A quasi-optimal energy resources management technique for low voltage microgrids

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Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
A quasi-optimal energy resources management technique for low voltage
microgrids
M. Crosa di Vergagnia, S. Massuccoa, M. Saviozzia,⁎, F. Silvestroa, F. Monachesib, E. Ragainib
a Department of Electrical, Electronics and Telecommunication Engineering and Naval Architecture, Università degli Studi di Genova, Italy
bABB SACE, Bergamo, Italy
A R T I C L E I N F O
Keywords:
Energy resources management
Distributed energy resources
Microgrid
Microgrid optimization
Demand response
Flexibility provision
Frequency control
A B S T R A C T
The increasing penetration of Distributed Energy Resources (DERs) in modern power systems is introducing new
challenges for system stability and control. The stochasticity of Renewable Energy Sources (RESs) and the un-
predictable behaviour of demand, make it necessary to develop intelligent Energy Resources Management (ERM)
methodology, able to actively regulate the actors of the electrical network. This paper proposes a new quasi-
optimal control algorithm, designed for LV breaker devices, aiming to manage DERs in a distributed and scalable
approach. The developed ERM technique is able: (1) to control the energy consumption at the Point of Common
Coupling (PCC) (with the possibility to join Active Demand Response (ADR) programs or to provide flexibility/
energy reserve), when the microgrid itself is connected to the main grid; (2) to control the frequency profile
when the microgrid is operating in islanded mode, using information provided by real time measures.
1. Introduction
1.1. Motivation
Nowadays the growing penetration of Renewable Energy Sources
(RESs), necessary to decrease generation costs and to foster a sustain-
able and low-emissions development, represents at the same time a
threat to power system reliability and stability. In addition, the spread
of active customers with Demand Side Management (DMS) installa-
tions, which can participate to Active Demand Response (ADR) pro-
grams [1–4], together with new flexibility markets [5,6], has increased
the operation complexity of power systems [78].
In this context, microgrids can represent a smart and efficient so-
lution accessing and controlling Distributed Energy Resources (DERs)
within their electrical area, providing also grid services (e.g. flexibility/
energy reserve, ADR, etc.) for the wider network [8]. Microgrids can
operate in both grid connected and stand-alone modalities, and they are
able to provide technical and economic benefits in cases wherein loads
and RESs uncertainties are managed with specific methodologies [9].
For these reasons, Energy Resource Management (ERM) techniques are
strongly recommended in order to increase the microgrid stability, re-
liability and performances [10].
1.2. Literature review
ERM is a very interesting topic that has been analysed with great
attention by the scientific community, which, in recent years, has
presented a great number of techniques for microgrid management
[8,11–13].
In [14] an ERM method has been proposed for an ADR application
in smart buildings considering controllable and non-controllable loads.
Authors in [15] propose an ERM methodology for the management
of multiple types of batteries in order to reduce diesel usage in micro-
grid with RESs.
ERM procedures for microgrids based on fuzzy logic are described in
[16,17], respectively for reducing power fluctuations and for the
minimization of operational costs.
Multi-agent based strategies are proposed in [18–21]. In particular,
[18,19] are designed for the minimization of microgrid operation cost,
[20] considers also power quality targets, while [21] takes into account
grid connected and islanded operation modes for economic dispatch
and frequency control.
Two stage ERM approaches for a generic microgrid, composed of a
day-ahead scheduler and a real time control are proposed in [22–24]. In
[25] a bi-level optimization is used to minimize the cost for residential
users and to provide services for the distribution grid.
ERM algorithms for the frequency control of isolated microgrids are
https://doi.org/10.1016/j.ijepes.2020.106080
Received 17 October 2019; Received in revised form 28 February 2020; Accepted 5 April 2020
⁎ Corresponding author.
E-mail address: matteo.saviozzi@unige.it (M. Saviozzi).
Electrical Power and Energy Systems 121 (2020) 106080
0142-0615/ © 2020 Elsevier Ltd. All rights reserved.
T
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analyzed in [26,27].
In [28] an ERM technique based on robust optimization is proposed
for the control of grid connected/isolated microgrids. These two op-
eration modalities are considered also by the authors in [29], where an
ERM methodology that couples distributed optimization with a Model
Predictive Control (MPC) is presented.
Finally, authors in [30–33] present a hierarchical approach for the
ERM of systems constituted of multiple microgrids.
Table 1 summarizes the main features on the ERM strategies dis-
cussed in this section.
1.3. Contributions and aims
Although the ERM techniques for microgrid management and con-
trol have been developed with very satisfying results (see literature
review in Section 1.2), it is possible to find some aspects that can be
improved:
• design of an ERM solution providing a suitable and available tech-
nological architecture for a real field implementation;
• management of both grid connected and islanded modalities of
operation. Notice that only three works described in the literature
review [21,28,30] consider the two aforementioned modes. In ad-
dition, it can be helpful to manage the transition from grid con-
nected scenario to the island operation;
• definition of an ERM procedure that is able to manage multiple
applications (ADR, flexibility provision, energy control, operational
cost minimization, etc.).
This work tries to address these aspects, describing an ERM that is
able to control dispatchable DERs (generators, storage systems and
loads), considering non-controllable loads and RES production, in a
microgrid scenario.
The proposed algorithm has been designed and implemented on
board of a commercial LV breaker [34] and therefore it is, at present,
suitable to a real field application. The algorithm is based on a novel
quasi-optimal formulation that does not require a high computational
effort limiting the hardware and software request for real field appli-
cations. This represents one of the main strong points of the proposed
methodology.
The ERM technique is capable of optimizing the energy flow of the
microgrid at the Point of Common Coupling (PCC) (where the afore-
mentioned breaker [34] is located) controlling dispatchable DERs and
exploiting information provided by real time measures (active power
consumption/production, breakers status, etc.) when the microgrid is
connected to the main grid, and it is able to regulate the frequency
when the microgrid operates in islanded mode. In addition, it is possible
to manage the transition among the grid connected operation and the
intentional islanding.
The proposed procedure can be exploited within different applica-
tions including ADR and/or flexibility provision. Moreover, the pro-
posed procedure can be employed also for the control of multiple mi-
crogrids according to the scalable implementation proposed in [22].
The proposed control algorithm has been patented [35] and has
clearly outperformed the ones described in [22,36,37] which have been
beforehand implemented on [34].
In summary, to the best of authors knowledge, this paper provides
the following contributions:
• a new mathematical formulationfor the microgrid optimization.
The proposed algorithm is inspired to the economical dispatch of
thermal units [38], wherein the optimized variables are the set-
point variations and the optimization is performed in real time;
• the modelling and the representation of the available contributions,
in terms of active power variations, related to the controllable mi-
crogrid devices;
• the extension of the Lambda Iteration Method [38] in order to in-
clude in its formulation controllable loads and storage systems, to-
gether with its application to the proposed problem.
All the above mentioned points have contributed to define and
implement a quasi-optimal ERM procedure characterized by a fast re-
sponse time.
