Optimal Capacitor Placement and Sizing for Enhancement of Distribution System Reliability and Power Quality Using PSO Pravin Machhindra Sonwane,Member IEEE
Bansidhar Eknath Kushare, Member IEEE
Electrical Engg. Dept., K.K.Wagh Inst. of Engg. Edu. & Research Nashik, India-422003
Professor and Head, Electrical Engg. Dept., K.K.Wagh Inst. of Engg. Edu. & Research Nashik, India-422003
[email protected]
[email protected]
Capacitor switching and number of capacitor used is always changing as per load and hence it is also responsible to introduce distortion in voltage and current waveforms results into increase in power quality problem. In this paper total harmonic distortion is considered as one of the constraint in addition to voltage profile and power factor constraints.
Abstract— This paper presents optimal capacitor placement and its sizing using Particle Swarm Optimization. Reactive power management and planning is one of the crucial issues in front of researcher from last four decades in addition to voltage profile, line losses and power factor problem in transmission and distribution system. Capacitor is a device which is a solution to above problem if utilized in proper way. IEEE 30 bus system is tested in this paper for optimal configuration of capacitor with broader multi-objective function. Reliability and its indices as discussed in IEEE std 493 and 1366 are benchmark studies followed by all researchers. Placement of capacitor will enhance the distribution system reliability and smart grid applicability. Particle Swarm Optimization technique is used to evaluate objective function for capacitor placement and sizing in IEEE bus system.
Numerous methods are discussed to evaluate similar problems are Artificial Neural Network[22], Fuzzy Logic [1], Search algorithm, Simulated Annealing, Genetic Algorithm[12-19], Tabu Search[10], Expert System[20] and Dynamic Programming. The fact of above methods is, they use certain control parameters that may be system dependent and difficult to determine. The major drawback of above methods is speed. In this paper more practical and easy to use and implement the multi-dimensional objective functions using particle swarm optimization technique is presented. This paper introduces OCP and PSO algorithm. Compensation of KVA, losses, voltage and power factor is discussed for before and after OCP.
Index Terms—OCP, Reliability, PSO
I. INTRODUCTION The unpredicted nature of load and increase in power demand in the electrical network forced the power system operation and control in complicated mode. Increase in power demand load results into (a) increase in number of feeder, (b) feeder capacity, (c) more generation and/or (d) expand the network by increasing substation capacity as well as equipment capacity. However such changes are not achievable in short time span and require putting lot of burden on economy. Therefore to increase KVA margin of substation, it will be more beneficial if system losses are minimized by means of reactive power management through capacitor placement. Such methods are already evaluated and employed [1-22].
Solution techniques treat nearest capacitor size as discrete variable rather than evaluated value of capacitor size. Actual cost of capacitor is considered. Active power losses and reactive power losses are evaluated separately. Most of the assumptions are minimized. For simplicity balanced distribution system is considered. II.
