</p><p>6.1.2 IPM Motor Nominal Tests</p><p>Using the IPM Motor parameters listed above is possible to prove the IPMSM model validation testing it</p><p>with all the nominal conditions.</p><p>Supplying the IPMSM with the nominal 3-phase stator voltages Vs1, Vs2 and Vs3 and applying on the rotor</p><p>shaft the nominal load torque value � !"�, should be checked if the 3-phase stator currents Is1, Is2 and Is3,</p><p>the electromagnetic torque ��� and the mechanical speed �� will correspond with the nominal values</p><p>expected and if these variables will have predictable trends from the theory.</p><p>As in the Table I is provided just the Bus DC Voltage VDC, the nominal voltage that the Inverter is able to</p><p>supply on the AC side for the IPMSM will be reached using the (6.2).</p><p>��? = @AB√# (6.2)</p><p>Being known all the necessary parameters for the test, the validation of the IPMSM can be implemented</p><p>like is shown in the Figure 6.7, checking the 3-phase stator currents, the electromagnetic torque and the</p><p>nominal speed,</p><p>respectively in the Figures 6.8, 6.9 and 6.10.</p><p>Figure 6.7 – MATLAB/Simulink implementation for the IPMSM model validation</p><p>126</p><p>Figure 6.8 – 3-Phase Stator Currents Trends during the IPMSM model test</p><p>Figure 6.9 – Mechanical Speed Trend during the IPMSM model test</p><p>Figure 6.10 – Electromagnetic Torque Trend during the IPMSM model test</p><p>127</p><p>Analyzing the results is evident that the electromagnetic torque and the speed values correspond with the</p><p>expected nominal values, while the maximum amplitude of the 3-phase stator currents during the IPMSM</p><p>steady-state response is equal to 2.72 A, namely very close to the expected value √2 Irms = 2.82 A. Such</p><p>results can be considered appropriate to say that has been realized a correct implementation of the</p><p>IPMSM.</p><p>6.1.3 SVPWM-VSI</p><p>The IPSM Drive System can be achieved using a Space Vector Pulse Width Modulated Voltage Source</p><p>Inverter (SVPWM-VSI) that will supply the motor with the right 3-phase stator voltage values according the</p><p>dq axis voltage references ���* and ���* imposed by the Control Algorithm and according the rotor</p><p>position >�. The SVPWM-VSI implementation in MATLAB/Simulink is ideal (Figure 6.11), so simplifying the</p><p>modeling and not considering the eventual harmonic contents, but it’s just inserted a saturation block for</p><p>doesn’t allow during some extreme operating conditions to supply the machine with three phase</p><p>overvoltage, more bigger than nominal value in the (6.2). Besides in the PWM-VSI block will be used the</p><p>Inverse Clarke and Park Transformations to reach the correct Vs1, Vs2 and Vs3 to apply.</p><p>Figure 6.11 – SVPWM-VSI Implementation for the IPMSM Drive System</p><p>6.2 IPMSM Control System Realization</p><p>To implement the IPMSM Control System has been choice a Feedback Control Algorithm than a Feed-</p><p>forward Control. Indeed when in the control loop the process is represented by an electric motor is very</p><p>likely that all the constant machine parameters as</p><p>�,</p><p>��,</p><p>�� and ���� will depend from the</p><p>Temperature, namely their values will change depending the operating conditions of the motor. As the</p><p>biggest advantage of the Feedback Control is represented by the high robustness for not predictable</p><p>interferences in the control system, it’s very suitable using this Closed Loop Control for the IPMSM. Instead</p><p>the disadvantages are mainly two: to have a non real-time response and to make unstable all the system if</p><p>128</p><p>the regulators are tuned in a wrong way. The basic principle of the Feedback Control is shown in the Figure</p><p>6.12.</p><p>Figure 6.12 – General Block Diagram for the Feedback Control Loop</p><p>The following analysis will treat the complete implementation of the Rotor Field Oriented Control (RFOC),</p><p>evaluating the best control strategy (MTPA, FWC, MTPV) for the IPMSM Drive System in each operating</p><p>region. Besides, proceeding step by step, will be designed and realized respectively the Current Controllers</p><p>for the current loop and the Speed Controller for the speed loop.</p><p>6.2.1 Decoupling d-q Axis</p><p>For simplifying the Current Controllers design can be very useful decoupling in the control system the d-q</p><p>axis voltage equations. Indeed from the electric model in the (5.1), rewrote below in the (6.3) in the Laplace</p><p>domain, it’s possible to observe that the d-axis stator voltage ��� doesn’t have influence only on the d-axis</p><p>stator current ���, but also on the q-axis stator current ��� due to the b-emf contribute −���</p><p>�����. The</p><p>same thing will happen for the ���, bound with the ��� and with the b-emf due to the PM effects �������.</p><p>E ��� =</p><p>���� + F</p><p>����� − ���</p><p>�������� =</p><p>���� + F</p><p>����� + ���</p><p>����� + ������� = (6.3)</p><p>So the two current loops don’t result independent between them, because the PI Regulator for the ���</p><p>current, despite acts on the ���* reference value, will modify also the ��� value. Indeed to balance the d-</p><p>axis equation, the PI Regulator for the ��� current will be constricted to act on the d-axis loop for every q-</p><p>axis variation.</p><p>Referring to the Figure 6.13, the Decoupling will be possible for the d-axis loop subtracting the term</p><p>���</p><p>����� to ���*’ and for the q-axis loop adding the term ����</p><p>����� + ����� to ���*’ (Forward</p><p>Compensation).</p><p>129</p><p>Figure 6.13 – d-axis and q-axis Decoupling for the IPMSM RFOC</p><p>Now it’s easy to comprehend that all the variables added to the reference ���*’ and ���*’ in the current</p><p>regulators will be erased with the real variables inside the IPMSM Model. Decoupling the d and q-axis</p><p>effects inside the RFOC Algorithm will be possible simplify also the control diagram blocks with the purpose</p><p>to make easier the current controllers design, like is possible to observe in the Figure 6.14.</p><p>Figure 6.14 – q-axis (a) and d-axis (b) simplification for the Current Controllers Design</p><p>The MATLAB/Simulink implementation for the d-q axis Decoupling block, according with the (6.3)</p><p>expressions is reported in the Figure 6.15.</p><p>130</p><p>Figure 6.15 – MATLAB/Simulink implementation for the d-q axis Decoupling</p><p>6.2.2 Current Loop Design</p><p>As discussed in the Chapter 4 and 5, the IPMSM torque control has a non linear dependence from the</p><p>stator current vector, which amplitude can be decomposed in the d-axis and q-axis current. So to realize a</p><p>torque control is first necessary realize the current closed loop and relative regulators.</p><p>The basic current loop implementation is shown in the Figure 6.16. Like is possible to watch, the VSI is</p><p>driven with the SVPWM that generates the appropriate switch command signals for each leg according the</p><p>d-q axis voltage references ���* and ���* on the inputs. The components of the d-q voltage references are</p><p>generated from a closed loop vector control regarding the stator current, namely will be controlled the</p><p>���* and ���* references controlling the components dq ���* and ���* of the stator current vector ��.</p><p>Figure 6.16 – Closed Loop Current Control with a RFOC Algorithm</p><p>131</p><p>The stator current vector will rotate in the d-q reference frame with a synchronous speed and will be</p><p>oriented according the rotor flux (alias the PM magnetic flux ����), so to implement a simpler form of</p><p>RFOC for the IPMSM can be considered (look the (5.1) torque expression) that the d-axis component ���</p><p>can be controlled placing a null reference signal because in this way the electromagnetic torque value will</p><p>be proportional only to the q-axis component ���, but will not be maximized.</p><p>To find the ��� and ��� values and using it in the feedback control system, is necessary to know, in addition</p><p>with the current probes measurements, the exactly position θr of the rotor magnetic flux ���� in the d-q</p><p>rotating reference frame. To achieve this information will be possible to use a mechanical position sensor</p><p>(Encoder or Hall Effect Probes) or adopting a particular Sensorless Control Algorithm capable to estimate</p><p>the rotor magnetic flux position (so also the rotor position).</p><p>The current measurements used in the Figure 6.16 is referred to a 3-phase system without neutral where</p><p>the value of the third phase current i3 can be reachable using the typical relation i1+i2+i3=0.</p><p>6.2.2.1 Current PI Controllers Design</p><p>The current regulation is ensured by two PI standard Controllers (Rq and Rd), both with already the</p><p>implementation regarding the d-q axis decoupling. To obtain correct references ���* and ���* for the</p><p>SVPWM-VSI must be tuned the corresponding PI Controllers, in particular the Proportional part Kp and the</p><p>Integral part Ki, like is possible to comprehend by the following (6.4) regarding a generic PI Controller</p><p>transfer function. Instead in the Figure 6.17 is reported a classic internal structure for a PID Controller.</p><p>GH�F� = I- + JK�</p><p>(6.4)</p><p>Figure 6.17 – PID Controller internal structure</p><p>Before to calculate the Kp and Ki gains for Rq and Rd, must be analyzed the transfer functions regarding the</p><p>q-axis and the d-axis from the IPMSM electrical equations. As It has already been realized the forward</p><p>compensation for the ���* and ���*, will be sufficient calculate the d-q axis transfer functions neglecting all</p><p>the coupling items, obtaining the following (6.5) and the corresponding blocks diagram in the Figure 6.18:</p><p>132</p><p>��</p><p>�</p><p>��G��F� = ������</p><p>.����� = L +�M</p><p>NO��P� �6LQ = R,TR,RR#T�6L = LLU,$V�6$WT,L$</p><p>G��F� = ������.����� = L +�M</p><p>NO��P� �6LQ = R,TR,RR##�6L = L$L,$L�6#R#,R#</p><p>= (6.5)</p><p>Figure 6.18 – Closed q-axis Current Loop Diagram for the IPMSM Control</p><p>To tune the q-axis PI Controller (like also the d-axis PI Controller) can be used different methods, between</p><p>which is possible to choose for example the Roots Locus or some analytic methods. However to analyze the</p><p>control system with the Roots Locus must be found before the closed loop transfer function Fq(s)</p><p>(considering unitary feedback), evaluating the closed loop poles position in the Real-Imaginary axes and</p><p>starting from the open loop transfer function Gq(s):</p><p>X��F� =</p><p>��F�G��F� = LLU,$VJY�6LLU,$VJK�46$WT,L$�</p><p>⇒ Z��F� = [����</p><p>L6[���� (6.6)</p><p>To tune the Integral gain Ki is very common to use a method that allows to erase the pole due to the</p><p>IPMSM electric time constant \� = ,��+� with the zero due to the q-axis PI Regulator. Such condition will be</p><p>valid if the module of the closed loop transfer function |Z��]��| will be equal to 0, namely when in the</p><p>Bode Diagram the module trend will cross the logarithmic axis in corresponding of the crossing frequency:</p><p>LL6^_`�→b [���� = 0 ⇒ L^_`�→b �[���� ≪ 1 ⇒ I� ≫ 2,53 (6.7)</p><p>To estimate the Proportional gain Kp is sufficient analyze the denominator of the (6.6), making the Roots</p><p>Locus, evaluating the closed loop poles position and using the Ki just found:</p><p>1 + X��F� = 0 (6.8)</p><p>From the (6.8) will be possible to obtain the value Kp=12,31</p><p>For the d-axis PI Controller can be repeated all the same considerations seen till this moment, so as the</p><p>inductances values Lsq and Lsd are almost the same will be possible to give the same Ki and Kp values to tune</p><p>133</p><p>the Controller gains, without commit big errors. However can’t be excluded eventual changes for Ki and Kp</p><p>values during the MATLAB/Simulink simulations due to eventual imprecision in the machine parameters.</p><p>It’s very important to comprehend how this issue will determine for the d-axis and q-axis current loops the</p><p>same control performances during the transient and the steady-state. Besides it’ useful to keep in mind</p><p>that generally a Controller without Integral gain Ki will give for the IPMSM Drive system a constant steady-</p><p>state error, while an excessive increase could be create fast responses and higher overshoots, so making</p><p>unstable all the IPMS Drive system.</p><p>6.2.3 Torque Control</p><p>Tuned the PI Current Controllers and found the corresponding Integral and Proportional gains, it’s possible</p><p>to implement in MATLAB/Simulink the RFOC Algorithm shown in the Figure 6.16. The following analysis will</p><p>treat at the beginning the Torque Control Algorithm without any type of optimization for the</p><p>electromagnetic torque, but then will be dealt the implementation for the TCA with MTPA (under the</p><p>IPMSM nominal velocity).</p><p>In Figure 6.19 is shown a classic feedback Torque Control scheme. In this scheme the torque reference is</p><p>transformed, through the Current Reference Generator action, in the d-axis and q-axis current reference</p><p>that will process successively in the d-axis and q-axis current loops. Besides, as is necessary to realize the</p><p>Decoupling between d and q-axis, there will be need to integrate the position signal from the encoder to</p><p>obtain the mechanical speed ωm or the electric speed ωr.</p><p>Figure 6.19 – Closed Loop Torque Control with a RFOC Algorithm</p><p>134</p><p>6.2.3.1 Non-Optimized Torque Control</p><p>As already discussed, in this case the Control Algorithm will impose a ���*=0 and a specular ���* with the</p><p>torque profile imposed from the reference Tem*. Indeed ���* can be considered proportional to Tem* if is</p><p>taken in examination the torque equation in the (5.1), where it’s easy to understand that each variation will</p><p>have mirror effect on the torque trend, without consider a scale factor regarding the amplitude (depending</p><p>from the poles pairs and from the PM Magnetic Flux).