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2016 IEEE PES Asia-Pacific Power and Energy Conference - Xi'an - China 
Optimal Reserve Model with Risk and Emergency 
Power Control Constraint 
Jibo Sun, Yanwei Wang, Yinguo 
Yang 
Yu Kou, Jiangfeng Jiang, Fan Liu, 
Tao Ding, Zhaohong Bie Yanlin Wu 
Electric Power Dispatching Control 
Center 
Guangdong Power Grid CO. ,Ltd 
Guangzhou 510600, China 
ky_921105@163.com 
State Key Labor-atory ofElectrical 
Insulation and Power Equipment 
Xi'an Jiaotong University 
Xi'an 710049, China 
kyallen@stu.xjtu.edu.cn 
State Grid Shaanxi Economic 
Research Institute 
Xi'an 710065, China 
wuyanlindq@126.com 
Abstract-In this paper, a new reserve model based on risk of 
the power system is proposed to considering both the reliability 
and the economy. In the meantime, the emergency DC power 
control are considered in this model. In the reserve model, the 
operating reserve are classified into load reserve and 
contingency reserve. The objective is to minimize the energy and 
reserve cost. Apart from system wide reserve requirements in 
the previous optimization model, constraints include emergency 
DC power support and contingency reserve requirements 
retlecting by risk. This model taking the reliability and the 
economy into account is insightful to guide the future 
development of reserve schedule for power system. 
Index Terms-- Optimal reserve, Contingency, risk, Emergency 
power control, Emergency DC power support 
I. INTRODUCTTON 
The operating reserve of power system is the important 
method to maintain the security, stability and economic 
operation. The energy reserves are left to cope with sudden 
changes in load, grid failures, generator failures, etc., which 
will minimize adverse effects of power shortage. Generally, 
the more proportion the reserve capacity is, the higher the 
reliability ofpower system, but the system operation economy 
decreases. How to ensure the reserve capacity under the 
premise of safety and reliability is one of the most important 
problems in operation dispatching. 
The traditional operation dispatching and control method 
based on the deterministic criteria has been difficult to adapt 
the development of power system. The studies of power 
system have been changed from the single deterministic way 
to the combination of certainty and uncertainty [1]. The 
traditional deterministic safety analysis method is based on 
"the most serious accident decision criteria", which means the 
systems is still safe in the most serious fault. The dispatching 
modes based on the "worst case" are often too conservative 
and unable to meet the economy requirements [2]. 
With the increasing of power system scale, the connection 
between the power systems is more closely. Because the 
reserve in the power system can support each regionss, how to 
ensure the reserve capacity of each region has important 
This work was supported in part by the National Natural Science 
Foundation of China under Grant 51577147 and the Independence research 
project of State Key Laboratory of Electrical Insulation and Power 
Equipment in Xi ·an Jiaotong University (EIPE I4I06). 
978-1-5090-5417-6/16/ $ 31.00 ©2016 IEEE 
theoretical and practical significance in maintaining reliability 
and improving in case of emergency. The reference [3]-[6] 
proposed a clearing model of the operating reserve market, 
which could ensure the optimal operating reserve capacity and 
operating reserve market. This model was based on the 
reliability evaluation of the generation system by cost-benefit 
analysis. [7] proposed a model of optimal reserve capacity 
(ORC) ofregional power system, which took the whole profit 
maxirnization as objective function. This model combined the 
minimization functions of both generation cost and grid loss. 
Besides, a survey on problems existing in current reserve 
capacity optimization of power system was given in [8] based 
on the viewpoint of risk management and coordination 
optimization. [9] presented a two-Ievel model considering 
some important constraints, including transmission capacity 
limit of tie line, minimum local reserve and total reserve 
requirement. In this paper, the concept of zonal electrical price 
was extended to zonal reserve price, which was a new method 
of cost-sharing problem. [10] presented an innovative 
methodological framework to optimize the locations of 
emergency rescue facilities in the contexts of large-scale urban 
environmental accidents. The method in this paper considered 
both the reliability and the economy, which is a new 
exploration to ensure the reserve capacity based on the risks. 
As the rapid development of HVDC technology, more and 
more power transmission project with large capacity put into 
operation in the actual system. Once the transmission channel 
failures, it will take a great threat to the power systems. The 
spinning reserves can maintain the stability of power system 
after the accident, which can quickly provide power support 
for power system to curb the system frequency reducing. [11] 
proposed an optimization method in which the transient 
frequency deviation of power system is taken into account and 
researched the optimization configuration of spinning reserve 
that is active during primary frequency regulation. [12] 
presented that the DC emergency power control can realize 
the DC transmission system for the AC power system support. 
What kind of intluence this new technology can bring to the 
optimal configuration of reserve capacity remains to be 
studied. 