The rest of the paper is organized as follows: Section 2 outlines the
adopted control strategy and the implemented algorithm, Section 3
describes the considered scenarios where the algorithm has been tested,
Section 4 gives an overview of the results and it is followed by the
concluding remarks exposed in Section 5.
2. Adaptive algorithm structure
The ERM program enables aggregators and end users to change
their energy consumption. In particular, medium size customers, or
aggregation of customers, which present interruptible processes and
controllable resources can successfully adopt ERM techniques for peak-
shaving, energy consumption control, participate to ADR programs,
provide flexibility/energy reserve or in order to offer other network
services helping the main grid to deal with uncertainties due to re-
newables and loads.
The implemented adaptive algorithm can be used to reach two main
objectives:
1. to maintain the energy consumption of the microgrid, while con-
nected to the main grid, below a target value (E t( )target ) (notice that
t( ) indicates the time dependency) at the end of a time window of
length T. The goal could be:
• to respect a contract threshold agreed with the local distribution
company or to respect an energy plan (day-ahead market parti-
cipation);
• to participate to ADR programs;
• to provide flexibility/energy reserve.
Thus, Etarget can vary in time according to signals given by the
customer or received within a demand response strategy/flex-
ibility request.
Moreover, if the goal is to have the microgrid operating autono-
mously, exchanging with the main grid a mean power equal to
zero over the predefined control interval T, the target value can be
set equal to zero. In this way, the microgrid would be ready to
disconnect from the main grid and start operating in islanded
mode;
2. to keep the frequency of the microgrid, while operating in islanded
mode, as close as possible to its nominal value ( fnom), over a pre-
defined control interval T. In this case the controlled variable is
represented by the estimation of the mean frequency error
( f t( )forecast ), which is calculated according to the measured fre-
quency of the microgrid [39]. This second objective can be con-
sidered a kind of secondary control on frequency, while the primary
control is performed by the local droop of the available generators.
All the possible use cases of the proposed ERM strategy are sum-
marized in Fig. 1. As can be seen from this figure in the grid connected
scenarios the exploitation of the ERM procedure can lead to important
economical benefits (respect of an energy contract avoiding penalties,
reward for ADR participation/flexibility provision).
Fig. 2 shows the logic of the ERM algorithm, for the Energy Con-
sumption Control case. The control is based on the estimated energy
consumption (E t( )forecast , black line in Fig. 2), that represents, at each
point, the expected consumption of the whole system at the end of the
control time window ( =t T ).
The main principle of the control algorithm is to keep the E t( )forecast
curve inside two boundaries, (UpperBound and LowerBound, respec-
tively depicted in red and blue in Fig. 2), which are two straight lines
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
2
Ta
bl
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1
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co
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th
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[2
3]
tw
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la
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da
y
ah
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an
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re
al
tim
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sc
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du
lin
g
sc
en
ar
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s
de
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lo
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fr
am
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or
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fo
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de
m
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sp
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se
[2
4]
tw
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la
pp
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da
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ah
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du
lin
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an
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to
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[2
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bi
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op
tim
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la
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no
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se
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m
an
ag
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m
od
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in
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of
fr
eq
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nc
y
se
cu
ri
ty
re
qu
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em
en
ts
[2
7]
hi
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ar
ch
ic
al
ap
pr
oa
ch
w
ith
m
ix
ed
in
te
ge
r
lin
ea
r
pr
og
ra
m
m
in
g
fr
eq
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nc
y
co
nt
ro
lo
fi
so
la
te
d
m
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gr
id
s
ge
ne
ra
to
rs
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oa
ds
m
od
el
in
g
of
th
e
st
ea
dy
st
at
e
hi
er
ar
ch
ic
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fr
eq
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nc
y
co
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ro
lf
un
ct
io
ns
of
a
dr
oo
p
co
nt
ro
lle
d
m
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gr
id
[2
8]
ro
bu
st
co
nv
ex
pr
og
ra
m
m
in
g
gr
id
on
:c
os
ts
m
in
im
iz
at
io
n
(i
m
po
rt
/e
xp
or
t)
;i
so
la
te
d
m
od
e:
m
in
im
iz
at
io
n
of
th
e
un
su
pp
lie
d
de
m
an
d
ge
ne
ra
to
rs
,s
to
ra
ge
sy
st
em
s,
lo
ad
s
ex
is
te
nc
e
of
so
lu
tio
n,
A
C
po
w
er
flo
w
gr
id
co
nn
ec
te
d/
is
ol
at
ed
op
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at
io
n
m
od
es
[2
9]
di
st
ri
bu
te
d
op
tim
iz
atio
n
an
d
M
PC
m
in
im
iz
at
io
n
of
m
ic
ro
gr
id
op
er
at
io
na
lc
os
t,
re
sp
on
d
to
ex
te
rn
al
pr
ic
e
si
gn
al
an
d
co
nt
in
ge
nc
y
ev
en
t
st
or
ag
e
sy
st
em
s,
lo
ad
s
M
PC
co
up
le
d
w
ith
di
st
ri
bu
tio
n
op
tim
iz
at
io
n
al
go
ri
th
m
[3
0]
hi
er
ar
ch
ic
al
op
tim
iz
at
io
n
fo
r
m
ic
ro
gr
id
co
m
m
un
ity
m
in
im
iz
at
io
n
of
m
ic
ro
gr
id
op
er
at
io
na
lc
os
t
ge
ne
ra
to
rs
,s
to
ra
ge
sy
st
em
s
no
ve
le
ne
rg
y
m
an
ag
em
en
t
sy
st
em
fo
r
m
ic
ro
gr
id
co
m
m
un
ity
[3
1]
pr
io
ri
ty
ba
se
d
en
er
gy
sc
he
du
lin
g
fo
r
m
ul
tip
le
m
ic
ro
gr
id
s
en
er
gy
sc
he
du
lin
g
gl
ob
al
m
ic
ro
gr
id
en
er
gy
no
n
pr
ic
in
g
ba
se
d
ap
pr
oa
ch
fo
r
en
er
gy
sc
he
du
lin
g
[3
2]
hi
er
ar
ch
ic
al
ER
M
fo
r
in
te
rc
on
ne
ct
ed
us
in
g
ch
an
ce
co
ns
tr
ai
ne
d
M
PC
op
er
at
io
n
m
an
ag
em
en
t
of
in
te
rc
on
ne
ct
ed
m
ic
ro
gr
id
s
ge
ne
ra
to
rs
,s
to
ra
ge
sy
st
em
s
hi
er
ar
ch
ic
al
st
oc
ha
st
ic
ER
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M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
3
that intersect the target value, E t( )target , at the end of the control period.
This is performed in order to maintain the energy consumption of the
microgrid (E t( )meas , green line in Fig. 2) below or close (depending on
its objective as previously explained) to E t( )target at =t T .
In the case depicted in Fig.1, the adaptive algorithm starts operating
after an inhibition time ti. If E t( )forecast happens to be out of the upper or
lower limit at a certain time t , the ERM procedure calculates the power
variation P t( )req to be requested to the microgrid in order to achieve
the desired energy consumption at the end of the control period.