PROBLEM FORMULATION
Optimal capacitor placement and sizing problem is formulated based on the requirements of benefits due to reliability cost, cost of capacitor, purchase cost, operating cost and maintenance cost and savings due to transmission and distribution loss is considered. Equation (1) represents reliability cost:
1
P. M. Sonwane, Member IEEE, is pursuing Ph.D. from research centre Electrical Department, K. K. Wagh Institute of Engineering Education & Research, Nashik, India and working as Associate Professor E-mail:
[email protected] 2 Dr. B. E. Kushare, Member IEEE, is with K. K. Wagh Institute of Engineering Education & Research, Nashik, Maharastra, India and working as Head & Professor of Electrical Engg. Department. He is Energy auditor and provides consultancy in the area of Power quality. E-mail:
[email protected]
(1)
1
ECOST λi Ccdf Lavg
– Reliability Cost – failure rate – customer composite damage function – average load
(7)
(8)
Failure rate λ is defined as the frequency of interruption. Number of interruption or faults in given system network is a result of weak systems and results into poor power system operation and control. Failure rate can be decreased with strengthening power system by means of proper reactive power management and control, maintaining power factor towards unity and voltage profile. Ccdf is a customer composite damage function which varies with customer type cost due to interruption for a customer like industrial, commercial, agricultural, municipal or domestic is different. Hence this factor is dependent and consider here as per the type of load selected for given system network for evaluation. Lavg is the average load converted to given bus which changes time to time at the same time as capacitor in discrete form is adding in a bus, the overall load is going to change. Then Capacitor cost is given by,
For the following constraint, Constraints Vmin < V< Vmax Pf min< pf THDi < THD max
Following assumptions are considered development of the objective function:
the
Balanced network is considered for simplicity Capacitors are available in step size. Capacitor placement affects only the flow of reactive power in the feeder. Dedicated software using visual studio with SQL server at back end to store huge data is developed and installed in research lab to evaluate above objective function for optimal capacitor configuration for enhancement of distribution system reliability and power quality. In addition to this load flow studies are carried out using ETAP and POWER FACTORY DIgSAILENT software. ETAP and POWER FACTORY software are having limitations to solve OCP program and hence solution of these software are denied. In PMS_PSO software the limitations are eliminated. Figure (1) shows dash view of software.
(2) (3) (4) First component of equation (4) is fundamental component where as second component of equation (4) is harmonic component treated separately for evaluation matrix of active and reactive power losses separately. CC Xi C0i Qci C1i Bi C2i T Ti PLi El Nbus
in
Cost of Capacitor bank 0/1 [0 for no capacitor / 1 for capacitor] installation cost KVAr rating of capacitor bank Rs/KVAr for bank number of capacitor in a bank operating cost / bank /yr Planning period in yr time duration in hours total system loss at load level Energy loss Bus number at evaluation is carried out
Fig. 1 PSO PMS software
III.
Now the problem can be stated as follows
PARTICAL SWARM OPTIMIZATION
PSO is developed by Kennedy and Elberhart in 1995. It is meta-heuristic method to optimize the function. In this method population called as swarm is randomly generated. The swarm consist of individuals called as particles. Each particle is represented here by coordinate and keeps the track in hyperspace which is based on best solution of fitness function and is represented by Pbest. [4-9,16] All such
(5)
(6)
2
Pbest values are remained with individual particles in a global space to achieve best amongst all solutions and is called as gbest.
in the range 0 to 1. The C1 and C2 are learning parameters and here it is taken as 2. Developed software is in two modules. First module is based on evaluation of objective function with various constraints. Regression analysis on objective function yields to polynomial equation which is used in PSO as second module. PSO which is suitably using rosenbrok equation now can work with OCP equation to find out fitness function. PSO is initialized with two dimensional, population size 40, maximum velocity 10, maximum positions 100, and maximum number of iterations 200, inertia weight 0.9 and minimum error as 0.00001.
As on today PSO algorithm is having much more better performance as compared with other intelligent tools based on calculation speed, required number of parameter to be evaluated and memory occupation and hence it is observed that PSO is most suitable to tackle multi-dimensional objective functions. Various structure of PSO is developed like Hybrid Particle Swarm Optimization (HPSO), Hierarchical Structure Poly-Particle Swarm Optimization (HSPPSO), Binary version of PSO developed by Kennedy and Mohan, Modified PSO by Hu.at el. In all methods of PSO only gbest information shared with others /neighbours. Then each particle update its coordinate based on search experience pbest and gbest according to the following equation.
vij
1
k 1 id
x
wvij k id
x
c1r1 ( pbi j k 1 id
v
xij ) c2 r2 ( gbdj
xidj )
IV.