2007 
In conclusion, it can be seen that the multi-objective 
coordination optimization problem of reserve capacity has 
been studied by some scholars, which considers the 
uncertainty based on the risks. However, most of the 
researches are based on the electricity market lacking of risk 
evaluation index and most studies are based on the academic 
level, which do not combine with the actual operation of 
power systems. 
Therefore, the optimal model of reserve capacity in this 
paper is based on the related concepts of risks, which 
combines with probability and consequences. It considers both 
the consequences of the failure events and the possibility of 
failure events in the process of capacity evaluation. Besides, 
the effects of DC emergency power control technology are 
considered in this paper. These innovations of optimal 
reserves capacity provide the corresponding reference in the 
new situation of power system and have important meanings 
to ensure the safety and economy of power system. 
11. EV ALUATlON INDEX OF RESERVE CAPAClTY 
CONSIDERING RISKS 
The traditional deterministic method for determining the 
reserve capacity is used in most parts of China, namely, 
according to the certain percentage of peak load or maximum 
generators capacity. This kind of method ignores the system 
operation parameters, which does not have areserves 
evaluation index system. Some probabilistic methods are 
considered in the foreign power systems, which ensure the 
reserve capacity based on the reliability requirements. 
However, this kind of method does not consider the cost of 
decision-making and the accident risks, which is unable to 
provide quantitative support for the economy. 
This section proposes a new reserves configuration 
evaluation index based on the power system reliability index 
EPNS. This index considers the economic and social effects of 
failures in different regions, which unifies the power supply 
reliability factor and economic factor through risks. This index 
is also the objective function of the reserve optimization 
model below. 
It is assumed that the start-up modes ofthe generators have 
been given, and only the output and reserve of each unit can 
be changed. Risk assessment quantitative index considering 
the capacity and cost of cutting loadin the lake of reserves can 
be expressed as follows: 
Ng Na Ng N 
SI = La)~ + Lßi(~+ +~-)+ LYiRi + LPj LCijillij ( 1) 
;eS 
Where P; means the planned output of the ith generator, ~+ 
means the purchases of the up load reserve capacity of ith 
AGC generator, ~. means the purchases of the down load 
reserve capacity of ith AGC generator, Ri means the 
purchases of spinning reserve capacity of the ith generator, 
ai , ß" Yi mean the price of electric energy, the price of load 
reserve and spinning reserve, respectively. The unit of the 
price is YuanlMW. Pi is the probability of ith accident. Cij 
means the amount of shedding loads of ith node, when the ith 
accident happened. ilIlj means the cost of shedding loads of ith 
node, when the ith accident happened. N means the total g 
number of schedulable generator in the power system, Na 
means the total number of AGC generator, N means the 
number of faults in the fault concentration, S means the set of 
all nodes in the power system. 
III. THE OPTIMAL DlSPATCHING OF RESERVE CAPACITY 
MODEL BASED ON RISKS 
A. The reserve optimization model based on risks 
1) Objec t i ve f unction 
The objective function of the optimal dispatching of 
reserve capacity model based on risks is minimize the total 
cost including electric energy, reserve and price of losing load. 
The objective function can be expressed as folIows: 
Ng Na Ng N 
min(La)~ + Lßi(Ai+ +~-)+ LY)\ + LPjLCijillij) (2) 
i eS 
The symbols in the equation (2) are explained in the section 
II. The generators in this model include all generators in the 
power systems, all high power tie Iines and all high-capacity 
transmission channels. 
2) Constraint conditions 
a) Equation ofpower balance 
N g Nd 
LP; = LD, 
i = l i = l 
(2) 
Where Di means the load of ith node, Nd means the 
number of all nodes in the power system. 
b) The constraint of generator output 
For all generators: 
(3) 
For AGC generators: 
P + A+ + R :s: P , P, - A,-, ~ P"m,'n I i I Imax (4) 
P + A+ :s: Li , P - A- ~ A 
I i L-'-;max ' I I imin 
(5) 
Where P; ma, means the maximum output of ith generator, 
P;min means the minimum output of ith generator, ~ma, 
means the ceiling of ith AGC generator, Aim," means the floor 
of ith AGC generator. 
For generators out of AGC control: 
(6) 
c) The constraint of generator c1imbing rate 
(7) 
Where POi means the active power output of ith generator 
before, which can get from the EMS. 
2008 
d) The constraint of reserve climbing rate Where ~:/1 means the active power output of kth line, after 
(8) the N-1 accident ofthe mth tie line happens. 