</p><p>To implement the IMPSM Drive system test in MATLAB/Simulink can be realized the control scheme in the</p><p>Figure 6.20, which reproduces exactly the real control scheme in the Figure 6.19.</p><p>The test has been executed applying for first a constant load torque equal to 20÷30% Tem nom and with a</p><p>such Tem* profile for 10 s, like shown in the Figure 6.21, while in the Figure 6.22 is shown the 3-phase stator</p><p>currents. In the Figure 6.21 will be possible to observe the comparison between the electromagnetic torque</p><p>reference Tem* imposed in the control system, the load torque Tload and the real electromagnetic torque</p><p>provided by the IPMSM. For a torque profile as faithful as possible with the reference, the Integral part of</p><p>the d-axis and q-axis Controller are set to zero, for avoid also eventual instability due to the wrong action of</p><p>the Current Controllers.</p><p>The 3-phase current trends in the Figure 6.22 will follow exactly the reference ���*/ Tem*, varying their</p><p>amplitude for every variation imposed. These values obviously are lower than the nominal values because</p><p>in the IPMSM Drive system is applied a load torque very low and because the torque profile is not</p><p>particularly pendant.</p><p>Figure 6.20 – MATLAB/Simulink implementation for the IPMSM Torque Control without MTPA</p><p>135</p><p>Figure 6.21 – IPMSM Electromagnetic Torque Trends for Torque Control without MTPA</p><p>Figure 6.22 – IPMSM 3-phase Stator Currents Trends for Torque Control without MTPA</p><p>Now applying a such profile of Tload depending from the time (Figures 6.23), the situation regarding the</p><p>electromagnetic torque provided by the IPMSM will change completely. Indeed the Torque Control, as is</p><p>not maximized, will not able anymore to follow the reference also increasing it. This means that the IPMSM</p><p>Drive system is having a performance degradation, namely the IPMSM torque will be able just to track the</p><p>load torque for each variation and for this reason that in Figure 6.24 the mechanical speed trend will start</p><p>to stabilize itself only when is found the mechanical balance in the D’Alambert equation.</p><p>136</p><p>Figure 6.23 – IPMSM Electromagnetic Torque Trends for a variable Load Torque</p><p>Figure 6.24 – IPMSM Mechanical Speed for a variable Load Torque</p><p>6.2.3.2 MTPA Control</p><p>To maximize the electromagnetic torque in function of the currents can’t be used anymore the</p><p>simplification to keep to zero the d-axis current reference. Indeed to implement the MTPA Control</p><p>Algorithm already analyzed (Chapter 5, paragraph 5.2.1) must be calculated and generated from special</p><p>blocks the d-axis and q-axis references ���* and ���* according the (5.11) and (5.3) equations.</p><p>Comparing this kind of control with the non-optimized torque control will be evident that the MTPA Control</p><p>has the possibility to provide much more torque for a same operating</p><p>condition because will benefit also of</p><p>the reluctance torque contribute. Besides such Control Algorithm has excellent dynamic performances and</p><p>will have less risks to make unstable all the IPMSM Drive system.</p><p>137</p><p>The implementation in MATLAB/Simulink of the ���* and ���* reference generators will use the (5.11) and</p><p>(5.3). Such realization is shown respectively in the following Figures 6.25 and 6.26.</p><p>Figure 6.25 – MATLAB/Simulink implementation for the d-axis Reference Generators in the</p><p>MTPA Control</p><p>Figure 6.26 – MATLAB/Simulink implementation for the q-axis Reference Generators in the</p><p>MTPA Control</p><p>To achieve the basic conditions for run the simulation must be retuned in a manual way the d-axis and q-</p><p>axis Current PI Controllers according the Torque*/Stator Current* that will be applied as input in the MTPA</p><p>Control Algorithm. The scheme used in the Figure 6.20 will be the same, with the only modify regarding the</p><p>blocks for the Current reference Generators (Figure 6.27).</p><p>Figure 6.27 – MATLAB/Simulink implementation for the Current References Generators in the</p><p>MTPA Control</p><p>138</p><p>Running the simulation, imposing a constant reference value of Tem*/���* and a step with the nominal load</p><p>torque value, will be obtained the following results shown in the Figures 6.28 and 6.29 respectively for the</p><p>Electromagnetic Torque and for the corresponding 3-Phase Currents.</p><p>Figure 6.28 – Electromagnetic Torque Trend for a Step of Load Torque with the MTPA</p><p>Figure 6.29 – 3-Phase Currents with the MTPA</p><p>Changing the constant torque reference with a variable reference and applying also for the load torque a</p><p>variable profile until the 70% of the nominal value, will be possible to see the following trends in the Figure</p><p>6.30 and in the Figure 6.31 respectively for the Electromagnetic Torque and the Mechanical Speed.</p><p>139</p><p>Figure 6.30 – Electromagnetic Torque Trend for a variable Load Torque with the MTPA</p><p>Figure 6.31 – Mechanical Speed Trend for a variable Load Torque with the MTPA</p><p>6.2.4 Speed Loop Control and Design</p><p>To comprehend till which point is possible to apply the FWC Strategy for IPMSM must be evaluated where</p><p>is placed the voltage ellipse center, easily reachable from the (5.5) already discussed. For the IPMSM used</p><p>in simulation the voltage ellipse center is localized outside the current circle (����/</p><p>��=5,54 > 2). This</p><p>means that the FWC Strategy is limited by a such speed value (calculable from the (5.20)) over the IPMSM</p><p>will not be able anymore to provide an useful torque value.</p><p>140</p><p>A basilar scheme for the implementation of the Speed Loop Control is shown in the Figure 6.32. In this</p><p>control scheme for the Simulink realization will not be tuned the Speed Regulator Rω because the</p><p>procedure is really difficult and often doesn’t produce significant results, so forcing to tune the Speed</p><p>Regulators in a practice way, observing when the system response will be admissible, converging according</p><p>the imposed speed reference. However being a cascade control, it’s very important that the bandwidth for</p><p>the internal current loop is much bigger than the external speed loop, namely the internal current loop will</p><p>be considered by the external speed loop like an ideal amplifier (always considered in the steady-state).</p><p>Figure 6.32 – Closed Loop Speed Control with a RFOC Algorithm</p><p>6.2.4.1 FWC Strategy</p><p>To realize the FWC Strategy and so extending the IPMSM Operating Domain over the nominal speed of the</p><p>motor means be able to understand when the machine surpassed the nominal velocity ωB, namely when is</p><p>the moment to pass from the MTPA Control Algorithm to the FWC, changing trajectory from the max T/I</p><p>curve to the current circle.</p><p>As the nominal speed is estimable from the (5.14) equation, it will depend just from the IPMSM</p><p>parameters, which are subject to have changes depending from the Operating region and in particular from</p><p>the temperature. For this reasons implement a Control Algorithm based on the (5.14) can be dangerous for</p><p>the IPMSM Drive System because the FWC action could start too early, making lose an useful contribution</p><p>for the torque motor.</p><p>To avoid the machine parameters dependence can be used a Control Algorithm that not implement the</p><p>(5.14), staying independent from the machine parameters. Such type of FWC Strategy is shown in the</p><p>Figure 6.33 and to solve this problem uses an external voltage loop to establish the correct FWC condition.</p><p>141</p><p>Figure 6.33 – Speed Control with FWC Strategy with an External Voltage Loop [Jang]</p><p>The big advantage for this control scheme is represented from the moment in whose the weakening starts.</p><p>Instead to implement the (5.18) and (5.19) equations to follow the trajectory on the current circle, in the</p><p>“Part II” are measured the voltage references ���* and ���*, calculating for them the module. This module</p><p>is compared with the maximum voltage that the Inverter will able to apply (6.2), while the adder output will</p><p>provide the voltage error to be integrated by the PI Voltage Regulator. If the error will be positive (no</p><p>saturation conditions for the regulators) there isn’t any type of action from the control system and the</p><p>IPMSM Drive System will continue to work in the Constant Torque Region. Instead when the voltage error is</p><p>negative the PI Voltage Regulator will provide a gradual decrease for the d-axis current component ���,</p><p>creating a new reference named ∆���j. The variation that ∆���j can have goes from the ����"k to -��? (look</p><p>Figure 5.10).</p><p>While the “Part I” is the MTPA Control Algorithm, the “Part III” is necessary to calculate the q-axis current</p><p>component and not allow that it will surpass the maximum value for the IPMSM currents. Such</p><p>implementation is exactly the same observed for the (5.3), but the expression uses ∆���j. In this part so will</p><p>possible to comprehend that when the IPMSM is working in the constant torque region will verify the</p><p>condition ���k*=���* so ���=����"k, namely will not have any type of limitation for the q-axis component.</p><p>To Implement the FWC Strategy in MATLAB/Simulink like in the Figure 6.33, will be possible to use the</p><p>scheme already adopted for the Torque Control, adding the external voltage loop and the “Part III” (Figure</p><p>6.34) and implementing them exactly as seen in Figure 6.33.</p><p>142</p><p>Figure 6.34 – Implementation in MATLAB/Simulink for the FWC Strategy with an External</p><p>Voltage Loop</p><p>Tuning with a very low gain the Integral part for the Current and Speed Regulators (to avoid instability into</p><p>the control system), will be possible to see the differences between the reference speed value imposed and</p><p>the real speed value for a generic speed profile before the nominal velocity (Figure 6.35) and over the</p><p>nominal velocity (Figure 6.36). The steady-state precision and the dynamic performance for the IPMSM</p><p>Drive System will depend from the tuning of the Regulators.</p><p>Figure 6.35 – Speed Reference vs real Mechanical Speed with FWC Strategy</p><p>143</p><p>Figure 6.36 – Speed Reference vs real Mechanical Speed with FWC Strategy (OVER nominal</p><p>speed)</p><p>144</p><p>7.1 Instrumentation and Configuration System</p><p>Chapter 7</p><p>IPMSM Drive System</p><p>Realization</p><p>Contents:</p><p>7.1 Instrumentation and Configuration System</p><p>7.2 PWM Generation</p><p>7.3 Currents Measurement</p><p>7.4 Encoder Measurement</p><p>7.5 IPMSM Open Loop Control</p><p>This Chapter will treat the basic implementation for the IPMSM Control and all</p><p>the useful measurements necessary to accomplish this task. Besides will</p><p>provide the basic knowledge to program the DSP Control Unit with the Simulink</p><p>blocks instead with the C Language. At the end will be tested the IPMSM with</p><p>an Open Loop Configuration.</p><p>145</p><p>7.1 Instrumentation</p><p>and Configuration System</p><p>For the practical realization of the IPMSM Drive System will be used the following instruments:</p><p>� Development board Spectrum Digital eZdsp™;</p><p>� Interface card to adapt the signal for the A/D and to convert the PWM electrical signal in an optical</p><p>signal;</p><p>� DSP 32 bit Texas Instrument TMS320F28335 @ 150 MHz Float Point Unit;</p><p>� Two Current trasducer LEM LA 100 P – SP 13 and one Current trasducer LEM LA 25-NP;</p><p>� Encoder WayCon A36 – 2000 counts/reverse incremental output A/B-Pulse;</p><p>� Inverter Danfoss 2.2 kW;</p><p>� IPM Synchronous Motor Yaskawa Electric Corporation SSR1-42P2AFNL.</p><p>The first step to deal is represented by the system configuration. It has been chosen to program the DSP</p><p>using the Simulink programming environment included in MATLAB. This decision has been taken because</p><p>this programming language allows to use the same programming blocks used in the simulations. Besides it’s</p><p>relatively easy to export the blocks used in the simulation for comparing the results.</p><p>To configure the DSP board is possible use the block F28335 (Figure 7.1) into the Simulink environment and</p><p>setting the parameters like listed below in the Figure 6.2:</p><p>Figure 7.1 – DSP board used in Simulink implementation</p><p>Figure 7.2 – DSP Parameters Setting in the Simulink Environment</p><p>146</p><p>Figure 7.3 – DSP Configuration Parameters in the Simulink Environment</p><p>After the parameters setting is possible start to program the DSP, inserting the necessary blocks for the</p><p>implementation. The scheme cannot be directly executed by Simulink, but first is necessary to convert its in</p><p>a C Language file, compiling the program by a software called Code Composer Studio (Figure 7.4)</p><p>distributed by Texas Instruments. Once that the program is compiled, will be possible to work on the DSP,</p><p>so monitoring the value of the variable and the status of the DSP.</p><p>Figure 7.4 – Code Composer Studio Programming Environment</p><p>147</p><p>7.2 PWM Generation</p><p>Once choice the programming environment and set all the parameters, will be possible to start the real DSP</p><p>programming. As first thing needs to generate the PWM signals that are required for the Inverter Control.</p><p>The generation of the three PWM signals is relatively easy, because the DSP adopted has some special</p><p>dedicated unit for this task. The blocks used in Simulink are shown in the Figure 7.5.