IEEE 30 bus system is described in Fig. (1). In this system five generators placed at bus numbers 1,2,5,8,11and 13. Transformers of rating 100MVA are placed between the buses as 4-12; 6-9; 6-10; 9-11; 12-13 and 28-27 respectively. IEEE bus system is benchmark system available for the study case and the operations like load flow study can be compared. The system is also represented in table (1) and table (2). This network consist of 30 buses, 41 branches, and 23 loads. It is observed that in this system 29 busses are rated with 33 kV, 9 buses are rated with 132 kV and 2 buses are rated with 11 KV. Considering this in mind we treat those buses which are 33 kV are part of distribution system. After load flow study, it is observed that 300.703MWand 80.538 Mvar. generation is required and this test system has initial losses in active power is 17.719 MW and 41.505 MW
(9) (10) (11)
2
ΔV= (Kvar)(XL) /10(KV)
Fig. 2
IEEE 30BUS SYSTEM
(12)
PSO Algorithm
If new velocity Then new velocity If new velocity Then new velocity Figure (2) indicates the flow chart of PSO process. Inertia weight is a parameter presents here is in the range of 0.4 to 0.9 as discussed in [25]. This parameter can be initialised within any value in between above range but this weight factor is continuously updated as per the equation (8). The parameters r1 and r2 are random variable generated
Fig. 3 IEEE 30 bus test system
Table 1 represents 41 branch information regarding branch resistance, reactance, failure rate and repair rate values.
3
10_21 10_22 12_14 12_15 12_16 12_13 25_27 27_29 27_30 28_27 14_15 15_18 15_23 16_17 18_19 19_20 21_22 22_24 23_24 24_25 25_26 29_30
0.9786 0.9612 0.9754 0.9598 0.9510 0.9838 0.9733 0.9808 0.9564 0.9818 0.9494 0.9236 0.9498 0.9494 0.9514 0.9509 0.9462 0.9506 0.9181 0.9483 0.9537 0.9537
Fig. 4 OCP Algorithm
0.0214 0.0388 0.0246 0.0402 0.049 0.0162 0.0267 0.0192 0.0436 0.0182 0.0506 0.0764 0.0502 0.0506 0.0486 0.0491 0.0538 0.0494 0.0819 0.0517 0.0463 0.0463
0.0348 0.0727 0.1231 0.0662 0.0945 0.0000 0.2198 0.2198 0.3202 0.22100 0.2210 0.1073 0.1000 0.0524 0.0639 0.0340 0.0116 0.1150 0.1230 0.1885 0.2544 0.2399
0.0749 0.1499 0.2559 0.1304 0.1987 0.14000 0.2087 0.0000 0.6027 0.4153 0.1997 0.2185 0.2020 0.1923 0.1292 0.0680 0.0236 0.1790 0.2700 0.3292 0.3800 0.45330
[SOURSE: IEEE PES]
TABLE I. BRANCH INFORMATION OF IEEE 30 BUS SYSTEM
Branch 1_2 1_3 2_4 2_5 2_6 3_4 4_6 4_12 5_7 6_7 6_8 6_28 6_9 6_10 8_28 9_10 9_11 10_17 10_20
Failure Rate 0.9783 0.9841 0.9532 0.9786 0.9497 0.9172 0.9828 0.9660 0.9760 0.9211 0.9494 0.9536 0.9494 0.9211 0.9537 0.9509 0.9535 0.9824 0.9666
Repair Rate 0.0217 0.0159 0.0468 0.0214 0.0503 0.0828 0.0172 0.034 0.024 0.0789 0.0506 0.0464 0.0506 0.0789 0.0463 0.0491 0.0465 0.0176 0.0334
R_pu
X_pu
0.01920 0.04520 0.05700 0.04720 0.05810 0.01320 0.01190 0.00000 0.04600 0.0267 0.0120 0.01690 0.0000 0.00000 0.0636 0.0000 0.0000 0.0324 0.0936
0.0575 0.1652 0.1737 0.1983 0.17630 0.03790 0.0414 0.2560 0.1160 0.0820 0.0420 0.0599 0.2080 0.5560 0.2000 0.1100 0.2080 0.0845 0.2090
TABLE 2 BUS DATA(GENERATOR AND LOAD DATA)
Bus PG(MW)
4
QG(MVAr)
PL(MW)
QL(MVAr)
Vpu
Ang
01
50-200
0
0
0
1.06
0.0
02
20-80
-20-100
21.700
12.700
1.045