(9) C;/1 means the amount ofshedding loads of ith node, when 
the N-1 accident of the mth tie line happens. The value is 
(10) limited by load gross of ith node, that is 
Where '1+ means the climbing rate of up load reserve of 
ith generator, '1- means the climbing rate of down load 
reserve of ith generator, I1 means the response time of load 
reserve, 12 means the response time of spinning reserve. 
e) The constraint of minimum reserve demand of power 
systems 
(18) 
1\/1 means the purchases of the spinning reserve capacity 
of the ith generator, when the N-1 accident of the mth tie line 
happens. The value is limited by the maximum output of ith 
generator, that is 
(19) 
No 
LA/ ?D~ 
h) The N-1 constraint of high-capacity transmission 
(11) channels considering risks 
i =1 
Where D~ means the minimum reserve demand of power 
systems, which is set to 2% in general. 
f) The constraint of line transmission capacity 
For all the lines in power systems: 
Ng Nd 
p" =" H k P, -" H kD k L...J I I ~ I I 
;=1 1=1 
(14) 
(15) 
All lines should satisfy the limit of line transmISSiOn 
capacity under the ground state trend. Where ~k means the 
active power output of kth line, ~k max means the maximum 
transmission capacity of kth line, H ki means the power 
transfer distribution factor matrix. 
g) The N-1 constraint of high power tie lines considering 
risks 
In general case, all tie lines should satisfy the limit of 
transmission capacity under N-1 condition, when the output of 
generators are fixed. However, for the high power tie lines, it 
is difficult to satisfy this constraint during the summer peak 
season. Therefore, in this paper, we assume alt generators 
have the expected plans of corrective control to call out 
reserves before accident happened. When the N-1 accident of 
the mth tie line happens, the topology of power grid network 
changes. Therefore, the new power transfer distribution factor 
matrix Hili should be calculated and the N-1 constraint of 
high power tie lines considering risks can be expressed as 
folIows: 
Ng Nd 
p,1II =" H III (P' +R,III)_" HIII(D -CIII ) (17) 
'k L..J kl I L..J kl f f 
i = ! i = ! 
The AC tie lines between provinces are equivalent to high-
capacity transmission channels, and we assume the operation 
mode ofthem is same with generators. When the N-1 accident 
of the nth high-capacity transmission channel happens, the 
fault line cannot provide electrical energy and reserves. Then, 
all of the generators in power systems and the other high-
capacity transmission channels should provide operating 
reserves. At this point, all Iines should satisfy the limit of line 
transmission capacity to ensure the safety of power systems 
after failures. The N-1 constraint of high-capacity 
transmission channels considering risks can be expressed as 
folIows: 
p" = O,Rn = 0 (20) 
N g Nd 
L R,n + Lcin = p" (21) 
i = l ,i'*-n 1=1 
-~k max :s;~: :s; ~k max (22) 
Ng Nd 
~: = LHk, (~+Rn-LHki (D, _C,n ) (23) 
;=1 ; =1 
(24) 
(25) 
The equation (21) means that the sum of the purchases of 
the spinning reserve capacity and the shedding load capacity 
should be equal to the active power deficiency. 
i) The N-1 constraint of large-capacity generator 
considering risks 
The maximum capacity generator in every region is 
selected as the large-capacity generator. It is assumed that the 
active power deficiency only can be made up by the 
generators without fault in each region, when the N-1 accident 
of the nzth large-capacity generator in zth region happens. At 
this point, alliines should satisfy the limit of line transmission 
capacity to ensure the safety of power systems after failures. 
2009 
The N-l constraint of large-capacity generator considering 
risks can be expressed as follows: 
P"z = 0, Rnz = 0 (26) 
N; Nd L R,nz + L qz = P"z (27) 
i=l,i;t:nz i=1 
- ~k max :;:; ~;z :;:; ~k max (28) 
Ng Nd 
~;z = LH/d(~ +R,nz)-LH/d(D; _c;nz) (29) 
i=1 ;= ] 
in the actual power system, which are equivalent to 11 high-
capacity transmission channels. The system is divide into 8 
regions according to the geographic position, where there are 
2350 nodes and 2556 lines. The diagram of actual system is 
shown in Fig.2. We assume that the 170 generators in the 
system are all controlled by AGC strategy, and the rate 
regulation of them is according to their minimum and 
maximum output. That is to say, the rate regulation of 
generators is satisfied A;max = ~max , A;mm = P'min • The 
response time of load reserve tl is 5 minutes and the response 
time of emergency reserve t2 is 10 minutes. The c1imbing rate 
of up load reserve and down load reserve are equal, that is to 
+ -(30) say lj = lj • 
(25) 
The meaning of the symbols in equations above are similar to 
the equations in constraint condition h). 