P t( )req is calculated once every tc, i.e. the interval of time which
defines the frequency of operation of the algorithm. P t( )req is de-
termined considering E t( ), i.e. the difference between E t( )forecast and
Etarget (see Fig. 2), and the control window length T. P t( )req is obtained
by acting on the available generators and controllable loads. According
to the resulting P t( )req , the system priority level ( t( )) is then cal-
culated and the contribution requested to each controllable device
( P t( )i ) is consequently defined. The distribution of the total requested
power variation P t( )req among the controllable loads and generators is
calculated according to pre-set priority levels ri, which are defined for
each controllable device and indicate the order whereby devices are
called by the algorithm to contribute to the energy regulation.
The logic of the algorithm for the Frequency Control case is basi-
cally similar, with the difference that the main purpose of the algorithm
is to keep the f t( )forecast curve inside the previously defined upper and
lower Bounds, in order to maintain the microgrid measured frequency
Fig. 1. Use cases for the proposed ERM procedure.
Fig. 2. ERM algorithm operation.
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
4
( f t( )meas ) as close as possible to its nominal value at =t T , providing a
sort of secondary control. The idea to have an average frequency is
inline with the microgrid concept that has lower power quality re-
quirements (i.e. shipboard power systems and isolated microgrids
[37]). Remember that in the considered approach the primary fre-
quency control is performed by the local droop of each generator.
Let G the set of the controllable generators, D the set of drivers
(i.e. controllable loads that can be continuously regulated), L the set of
the on/off loads ad S the set of storage systems. The following power
limits are defined:
• P i( )i max G D L S, represents the maximum active
power available of the ith device (i.e. the mean active power ab-
sorbed for loads and the technical limits for generators/storage
systems);
• P i( )i min G D L S, defines the minimum active power
available of the ith device (i.e. zero for loads and the technical limits
for generators/storage systems).
The controllable generators/storage systems are characterized by an
initial active power set-point P t i( ) ( )i set G S, , which represents
the optimum power to be dispatched at the beginning of each control
window (e.g. interval T[0, ] in Fig. 2). These values are considered as
scheduled by an external optimization process [22,40]. Thus, the pro-
posed ERM algorithm operates as a microgrid real time controller.
Finally, let ti dis, and ti rec, be respectively the last disconnection and
reconnection time of the ith load within the control interval T[0, ], the
controllable On/Off loads connected to the microgrid are characterized
by:
• t i( )i max off L, , representing the maximum disconnection time. If
the ith load gets disconnected at =t ti dis, , it has to be reconnected
before the maximum disconnection time. If this does not happen, the
load is automatically reconnected at = +t t ti dis i max off, , , ;
• t i( )i min off L, , defining the minimum disconnection time. When
the ith load gets disconnected at =t ti dis, , it cannot be reconnected
before = +t t ti dis i min off, , , ;
• t i( )i min on L, , representing the minimum reconnection time. Once
a load is reconnected at =t ti rec, , it cannot be disconnected again
before = +t t ti rec i min on, , , .
Notice that if an On/Off load has never been disconnected/re-
connected ti dis, and ti rec, are respectively defined as =t ti dis i min off, , , and
=t ti rec i min on, , , .
The operational steps of the proposed ERM algorithm are shown in
Fig. 3, while the time parameters that can be defined by the operator
are:
• T: time window of the controller;
• t : acquisition time width;
• tc: interval of time between two operations of the proposed ERM
algorithm;
• ti: inhibition time at the beginning of the control window;
• tm: time width for the evaluation of the mean values.
With this notation t during the control interval starts from 1 and
reaches T with a granularity equal to t . The fundamental blocks of the
proposed ERM procedure are described in the following subsections.
2.1. Acquisition and average
The controllable loads status and power demand are taken from the
field and stored once every t . For any load that cannot be monitored,
the algorithm takes pseudo measurements into account (e.g. load size
multiplied by a utilization factor). The Acquisition and Average task
itself is performed once every t .
2.1.1. Energy consumption control
When the microgrid is connected to the main grid, the actual power
consumption at the PCC is directly measured every t . The average
power consumption of each load (P t( )i meas, ) is determined according to
the acquired measurements (P t( )i ) and each mean power demand is
calculated over a time interval tm. If a load has been turned off, the
acquired measurements (equal to 0) taken during the switch off period
are not considered in the average value calculation.
The mean power consumption at the PCC is calculated over the
same time interval tm, according to the actual power consumption
measured at the PCC. This value is then used to determine the energy
consumption of the microgrid over time (E t( )meas ). The Average task is
performed every ( t).
2.1.2. Frequency control
When the microgrid operates in islanded mode, the frequency
measurements ( f t( )meas ) are taken from the field and stored once every
Fig. 3. Block diagram of the proposed ERM algorithm architecture.
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
5
t . Loads average power consumption is calculated the same way as for
the Energy Consumption Control.
Field frequency measurements are used to calculate the frequency
signal f t()mean , which will determine the power variation P t( )req that
will be requested to generators and available loads [39].
The frequency signal is calculated as:
= = +f t
f z f
t num T
( )
( )
·mean
z num T
t
meas nom
T
1 ·T
(1)
where:
• f t( )meas is the microgrid frequency measurement;
• fnom is the nominal frequency;• T is the lenght of the control period, as previously defined;
• numT is the number of control intervals already passed.
2.2. Forecast
The forecast function estimates the expected global consumption at
the end of the time period ( =t T ) for the Energy Consumption Control,
while for the Frequency Control it provides the expected frequency
error at =t T . The two different implementations are described below.
2.2.1. Energy consumption control
The estimated global energy consumption curve E t( )forecast is calcu-
lated with a granularity defined by t as:
= + =E t E t E t
t
T t E t T
t
( ) ( ) ( ) · ( )·forecast meas meas meas
(2)
Notice that the forecast is based on the assumption that the active
power flow through the PCC remains constant for the rest of the period
(from t to T).
2.2.2. Frequency control
The estimated frequency signal curve is calculated once every t ,
with the same logic as the estimated energy consumption, as described
by the following equation:
= + =f t f t
f t
t
T t
f t T
t
( ) ( )
( )
·
( )·
forecast mean
mean mean
(3)
2.3. Displacement estimation
The Displacement Estimation function establishes, for both the
control modalities, if the proposed algorithm has to operate. Notice that
this functionality works only if t is greater than the inhibition time ti
(see Fig. 3). Once again, the Displacement Estimation block has two
different implementations, one for the Energy Consumption and one for
the Frequency Control, as presented below.
2.3.1. Energy consumption control
The Displacement Estimation function for the Energy Consumption
Control mode compares the estimated energy consumption value with
the upper and lower bounds: two lines that define the tolerance band
and intersect Etarget at the end of the control period T[0, ]. The com-
parison is performed once every tc. The first action of the controller is
taken as soon as the E t( )forecast at time t (with =t k t· c) exceeds one
of the two bounds. From the second action on, if Eforecast t( ) exceeds the
upper or lower bound, a convergence test is performed. Let analyze the
case wherein the upper bound is exceeded, as reported in Fig. 4. In this
case the slope =mAT
E E t
T t
( )target forecast 1
1
is compared with
=m E t E tt t
( ) ( )forecast forecast2 1
2 1
.