-5.5
03
0
0
2.400
1.200
1.021
-8.0
04
0
0
7.6
1.6
1.012
-9.6
05
15-50
-15-80
94.2
19.0
1.01
-14.4
06
0
0
0
0
1.01
-11.3
07
0
0
22.8
10.9
1.002
-13.1
08
10-35
-15-60
30
30
1.01
-12.1
09
0
0
0
0
1.051
-14.4
10
0
0
5.8
-18.752
1.045
-16.0
11
10-30
-10-50
0
0
1.082
-14.4
12
0
0
11.200
7.500
1.057
-15.2
13
12-40
-15-60
0
0
1.071
-15.2
14
0
0
6.200
1.600
1.042
-16.1
15
0
0
8.200
2.500
1.038
-16.2
16
0
0
3.500
1.800
1.045
-15.8
17
0
0
9.0
5.800
1.04
-16.1
18
0
0
3.2
0.900
1.028
-16.8
19
0
0
9.500
3.400
1.026
-17.0
20
0
0
2.200
0.700
1.03
-16.8
21
0
0
17.500
11.200
1.033
-16.4
22
0
0
0
0
1.033
-16.4
23
0
0
3.200
1.600
1.027
-16.6
24
0
0
8.700
2..213
1.021
-16.8
25
0
0
0
0
1.017
-16.4
26
0
0
3.500
2.300
1.00
-16.8
27
0
0
0
0.000
1.023
-15.8
28
0
0
0
0
1.007
-12.0
29
0
0
2.400
0.900
1.003
-17.1
30
0
0
10.600
1.900
0.992
-17.9
in amount so overall objective function suggest the solution as given in table [5]. Figure (4) is a flow chart that represents the PSO based OCP algorithm. Load flow data is provided in addition to capacitor information. PMS_PSO software evaluates the objective function considering all constraint and memorised in the backend database. As per the requirements and customer type reliability cost is evaluated based on above equations. PSO will initialize it’s parameters as per constraint selected and evaluated a fitness function as given in figure (4). Table [5] shows the loss reduction in branches in the system shown. The capacitor placement can help to modify voltage parameters in the system. In Figure (6), profit during planning period is shown. It is observed that within two year the capacitor cost including operating cost is recovered and accumulative profit starts afterwards. Apart from this before and after capacitor placement evaluates as 13.81MVA capacity is released in this system. In most of cases power factor is improved and voltage is within the limits as per standard as shown in table [6]. Harmonic distortion as per equation (8) is also not violated.
Reliability Indices:
At the same time capacitor bank also contribute in reactive power, so wherever local reactive power is required, capacitor placed as suggested by PSO and it is general practice that the distribution engineer locally apply the capacitor for this purpose, which is the solution for local case. PSO evaluates its fitness function in local and global platform as shown in figure (5).
(15)
TABLE [5]. BRANCH LOSSES BEFORE AND AFTER OCP
Source of equations (13-15) is from IEEE standard 1366, 2001. These indices are depending on failure rate, duration of interruptions and number of customers interrupted. Most of the time, it is observed that as capacitor as a component is added in the network, overall system failure is increasing. For simplicity this fact is neglected in this paper also it is presumed that capacitor placement is decreasing. In previous research paper, modified failure rate is depending on compensated and uncompensated failure rate and in most cases it was predicted values. Modified failure rate, in this paper is calculated as per thermal loading of transformers and line loading and then used in evaluation process of objective function. V.