</p><p>Figure 7.5 – PWM Blocks Implementation</p><p>For choosing the PWM generation parameters, like for example the switching frequency and the duty cycle,</p><p>will be changed the configuration parameters for the signals applied to the PWM generation blocks. In</p><p>particular for setting the switching frequency it has been modified the signal on the T ports, while for</p><p>setting the duty cycle it has been changed the signal on WA ports.</p><p>To select which modules PWM enable and all the related parameters it’s possible to open the blocks and</p><p>modify the internal parameters, as shown in the Figure 7.6 below.</p><p>Figure 7.6 – Setting Parameters PWM Blocks</p><p>148</p><p>To check the correct generation of the PWM can be made an acquisition with the oscilloscope regarding</p><p>the Voltage signal on the DSP output. The acquired PWM is shown in the Figure 7.7.</p><p>Figure 7.7 – DSP generated PWM Signal</p><p>149</p><p>7.3 Currents Measurement</p><p>Another important operation can be conducted before to realize the control system for the motor. Indeed</p><p>to implement the IPMSM Drive system are fundamental the acquisitions about the 3-phase currents that</p><p>flow into the motor (to act properly on the control parameters). To make this are used Hall effect current</p><p>sensors, capable to read both AC and DC current, produced by LEM. Besides are chosen these modules</p><p>because are very easily to interface with the DSP. The current probes are connected to the analog digital</p><p>converter (with a resolution of 12-bit) contained inside the DSP. However is not possible connect directly</p><p>the probe to DSP, because the analog digital converter accepts values of voltage from 0 to 3.3 V, so causing</p><p>reading problems when on input there are AC currents. To solve this problem can be used an interface card</p><p>that adapts the values read by the sensors with the compatible values that the DSP can support. The block</p><p>ADC that will acquire the current signals is represented in the following Figure 7.8.</p><p>Figure 7.8 – 3-phase Currents Measurement and ADC acquisition</p><p>After the acquisition blocks are connected Buffer blocks because without them could not be possible to</p><p>observe the signals acquisition with the Code Composer.</p><p>The fundamental parameters for the ADC blocks configuration are shown in the next Figure 7.9, and in</p><p>particular will be very important the Sample Time that allows to acquire the correct signal and the Channels</p><p>menu for choose from which input acquiring the signals.</p><p>150</p><p>Figure 7.9 – Setting Parameters ADC Blocks</p><p>The set-up for the 3-phase Currents measurements is shown in Figure 7.10, where will be possible to</p><p>observe the three current sensors and the interface board that allows to connect the sensor to DSP board.</p><p>Figure 7.10 – Set-up Bench for 3-phase Currents Measurements</p><p>Executing this test will be possible finally to acquire and read the 3-phase currents to implement</p><p>successively the IPMSM current control. In the Figure 7.11 are displayed in Code Composer the currents</p><p>trends due to measure with the currents probes.</p><p>151</p><p>Figure 7.11 – 3-phase Currents Measurements in Code Composer Studio</p><p>7.4 Encoder Measurement</p><p>If there is the necessity to implement for the IPMSM Drive also the speed loop, must be read the speed</p><p>value (or the position) from the encoder, so allowing to maximize the IPMSM performances. The DSP used</p><p>for the practical realization has a specific input for the read from the incremental encoder. However is not</p><p>possible connect directly the incremental encoder to the DSP because it accepts only input Voltage</p><p>between 0 to 3.3 Volts. To solve this problem it has been used a simple circuit with Zener diodes able to</p><p>transform the encoder output to have a compatible level with the DSP range voltages. The block in Simulink</p><p>that allows to solve this problem is shown in the Figure 7.12.</p><p>Figure 7.12 – Position Read Block Implemented inside the DSP</p><p>To control the encoder reading, like first step must be established the input port where is desired to receive</p><p>the encoder signal. The second step regards the correct choice about the sample time in according to the</p><p>152</p><p>maximum motor rotational speed that allows the correct acquisitions. All these parameters can be choice</p><p>through the configuration dialogs shown in the Figure 7.13 listed below.</p><p>Figure 7.13 – Setting Parameters Position reading Blocks</p><p>7.5 IPMSM Open Loop Control</p><p>The simplest type of control that is realizable for the IPMSM is the Open Loop Control. This type of control</p><p>allows to observe if the generation of the PWM made by the DSP is correct, if the reading encoder works,</p><p>and if the current probes are working properly. The general diagram that allows to make this control is</p><p>shown below in the Figure 7.14.</p><p>153</p><p>Figure 7.14 – Open Loop Control Implementation inside the DSP</p><p>154</p><p>From the general Implementation into the DSP from the Figure 7.14 can be explained in detail the</p><p>functionality for each individual sub-block.</p><p>The sub-system reported in the Figure 7.15 realizes the acquisitions (it is the block for the digital/analogic</p><p>conversion) regarding the three currents by A0, A1, A2 and receives the speed reference by A3 to impose</p><p>the desired speed profile. Instead the Figure 5.16 shows the position reading block implemented in</p><p>Simulink.</p><p>Figure 7.15 – 3-Phase Currents Acquisitions and Speed</p><p>5</p><p>15÷40 kW BDC IM PMSM BLDC</p><p>Average Efficiency 77÷80 % 86÷90 % 90÷93 % 90÷93 %</p><p>Power Density 0,135 kW/kg 0,220 kW/Kg 0,510 kW/Kg 0,470 kW/Kg</p><p>Control Strategy Full Bridge DC/DC Converter</p><p>with PWM Modulation</p><p>Inverter VSI</p><p>(Current Controlled)</p><p>with SV Modulation</p><p>Inverter VSI</p><p>(Voltage Controlled)</p><p>with SV Modulation</p><p>Inverter VSI</p><p>(Voltage Controlled)</p><p>with SV Modulation</p><p>Cost Low Medium High High</p><p>Maintenance Frequently for the brushes Almost absent Demagnetization limit Demagnetization limit</p><p>Table 1.1 – Performance Compared between BDC, IM, PMSM and BLDC (Size 15÷40 kW)</p><p>How is easy to understand an ideal choice should be take a Motor with high Efficiency and Power Density,</p><p>low Cost, very little Maintenance and a Type of Control as simple as possible in terms of Hardware,</p><p>Programming Software and Practical Implementation. Obviously all these skills in a single Electric Motor</p><p>can’t be achieved and for this reasons will be choice a couple of Electrical Motors capable to optimize our</p><p>requirements.</p><p>In the Project will be choice a Permanent Magnet Synchronous Motor (the exactly PMSM size will be</p><p>discussed and selected in the Chapter 2) because there are some Advantages extremely appreciated for a</p><p>HEV, like for example high Efficiency and Power Density values and any particular problem with the</p><p>Maintenance (in a HEV is more important to minimize weight, bulk and losses). The Disadvantages related</p><p>with this decision regard a non-moderated Cost and a more larger sophistication with the Control and the</p><p>Implementation for the entire AC-Drive than a DC-Drive.</p><p>1.2.2 Inverter Operating</p><p>As the Power flow into the Drive could be changed in some situations like a Regenerative Braking with the</p><p>Traction Motors or when Charging from the External Grid, it’s necessary to use an Inverter Configuration</p><p>capable to make work the Converter both as DC/AC Converter (Inverter Working) and as AC/DC Converter</p><p>(Rectifier Working).</p><p>Other problem to ponder for the Inverter regards is the Power sizing. In general, when is using an Electric</p><p>Motor with a such Power (for example 30 kW), is always advisable not choose a Converter with the same</p><p>Motor Power, because Electrical Machines have a thermal overload capability larger than a Converter and</p><p>besides they can sustain Over-Currents for more time among this electronic device (minutes against</p><p>milliseconds). In these cases can be suitable oversize the Converter (for example choosing an Inverter with</p><p>40 kVA), doing to work it with a Current value more lower than the nominal Current value.</p><p>6</p><p>Other fundamental issues for the Converter Operative Mode are the choice regarding the type of the</p><p>Power Devices (MOSFET, IGBT, etc.) and at the same time the Switching Frequency.</p><p>The first item is given by the Nominal Power of the Converter, so to pick out the most suitable Power</p><p>Device must be taken in consideration several factors as the Drain-Source Voltage (VDS) and the Drain</p><p>Current (ID) for the Switch. In the Figure 1.2 is possible to see which are the possible ranges application for</p><p>the Power Electronic Devices related with the Voltage and Power Values. Even if these values match with</p><p>the nominal values required by the Motor, when is selecting a Power Device is impossible for the designer</p><p>doesn’t consider notable modification due to the device dynamics. Indeed, during the commutation of the</p><p>Switches, there are extra-voltages that will bring on further stress for the devices and for this reason must</p><p>be used a safety-factor when is estimating the size of the Switches. Usually this safety-factor is 2 times for</p><p>VDS and 3�4 times for ID related with the Nominal Value.</p><p>Figure 1.2 – Range Application for the Power Devices [University of Cassino]</p><p>To choose the best Switching Frequency must be done an optimization between the Power Losses of the</p><p>Devices (the Conduction and Commutation Losses should be minimized) and an acceptable Efficiency for</p><p>the Switch conversion (increasing the Switching Frequency is possible to improve the conversion efficiency).</p><p>An High Switching Frequency value is also desired (in general for any type of Converter) to reconstruct as</p><p>faithfully as possible an ideal waveform on the Output Load, so when is moving towards high Switching</p><p>Frequency values must be considered that the Power Losses should become too high and could overheat</p><p>the device, probably damaging it an reducing the lifetime due to the excessive temperatures.</p><p>7</p><p>The last aspect to consider when is evaluating the exactly Converter to use for a specific application regards</p><p>the Type of Control and the Modulation Technique (Pulse Width Modulation, Space Vector Modulation,</p><p>Current Hysteresis Control, Direct Torque Control, etc.). Each type of Control and Modulation have several</p><p>advantages and disadvantages that do prefer one to another.</p><p>For example a Space Vector Modulation (SVM) has the big benefit to reduce the Total Harmonic Distortion</p><p>(THD) on the Grid and on the Load among Pulse Width Modulation (PWM), but a SVM realization and</p><p>digital implementation results more difficult than a PWM. However both the Modulations use a technique</p><p>to modify the voltage spectrum to reduce in a strong way the Current Harmonic contents and is always</p><p>appreciated to use as high as possible Modulation Index (ratio between Carrier Frequency and Modulation</p><p>Frequency) to shift the Harmonic Content far from the Fundamental Frequency (not for reduce the</p><p>Harmonic values of each component). This aim is reachable if the Switching Frequency is increased for the</p><p>Converter.</p><p>In the Project will be used an Inverter with IGBT as Power Devices, because applications like HEV requires</p><p>too high Power Range for the MOSFET. The Switching Frequency value will be chosen in parallel with the</p><p>Type and Control Techniques in the next chapters (these two decisions are linked and require other</p><p>analysis).</p><p>1.2.3 Recharge Battery Pack</p><p>To ensure an optimal support for the Fuel Cell during the start-up phase of the device and while the Vehicle</p><p>is climbing hills must be used a Battery Pack with specific characteristics.</p><p>The basic problem is to select the most appropriate type and size of Battery for our Drive, basically for</p><p>adapt the charge and discharge cycles to the operative conditions of the Vehicle. Besides, the Batteries</p><p>must be recharged by flowing current in the direction opposite of discharge, so the Battery Pack will have</p><p>need of Buck-Boost DC/DC Converter to work with negative currents, inverting the power flow into the</p><p>Drive.</p><p>In general a desirable list of skills for the batteries are listed below:</p><p>� High Peak Power</p><p>� High Specific Energy at Pulse Power</p><p>� High Charge Acceptance</p><p>� High Capacity Value</p><p>� Long Calendar and Cycle life</p><p>� Cost</p><p>8</p><p>The Batteries that can be used as suitable for typical HEV/EV applications are the following:</p><p>Lead-Acid (Pb-acid)</p><p>Nickel-Cadmium (Ni-Cd)</p><p>Nickel-Metal-Hydride (NiMH)</p><p>Lithium-Ion (Li-ion)</p><p>Lithium-Polymer (Li-poly)</p><p>Sodium-Sulfur (NaNiCl)</p><p>Zinc-Air (Zn-Air)</p><p>The actual technological limitation doesn’t allow to use a Battery Pack with high Peak Power and high</p><p>Specific Energy at Pulse Power, so this can explain because on the Vehicles is often need also of a Super-</p><p>Capacitor while is requiring a strong increase of speed. Indeed the Batteries don’t able to provide high</p><p>current values in short time cause the burst limit. However is ever reasonable for a HEV/EV to choose a</p><p>type of Battery oriented towards high Specific Energy values. In the Figure 1.3 are displayed the application</p><p>fields for the most common Batteries listed above (named Ragone Plot).