In the convergence test two different cases can occur:
1. the energy forecast curve (orange line in Fig. 4) is converging fast
enough to respect the energy target by the end of the control period,
since <m mAT1 ;
2. the energy forecast curve (red line in Fig. 4) is not converging fast
enough, being >m mAT2 .
Notice that the case related to a lower bound violation is completely
symmetric.
If E t( )forecast is both out of the boundaries and is not converging
(case 2), then an action is required. The total power variation P t( )req
to be requested to the microgrid is then calculated, according to the
following equation:
=P t
E t E T
t T
( )
( ) ( )
req
forecast target
(4)
It is possible to observe that if E t( )forecast is above the energy target then
Preq is positive, and therefore the microgrid has to decrease the load
and/or the controllable generation. If Preq is negative the microgrid has
to decrease the generation and/or increase the load.
Notice that the algorithm does not act every time that the forecast
exceeds the bounds. For this reason, the proposed ERM technique can
be called adaptive. The same stands for the Frequency Control.
2.3.2. Frequency control
The Displacement Estimation function for the Frequency Control
case compares the estimated f t( )forecast with the upper and lower
bounds, that intersect the x-axis at the end of the control period T. The
granularity of the comparison is defined by tc. If at a certain time
=t t f t, ( )forecast gets out of the boundaries, the algorithm calculates
the amount of power variation to be requested according to the fol-
lowing equation [41]:
=P t E f t( ) · ( )req p forecast (5)
with = =Ep i
S P
f b1 ·
eff i
nom p i
,
,
, where S is the total number of synchronous
generators connected to the grid, Peff i, is the maximum active power that
can be continuously delivered by the ith generator, and bp i, is the statism
degree of the ith generator. The sign of P t( )req has the same inter-
pretation of the case related to the Energy Consumption Control.
2.4. Curves calculation
The total power variation is distributed among the controllable
devices according to their priority values ri, which defines the order
whereby devices are called by the algorithm to contribute to energy
regulation. This implies that the proposed control algorithm is based on
hierarchical strategy.
The available contribution of each device at time =t t can be re-
presented in the r P plane with a line, where r stands for priority.
The single contribution varies depending on the sign of P t( )req , the
actual power demand/generation, the priority ri and the number of
steps si, which defines the slope of the curves. The curves calculation
logic, i.e. the contribution evaluation P t( )i , of each controllable de-
vice will be described in the following.
2.4.1. Generators (i G)
Controllable generators are assumed to be scheduled by an external
optimization process as a day-ahead scheduler based on economic
dispatch [40]. Thus, each generator has a set-point of active power
(P ( )i set, , where = = …k T k P· , 1, , and P is the number of control
periods) defined at the beginning of each period (with a granularity set
by T).
During the algorithm operation, within the period, the generators
set-points can be changed between the technical limits Pi min, and Pi max, .
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
6
If no actions are required the generators set points are fixed to P ( )i set,
for the whole control period.
At time t , a generator with priority ri, which is generating P t( )i , can
be represented as shown in Fig. 5, where the green line represents the
feasibility range of P t( )i (in the plane r P) and:
=
>
<
P t
P P t if P t
P P t if P t
( )
( ) ( ) 0
( ) ( ) 0i max
i max i req
i min i req
,
,
, (6)
Observe that si in Fig. 5 indicates the number of steps on which the ith
generator shares its regulating power. In particular, si determines the
slope of the curve. Notice that the quantity +r si i defines the maximum
priority level at which the ith generator performs a regulation.
The blue line in the left plot of Fig. 5 (case >P t( ) 0req ) indicates
that as long as the priority level of the system ( t( )) is below the
priority value of the device (ri), no contribution is requested. When
t( ) is above the maximum priority of the device ( +r si i) the generator
changes its set-point to P t( )i max, reaching its technical limit. The case
<P t( ) 0req operates symmetrically.
Finally, in both cases, if t( ) is included between +r r s[ , ]i i i , the ith
generator modifies its set-point of P t( )i according to the curve de-
picted in Fig. 5.
2.4.2. Drivers (i D)
A driver is a controllable load that can be continuously regulated
between 0 and 100% of its power demand by applying an external signal
generated by the control algorithm. Drivers can increase/decrease their
power demand as generators with their output power. The most
significant difference is that P t( )i max, changes in the time according to
the amount of power absorbed by the load, which cannot be prior de-
fined. Notice that the response time of each driver to an action of the
proposed control algorithm depends on the load type (e.g.: thermal,
pumps, etc.).
Therefore, in this case, referring to Fig.4, the green line represents
the feasibility range of P t( )i, and P t( )i max, is defined by the mean load
power consumption (P t( )i meas, , evaluated by the Average function) of
the device in the last tm minutes. In particular:
=
>
<
P t
P t if P t
P t P t if P t
( )
( ) ( ) 0
( ) ( ) ( ) 0i max
i meas req
i i meas req
,
,
, (7)
2.4.3. On/Off Loads (i L)
An On/Off load is a controllable load which can be only dis-
connected or reconnected (through a binary variable), implying that its
power demand can be set either equal to 0 or to P t( )i max, . Also in this
case, P t( )i max, changes in the time and is evaluated as the mean active
power absorbed P t( )i meas, in the last tm minutes. In order to be able to
include the On/Off loads into a convex optimization problem, that
characterizes the proposed ERM algorithm, their corresponding curves
in the plane r P have been represented again as reported in Fig. 5.
Differently from other devices, P t( )i is able to assume only two values:
0 and P t( )i max, , represented by the two green points in Fig. 5. In
particular:
=
> +
< + +P t
P t if P t t r t t t
P t if P t t r s t t t
otherwise
( )
( ) ( ) 0, ( ) ,
( ) ( ) 0, ( ) ,
0
i
i max req i i rec i min on
i max req i i i dis i min off
, , , ,
, , , ,
(8)
Eq. (8) introduces a simplification on the modelling of the On/Off loads,
since their final contributions are obtained approximating the con-
tinuous line of Fig. 5 with only two points. This simplification designed
for the On/Off loads will lead to a quasi-optimal formulation for the
ERM algorithm.
2.4.4. Storage systems (i S)
Storage systems can be described similarly to generators and dri-
vers. Also these systems are assumed to be scheduled by an external
optimization process. Thus, each storage system has a set-point of ac-
tive power (P ( )i set, , where = = …k T k P· , 1, , and P is the number of
Fig. 4. Convergence test of the Displacement Estimation function - Upper bound violation.
Fig. 5. Available power and Pi identification (plane r P).
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
7
control periods) defined at the beginning of each period.
During the algorithm operation, within the period, the storage
systems set-points can be changed between their technical limits de-
fined by the maximum discharge power Pi st dch, , , the maximum charge
power Pi st ch, , and the battery nominal energy Ei nom, . If no actions are
required the storage set-points remain equal to P ( )i set, for the whole
period.