RESULTS
It is observed that the capacitor placement reduces the power losses as active power reduction is (17719.8317484.9)=234.93KW and reactive power reduction is (41505.82-41246.02)=259.8KVAR. It is observed that Reliability Indices are improved as compared in Table [3] before capacitor placement and Table [4] after capacitor placement. Few branches are found that KW and KVA losses are increasing, it is due to (a)it is small in amount and (b)cost due to losses as compared to reliability cost is small
5
Branch
Before kW Losses
Before kvar Losses
After kW Losses
After kvar Losses
1_2
5176
9675
5180
9676
1_3
3129
7038
3115
6968
2_4
1035
703
1017
783
2_5
2981
8134
2954
8007
2_6
1960
2037
1945
1964
3_4
862
1617
858
1596
4_6
614
1229
625
1256
5_7
202
1543
177
1617
6_7
387
513
382
544
6_8
116
500
116
513
6_28
59.783
1093
60.002
1108
8_28
3.553
4286
2.139
4345
9_10
0
761
0
765
10_17
9.253
24.131
8.311
21.675
72.49
162
74.072
165
10_21
107
229
96.992
209
10_22
49.101
101
43.787
90.284
12_14
81.393
169
73.125
152
12_15
246
484
214
422
12_16
77.09
162
49.213
103
14_15
8.944
8.082
5.502
4.972
15_18
49.304
100
44.535
90.688
15_23
40.505
81.819
24.791
50.077
16_17
14.845
54.48
12.339
45.282
18_19
8.179
16.538
6.765
13.679
19_20
14.498
28.996
15.044
30.087
21_22
1.106
2.25
1.805
3.673
22_24
33.759
52.547
29.546
45.989
23_24
11.46
23.44
9.709
19.859
24_25
7.346
12.828
5.755
10.05
25_26
45.742
68.326
30.858
46.093
25_27
28.074
53.605
29.354
56.049
27_29
88.121
166
85.142
161
27_30
166
312
160
301
29_30 Total Losses
34.282
64.776
33.112
62.567
17719.83
41505.82
17484.9
41246.02
Fig. 5
PSO for OCP
Cost
600 Thousands
10_20
500 400 300 200 100
0 1
2
3
4
5
Year
Fig. 6 Figure 5 Profit curve P.F.
TABLE [6].CAPACITOR PLACEMENT AND SIZING USING OCP
Bus 14 15 16 20 22 23 27 29
Vold 1.042 1.038 1.044 1.026 1.033 1.027 1.023 1.003
Vmod 1.043 1.040 1.045 1.028 1.035 1.028 1.024 1.004
Total KVAr 800 2400 1200 2400 2400 1200 1200 800
PFold 92.59 91.63 93.18 92.22 83.50 82.30 97.84 98.69
PFmod 93.00 93.00 94.00 94.00 84.95 83.40 98.20 98.80
No of Capacitor
Fig. 7 power factor improvement for a sample bus 10
6
Thousands
CONCLUSION
Objective function
900000 800000
Particle swarm optimization is a tool to evaluate multidimensional objective function. Evaluation of loss reduction yield to conclude that to decide cost recovery period due to cost of capacitor and installation cost. Result analysis shows that optimal capacitor configuration find proper places and size of capacitor. This placement improves power factor, reduces active and reactive losses, maintain voltage profile and KVA release. Apart from this indices shows that Reliability of the system is also improved.
700000 600000 500000 400000 300000 200000 100000
No of Capacitor
0
0
5
10
15
ACKNOWLEDGMENT
Fig. 8 objective function for sample of bus 10
Author thanks to Principal Prof. Dr. K. N. Nandurkar and management of K. k. Wagh Institute of Engineering education nashik for supporting to conduct this research work in the institute research laboratory, BCUD section to consider the research proposal and provide funding from university to this research work, without which research work may not be completed.