</p><p>High Capacity and Charge Acceptance values can be important to know the maximum Nominal Current</p><p>value and the maximum Instantaneous Current value that is possible to supply respectively in continuous</p><p>discharge conditions</p><p>Reference for the Open Loop Control</p><p>Figure 7.16 – Position Measurement for the Open Loop Control</p><p>The sub-system shown below in the Figure 7.17 is very important because it generates the three sinusoidal</p><p>signals with a phase difference of 120° between them, and with external control (practically realized with a</p><p>trimmer) is possible to change the frequency regarding the control signal for the switches inside the</p><p>Inverter and consequently also the motor speed.</p><p>155</p><p>Figure 7.17 – Control Signals Generation to regulate the Switching Frequency</p><p>Instead the sub-system shown below (Figure 7.18) will allow to control directly the PWM generation unit,</p><p>namely imposing a such signal on the WA input the ePWM block will generate for the Inverter switches a</p><p>PWM control signal able to obtain on the IPMSM exactly the original reference imposed previously in WA.</p><p>Figure 7.18 – PWM Generation Unit inside the DSP</p><p>156</p><p>Finally this last sub-system in the Figure 7.19 is not necessary for the control of the motor, but it has the</p><p>function to send to the Inverter the Enable Signal to activate it, when the velocity signal is bigger than the</p><p>specified velocity in the Constant block.</p><p>Figure 7.19 – Enable Signal Generation for the Inverter</p><p>The 3-phase currents values imposed by the Inverter during the IPMSM Open Loop test are shown in the</p><p>Figure 7.20. It’s important to note that the amplitude for the Ch3 current is different compared with the</p><p>other two currents. This aspect is due to the different Current Probe used for the practical realization.</p><p>Figure 7.20 – 3-Phase Currents Trends measured with the Current Probes</p><p>157</p><p>Chapter 8</p><p>Conclusion</p><p>This project deals with the study of the physical characteristics of an electric vehicle, and implementing of</p><p>the components necessary for the function, this is perform by studying the system and through simulations</p><p>conducted by MATLAB\Simulink.</p><p>The project is divided into three parts. The first part deals with the study of the characteristics of a typical</p><p>vehicle (the characteristics are choosing considering the dimensions of a small vehicle for urban use). Are</p><p>studying the forces that interact with the vehicle, what forces are relevant and which are negligible for the</p><p>study, and the calculation of theoretical performance of the vehicle. After pass to determine the size of the</p><p>components necessary to implementation. Focus on the type and the size of the motor, the type and</p><p>power of batteries, the type of fuel cell and the choosing of system control. Decided to use a PMSM motor,</p><p>and for control system DSP of C2000 series product by Texas Instrument. The fuel cell and the batteries</p><p>were not used practically due to the limited amount of time.</p><p>The second part of the project treats the study through simulation perform by Simulink of engine behavior</p><p>for different load torque both constant that variable. This is because it has been tried, also in approximated</p><p>mode, the simulation of a typical cycle of a vehicle.</p><p>The third part it has been chosen the typology of device for implementing the algorithm of control of</p><p>motor. It has been chosen to use the DSP TMS320f28335 product by Texas Instrument. It is many adapt for</p><p>the control of motor, because it has inside the unit for direct control of motor. The mains unit that has</p><p>been used are ADC unit for acquire the analog inputs, the PWM units for generate the signals for control</p><p>the output of inverter and the unit of read of encoder. The programming of DSP it has been made whit use</p><p>of Simulik and after exported to CodeComposerStudio for the build and the load of the program on DSP.</p><p>The practical realization of system has affronted the practical problems, such as the connection of current</p><p>probes, the connection of the encoder, the control of inverter and the connection with the motor. It has</p><p>been made only the control of the motor in open loop, because to implement the other control type would</p><p>require much more time for the development of system.</p><p>158</p><p>8.1 The project put into perspective</p><p>Due to vastness of the project, the limited amount of time and specially for the limited human resource in</p><p>the group there are only two persons, it not has been possible development and depth all the aspect of the</p><p>project. A possible perspective for the future are the development of more sophisticated control</p><p>techniques such as torque control and position control.</p><p>159</p><p>Bibliography</p><p>[Wikipedia 2010] Wikipedia (2010). Wikipedia the free encyclopedia. Wikipedia.</p><p>http://en.wikipedia.org/wiki</p><p>[Mehrdad Yimin Ali 2010] Mehrdad Ehsani, Yimin Gao, Ali Emadi(2010) Modern Electric, Hybrid Electric,</p><p>and Fuell Cell Vehicles, second edition. ISBN 978-1-4200-5398-2</p><p>[Acampa] Mario Simone Davide Acampa, thesis Operating characteristics and control techniques drives</p><p>brushless permanent magnet University of Naples “Federico II”</p><p>[Iqbal 2003] Iqbal Husain (2003) Electric and hybrid vehicle Design Fundamentals ISBN 0-8493-1466-6</p><p>[Jang] Jang-Mok Kim, Seung-Ki Sul, "Speed Control of Interior Permanent Magnet Synchronous Motor Drive</p><p>for Flux Weakening Operation" IEEE publication</p><p>[Jordi] Jordi Espina, Toni Arias, Josep Balcells and Carlos Ortega , "Speed Anti-Windup PI strategies for Field</p><p>Oriented Control of Permanent Magnet Synchronous Machines" IEEE publication</p><p>[Buso] Simone Buso, Paolo Mattavelli “Digital control in Power Electronics” ISBN-10: 1598291122</p><p>[Salvatore] L. Salvatore “MOTORE SINCRONO A MAGNETI PERMANENTI” Politecnico di Bari</p><p>[Jun Kang] Jun Kang, General Purpose Permanent Magnet Motor Drive without Speed and Position Sensonr</p><p>Yaskawa Electric America.Inc</p><p>[University of Cassino] course of “Veicoli Elettrici” 2009</p><p>[www.energymatters.com] www.energymatters.com , images</p><p>160</p><p>[www.hdtlovato.com] www.hdtlovato.com</p><p>[www.ballard.com] www.ballard.com</p><p>[http://www.gmbattery.com/English/Li-ion_Cylindrical_Battery.html]</p><p>[http://www.maxwell.com] www.maxwell.com Maxwell super capacitor</p><p>[Giovannitonzig] http://www.giovannitonzig.it/integrazioni/meccanica/meccanica_10_attrito.pdf</p><p>[Texas instrument] “TMS320F28335, TMS320F28334, TMS320F28332 TMS320F28235, TMS320F28234,</p><p>TMS320F28232 Digital Signal Controllers (DSCs)” Data Manual</p><p>[Petrella] Roberto Petrella “Strategie di controllo del motore brushless” University of Udine</p><p>[Omron] “Encoder incrementali e assoluti” Omron</p><p>[Direct industry] http://img.directindustry.it/images_di/photo-g/pinza-amperometrica-364159.jpg</p><p>[gmbattery] http://www.gmbattery.com/English/Li-ion_Cylindrical_Battery.html</p><p>• Incremental output A/B-Pulse</p><p>• Housing diameter 36 mm or 58 mm</p><p>• Protection class IP64, max. IP67</p><p>• Output frequency up to 300kHz</p><p>• Max. rotation speed 12.000 rpm</p><p>• Torque: 0,05-0,5 Nm</p><p>• Aluminium housing</p><p>• Customised versions available</p><p>Incremental Angle Transducer</p><p>Encoder</p><p>13.09.05</p><p>Series A36</p><p>and A58</p><p>Technical drawing A36</p><p>Solid shaft</p><p>Through hollow shaft / Hollow shaft</p><p>Solid shaft Through hollow shaft / Hollow shaft</p><p>Shaft diameter 6 mm 6 / 6,35 / 8 mm (depth=2xD for holl. sh.)</p><p>Max. rotation speed 12.000 rpm 12.000 rpm</p><p>Shaft load 40 N radial, 25 N axial 45 N radial, 30 N axial</p><p>Moment of inertia approx. 0,2x10-6 kgm2 approx. 0,3x10-6 kgm2</p><p>Starting torque (20°C) <0,05 Nm <0,5 Nm</p><p>Ball bearing 626ZZ 6800ZZ</p><p>Shaft material stainless steel brass</p><p>Working temperature -30...+85°C</p><p>Protection class IP64</p><p>Shock resistance 1000 m/s2; 6 ms</p><p>Vibration resistance 100 m/s2; 55-2000 Hz</p><p>Mass approx. 80 g</p><p>Housing material aluminium</p><p>Available resolution 25 / 100 / 125 / 200 / 360 / 500 / 1000 / 1024 / 1500 /</p><p>2000 / 2048 / 2500 / 3600 counts/rev. (more on request)</p><p>A36</p><p>A36</p><p>See page 5</p><p>for electr. data</p><p>Note:</p><p>Through hollow shafts are not</p><p>available with axial cable</p><p>output</p><p>- 2 -</p><p>A58</p><p>Technical drawing A58</p><p>Solid shaft</p><p>Through hollow shaft</p><p>Solid shaft Through hollow shaft</p><p>Shaft diameter 6 / 10 / 12 mm 12 / 20 / 25 / 28 mm</p><p>Max. rotation speed 12.000 rpm 5.000 rpm</p><p>Shaft load 40 N radial, 60 N axial 60 N radial, 80 N axial</p><p>Moment of inertia approx. 1,4x10-6 kgm2 approx. 35x10-6 kgm2</p><p>Starting torque (20°C) <0,05 Nm <0,1 Nm</p><p>Ball bearing 6000 2RS 2RS</p><p>Shaft material stainless steel stainless steel</p><p>Working temperature -30...+85°C</p><p>Protection class IP64 or IP67 (for IP67 max. rotation speed reduced to 50%)</p><p>Shock resistance 1000 m/s2; 6 ms</p><p>Vibration resistance 100 m/s2; 55-2000 Hz</p><p>Mass approx. 250 g</p><p>Housing material aluminium</p><p>Available resolution 60 / 100 / 250 / 400 / 500 / 960 / 1000 /</p><p>1024 / 2000 / 5000 counts/rev. (more on request)</p><p>A58</p><p>See page 5</p><p>for electr. data</p><p>- 3 -</p><p>Connection</p><p>Values for impulse and resolution in the according manuals</p><p>* For line driver L only (RS422 TTL-compatible). For long line lengths it may occur that the operating voltage at the sensor does not</p><p>suffice due to the output resistance. With the sensor lines 0Vsens and +UBsens the operating voltage can be checked and, if</p><p>necessary, be readjusted at the input connection.</p><p>Signal 0V +UB 0Vsens* +UBsens* A A- B B- Z Z- Screen</p><p>12pin connector 10 12 11 2 5 6 8 1 3 4 Housing</p><p>Wire colour white brown black violet green yellow grey pink blue red Housing</p><p>90°</p><p>A</p><p>B</p><p>Z 90°</p><p>360°</p><p>Z-signal with A/B</p><p>AND-related</p><p>Output signal</p><p>Pulses A and B are 90° phase-delayed</p><p>(detection of direction). The Z-signal recurs</p><p>with pulse distance Z and may be used as</p><p>point of reference.</p><p>Display of signal without inverted signals.</p><p>Clockwise rotation - view onto shaft</p><p>12pin connector output</p><p>(socket) for A58 only</p><p>Profile/view on solder side</p><p>of mating connector</p><p>Cable:</p><p>radial/axial 1,5 m standard</p><p>other lengths optional</p><p>Type: UL2464/1061, LIYY, flexible</p><p>Diameter: approx. 6,5 mm</p><p>Core: 0,25 mm²</p><p>Temperature range: fixed in installation -30...+80°C</p><p>flexible -20...+80°C</p><p>1 9 8</p><p>2 10 12 7</p><p>3 11</p><p>54</p><p>6</p><p>Power supply: 5 VDC ±5% 8 up to 30 VDC</p><p>Current consumption without load: typ. 70 mA, max. 100 mA typ. 80 mA, max. 150 mA</p><p>Max. load/canal A36: ±10 mA ±30 mA</p><p>Max. load/canal A58: ±20 mA ±30 mA</p><p>Max. pulse frequency A36 : 125 kHz 100 kHz</p><p>Max. pulse frequency A58: 300 kHz 300 kHz</p><p>Min. signal level high: 2,5 V UB - 3 V</p><p>Max. signal level low: 0,5 V 2,5 V</p><p>Working temperature -30...+85°C -30...+85°C</p><p>Protection class IP64 (IP67 on request) IP64 (IP67 on request)</p><p>Max. line length 1000 m 250 m</p><p>Recommended circuit</p><p>Data Electronics Line driver L Push-Pull G</p><p>RS 422 (TTL-compatible)</p><p>0V</p><p>+5V</p><p>A</p><p>Ā</p><p>sensor circuit</p><p>Z = 120 Ohm</p><p>Z</p><p>0V</p><p>+5V</p><p>0V</p><p>UB = 8..30 VA</p><p>Ā</p><p>sensor circuit</p><p>RL = 1 k Ohm</p><p>RL</p><p>Technical data</p><p>- 4 -</p><p>Digital angle and rotation speed measurement - PAX</p><p>Use PAX to visualise the angle of rotation or the rotation speed (Tacho sensor) of the encoder.</p><p>It enables a transmission of the measurement data on the computer via interface.</p><p>The comparator allows a Good-Bad-evaluation (limiting values function).</p><p>Inputs: Incremental/Analogue, 2 independent counter, 1 Tacho sensor</p><p>2 or 4 limiting values (plug in card)</p><p>Analogue output (0)4...20 mA, 0...10 V (plug in card)</p><p>Serial interfaces: RS 485, RS232, DeviceNet (plug in card)</p><p>Protection class (front panel) IP 65</p><p>6-digit display and power supply 11...36 VDC or 85...250 VAC</p><p>For further information please ask for the data sheet for the PAX display series.</p><p>Options</p><p>Mating connector M23 for A58 - CON012-S</p><p>M23, straight</p><p>12pin connector clockwise</p><p>(fits in anticlockwise encoder sockets)</p><p>Metal housing</p><p>Accessories</p><p>Synchro flange (for A58)</p><p>Encoder A58 can also be conducted with a synchro</p><p>flange. The shaft diameter is 6 mm (see sketch).</p><p>To mount the sensor the excentrics BX58 may be</p><p>used.</p><p>Mounting excentric kit - BX36 and BX58</p><p>The encoder can be mounted with the excentrics.</p><p>The kit includes 3 excentrics and 3 screws.</p><p>Required drill holes:</p><p>BX36: M2,5-screw thread, depth 5 mm, ø screw-hole circle 42 mm</p><p>BX58: M3-screw thread, depth 6 mm, ø screw-hole circle 65 mm</p><p>IP67 (for A58)</p><p>Option IP67 applies when the sensor is completely immersed in water (temporarily). Please bear in mind that this option implicates</p><p>a higher starting torque due to the specific sealing. The max. torque is reduced to 50% of the specified value. This option is</p><p>available for series A58 only.</p><p>Extended connector cable for cable output</p><p>The cable length for sensors with cable output is 1,5 m standard. The cable can be ordered in any length as needed. Please</p><p>specify your request in your order.</p><p>Coupling</p><p>We offer a range of fixed or pluggable (disk) couplings (bellows coupling) for</p><p>all current shaft diameters.</p><p>Application for shaft unsymmetries, angle errors, axial play, as adapter for</p><p>various shaft diameters or as disk couplings to disconnect or disassemble.</p><p>- 5 -</p><p>Office Köln</p><p>Alte Fischenicherstr. 