At time t , a storage system that is generating P t( )i , can be re-
presented as shown in Fig. 5. These systems adopt the generators
convention:
=P t P t P t( ) ( ) ( )i max i max i, , (9)
P t( )i max, for storage systems is evaluated according to the sign of
P t( )req :
=
>
<
P t
P if P t
P if P t
( )
min , ( ) 0
min , ( ) 0
i max
E t
T t i st dch req
E E t
T t i st ch req
,
( )
( ) , ,
( )
( ) , ,
i
i nom i,
(10)
where E t( )i is the actual energy of the storage system at time t . This
formalization can be performed if an estimation of E t( )i is available,
otherwise the storage system can be modeled as a generator.
2.5. Priority identification
The priority identification module identifies the priority level of the
system ( t( )). Observe that also in this section t identifies a multiple
of tc and consequently an instant wherein the algorithm is enabled to
operate.
The procedure is based on the definition of an optimization pro-
blem. The optimal priority identification procedure provides to each
dispatchable devices of the microgrid the active power variation
= …P t P t P t( ) ( ( ), , ( ))N1 , where N is the number of the con-
trollable devices. Thus, = …P t i N( ) ( 1, , )i represent the variables of
the proposed algorithm. The optimization problem is defined for each
time that the microgrid needs a control operation as the sum of the
weight priority curve of each controllable device. Let assume to be at
=t t , the optimization problem objective function has the following
mathematical form:
=
=
W P t W P tmin ( ) min ( )
P t P t i
N
i i
( ) ( ) 1 (11)
where W P t( ( ))i i is the weight priority curve for the ith device and
P t( )i is the set-point variation. The weight priority curves can be
described as [38] (following the example of the standard cost of
thermal units):
= + = …W P t a P t b P t i N( ( )) ( ) ( ) , 1 ,i i i i i i 2 (12)
The constraints of the optimization problem solved by the ERM algo-
rithm within the Priority Identification function can be described as:
+P P t P t P i( ) ( ) ,i min i i i max G, , (13)
P t P t i0 ( ) ( ),i i meas D L, (14)
+P P t P t P i( ) ( ) ,i min i i i max S, , (15)
+ +E t P t P t T t E i( ) ( ( ) ( ))·( ) ,i i i i max S, (16)
=
=
P t P t( ) ( ) 0req
i
N
i
1 (17)
where (13) defines generators limits, (14) represents loads constraint,
(15) imposes power limits on storage systems and (16) defines the en-
ergy constraints on batteries. In this last equation E t( )i represents the
current energy of the ith storage system at time t, while Ei max, is the
maximum energy. Finally, (17) imposes the Etarget chase. The
optimization algorithm defined by (11), (13)–(17) is a convex optimi-
zation problem, since the objective function is (convex) quadratic and
the constraints are affine. In this type of problem, the local solutions are
also global [42]. Remember that the approximation in the modelling of
the On/Off loads leads to a quasi-optimal formulation (see (8) in Sec-
tion 2.4).
A method based on Lagrange multipliers and Lambda Iteration
method is used to solve the optimization problem defined by the ob-
jective function (11) and constraints (13)–(17).
Let t( )opt be the Lagrange multiplier which, at time t , satisfies
[42]:
= = …dW P t
d P t
t i N( ( ))
( ( ))
( ) 0, 1, ,i i
i
opt (18)
In this case t( )opt can be called optimal priority. Eqs. (13)–(17) have
to be satisfied by the solution of the problem described by (11). In
particular, these equations represent the first order necessary condi-
tions for the optimization problem previously presented.
Considering the weight priority curves described in (12), Eq. (18)
can be re-written as:
= + = …dW P t
d P t
a b P t i N( ( ))
( ( ))
2 ( ), 1, ,i i
i
i i i (19)
Since Eq. (19) corresponds to a linear function, its inverse can be easily
calculated as [38]:
= + = …P t A B t i N( ( )) ( ), 1, ,i i i (20)
where t( ) represents now the continuous priority level.
Notice that all the curves presented in Section 2.4 and evaluated
through the curve calculation function can be described with Eq. (20)
by choosing the correct parameters Ai and Bi. This is a crucial step as it
connects two important functions of the proposed ERM algorithm:
curve calculation and priority identification. It can be observed now
that with Eq. (20), given a priority level t( ), it is possible to evaluate
the total P t( ) associated to the microgrid, summing all the con-
tributions P t( )i . Knowing P t( )i as a continuous function of priority
t( ) it is possible to solve the optimization problem (Eqs. (11)–(13),
(12)–(17)) with the Lambda Iteration method [38].
Notice that this optimization algorithm is modeled as the optimal
dispatch problem with the main difference that the optimization vari-
ables are Pi instead of Pi [38].
2.5.1. Lambda iteration method
Let t( )opt be the Lagrange multiplier defined in Eq. (18) for =t t ,
i.e. the priority level which defines the solution of the optimization
problem. The Lambda Iteration method starts from two values L and
< t: ( )H L opt and > t( )H opt . In order to respect the constraints
(13)–(17) the following definition is necessary:
2.5.2. Definition
Let be a generic priority level and P ( )i the active power varia-
tion of the ith device (evaluated through the curves calculation block
and generalized in (20)). Pi for the optimization problem (11) is de-
fined as:
case >P t( ) 0req
generators (i G)
=
+ <
+ >P
if P t P P
P P t if P t P P
P otherwise
( )
0 ( ) ( )
( ) ( ) ( )
()
i
i i i min
i max i i i i max
i
,
, ,
(21)
drivers (i D)
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
8
=
<
>P
if P
P t if P P t
P otherwise
( )
0 ( ) 0
( ) ( ) ( )
( )
i
i
i meas i i meas
i
, ,
(22)
on/off loads (i L)
=
<
>P
if P
P t if P P t
P t otherwise
( )
0 ( ) 0
( ) ( ) ( )
( )
i
i
i meas i i meas
i meas
, ,
, (23)
storage systems (i S)
=
+ <
>
P
if P t P P
M t if P M t P otherwise
( )
0 ( ) ( )
( ) ( ) ( ) ( )i
i i i min
i i i i
,
(24)
where =M t P P t( ) min , ( )i
E t
T t i i set
( )
,max ,
i . Notice that the second
equations in (24) has been introduced to deal with the two constraints
(15) and (16) related to the storage systems.
Case <P t( ) 0req is symmetrical with respect to case >P t( ) 0req .
The novel definition composed by (21)-(24) allows to extend the
Lambda Iteration Method including in its formulation also On/Off
loads, drivers and storage systems, together with all the technical
constraints of the controllable devices.
After this definition, Lambda Iteration Method can be described in
detail.
2.5.3. Lambda iteration method
Let us suppose to be at time t . Let’s define L and H :
<
=
P P t( ) ( ) 0
i
N
i
L
req
1
>
=
P P t( ) ( ) 0
i
N
i
H
req
1
while <L H , do
= +M
L H
2
if >= P P t( ) ( ) 0i
N
i M request1 then
=H M
else
=L M
end if
=t( )opt M
end while
Notice that also the proposed version of the Lambda Iteration
Method is essentially a bisection procedure which is able to solve the
problem defined by Eqs. (11)–(13), (12)–(17). The implementation
simplicity and the low computational cost of this solution technique is
crucial for the implementation on board of a LV commercial breaker,
allowing a real time control in a real field application.