B. The emergency DC power control 
In the optimal dispatching ofreserve capacity model ofthe 
past, the transmission power of DC tie lines between 
provinces is fixed. However, as the emergency DC power 
control technology develops, the active power support of DC 
tie Iines is feasible in case of emergency. 
p 
!!P,lImax 
Fig. I OCemergency power control process 
Therefore, in this paper, the emergency DC power control 
are considered in the optimal dispatching of reserve capacity 
model. The emergency DC power control process has been 
simulated in Fig.l, where the symbol of means the power 
limit of the DC transmission line, the symbol of means the 
time been taken. 
The DC tie lines between provinces also can be equivalent 
to high-capacity transmission channels. When the emergency 
fault happens, the DC tie lines can provide reserves through 
emergency DC power control. The model and the constraint 
condition of DC tie Iines is same as the AC tie lines between 
provinces above. 
IV. RESULTS ANO ANAL YSES BASED ON THE ACTUAL 
POWER SYSTEM IN A PROVINCE 
In this section, the proposed model is performed using 
MATLAB and MOSEK based on the actual power system in a 
province. The information of every generator and line are 
according to the actual data under a certain operation mode in 
summer. 
The information of every generator and line are according 
to the actual data. There are 8 DC tie lines and 8 AC tie lines 
Fig.2 The 8 regions ofthe actual power system 
0011lJ 
+ fftf,f 
@ :i<:l!!tJL 
- ~Ul\ 
The total load ofthe actual power system is 92232.98MW. 
The total generators capacity and the maximum generator 
capacity in every regions are Iisted in Table 1. We can see 
from the Table 1 that the total instalIed capacity of all regions 
is 68058.5, therefore, the AC and DC tie lines must provide 
active power to balance the loads in the system. 
Table I The information ofgenerator in each region 
Region Generator Total Maximum 
number number capacity/MW capacity/MW 
41 18436.5 1036 
2 18 4203 650 
3 19 6975 660 
4 11 3800 600 
5 18 5110 390 
6 16 4500 370 
7 23 14124 1086 
8 24 10910 1000 
Total 170 68058.5 5792 
The fault concentration is set accord ing to section III , 
where there are 10 high power tie lines, 3 high-capacity 
transmission channels and 8 maximum large-capacity 
generators in each regions. The high power tie lines N-l 
failures are the 500KV tie Iines connecting each regions. The 
high-capacity transmission channels N-l failures are the 
maximum DC high-capacity transmission channel (SI #), the 
second-highest DC high-capacity transmission channels (S2# 
and S3#). The active power deficiency of them are 6400MW 
5000MW respectively. 
2010 
According to the actual data, the forced outage rates of 
high-capacity transmission channels, high power tie lines and 
large-capacity generators are 0.06, 0.05 and 0.02. We assume 
that there are 20% interruptible loads in region 3, the cost of 
which is 0.06 YuanJMW. 
Based on the proposed model, the minimum cost of energy 
and reserve considering risks is 18.17633 million Yuan and 
the results of optimal power, load reserves and spinning 
reserves for every region are shown in Table 2. 
Table 2 The results of optimal dispatching model based on risks 
Region Electric Up load Down load Spinning 
number energy reserves reserves reserves /MW /MW /MW /MW 
18192.47 710.00 770.59 1320.00 
2 11841.00 279.00 37.71 558.00 
3 13755.74 178.16 109.42 798.00 
4 3237.67 47.50 120.00 450.00 
5 10501.46 375.00 51.94 618.50 
6 6188.87 135.00 45.00 803 .80 
7 13399.78 65.00 155.00 550.45 
8 15116.00 55.00 555.00 643.00 
Total 92232.98 1844.66 1844.66 5741.75 
From the Table 2, we can see that the optimal results meet 
the load demands and reserve demands in the system. In 
addition, we can also get the plan of calling up reserves in 
each regions afar failures. Some results of N-l faults are 
shown in Table 3. 
Table 3 The results of3 high-capacity transmission channels N-l failures 
Region 
number 
2 
3 
4 
5 
6 
7 
8 
Total 
The capacity of calling up reserves afar failures/MW 
S1# fault S2#fault S3#fault 
1402.28 1180.93 1195.3 
640.28 0 487.84 
880.28 798 679.56 
532.28 160 403.79 
700.78 393 497.54 
886.08 803.8 705.24 
632.73 550.45 473.91 
725.28 643 556.83 
6400.00 5000.00 5000.01 
V. CONCLUSIONS 
The main contributions ofthis paper are listed as followed: 
• Based on the conception of risk, this paper will 
propose an index to quantify the reserve capacity of a 
renewable power integrated system, which 
considering ofthe reliability and the economy. 
• Simultaneously, the new reserve model in this paper 
studies the emergency DC power control, which 
reflects the DC power connection. 
Based on the traditional reserve model, this paper will 
construct a new reserve model while considering DC power 
connection. 
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