46</p><p>50997 Köln</p><p>Tel. +49 (0)2232 96 58 03</p><p>Fax +49 (0)2232 96 58 05</p><p>Head Office</p><p>Inselkammerstr. 8</p><p>82008 Unterhaching</p><p>Tel. +49 (0)89 61 20 84 70</p><p>Fax +49 (0)89 61 20 84 83</p><p>WayCon Positionsmesstechnik GmbH</p><p>e-mail: info@waycon.de</p><p>internet: www.waycon.de</p><p>Order code A36</p><p>Order code A58</p><p>Shaft type/flange</p><p>Solid shaft with clamp flange</p><p>Solid shaft with synchro flange</p><p>Through hollow shaft</p><p>W</p><p>WY</p><p>H</p><p>A58</p><p>Shaft diameter</p><p>Solid sh. with clamp fl.: 6/10/12 mm</p><p>Solid sh. with synchro flange: 6 mm</p><p>Thr. hollow sh.: 12/20/25/28 mm</p><p>z.B. 6</p><p>6</p><p>z.B. 28</p><p>Output</p><p>Line driver RS422 (5V)</p><p>Push-pull antivalent (8..30V)</p><p>L</p><p>G</p><p>Connection</p><p>Connector output axial</p><p>Connector output radial</p><p>Cable output axial (not thr. hollow sh.)</p><p>Cable output radial</p><p>SA</p><p>SR</p><p>KA</p><p>KR</p><p>Resolution</p><p>60/100/250/400/500/960/</p><p>1000/1024/2000/5000</p><p>z.B.</p><p>5000</p><p>A36-W Solid shaft 135 €</p><p>A36-H/SH Through hollow shaft or hollow shaft 140 €</p><p>Price list</p><p>A58-H-12/20 Through hollow shaft ø 12 or 20 mm 199 €</p><p>A58-H-25/28 Through hollow shaft ø 25 or 28 mm 219 €</p><p>A58-W/WY Solid shaft 155 €</p><p>Accessories:</p><p>BX36 Mounting excentric kit for A36</p><p>BX58 Mounting excentric kit for A58</p><p>mating connector M23, SA/SR</p><p>CON012-S mating connector M23 straight</p><p>PAX Digital display of angle and rotation speed</p><p>(see separate data sheet for the PAX display series)</p><p>7 €</p><p>9 €</p><p>19 €</p><p>ab 324 €</p><p>Options</p><p>water-proof IP67 (not thr. hollow sh.)IP67</p><p>Options:</p><p>IP67 water-proof IP67</p><p>Extended connector cable for axial/radial</p><p>cable output KA/KR</p><p>each additional metre of PVC cable</p><p>15 €</p><p>6 €</p><p>- 6 -</p><p>Shaft type</p><p>Solid shaft</p><p>Through hollow shaft</p><p>Hollow shaft</p><p>W</p><p>H</p><p>SH</p><p>A36</p><p>Shaft diameter</p><p>Solid shaft: 6 mm</p><p>Through hollow shaft: 6/6,35/8 mm</p><p>e.g. 6</p><p>e.g. 8</p><p>Output</p><p>Line driver RS422 (5V)</p><p>Push-Pull (8..30V)</p><p>L</p><p>G</p><p>Connection</p><p>Cable output axial (not thr. hollow sh.)</p><p>cable output radial</p><p>KA</p><p>KR</p><p>Resolution</p><p>25/100/125/200/360/500/1000/1024/</p><p>1500/2000/2048/2500/3600</p><p>e.g.</p><p>3600</p><p>We reserve the right to alter the specification without prior notice.</p><p>Current Transducer LA 100-P</p><p>For the electronic measurement of currents : DC, AC, pulsed...,</p><p>with a galvanic isolation between the primary circuit (high power)</p><p>and the secondary circuit (electronic circuit).</p><p>Electrical data</p><p>I</p><p>PN</p><p>Primary nominal r.m.s. current 100 A</p><p>I</p><p>P</p><p>Primary current, measuring range 0 .. ± 150 A</p><p>R</p><p>M</p><p>Measuring resistance @ T</p><p>A</p><p>= 70°C T</p><p>A</p><p>= 85°C</p><p>R</p><p>M min</p><p>R</p><p>M max</p><p>R</p><p>M min</p><p>R</p><p>M max</p><p>with ± 12 V @ ± 100 A</p><p>max</p><p>0 50 0 42 Ω</p><p>@ ± 120 A</p><p>max</p><p>0 22 0 14 Ω</p><p>with ± 15 V @ ± 100 A</p><p>max</p><p>0 110 20 102 Ω</p><p>@ ± 150 A</p><p>max</p><p>0 33 20 25 Ω</p><p>I</p><p>SN</p><p>Secondary nominal r.m.s. current 50 mA</p><p>K</p><p>N</p><p>Conversion ratio 1 : 2000</p><p>V</p><p>C</p><p>Supply voltage (± 5 %) ± 12 .. 15 V</p><p>I</p><p>C</p><p>Current consumption 10(@± 15 V)+ I</p><p>S</p><p>mA</p><p>V</p><p>d</p><p>R.m.s. voltage for AC isolation test, 50 Hz, 1 mn 2.5 kV</p><p>Accuracy - Dynamic performance data</p><p>X Accuracy @ I</p><p>PN</p><p>, T</p><p>A</p><p>= 25°C @ ± 15 V (± 5 %) ± 0.45 %</p><p>@ ± 12 .. 15 V (± 5 %) ± 0.70 %</p><p>ε</p><p>L</p><p>Linearity < 0.15 %</p><p>Typ Max</p><p>I</p><p>O</p><p>Offset current @ I</p><p>P</p><p>= 0, T</p><p>A</p><p>= 25°C ± 0.10 mA</p><p>I</p><p>OM</p><p>Residual current 1) @ I</p><p>P</p><p>= 0, after an overload of 3 x I</p><p>PN</p><p>± 0.15 mA</p><p>I</p><p>OT</p><p>Thermal drift of I</p><p>O</p><p>- 25°C .. + 85°C ± 0.05 ± 0.25 mA</p><p>- 40°C .. - 25°C ± 0.10 ± 0.50 mA</p><p>t</p><p>ra</p><p>Reaction time @ 10 % of I</p><p>P max</p><p>< 500 ns</p><p>t</p><p>r</p><p>Response time 2) @ 90 % of I</p><p>P max</p><p>< 1 µs</p><p>di/dt di/dt accurately followed > 200 A/µs</p><p>f Frequency bandwidth (- 1 dB) DC .. 200 kHz</p><p>General data</p><p>T</p><p>A</p><p>Ambient operating temperature - 40 .. + 85 °C</p><p>T</p><p>S</p><p>Ambient storage temperature - 50 .. + 95 °C</p><p>R</p><p>S</p><p>Secondary coil resistance @ T</p><p>A</p><p>= 70°C 120 Ω</p><p>T</p><p>A</p><p>= 85°C 128 Ω</p><p>m Mass 18 g</p><p>Standards 3) EN 50178</p><p>Notes : 1) The result of the coercive field of the magnetic circuit</p><p>2) With a di/dt of 100 A/µs</p><p>3) A list of corresponding tests is available</p><p>Features</p><p>• Closed loop (compensated) current</p><p>transducer using the Hall effect</p><p>• Printed circuit board mounting</p><p>• Insulated plastic case recognized</p><p>according to UL 94-V0.</p><p>Advantages</p><p>• Excellent accuracy</p><p>• Very good linearity</p><p>• Low temperature drift</p><p>• Optimized response time</p><p>• Wide frequency bandwidth</p><p>• No insertion losses</p><p>• High immunity to external</p><p>interference</p><p>• Current overload capability.</p><p>Applications</p><p>• AC variable speed drives and servo</p><p>motor drives</p><p>• Static converters for DC motor drives</p><p>• Battery supplied applications</p><p>• Uninterruptible Power Supplies</p><p>(UPS)</p><p>• Switched Mode Power Supplies</p><p>(SMPS)</p><p>• Power supplies for welding</p><p>applications.</p><p>I</p><p>PN</p><p>= 100 A</p><p>980717/6</p><p>LEM Components www.lem.com</p><p>Secondary terminals</p><p>Terminal + : supply voltage + 12 .. 15 V</p><p>Terminal - : supply voltage - 12 .. 15 V</p><p>Terminal M : measure</p><p>Connection</p><p>Remarks</p><p>• I</p><p>S</p><p>is positive when I</p><p>P</p><p>flows in the direction of the arrow.</p><p>• Temperature of the primary conductor should not exceed</p><p>100°C.</p><p>• Dynamic performances (di/dt and response time) are best</p><p>with a single bar completely filling the primary hole.</p><p>• In order to achieve the best magnetic coupling, the primary</p><p>windings have to be wound over the top edge of the device.</p><p>• This is a standard model. For different versions (supply</p><p>voltages, turns ratios, unidirectional measurements...),</p><p>please contact us.</p><p>Mechanical characteristics</p><p>• General tolerance ± 0.2 mm</p><p>• Primary through-hole 12.7 x 7 mm</p><p>• Fastening & connection of secondary 3 pins</p><p>0.63 x 0.56 mm</p><p>Recommended PCB hole 0.9 mm</p><p>Dimensions LA 100-P (in mm. 1 mm = 0.0394 inch)</p><p>Bottom view</p><p>Front view</p><p>Left view</p><p>LEM reserves the right to carry out modifications on its transducers, in order to improve them, without previous notice.</p><p>Standard 00 Year Week</p><p>or N° SP ..</p><p>swiss</p><p>made</p><p>1</p><p>aalborg</p><p>Ch1-Problem Analysis and Project Approach</p><p>Ch2-Estimation HEV Traction System Drive</p><p>Ch3-Drive Design</p><p>Ch4-PMSM Modeling</p><p>Ch5-IPMSM Control Strategy</p><p>Ch6-IPMSM Control System Development</p><p>Ch7-IPMSM Drive System Realization</p><p>Ch8-Conclusion</p><p>Incremental_Encoder_A_Enco_e</p><p>lem</p><p>and in peak discharge conditions. For a correct utilization of the batteries it’s advisable</p><p>to not overtake these Nominal Limits. However these values must be observed and valuated when</p><p>choosing a Battery Pack to supply an arbitrary load, keeping in mind that a high Capacity value may mean a</p><p>less autonomy for the Battery Pack if the Capacity value is fully exploited.</p><p>Figure 1.3 – Ragone Plot for the Storage Systems [University of Cassino]</p><p>9</p><p>Another important parameter for the Batteries is their Cycle life, intended as the number of Charge-</p><p>Discharge Cycles that can be approached from the device. This number will suffer for a decrease if during</p><p>the normal utilization of the Battery Pack comes surpassed the maximum Depth of Discharge, so for a long</p><p>life utilization it’s ever advisable not to overpass the Specific Limit provided by the constructor. For example</p><p>in the Figure 1.4 these behaviors are shown for a typical Lead-Acid Battery with 3 different percentage</p><p>value of discharge.</p><p>Figure 1.4 – Cycle Life vs Depth of Discharge for a Lead-Acid Battery [www.energymatters.com]</p><p>As is possible to watch in Figure 1.3, the Types of Batteries with the highest Specific Energy value are the</p><p>Sodium-Sulfur, Lithium-Ion and Lithium Polymer and this skill is right for HEV applications and for the</p><p>Project development. In this HEV Drive will use a Lithium Polymer Battery because is a the best choice that</p><p>can join good Capacity, Charge Acceptance and Cycle Life values against an high Cost.</p><p>1.2.4 Ultra-Capacitor Use</p><p>This particular Energy Storage System must be used to capture the braking energy during the deceleration</p><p>of the Vehicle and also to provide Current Pulse values to the Traction System when is required an high</p><p>Torque value (for strong acceleration). The characteristic to accumulate (or to supply) a large amount of</p><p>Electric Charge than a conventional Capacitor or than a Battery Pack makes these devices useful when are</p><p>necessary high Current Pulse values.</p><p>The biggest Advantage of this Energy Storage System regarding the possibility to charge or discharge it</p><p>almost instantly (typical time 1÷10 s), so ensuring an highest Specific Power (required when the Vehicle</p><p>demands a powerfully acceleration). This aspect can also introduce a simplification for the entire Drive of</p><p>the Vehicle, because could be possible to avoid the use of a Converter to manage and control the Current</p><p>10</p><p>value during the braking and acceleration. However if will be used or not a Converter will depend from the</p><p>Current and Voltage values obtained after the sizing of the Drive. Eventually to achieve this Purpose will be</p><p>used a Bidirectional Converter capable to work in Boost Mode when there is a strong acceleration and in</p><p>Buck Mode when the Vehicle is braking (Buck/Boost Converter).</p><p>Other types of Advantages for these devices are:</p><p>� High Cycle Efficiency (95 % or more because have an extremely low internal resistance)</p><p>� High number of Charge-Discharge Cycles (one million about)</p><p>� Low Heating Level</p><p>� Safety Mode to charge (no full-charge control is required, no danger of overcharge)</p><p>The main Disadvantage of the Super-Capacitors is mitigated by the Battery use, because they have a low</p><p>value of storable energy if compared with any other type of battery (for this reason the Super-Caps are not</p><p>used to supply completely an EV).</p><p>Besides another important problem regards the Voltage variation with the Energy stored (if the energy</p><p>stored improves also the voltage value will improve), so could be important about the decision to use or</p><p>not a Converter to minimize losses of energy.</p><p>Finally another problem could affect the high self-discharge ratio for these items, because may cause some</p><p>difficult to obtain good dynamic performance for the HEV after a long inactivity period. However this type</p><p>of problem depends by the actual technology, so is difficult to do something for arrange this situation.</p><p>For this particular application is required a Super-Capacitors stock capable to deliver rapid Bursts of Power,</p><p>to have a right Time Constant Value compatible with HEV Dynamics, to work with admissible Voltage and</p><p>Current Drive values and with as more as possible low Mass value. Ultra-Capacitors typically suitable for</p><p>these tasks are the BOOSTCAP (Maxwell Technologies) for mix of good Energy Density-Peak Power-Price</p><p>values. However an exact Capacity value for the stock will be determined in Chapter 2.</p><p>1.2.5 DSP Tasks</p><p>For the Control and the Implementation on the HEV is necessary to use a fast Digital Signal Processor Unit</p><p>(DSP) to coordinate all the actions inside the Drive aboard. The main tasks for DSP in this application are:</p><p>• Measurement of the Real Signal, Comparison with the Reference Signal, Regulation of the Error</p><p>Signal and Supply the due Control Signal for every Power Switch of each Converter in the Drive.</p><p>• Intelligent Management of the Power Flow during each HEV phase (Start-up, Cruise, Plug-in from</p><p>the Grid, Braking and Acceleration).</p><p>• Implementation of a Strategy and Algorithm Control for the Drive.</p><p>11</p><p>How every device, the DSP has a several proprieties that must be evaluated when is selecting this Unit:</p><p>� Real Time Performance</p><p>� Peripherals I/O, ADC, PWM</p><p>� Architecture</p><p>� Program Flow</p><p>� Data Operations</p><p>� Instructions Sets</p><p>In the Digital Real Time Elaboration is more important the number of elaboration done by the DSP in a</p><p>specific period. This number is represented by the Clock Frequency and the actual technology standards</p><p>can achieve 1 GHz about.</p><p>The Architecture of DSP is another important requirement to understand the various uses of this item. A</p><p>basic Architecture of a DSP is composed by: an Arithmetic Logic Unit (ALU), a Memory to storage the data</p><p>and the instructions of the program and a Bus Data to transfer instructions and data between the Memory</p><p>and ALU. The different types of Architecture can determine Computing Power, Flexibility and Processing</p><p>Time for a DSP, making it less or more appropriated for a such application.