2.6. Switching
The switching function operates in two cases:
1. after the priority identification module, providing the new set-points
of the controllable devices according to the solution ( P t( )) of the
optimization problem (solved in the priority identification block).
The new set-points for all the controllable devices of the system are
obtained by adding P t( )i ( = …i N1, , ) to the current set-points,
whereas the On/Off loads will have their breaker status eventually
updated;
2. In order to reconnect the On/Off loads in cases wherein the max-
imum disconnection time (ti max off, , ) has been overcome.
3. Study case
The proposed ERM algorithm has been developed in the Matlab
environment and tested in a simulated microgrid, whose dynamic
model has been developed in DIgSILENT Power Factory. The commu-
nication among the two software has been operated through an Open
Platform Communications (OPC) layer [43]. The test system has been
set to simulate one hour of the ERM algorithm operation.
3.1. Microgrid model
The test case microgrid is a Low Voltage (LV) System at 400 V,
connected to the main grid through a 10/0.4 kV transformer with a
rated power of 1 MVA. The single line diagram is shown in Fig. 6, where
the blue boxes indicate the measurement devices which communicate
with the ERM algorithm at the PCC. The external grid represents the
distribution system, modeled with a general load of 400 MW and a
synchronous generator of 1000 MW.
The generating capacity of the microgrid is supplied by two diesel
generators (DG1 and DG2), each of them with a rated power (Pnom) of
300 kVA and a nominal voltage of 400 V, and a PhotoVoltaic system
(PV) with a rated power of 300 kVA.
The local energy demand is composed of two non-dispatchable
loads: a thermal load with an apparent power of 313 kVA and a con-
stant load (NCL) with a power of 222 kVA. Moreover there are 20
controllable loads connected at line 4.
The dynamic models of electrical machines, regulators and loads
have been implemented as shown in [44].
The described microgrid can be considered a model of building,
wherein the 20 controllable loads can represent the loads of the dif-
ferent floors, or a industrial/commercial site with various assets (in
accordance to microgrid architecture typologies presented in [45]).
3.2. Simulation scenarios
Each one of the two different applications of the proposed ERM
algorithm, the Energy Consumption and the Frequency Control, has
been tested on specific scenarios, with different objectives and control
parameters. In all the cases the test system has been arranged to si-
mulate one hour, in real time, divided in control periods defined by T.
Table 2 collects the scenarios description with the objectives and the
time settings adopted in the simulations. As can be seen from this table
the first two scenarios (A,B) are dedicated to the test of the energy
consumption control, while scenario C is focused on the energy target.
Fig. 6. Test case microgrid.
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3.3. Load/generation characterization and microgrid operating scenario
This section describes in detail the characterization of the loads and
generators of the considered microgrid model.
3.3.1. Non-dispatchable loads
The thermal load has a nominal capacity of 315 kVA and has been
characterized with the profile reported in Fig. 7. The adopted char-
acteristic derives from a measure campaign [46]. The granularity of the
data is 5 s.
The non-controlled load (NCL) has been defined by assigning a fixed
active power set point.
Table 3 collects the operating set-points and parameters of non-
controlled loads in the scenarios presented in Section 3.2.
Notice that in order to test the frequency control logic (scenario C,
at =t 634 s the thermal load is disconnected to simulate a power im-
balance in the microgrid, and a sudden frequency deviation.
3.3.2. Controllable loads
The 20 loads connected at line 4 of the test microgrid (see Fig. 6) are
controlled by the ERM algorithm. Table 4 reports the technical data
related to these loads that have been used in all the simulation sce-
narios.
Eleven priority levels (ri varies from 5 to 15) have been adopted to
characterize the controllable loads. According to their absorption pro-
file, the 20 loads can be grouped as:
• Load 1–6: these loads are characterized by a highly variable profile
and a low value of priority (they are considered the least important
in the group), except Load 6. This load has a high priority value in
order to maintain a little variability in the system when the first
levels of priority are reached during the simulation;
• Load 7–13 are characterized with profiles that present slow varia-
tions and with a priority between 9 and 13;
• Load 14–20 are considered the most important in the ensemble,
therefore their priority values are the highest.
The graphical representations of the loads consumption profiles are
reported in Figs. 8–11. The loads have been grouped based on their
priority values.
All the consumption profiles assigned to the 20 controllable loads
derive from historical database of field measurement campaign [46].
The data granularity is again 5 s.
Notice that t t,i max off i min off, , , , and ti min on, , have not been considered in
these simulations scenarios in order to facilitate the results analysis.
The global power consumption of all the controllable loads is
reported in Fig. 13 and highlights a variability around a mean value of
200 kW.
3.3.3. PV system
The PV system has been characterized with the profile reported in
Fig. 12. Also in this case the data are derived from real measurements
related to one hour of PV production [46].
It is very important to highlight that the PV profile represented in
Fig. 12 and the thermal load represented in Fig. 7 have been considered
in order to increase the microgrid variability and to give to the ERM
technique a target more ambitious since it cannot manage all the system
variables (notice that the PV system and the thermal load are not
controllable). With this characterization of non-controllable loads and
renewable production, the simulation scenarios considerthe un-
certainties due to load and RES.
3.3.4. Controllable generators
The two diesel generators (DG1 and DG2) of the microgrid are
considered as controllable. The operating set-points and parameters of
controllable generators are collected in Table 5.
Notice that the columns related to the priority ri and the definition
of the steps si are crucial for the evaluation of the possible contributions
in terms of active power in order to respect Etarget (see Section 2.4).
Table 2
Objectives and parameters adopted in the simulations.
ID Objective T[s] t [s] ti [s] tc [s] tm[s]
A E 0target 900 1 180 60 10 0.01
B =E 0target 300 1 45 20 20 0.01
C fnom 900 1 180 30 10 0.01
Fig. 7. Thermal load profile assigned for the test case simulations.
Table 3
Operating set-points of non-controllable loads.
ID Pset Scenario Control ri si
[kW] [kW] [kW]
Thermal Load Dynamic (see Fig. 7) A/B/C – –
Non-controllable load (NCL) 220 A – –
55 B/C – –
Table 4
Priority value and rated power of controllable loads.
ID Pnom [kW] Priority ri Steps si Type
Load 1 12.5 5 1 On/Off
Load 2 12.5 5 5 driver
Load 3 25 6 1 On/Off
Load 4 25 6 5 driver
Load 5 35 6 1 On/Off
Load 6 10 13 5 driver
Load 7 22.5 8 1 On/Off
Load 8 17.5 9 5 driver
Load 9 21.25 9 1 On/Off
Load 10 18.75 9 5 driver
Load 11 37.5 9 1 On/Off
Load 12 26.5 10 5 driver
Load 13 20 11 1 On/Off
Load 14 12.5 11 5 driver
Load 15 15.25 12 1 On/Off
Load 16 13.75 12 5 driver
Load 17 30 13 1 On/Off
Load 18 12.75 13 5 driver
Load 19 11.25 14 1 On/Off
Load 20 10.75 15 5 driver
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Fig. 8. Highly variable power consumption profiles of the loads with priority value between 5 and 9.
Fig. 9. Slowly variable power consumption profiles of loads 8–13 with priority value between 9–11 and the barely variable absorption profile of Load 14.
Fig. 10. Consumption profiles of high priority (12–15) loads, little variability except for the Load 6 with priority equal to 13.
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
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3.3.5. PCC global exchange
Finally, the microgrid global exchange at the PCC is depicted in
Fig. 13.
In this figure all the contributions (generators, controllable/non-
controllable loads) are considered. The resulting behavior of the grid is
representative of a real study case and represents a realistic challenge
for an ERM algorithm.
3.4. Communication architecture
The simulation environment is represented in Fig. 14.
The proposed simulation architecture considers the implementation
of the simulated field, i.e. the fully dynamic model of the LV microgrid
(see Section 3.1), in the DIgSilent PowerFactory [47] software en-
vironment. This software allows to perform a real time simulation of the
test network. This peculiarity coupled with the characterization of the
system presented in Section 3.3 allows to have a simulated field with a
behaviour which is close to a real test facility (see the field tests per-
formed in [22] related to an old version of the proposed ERM algo-
rithm).
The presence of virtual measurement devices in the simulated field
(represented with blue lines in Fig. 6) permits the acquisition of the
measures (active power consumption of controllable loads, switches
status of on/off loads, controllable generators/storage systems active
power production/absorption, storage systems state of charge and
global exchange at the PCC).
The data flow from the simulated microgrid to the ERM application
is managed by using the Open Platform Communication (OPC) stan-
dard, which is based on a client–server structure (see Fig. 14).
The ERM application runs in Matlab environment and performs the
routine presented in Section 2 and depicted in Fig. 3. Once the ERM
algorithm has been executed the possible output signals (modification
Fig. 11. Global active power consumption of the controllable loads (Load 1–20) and mean value.
Fig. 12. PV production profile for all the simulation scenarios.
Fig. 13. Active power exchange at the PCC of the whole microgrid adopted as a test case for the proposed ERM algorithm.
Table 5
Operating set-points and parameters of controllable generators.
ID Pset Scenario Pmax Pmin Control ri si
[kW] [kW] [kW]
Diesel 1 (DG1) 210 A 270 150 ✓ 1 14
210 B/C 270 50 ✓ 1 14
Diesel 2 (DG2) 210 A 270 150 ✓ 1 14
210 B/C 270 50 ✓ 1 14
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of the controllable devices set points in terms of active power) are sent
to the simulated field exploiting again the path through the OPC server.
In addition, all the measures from the simulated field and all the
ERM control actions performed during the simulation are stored in
Matlab for the post process analysis. This task in crucial for the per-
formance evaluation of the proposed ERM algorithm.
3.5. Key performance indicators
Four different Key Performance Indicators (KPIs) have been pro-
posed and used to evaluate the performances of the proposed ERM
procedure:
• Absolute Error (errabs j, ), defined slightly differently for the Energy
Consumption [kWh] and the Frequency Control [Hz], respectively,
as:
=err E Eabs j target j meas j, , , (25a)
=err fabs j mean j, , (25b)
where Etarget j, is the energy target at the end of the jth period, Emeas j,
is the measured energy absorption of the microgrid at the PCC at the
end of the same control window and fmean j, is the measured mean
frequency deviation from its nominal value at the end of the same
control period. This index provides a measure of the error for each
control period.
• Mean Absolute Error (MAE), defined for both the Energy
Consumption [kWh] and the Frequency Control [Hz] as:
=
=
MAE
N
err1
P j
N
abs j
1
,
P
(26)
where NP is the number of control periods.
• Percentage Error (errperc j, , [%]), evaluated only for the Energy
Consumption Control according to the following formula:
=err
err
E
·100perc j
abs j
target j
,
,
, (27)
Fig. 14. Communication architecture for the test simulations.
Table 6
Computer specifications.
Processor RAM Operating System
Intel(R) Core(TM) i7-7Y75 1.30 GHz 16 GB Windows 10 Professional
Fig. 15. Simulation results for Scenario A.
Table 7
Numerical KPIs for scenario A.
errperc,1 errperc,2 errperc,3 errperc,4 MAPE
No Control 40.55% 20.70% 48.49% 65.85% 43.90%
ERM −0.32% −0.51% 1.23% 1.70% 0.95%
[22] −12.50% −4.61% 9.10% 7.25% 8.36%
[36] −4.72% −3.73% 4.03% 3.55% 4.00%
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• Mean Absolute Percentage Error (MAPE, [%]), calculated for the
Energy Consumption Control as:
=
=
MAPE
N
err
E
1 ·100
P j
N
abs j
target j1
,
,
P
(28)
This KPI provides a measure of the percentage error for the whole
simulation.
• Computational time: the specifications of the computer used in all
the simulations are reported in Table 6.
4. Simulation results
This section presents the results of the simulation in the above-
mentioned scenarios.
Fig. 16. Active power set-points provided by the ERM procedure in Scenario A. Top plot: active power set-points for diesel generators. Bottom plot: set-points for two
controllable loads.
Fig. 17. Simulation results for Scenario B.
Table 8
Numerical KPIs for scenario B.
errabs,1 errabs,2 errabs,3 errabs,4 errabs,5 errabs,6
No Control −0.43 kWh 1.04 kWh 0.40 kWh 0.29 kWh −0.18 kWh 1.35 kWh
ERM −0.05 kWh −0.17 kWh 0.22 kWh 0.03 kWh −0.08 kWh −0.28 kWh
[22] −0.20 kWh −0.31 kWh 0.36 kWh 0.29 kWh −0.11 kWh 0.26 kWh
[36] −0.13 kWh −0.25 kWh 0.30 kWh 0.28 kWh −0.10 kWh −0.28 kWh
errabs,7 errabs,8 errabs,9 errabs,10 errabs,11 errabs,12 MAE
0.82 kWh 3.13 kWh 3.52 kWh 4.23 kWh 2.30 kWh 2.60 kWh 1.83 kWh
−0.43 kWh −0.09 kWh 1.26 kWh −0.07 kWh −0.09 kWh 0.00 kWh 0.23 kWh
−1.00 kWh −0.33 kWh 1.91 kWh −1.72 kWh −0.65 kWh 0.39 kWh 0.62 kWh
−0.54 kWh −0.15 kWh 1.89 kWh −1.50 kWh −0.70 kWh 0.36 kWh 0.54 kWh
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4.1. Energy consumption control
This subsection is dedicated to the analysis of the scenarios and the
simulation results related to Energy Consumption Control (A,B).