</p><p>The DSP are classified according type and amplitude for the Flow Data that they are able to process. Indeed</p><p>is possible to talk about DSP with 32, 24 or 16 bit and with Floating-point or Fixed-point. For example a 16</p><p>bit Fixed-point DSP will be used for low cost application like Industrial cases (Figure 1.5), while a 32 bit</p><p>Floating-point DSP will be used for high cost application like Graphical Elaboration, however when is</p><p>required a good dynamic representation range, a relatively small error and a low probability that overflow</p><p>occurs (but they have a big disadvantage due to the slowness of the processing). These considerations push</p><p>to select for the Project a 32 bit Fixed-point DSP for his good dynamic performance (the exactly type will be</p><p>choice in the next Chapters after other evaluations).</p><p>Figure 1.5 – Block Diagram for a basic Fixed-point DSP [http://lesim1.ing.unisannio.it]</p><p>12</p><p>1.3 Problem Formulation</p><p>The Project guidelines until this point have emphasized only the principal problems for each device, but it’s</p><p>already enough to make a first brief concerning the complete HEV Drive, putting together the preliminary</p><p>solutions found up to now. A basic way to set and develop the Project is already shaping and in the Figure</p><p>1.6 is possible to observe a more detailed HEV Drive than that shown in Figure 1.1 at the beginning of this</p><p>work.</p><p>Figure 1.6 – Schematic and Block Diagram for the HEV Drive</p><p>NOTE: In the Chapter 2 will be dealt the Calculations regarding the HEV mechanics, resistances and dynamic</p><p>equations, to achieve at last the desirable Vehicle Performance, and so be able to choose every device size</p><p>in the Drive. These values will be calculated for a REAL HEV POSSIBLE APPLICATION, while in the part about</p><p>Modeling and Testing of the devices will be used a LOWEST NOMINAL POWER VALUES</p><p>for each</p><p>components, for reasons due to the difficult Practical Realization of the Project, meanly high Costs and hard</p><p>Availability of those power values.</p><p>The most important topics to deal and solve for the rest of the Project are listed below:</p><p>� How to Estimate the exactly size for each components aboard using the Physical Relation of the</p><p>Vehicle?</p><p>� How Choose in every detail the rest of the Parameters for the Drive?</p><p>� Which kind of Architecture for the Control Strategy is possible to use?</p><p>13</p><p>� Which Method is possible to Recharge the Battery with any type of configuration?</p><p>� Which are the required Mathematical Model to implement for the main devices?</p><p>� How is possible to set all the Tests during the Practical Realization ?</p><p>Every of these Targets will be analyzed in the next Chapters and will be treated into a several sub-analysis.</p><p>1.4 Project Strategy</p><p>To Comprehend the approach about the project is better to divide its in three different parts, where will be</p><p>described the following issues:</p><p>I. Electric Design</p><p>In this part of the project will be dealt mainly issues like:</p><p>� Estimation and Selection of all electric components for the HEV Traction System Drive:</p><p>o Fuel Cell</p><p>o DC/DC Converters</p><p>o DC/AC Converters</p><p>o Battery Pack</p><p>o Ultra-Capacitors</p><p>o Traction Motors</p><p>o Control Unit</p><p>� Complete Architecture and Strategy Control used for the Electric Drive.</p><p>� Operation Mode for the Traction System Drive regarding:</p><p>o PMSM Speed Control</p><p>o PMSM Torque Control</p><p>II. Modeling Section</p><p>The second part of the project will regard:</p><p>� Analysis, Modeling and Software Implementation of the main components for the HEV:</p><p>o PMSM and Equivalent Load</p><p>o Inverter</p><p>o DSP, Encoder and Current Probes</p><p>� Simulation and Result Analysis.</p><p>� Comparison Versus Theoretical and Ideal Performance.</p><p>All Models will be implemented with MATLAB/Simulink™.</p><p>14</p><p>III. Test and Practical Realization</p><p>The topics for this part will regard only analysis e and laboratory tests about the Operative Mode</p><p>for the Traction System:</p><p>� Current and Speed Sensors measurements</p><p>� Control Speed Test with PMSM+Inverter.</p><p>� Programming and Implementation on a DSP Controller.</p><p>15</p><p>Chapter</p><p>Chapter 2</p><p>Estimation HEV Traction</p><p>System Drive</p><p>Contents:</p><p>2.1 Physical Relations for the HEV</p><p>2.1.1 Free Body Diagram</p><p>2.2 Design Features</p><p>2.3 Propulsion Electrical Motors Choice</p><p>2.4 Estimation HEV Performance</p><p>2.5 HEV Motion Model Implementation</p><p>2.6 Primary and Secondary Energy Sources Estimation</p><p>2.6.1 Fuel Cell</p><p>2.6.2 Battery</p><p>2.6.3 Ultra-Capacitors</p><p>This Chapter will treat at first the Physical relations necessary to size an HEV</p><p>and then will be develop all the mathematical calculation necessary to achieve</p><p>specific performance for the HEV Traction System Drive. Besides will be</p><p>simulated in MATLAB/Simulink the Motion Model regarding the HEV,</p><p>comparing the results obtained between the analytical expressions and the</p><p>HEV Implemented model. At last will be show the calculation to size primary</p><p>and secondary energy sources aboard of Vehicle.</p><p>16</p><p>2.1 Physical Relations for the HEV</p><p>Before to make the design of the Vehicle and choose which are the most suitable devices to achieve</p><p>specific performance is necessary to analyze all the forces that will influence the HEV motion. To consider</p><p>and to calculate these forces can be used the following Free Body Diagram.</p><p>2.1.1 Free body diagram</p><p>While the Vehicle is running some Resistance Forces will oppose to the Traction Force, which will be direct</p><p>towards the HEV motion direction. The Resistance Forces can be divided into two categories:</p><p>• Rolling Resistance Force Fpe: this kind of force is caused by friction between the pin and bearing.</p><p>• Rolling Resistance Force Fwg: caused by the rolling of the wheel on the ground.</p><p>• Air Resistance Force Fair: this force is caused by the resistance that the air generates on the car.</p><p>• Accidental Resistance Forces Fslope: will be determined force by eventual slope of the road.</p><p>• Gravitational Force Fcurve: these resisting forces are caused by eventual curves.</p><p>All the Forces reported above are shown in Figure 2.1. The total driving resistances will be the sum of all</p><p>these resistant forces.</p><p>Figure 2.1 – Forces Acting on the Vehicle</p><p>The resulting force is the driving force Fdr, which represents the force required to advance:</p><p>��� = ��� − ��� − �</p><p>− ���� [(�)] (2.1)</p><p>Fpe force rolling resistance can be calculated as:</p><p>��� = µ� �� ����</p><p>�</p><p>� [(�)] [University of Cassino] (2.2)</p><p>17</p><p>Where:</p><p>μ� ��: Friction coefficient between pin and bearing; ([−])</p><p>����: weight of car; ([N])</p><p>�: diameter pin; ([m])</p><p>�: diameter wheel. ([m])</p><p>Figure 2.2 – Coupling pin-bearing</p><p>Inserting data of the components selected:</p><p>�: 0.05 ([m])</p><p>�: 0.76 ([m])</p><p>����: 11000 ([N])</p><p>and considering the typical friction coefficient between pin and bearing [Wikipedia 2010]:</p><p>μ� ��: 0.001 ([−])</p><p>obtain:</p><p>��� = 0.001 ∙ 11000 ∙ 0.05</p><p>0.76 ≅ 1 �</p><p>(2.3)</p><p>Fwg force rolling resistance</p><p>�</p><p>= ����</p><p>$%</p><p>� [(�)] [University of Cassino] (2.4)</p><p>where,</p><p>����: weight of car; ([N])</p><p>&: displacement the weight force G in the direction of motion; ([m])</p><p>18</p><p>�: diameter wheel. ([m])</p><p>Figure 2.3 – Unbalanced Pressure Distribution</p><p>where,</p><p>����: weight of car; ([N])</p><p>&: moving the weight force G in the direction of motion; ([m])</p><p>': velocity; ([m/s])</p><p>Fwg: force rolling resistance. ([N])</p><p>Inserting data of the components selected:</p><p>����: 11000 ([N])</p><p>�: 0.76 ([m])</p><p>and considering,</p><p>the typical value of δ [Giovannitonzig]:</p><p>&: 0.01 ([m])</p><p>obtain:</p><p>�</p><p>= 11000 2 ∙ 0.01</p><p>0.76 = 289.47 �</p><p>(2.5)</p><p>19</p><p>Fair force caused by the resistance of the air (consider negligible component side Fairy=0):</p><p>Figure 2.4 – Resistances Forces caused by the air</p><p>���� = 1</p><p>2 ,�-.'/01$ [(�)] (2.6)</p><p>where,</p><p>,2: Frontal area of the vehicle; ([m</p><p>2</p><p>])</p><p>-: air density; ([kg/m</p><p>3</p><p>])</p><p>.: coefficient of penetration of the vehicle; ([−])</p><p>'/01: reachable maximum velocity. ([m/s])</p><p>Inserting the characteristics of the vehicle:</p><p>,2: 2 ([m</p><p>2</p><p>])</p><p>'/01: 20 ([m/s])</p><p>and considering the typical value of ρ and γ [Modern electric, hybrid electric and fuel cell vehicles]:</p><p>-: 1.25 ([kg/m</p><p>3</p><p>])</p><p>.: 0.3 ([−])</p><p>obtain:</p><p>���� = 1</p><p>2 ∙ 2 ∙ 1.25 ∙ 0.3 ∙ 20$ = 150 �</p><p>(2.7)</p><p>20</p><p>Figure 2.5 - Resistance Force caused by the slope of the road</p><p>Fslope force caused by the slope of the road:</p><p>�256�� = ���� tan (:) [(�)] (2.8)</p><p>where,</p><p>����: Weight of car; ([m</p><p>2</p><p>])</p><p>:: slope. ([kg/m</p><p>3</p><p>])</p><p>Inserting the characteristic of the vehicle:</p><p>����: 11000 ([N])</p><p>and considering an typical slope of 10%</p><p>α</p><p>21</p><p>Figure 2.6 - Slope of the road</p><p>And for obtain the angle α:</p><p>: = tan;< = 10 ></p><p>100 >? = 5.71° �AB</p><p>(2.9)</p><p>corresponding at:</p><p>:: 5.71 ([°deg])</p><p>obtain:</p><p>�256�� = 11000 tan(5.71) = 1099.88 � (2.10)</p><p>Fcurve force caused by the curves of the road (caused by centrifugal force and centripeda force):</p><p>�CD�E� = ([N]) (2.11)</p><p>Figure 2.7 – Resistance Force caused by the curves on the road</p><p>where,</p><p>-: amplitude of the curve; ([rad])</p><p>G: mean radius of the curve. ([m])</p><p>However this force is not considerate in the project because are negligible.</p><p>X</p><p>Y</p><p>ΘY</p><p>22</p><p>2.2 Design Features</p><p>In order to estimate the size of the engine to use, it’s possible to start deciding the speed, acceleration and</p><p>autonomy that the car should have. The</p><p>specific assumed for the HEV design are:</p><p>� Type of vehicle: city car for 2 persons</p><p>� Max speed: 70 km/h</p><p>� Autonomy: 50 km</p><p>� Mass of car: about 1100 kg</p><p>� Power supply: Main supply by fuel cell, secondary supplies by batteries and super-capacitors</p><p>� Motor type: AC motor permanent magnet synchrony motor (PMSM)</p><p>2.3 Propulsion Electrical Motors Choice</p><p>So now having calculated all the resisting forces acting on the vehicle, can be estimate the power HI5��</p><p>required by the car for run on flat road at velocity of 13.89 m/s (50 km/h):</p><p>HI5�� = JFLM + FOP + FQRST ∙ v = (1 + 289.47 + 150) ∙ 13.89 = 6.12 kW (2.12)</p><p>where,</p><p>': velocity. ([m/s])</p><p>If instead considering that the car is running an climb with slope of 10%, at velocity of 5.56 m/s (20 km/h),</p><p>the power HC5�XY required is:</p><p>HC5�XY = JFLM + FOP + FQRS + FZ[\LMT ∙ v [(kW)] (2.13)</p><p>However should be recalculate the force Fair caused by the resistance of the air at new velocity of 5.56 m/s</p><p>using 2.6:</p><p>���� = 1</p><p>2 ∙ 2 ∙ 1.25 ∙ 0.3 ∙ 5.56$ = 11.59 �</p><p>(2.14)</p><p>So the power required is:</p><p>HC5�XY = (1 + 289.47 + 11.59 + 1099.88) ∙ 5.56 = 7.80 kW (2.15)</p><p>23</p><p>Therefore would sufficient two motors of power of about 4 kW, but to have a reserved of power of to use</p><p>also for recharge the batteries and the super capacitor, then decide to choice two motors of about 30 kW</p><p>for an total power available of 60 kW.</p><p>Detailed features of motors [www.hdtlovato.com]:</p><p>AC Brushless Motor product by HDT Lovato Group;</p><p>Type motor: AC Brushless Motor;</p><p>Model: B20L F;</p><p>Supply voltage: 400V;</p><p>Power: 31958 W;</p><p>Nominal torque: 118 Nm;</p><p>Nominal speed: 3000 rpm;</p><p>Weight: 62 kg.</p><p>Figure 2.8 - AC Brushless Motor B20L F [www.hdtlovato.com]:</p><p>So considering that we have needed of two motor:</p><p>Total power available is: power of every motor for two = 63916 W;</p><p>Total torque available is: torque of every motor for two = 236 Nm;</p><p>The total weight is: mass of every motor for two = 124 kg;</p><p>The other parameters are the same.</p><p>24</p><p>2.4 Estimation HEV Performance</p><p>At this point the parameters of the engines selected, and assuming the engines to work at maximum</p><p>torque, can calculate the maximum acceleration of the vehicle ]^�,X�^, setting a standard gear ratio and</p><p>starting from standstill, whereas Fair is equal to zero because at start the velocity is zero and increase</p><p>slowly.</p><p>]^�,X�^ = <</p><p>X `a�^_X�^</p><p>cde</p><p>� f − <</p><p>X gFpe + Fwg + Fslopeo pqX</p><p>2rst</p><p>(2.16)</p><p>where,</p><p>>: Mass of car; ([kg])</p><p>a�^_/01: maximum torque of motors; ([Nm])</p><p>uX�: gear ratio; ([−])</p><p>v: radius of wheel. ([m])</p><p>inserting data of the components selected,</p><p>>: 1100 ([kg])</p><p>a�^_/01: 236 ([Nm])</p><p>uX�: 6 ([−])</p><p>v: 0.38 ([m])</p><p>we have</p><p>]^�,X�^ = <</p><p><<ww `236 ∙ x</p><p>w.yzf − <</p><p><<ww {1 + 289.5 + 1099.8| = 2.12 X</p><p>2r (2.17)</p><p>Acceleration is definite in this mode:</p><p>] = Er;E}</p><p>�r;�}</p><p>pqX</p><p>2rst (2.18)</p><p>where:</p><p>'<: Initial velocity; ([m/s])</p><p>'$: final velocity; ([m/s])</p><p>~<: initial time; ([s])</p><p>~$: final time. ([s])</p><p>25</p><p>To find the time to accelerate up to 100 km/h, starting from a stationary, we start by the relation of</p><p>acceleration that is definite in this mode:</p><p>] = Er;E}</p><p>�r;�}</p><p>pqX</p><p>2rst (2.19)</p><p>where:</p><p>'<: Initial velocity; ([m/s])</p><p>'$: final velocity; ([m/s])</p><p>~<: initial time; ([s])</p><p>~$: final time. ([s])</p><p>and considering that starting from a stationary, we have that:</p><p>'<: 0 ([m/s])</p><p>~<: 0 ([s])</p><p>so the time for go up to 27.78m/s (100 km/h) is :</p><p>~(w;<ww)�d</p><p>�</p><p>=</p><p>E}�� �d</p><p>�</p><p>���,d��</p><p>= $�.�z d�</p><p>$.<$ d�r</p><p>= 13. 1 �</p><p>(2.20)</p><p>26</p><p>2.5 HEV Motion Model Implementation</p><p>With this model in the Figure 2.9 is implemented the law of motion that describes the main characteristics</p><p>of vehicle, as the maximum acceleration, the maximum speed and the position reached after a certain</p><p>period. The inputs of the system (orange blocks) are the torque of motor, called Mtx, expressed in Nm and</p><p>the slope of the road, called Slope, expressed in perceptual. The parameters that considerate constant are</p><p>friction coefficient pin and bearing called udSB, weight of car called GTOT expressed in N, diameter pin</p><p>called d expressed in m, diameter of wheel called D expressed in m, displacement caused by weight force G</p><p>called delta expressed in m, frontal area of the vehicle called As expressed in m</p><p>2</p><p>, air density called ro</p><p>expressed in kg/m</p><p>3</p><p>and coefficient of penetration of the vehicle called lambda dimensionless. The three</p><p>resistance forces that escape from the three blocks of multiplication Fpe resistance pin bearing, Fwg</p><p>resistance of rolling and Fair resistance of air, that depend on the velocity of vehicle. These three forces are</p><p>divided for the mass of the vehicle called m for obtain the negative acceleration. This negative acceleration</p><p>is subtracted to the positive acceleration generate by the motor. The positive acceleration of the motor</p><p>depends by torque of motor, by ration gear and by the radius of wheels. At this point at the out of the</p><p>adder node there is the net acceleration. Integrated the acceleration obtain the velocity and integrated the</p><p>latter obtain the position.</p><p>Figure 2.9 – HEV Motion Model Implementation in MATLAB/Simulink</p><p>27</p><p>This three graphs show the results of the simulation. The first graph In Figure 2.10 shows the net</p><p>acceleration applied to vehicle. Note that this decreases non-linearly, because the Fair, resistance force of</p><p>air, increases non-linearly with speed.</p><p>Figure 2.10 – HEV Acceleration Trend</p><p>This second graph in the Figure 2.11 shows the velocity of the vehicle. From this graph is possible kwon the</p><p>maximum velocity of vehicle about 78 m/s, and the time for accelerate from 0 to 100 km/h about 14</p><p>seconds.</p><p>Figure 2.11 – HEV Speed Trend</p><p>28</p><p>From this last graph in Figure 2.12 show the position of vehicle with increase of the time. From this graph is</p><p>possible know the time necessary to reach a kilometer, and this value is about 32 seconds.</p><p>Figure 2.12 – HEV Position Trend</p><p>29</p><p>2.6 Primary and Secondary Energy Sources Estimation</p><p>2.6.1 Fuel Cell</p><p>The fuel cell is an electrochemical device that can generate electricity exploiting the chemical reaction</p><p>between hydrogen and oxygen, without making a combustion process. There are many types of fuel cells, a</p><p>good type for use on the car are the proton exchange membrane PEM, because not take more time for the</p><p>start, have a good efficiency, have a good ratio mass power, and they are easy to use and control.</p><p>Figure 2.13 - Fuel Cell [Mehrdad Yimin Ali 2010]</p><p>It was decided that the power of fuel cells must be sufficient to feed the motors at full power. Then the</p><p>power of fuel cell must be of about 60 kW. It was chosen for reliability issues to use three cells of</p><p>approximately 20 kW each (because if break a cell we changed only that does not work, save lots of</p><p>money).</p><p>Detailed features of fuel cells [www.ballard.com]:</p><p>Fuel Cells product by Ballard;</p><p>Type of fuel cell: PEM fuel cell;</p><p>Model: FC Velocity – 9SSL;</p><p>Rated Power: 19.3 kW;</p><p>DC voltage (at 300A): 64.3 V;</p><p>Mass: 17 kg.</p><p>30</p><p>Figure 2.14 - Fuel cell [www.ballard.com]</p><p>A possible connection diagram is as follows (only as a basic diagram because in practice should be tested if</p><p>feasible):</p><p>Figure 2.15 - Connection diagram</p><p>So considering that need of three fuel cells connected in series:</p><p>Total power available is: power of every fuel cell for tree = 57.9 kW;</p><p>The total mass is: mass of every fuel cell for three = 51 kg;</p><p>The other parameters are the same.</p><p>31</p><p>2.6.2 Battery</p><p>The batteries are an electrochemical device that convert chemical potential energy into electrical energy</p><p>during the phase of discharge or use, the reverse process takes</p><p>place during the charging. A battery pack is</p><p>made of more cells connected in series or in parallel to each have a voltage or a higher current, in function</p><p>of specific load. Important parameters for the batteries are the voltage, the capacity, the cycles of charging,</p><p>and weight. The types of batteries are many, a good type for use on the car are lithium battery, because</p><p>have an high specific energy and so has a limited weight in relation with their capacity.</p><p>Figure 2.16 - A typical electrochemical battery cell[Mehrdad Yimin Ali 2010]</p><p>To estimate the required capacity of the battery is consider that the batteries should supply the motors in</p><p>the start-up, when the fuel cells still have not reached the optimal values of operating, or in the transitional</p><p>phases, as acceleration, in aid to super capacitors, however, for a maximum time (that only for test</p><p>considered of six minutes, but this time is only indicative and another value of time is possible).</p><p>Sizing of the battery pack. Estimation of the energy needed to power the engines at full power for six</p><p>minutes.</p><p>�Y��� = qP�\�\SZ ∙ x�</p><p>xws � �63916 W ∙ 0.1 h� � 6391.6 Wh (2.21)</p><p>Detailed features of cell [http://www.gmbattery.com/English/LiPo_Battery.html]:</p><p>Cell product by GMBPOWER;</p><p>Type of cell: Li-ion;</p><p>Model: 5069114;</p><p>Capacity for single cell: 4100 mAh;</p><p>32</p><p>DC voltage: 3.7 V;</p><p>Weight: 85 g.</p><p>Figure 2.17 - Li-ion cells [Gmbattery]</p><p>To obtain an energy of 6391.6 Wh we need to realize series and parallel of cells. Start of the voltage, fix the</p><p>voltage at the same value of that provided by fuel cells about 65 V . So for obtain this value of voltage we</p><p>calculated the number of cells needed, considering that the voltage for every cell is 3.7 V.</p><p>�C�552 �� 2����2 = �65��</p><p>� ���D����</p><p>�65��</p><p>� I6� 2��</p><p>5� C�55 = x�</p><p>y.� ≅ 18 (2.22)</p><p>Then considering that every cell has a capacity of 4.1 Ah, and that the series of 18 cells has voltage of 66.6</p><p>V, we calculate the number of the parallels needed to obtain the energy of 6391.6 Wh.</p><p>��~v��B = (�C�55 ∙ N�M[[Z) ∙ Capacity = 3.7 ∙ 18 ∙ 4.1 = 273.06 Wh (2.23)</p><p>So calculating the number of parallels:</p><p>A = “Total energy required”</p><p>B = “Energy series of 18 cells”</p><p>�����55�52 = 0</p><p>� = xy�<.x</p><p>$�y.wx ≅ 24 (2.24)</p><p>So the total cells are:</p><p>� 6I C�552 = �C�552 �� 2����2 ∙ NLQSQ[[M[Z = 18 ∙ 24 = 432 (2.25)</p><p>Connection diagram is as follows:</p><p>33</p><p>Figure 2.18 - Battery pack</p><p>So considering that we have needed of 432 cells:</p><p>Total energy available is about 6550 Wh;</p><p>The total weight is: weight of every cell for 432, is about 37 kg.</p><p>2.6.3 Ultra-Capacitors</p><p>When need strong accelerations or affront steep climb is necessary to have a power source that is able very</p><p>quickly, more quickly of batteries, to provide the energy needed, for that are used the super capacitor. For</p><p>estimate the characteristic of super capacitor, we consider the need of energy to power the motors at full</p><p>power for a maximum time (that only for test considered of 8 seconds, but this time is only indicative and</p><p>another value of time is possible). The energy for 8 seconds is:</p><p>�<w2 � qP�\�\SZ ∙ z��</p><p>yxwws = (63916 W ∙ 0.00278 h) = 142.04 Wh (2.26)</p><p>Detailed features of super capacitor [http://www.maxwell.com]:</p><p>Super capacitor product by: MAXWELL;</p><p>Model: BMOD0094 P075 B02;</p><p>Capacity: 94 F;</p><p>Voltage: 75 V;</p><p>Total energy 73.2 Wh;</p><p>Weight: 25 kg.</p><p>34</p><p>Figure 2.19 – Super-Capacitor [http://www.maxwell.com]</p><p>Whereas the super capacitor choice gives an energy of 72.2 Wh, and we need of about 142 Wh we use two</p><p>in parallel.</p><p>Connection diagram is as follows:</p><p>Figure 2.20 - Connection diagram</p><p>So considering that we have needed of 2 super capacitors:</p><p>Total energy available is about 147 Wh;</p><p>The total weight is: weight of every super capacitor for two, is about 50 kg.</p><p>Chapter 3</p><p>Drive Design, Control and</p><p>Measurements for HEV</p><p>Contents:</p><p>3.1 General Operation for HEV Drive</p><p>3.2 PEM Fuel Cell</p><p>3.3 Electric Schematic and Architecture for HEV</p><p>3.4 Operation for each Control and Measurement Device</p><p>3.4.1 Digital Signal Processor</p><p>3.4.1.1 DSP Common Structure</p><p>3.4.1.2 Texas Instruments TMS320F28335 Peripherals</p><p>3.4.2 Encoder</p><p>3.4.2.1 General Features</p><p>3.4.2.2 Encoder Structure</p><p>3.4.2.3 Incremental Encoder</p><p>3.4.2.4 Absolute Encoder</p><p>3.4.3 Voltage and Current Hall Effect Probe</p><p>3.4.3.1 General Features</p><p>3.4.3.2 Current Probes</p><p>3.4.3.3 Voltage Probes</p><p>This Chapter will take in examination the different operating modes for the</p><p>HEV Drive, analyzing which could be the most appropriate Electrical</p><p>Architecture and the best Control Strategy to achieve the basic targets of the</p><p>Project and which is the behavior regarding the Primary Energy Source aboard.</p><p>Besides will be discussed in detail each Components for the HEV Drive control</p><p>and for the measurements of the main variables, treating at first their general</p><p>functioning and then the specific tasks, characteristics and advantages for this</p><p>application.</p><p>36</p><p>3.1 General Operation for HEV Drive</p><p>The Design of the HEV Drive has been made to allow the achievement of the main targets. Indeed is</p><p>necessary plan and realize an Electrical Drive for the Traction System capable to accomplish important</p><p>issues like primary the PMSM Speed Control and then other tasks like the Power Flow Management and Li-</p><p>Poly Battery Recharge from the Grid.</p><p>To realize the Operating modes of the HEV Drive is important start from the Primary Energy Source</p><p>parameters. The PEM FC aboard the Vehicle must be able to provide the most of Power, with appropriate</p><p>Voltage and Current values for the DC Bus, but the actual technological limits for this device give some</p><p>problems about the Voltage values. Indeed each type of FC available today don’t able to produce an high</p><p>Voltage value on clamps, also for high Power like the PEM FC used in the Project (3 stk. from each 19,3 kW).</p><p>This means that the output Voltage of the PEM FC (65 V) must be increased through a DC/DC Boost</p><p>Converter, thus adapting the Voltage (380 V) and the Current required by the DC Bus to supply Inverter and</p><p>PMSM with nominal values.</p><p>On the DC-Bus the Voltage value must be maintained as constant as possible, to avoid dangerous swings</p><p>that could damage some devices in the HEV Drive. This task can be accomplished using a Capacitor (or a</p><p>bench of Capacitors) capable to keep the DC-Bus Voltage value near to the desired value.</p><p>In parallel on the DC-Bus is connected the DC/DC Buck-Boost Converter to allow the recharge of the Li-Poly</p><p>Battery from the PEM FC during the normal run of the Vehicle and from plug-in during the parking of it</p><p>(Buck Mode), but also to provide the necessary Power for the motion when the Vehicle climbs hills (Boost</p><p>Mode), because the PEM FC don’t able to give on the output big changes about the required current value.</p><p>The same type of Converter could be used for the Ultra-Capacitors bench, which will have the task to</p><p>provide high peak power values or to absorb high power values in a limited time range. To simplify the HEV</p><p>design it’s also possible to avoid the use of the DC/DC Buck-Boost Converter for the Ultra-Capacitors bench</p><p>if them will be capable to storage or provide the required peak power value in the worst case (maximum</p><p>HEV braking or maximum HEV acceleration) without any kind of control for the Voltage applied on it.</p><p>To control the PMSM operating conditions can be used an Inverter driven by a DSP, which according the</p><p>current</p><p>and the speed values read from the probes will apply the correct switching frequency for the</p><p>modulation signals on the gate for each switch. Besides the Control Unit must be able to comprehend when</p><p>the HEV Drive will invert the power flow due to other operating modes (Recharge from the Grid, HEV</p><p>Braking), so making pass the Inverter to work like a Rectifier.</p><p>From the following Figure 6.1÷6.7 is shown the Power Flow Management inside the HEV Drive for every</p><p>possible operating condition.</p><p>37</p><p>Figure 3.1 – Normal Run Power Flow for the HEV Drive</p><p>Figure 3.2 – Start-Up Power Flow for the HEV Drive</p><p>38</p><p>Figure 3.3 – Climb Hill Power Flow for the HEV Drive</p><p>Figure 3.4 – Normal Run/Strong Acceleration Power Flow for the HEV Drive</p><p>39</p><p>Figure 3.5 – Braking Recovery Power Flow for the HEV Drive</p><p>Figure 3.6 – Climb Hill/Strong Acceleration Power Flow for the HEV Drive</p><p>40</p><p>Figure 3.7 – Recharge from External Grid Power Flow for the HEV Drive</p><p>3.2 PEM Fuel Cell</p><p>The PEM FC (Polymer Electrolyte Membrane or Proton Exchange Membrane Fuel Cells) are devices that</p><p>allow to convert directly and with good efficiency the chemical energy of the fuel (H2) in electric energy</p><p>through oxidation, without passing through the conversion heat-work-electric energy, usually used in the</p><p>most common thermodynamics power cycles. If pure hydrogen is used as a fuel, fuel cells emit only heat</p><p>and water, eliminating concerns about air pollutants or greenhouse gases, like is possible to see in the</p><p>Figure 3.8.