4.1.1. Scenario A
The control algorithm aims to keep the energy consumption below
the Etarget , which assumes different values for each one of the four
control periods, as shown in Fig. 15. The length of the control window
is 15 min. The lower and upper bounds initial values are ± 25% of
Etarget . Fig. 15 shows the results of the simulation for scenario A. This
figure reports respectively in black and green line the estimated and
measured energy consumption under the control of the proposed ERM
procedure, while the dotted lines represent the microgrid behavior
without control.
As can be seen from Fig. 15 the goal of the ERM algorithm is
achieved with a good accuracy, since the green curve (Emeas) at the end
of each control period is very close to the Etarget , represented by the
intersection of the blue and the red line. Table 7 collects the results in
terms of percentage error and MAPE for scenario A with and without
ERM control. In addition, this table reports also a comparison with the
two algorithms which have been implemented in [34].
KPIs in Table 4 provide the validation for the ERM algorithm in
cases wherein the Etarget is dynamic and varies in the periods. In parti-
cular, the MAPE value for the whole simulation is under 1%, improving
clearly the results of the procedure proposed in [22,36].
The set-points provided by the proposed ERM algorithms for the
diesel generators are reported in the top plot of Fig. 16. Diesel 1 (re-
presented with the red line) is asked to perform larger variations of its
power generation, with respect to Diesel 2 (black line in Fig. 16),
having a lower priority value (see Table 5). As can be seen from Fig. 16,
at the end of each control period, both generators are brought back to
their power set-points (P ( )i set, , equal to 210 kW). In addition, it is
possible to observe that they never violate their maximum power limit
(Pi max, ) set to 270 kW. The bottom plot of Fig. 16 depicts the behavior of
an On/Off load (orange line) and a driver (grey line) during the si-
mulation. As can be observed from this plot the On/Off load cannot be
continuously regulated by the ERM algorithm.
Finally, the mean computational time of the functionalities
Displacement Estimation, Curves Calculation, Priority Identification
and Switching (see Section 2 and Fig. 3), which are responsible of the
resolution of the optimization problem and the microgrid control, is
close to 0.29 s with a maximum of 1.53 s. These values are satisfactory,
allowing a real time application of the proposed ERM strategy.
4.1.2. Scenario B
In this case, the goal of the adaptive algorithm is to keep the mi-
crogrid energy consumption as close as possible to Etarget , that has been
set equal to zero. The lower and upper bounds start from −0.25 and
0.25, respectively, and both converge to zero. The length of the control
window is 5 min. Fig. 17 shows the results of the simulation for scenario
B. This figure proves that with the proposed procedure, the actual en-
ergy exchange at end of control period is widely closer to the energy
target with respect to the case with no control enabled.
Table 8 collects the results of Scenario B in terms of Absolute Error
and MAE confirming that the ERM algorithm is a robust controller that
can achieve different objectives. Finally, also in this case the proposed
procedure outperforms [22,36].
The results related to the computational speed are similar to the
ones obtained in Scenario A with a mean value close to 0.23 s and a
maximum around 0.96 s.
4.2. Frequency control
This subsection reports the analysis for Scenario C that has been
designed in order to test the Frequency Control strategy.
4.2.1. Scenario C
In this case, the goal of the adaptive algorithm is to keep the fre-
quency of the microgrid as close as possible to its nominal value, that
has been set equal to 50 Hz. The controlled variable is the estimated
mean frequency error fforecast. The length of the control window is
15 min. Fig. 18 shows the results of the simulation for scenario B. This
figure proves that with the proposed procedure, the actual mean fre-
quency error at end of the control period is widely closer to zero with
respect to the case with no control enabled.
Fig. 19 displays the frequency distribution that, with the ERM
control logic in operation, is narrowly concentrated around its nominal
value.
Table 9 collects the results of scenario B in terms of absolute error
and MAE, confirming that the ERM algorithm is a robust microgrid
controller that can achieve different objectives.
Fig. 18. Simulation results for Scenario C.
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
15
Furthermore, Fig. 20 shows the actual power generated by the two
diesel generators during Scenario C. From this figure it is possible to
observe that the models of DG1 and DG2 are fully dynamic.
Also in this case the results related to the computational time are
satisfactory, since the mean value is close to 0.19 s, while the maximum
is around 0.69 s.
5. Conclusions
The adaptive control algorithm, based on a quasi-optimal ERM
technique, is meant to operate in a microgrid scenario. The proposed
procedure aims to regulate the dispatchable DERs in order to control
the energy exchanged at the PCC when the microgrid is connected to
the main grid, and the frequency profile when the microgrid is oper-
ating in islanded mode.
The proposed ERM strategy can be implemented on board of LV
breaker devices, able to control DERs with satisfying results, as showed
by the performed simulations. This has been achievable since the ERM
algorithm is based on a sub-optimal formulation that can be solved by a
simple iterative method without a great computational effort. This
peculiarity represents one of the main advantages of the presented
methodology for a real field implementation.
Future developments may investigate a more sophisticated forecast
functionality for the ERM procedure that could lead to a more precise
and efficient control.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Table 9
Numerical KPIs for Scenario C.
errabs,1 errabs,2 errabs,3 errabs,4 MAE
No Control 0.25 Hz 0.94 Hz 0.96 Hz 0.90 Hz 0.76 Hz
Control 0.23 Hz 0.07 Hz 0.08 Hz 0.03 Hz 0.10 Hz
Fig. 20. Active power produced by diesel generators during Scenario C.
Fig. 19. Histogram of the Frequency Distribution for Scenario C.
M. Crosa di Vergagni, et al. Electrical Power and Energy Systems 121 (2020) 106080
16
CRediT authorship contribution statement
M. Crosa di Vergagni: Software, Validation, Data curation, Writing
- original draft. S. Massucco: Resources, Supervision, Writing - review
& editing. M. Saviozzi: Conceptualization, Methodology, Software,
Validation, Formal analysis, Investigation, Data curation, Writing -
original draft, Writing - review & editing. F. Silvestro:
Conceptualization, Methodology, Supervision, Writing - review &
editing, Funding acquisition. F. Monachesi: Conceptualization,
Investigation, Supervision. E. Ragaini: Conceptualization, Supervision,
Project administration, Funding acquisition.
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	A quasi-optimal energy resources management technique for low voltage microgrids
	Introduction
	Motivation
	Literature review
	Contributions and aims
	Adaptive algorithm structure
	Acquisition and average
	Energy consumption control
	Frequency control
	Forecast
	Energy consumption control
	Frequency control
	Displacement estimation
	Energy consumption control
	Frequency control
	Curves calculation
	Generators (i∈ΩG)
	Drivers (i∈ΩD)
	On/Off Loads (i∈ΩL)
	Storage systems (i∈ΩS)
	Priority identification
	Lambda iteration method
	Definition
	Lambda iteration method
	Switching
	Study case
	Microgrid model
	Simulation scenarios
	Load/generation characterization and microgrid operating scenario
	Non-dispatchable loads
	Controllable loads
	PV system
	Controllable generators
	PCC global exchange
	Communication architecture
	Key performance indicators
	Simulation results
	Energy consumption control
	Scenario A
	Scenario B
	Frequency control
	Scenario C
	Conclusions
	Declaration of Competing Interest
	CRediT authorship contribution statement
	References