</p><p>Figure 3.8 – Basic Operation for PEM Fuel Cells [University of Salerno]</p><p>41</p><p>The Operating Principles of a PEM FC is based on the continue injection of H2 from the Anode electrode</p><p>(Positive electrode) and of O2 on the other Cathode electrode (Negative electrode), so the fuel and the</p><p>oxidizing agent are continuously and separately supplied to the two electrodes of the cell, where they</p><p>undergo a reaction. To make this, the PEM FC will need of a Electrolyte (Perfluorosulfonic Acid) in the</p><p>middle of the cell to conduct the ions H</p><p>+</p><p>from one electrode (Anode) to the other (Cathode).</p><p>During this procedure the electrons e</p><p>-</p><p>will be released from the fuel under catalyst, going to flow through</p><p>the external circuit from Anode to the Cathode due to the potential difference between the electrodes. In</p><p>this way the positive ions H</p><p>+</p><p>and Oxygen O2 will combine to have H2O on the exhaust. A brief graphical</p><p>explanation of a single PEM FC stack Operating is shown in the Figure 3.9.</p><p>Figure 3.9 – Graphical Operating of a single PEM FC Stack [Wikipedia 2010]</p><p>The chemical-electric energy transformation can be explained using thermodynamics parameters like</p><p>Enthalpy H, Entropy S and Temperature T, evaluating the Free Energy changes ΔG with the Gibbs Equation</p><p>(3.1 – 3.2), which established: “the Useful Work ΔLu that a system can make is due by decrease of his Free</p><p>Energy changes ΔG”:</p><p>−∆� = �� (3.1)</p><p>∆� = ∆� − 	∆</p><p>(3.2)</p><p>A kind of Useful Work is the Electric Work Le, which can be expressed with the (3.3):</p><p>�� = �� = −∆� = �</p><p>� (3.3)</p><p>42</p><p>Where:</p><p>n= number of electrons e</p><p>-</p><p>involved into the reaction</p><p>E= Cell Voltage [V]</p><p>F= Faraday constant [96,44*10</p><p>3</p><p>C/mol]</p><p>Consequently, the produced Heat Quantity Q will be:</p><p>� = 	∆</p><p>= ∆� − ∆� (3.4)</p><p>For a general chemical equation like aA+bB→cC+dD will be possible have the following equation:</p><p>∆� = ∆�� + �	��</p><p>��������</p><p>�������� (3.5)</p><p>Using the (3.3) equation and evaluating the (3.5) for an ideal gas will obtain the Nernst Equation:</p><p>� = �� + �	��</p><p>∏� !"#�$�%&'</p><p>()</p><p>∏� "*�+*,%&'</p><p>() (3.6)</p><p>Where:</p><p>E0= Cell Voltage [V] due to the Gibbs Free Energy ΔG0 in Standard Conditions (p=1atm, T=25°C)</p><p>pproducts = products partial Pressure [atm]</p><p>preagents = reagents partial Pressure [atm]</p><p>vi= Stoichiometric coefficient for the reaction</p><p>R= Gas constant [J/K*mol]</p><p>For an ideal PEM cell and in Standard Conditions will result E=E0=1,229 V. For a real PEM cell, considering a</p><p>normal utilization and each possible loss, will have a Cell Voltage E≈0,7 V and a Current value I=300 Ma. To</p><p>obtain significant Power values must be stacked more cells in series to make a single PEM FC Stack.</p><p>Real PEM FC reduces Cell Voltage value (calculable with Nernst Equation (3.6)) because there are negative</p><p>effects caused by Irreversibility inside the device. These Irreversibility are three:</p><p>� Ohmic Polarization ΔVohm: is due to the resistance phenomena for the passing of electrons e</p><p>-</p><p>on</p><p>the electrodes and of ions H</p><p>+</p><p>through the electrolyte. However for these reasons will have an</p><p>Internal Resistance that will provoke a voltage drop, creating a linear dependence with the Current</p><p>Density J (Ohm’s Law).</p><p>� Concentration Polarization ΔVconc: the waste of reagents and ions near the electrodes generates,</p><p>inside the cell, a little concentration cell that causes an opposite Voltage compared with the Cell</p><p>Voltage direction. This kind of problem is caused by the limitation about speed mass transit, which</p><p>determines a slow diffusion for the gas on the electrodes and for the ions inside the electrolyte.</p><p>The effect due to the Concentration Polarization will increase in an exponential way the</p><p>dependence from the Current Density (Fick’s Law).</p><p>43</p><p>� Activated Polarization ΔVact: is due to the energy required to break the molecular bonds of the</p><p>reagents and between reagent atoms and catalyst atoms. This kind of phenomena create a</p><p>logarithmic dependence with the Current Density, that will increase the ΔVact and so decrease the</p><p>Cell Voltage E (Tafel’s Law).</p><p>These Irreversibility make decrease the ideal Cell Voltage E, defining a new real Cell Voltage value VC like:</p><p>-� = � − ∆-./0 − ∆-1.21 − ∆-314 (3.7)</p><p>With this analysis is possible to understand which is the real behavior of these devices, namely the PEM FC</p><p>Voltage changes linearly with the Current Density if considering only the Ohmic Polarization, with a</p><p>logarithmic trend if considering in addition the Activated Polarization and with an exponential way if</p><p>considering still in addiction the Concentration Polarization. In the Figure 3.10 is shown a PEM FC</p><p>Characteristic regarding Cell Voltage-Current Density, in different conditions from that Standard.</p><p>Figure 3.10 – Voltage-Current Density PEM FC Characteristics (no Standard Conditions)</p><p>[University of Cassino]</p><p>The Concentration Polarization can be neglected if the PEM FC doesn’t work near the Current Density limit</p><p>value and for this reasons often the Manufactures produce fuel cells to operate far from such limit. The</p><p>Activated Polarization is more important for low values of Current Density, but then loses progressively</p><p>importance because becomes not so big compared with the Ohmic Polarization. Besides the Activated</p><p>Polarization is strongly bound with the Temperature</p><p>e becomes negligibly for high values of it.</p><p>For these reasons is possible to use an analytic and simplification expression to calculate the real Cell</p><p>Voltage for a PEM FC:</p><p>-� = 5 − 67 − 8��(7) (3.8)</p><p>Where a, b and c are coefficient provided by the Manufactures and J is the Current Density for the cell.</p><p>44</p><p>The Voltage Efficiency ηV can be expressed like the ratio between the real Cell Voltage VC and the ideal Cell</p><p>Voltage E:</p><p>;- =</p><p>-<</p><p>�</p><p>(3.9)</p><p>The Voltage Efficiency can be increased modifying parameters for the fuel cells like Temperature and</p><p>Pressure.</p><p>The open circuit Voltage value will be larger for the fuel cells with low operating Temperature, like the PEM</p><p>FC used (operates with 60÷100 °C), but also the Polarization effects will improve. Indeed, the Ohmic</p><p>Polarization is increased cause the favorable Temperature effect about the electrolyte ionic resistance,</p><p>adding to the Activated Polarization. In the Figure 3.11 is possible to observe the dependence of the PEM</p><p>FC from the Temperature and how conditions the Cell Voltage behavior.</p><p>The Pressure influence on the PEM FC is important, because raising the operating Pressure will have</p><p>advantages and improvements about the Cell Voltage and the Polarization effects. Indeed increasing the</p><p>Pressure will also increase the Cell Voltage, but this improvement have a rapid damping if passed a critical</p><p>Pressure, like is understandable by Figure 3.12. The same thing happens if evaluates the Power Density</p><p>changes compared with the Pressure variation (Figure 3.13).</p><p>Figure 3.11 – Cell Voltage-Temperature for each type of FC [University of Cassino]</p><p>45</p><p>Figure 3.12 – Voltage Efficiency improvement related with operating Pressure [University of</p><p>Cassino]</p><p>Figure 3.13 – Power Density trend related with operating Pressure [University of Cassino]</p><p>The advantages that make good the PEM FC choice for HEV Drive (or in general for automotive</p><p>applications) are represented by:</p><p>• Low Operation Temperature (60÷100 °C)</p><p>• “Fast” Start-Up Time (1÷5 minutes)</p><p>• Highest Power Density (0,5÷1,2 kW/kg)</p><p>• Solid Electrolyte Reliability (no changes, no moves, no vaporizations, delimited corrosions)</p><p>An important critical issue for the PEM FC is the Water Management. In order to operate properly, the</p><p>polymer membrane needs to be kept humid, because the ions require humidity to move. So if the</p><p>membrane is too dry, there will not be enough acid ions to carry protons, but if the membrane is too wet</p><p>46</p><p>(Flooded Phenomena), the pores of the diffusion layer will be blocked and reactant gases will not able to</p><p>reach the catalyst.</p><p>These devices have a lot of others fabrication disadvantages like expensive membrane, expensive noble</p><p>metal for the electrodes and easily poisoned catalyst and membrane. However these problems don’t are to</p><p>analyze in this work.</p><p>To allow an optimal operation for the PEM FC inside the HEV Drive should be always known the Working</p><p>Point on Voltage-Current Characteristic, but such Working Point is imposed from the natural operative</p><p>modes due to the External Load. To control the PEM FC supply and comprehend where will work on the</p><p>Voltage-Current Characteristic (if near the max efficiency point or near the max power point) exist 3</p><p>different methods:</p><p>1. Power Control</p><p>2. Voltage Control</p><p>3. Current Control</p><p>Power Control</p><p>For each Power value there are two possible Working Point whose one, that with a less Current value, will</p><p>have a better value of Efficiency. Unfortunately, the other Operation Point that ensure the greater Power</p><p>output is unstable, because for high Current values will be strong the diffusion losses due to the</p><p>Concentration Polarizations, so not allowing to use the Maximum Power Point Tracker (MPPT) control to</p><p>follow and to work ever near the maximum Power point.</p><p>So this type of control for the PEM FC doesn’t maintain on a constant value the output Voltage on the fuel</p><p>cell clamps (or the output Current), but needs of a DC/DC Boost Converter to step-up the Voltage on the DC</p><p>Bus and to stabilize Voltage and Current for every External Load variation (Figure3.14). Indeed, when there</p><p>is a Pload variation, the PEM FC will provide VFC and IFC on output, but then will be the Boost Converter to</p><p>maintain into the tolerance values the Voltage DC Bus, how is observable in Figure 3.15, where for Load is</p><p>intended all the HEV Drive downstream the device.</p><p>47</p><p>Figure 3.14 – Power Control Operation Points for a PEM FC</p><p>Figure 3.15 – Power Control Scheme for a PEM FC</p><p>Voltage Control</p><p>Using this type of control the PEM FC will work with a fixed Voltage output value, acting like a Current</p><p>Generator. This operating mode can be obtained linking in parallel on the PEM FC output a Storage Device</p><p>(Auxiliary Voltage Source), interposing between them a DC/DC Converter to adapt the Voltage (Figure</p><p>3.16).</p><p>Figure 3.16 – Voltage Control Scheme for a PEM FC</p><p>The main task of the Battery used like a Storage Device will be supply with a Current value the DC Bus to</p><p>ensure the Nominal Voltage on it. For every type of External Load variation, the system placed in parallel to</p><p>48</p><p>the PEM FC will be able to maintain the DC Bus Voltage near the right value, without significant changes for</p><p>the PEM FC operating conditions (Figure3.17 and 3.18).</p><p>Figure 3.17 – Voltage Control Operating Point for a PEM FC</p><p>Figure 3.18 – Parameters Trend in the Voltage Control for a PEM FC</p><p>Current Control</p><p>This control technique for a PEM FC is based on the same principle of the Voltage Control, with the</p><p>difference regarding the way which the desired values on the DC Bus are reached. Indeed using an Auxiliary</p><p>Current Source (DC/DC Converter plus a Storage Device like Battery Pack) and an Inductance, all connected</p><p>in parallel with the DC Bus (Figure 3.19), will be possible to impose the Current Working Point for the FC.</p><p>This technique must be used with attention, because can be dangerous for the PEM FC if for any reason</p><p>occurs a Flooded Phenomena (meanly on the Anode electrode). Indeed in this case will continue the</p><p>Current request with possible irreversible damage for the entire Fuel Cell.</p><p>49</p><p>Figure 3.19 – Current Control Scheme for a PEM FC</p><p>3.3 Electric Schematic and Architecture for HEV</p><p>According with the scheme in the Figure 1.6, can be designed the basic electric circuit regarding all the HEV</p><p>Drive, like shown in the Figure 3.20.</p><p>The PEM FC can be schematized like real voltage generator with internal resistances due respectively to the</p><p>Ohmic, Activation and Concentrated polarization effects and will supply the DC/DC Boost Converter with a</p><p>voltage value equal to 65 V. This voltage value will be pull-up till 540 V from the Chopper step-up, obviously</p><p>reducing the current value on the DC Bus. The switching frequency for the power switch Tu of this</p><p>converter will be driven by a DSP Controller, which will provide the correct PWM signal. As the power of</p><p>the DC/DC Boost Converter is very high (60 kW about), will be a good choice to not drive the IGBT with a</p><p>switching frequency (for minimize the power losses during the commutation).</p><p>On the DC Bus is linked the DC/DC Buck-Boost Converter necessary to use the Battery Pack like secondary</p><p>energy sources. Indeed as the Battery pack must be recharged with a controlled cycle (to impose the</p><p>voltage and current characteristic provided by the manufacturer), it’s impossible to link directly this</p>