ECOST
REFERENCES [1]. Hu, W. ; Chen, Z. ; Bak-Jensen, B. ; Hu, Y., "Fuzzy Adaptive Particle Swarm Optimisation For Power Loss Minimisation In Distribution Systems Using Optimal Load Response” Generation, Transmission & Distribution, IET Journals & Magazines Volume: 8 , Issue: 1 Publication Year: 2014, Page(S): 1 - 10 [2]. El-Fergany, A.A. ; Abdelaziz, A.Y., “Efficient Heuristic-Based Approach For Multi-Objective Capacitor Allocation In Radial Distribution Networks” Generation, Transmission & Distribution, IET Journals & Magazines Volume: 8 , Issue: 1 Publication Year: 2014 , Page(S): 70 - 80 [3]. Abdelsalam A. Eajal, And M. E. El-Hawary, “Optimal Capacitor Placement And Sizing In Unbalanced Distribution Systems With Harmonics Consideration Using Particle Swarm Optimization”, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010 [4]. Kennedy, J., "Social Interaction Is A Powerful Optimiser: The Particle Swarm Bio-Inspired Computing: Theories And Applications”, 2008. BICTA 2008. 3rd International Conference Publication Year: 2008 , Page(S): 9 – 10 [5]. Nissrine Krami, Mohamed A. El-Sharkawi, “Pareto Multiobjective Optimization Technique For Reactive Power Planning” 2008 IEEE. [6]. Naing Win Oo, “A Comparison Study On Particle Swarm And Evolutionary Particle Swarm Optimization Using Capacitor Placement Problem” 2nd IEEE International Conference On Power And Energy (Pecon 08), December 1-3, 2008, Johor Baharu, Malaysia [7]. Kennedy, J. “Some Issues And Practices For Particle Swarms” Swarm Intelligence Symposium, 2007. SIS 2007. IEEE Publication Year: 2007 , Page(S): 162 - 169 IEEE Conference Publications [8]. Poli, R. ; Brattonx, D. ; Blackwell, T. ; Kennedy, J., “Theoretical Derivation, Analysis And Empirical Evaluation Of A Simpler Particle Swarm Optimiser” Evolutionary Computation, 2007. CEC 2007. IEEE Congress On Publication Year: 2007 , Page(S): 1955 - 1962 [9]. Bratton, D. ; Kennedy, J., “Defining A Standard For Particle Swarm Optimization” Swarm Intelligence Symposium, 2007. SIS 2007. IEEE Publication Year: 2007 , Page(S): 120 – 127
No of Capacitor Fig. 9 Reliability Cost for a sample bus 10
Voltage (V=V+ΔV)
No of Capacitor Fig. 10 Voltage profile for a sample bus 10
All above graphs are plotted on the basis of sample for a bus number 10. Almost all other buses where capacitors are placed are of the same nature and where capacitors are not placed graphs will be generated with opposite nature reasons may be due to power factor in leading mode or voltage profile may be violating limits or VTHD may not as per IEEE standard 519. Considering this, only sample bus 10 graphs are plotted here. PMS_PSO is capable to plot any graph as per the selection of programmer.
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Method Of Local Variations,” IEEE Trans. PAS, Vol. 102, No. 6, Pp. 1607–1614, June 1983. [25]. Maurice Clerc, “Particle Swarm Optimization” ISTE Publication, Indian Print 2006
ABOUT THE AUTHOR Prof. P. M. Sonwane graduated in Electrical Engineering from Chandrapur Engineering College, Nagpur University. He obtained M.Tech. in Integrated power systems From V.R.C.E. Nagpur in 2005 and pursuing Ph.D. in University of Pune. His area of interest is power system. Planning and Reliability, microprocessor, microcontroller, robotics and automation, artificial Intelligence and distribution system. He worked in Mumbai and Pune University and taught various subjects in last 14 Years. Currently he is working with Electrical Engineering Department, K. K. Wagh Institute of Engg. Edu. & Research, Nashik as Associate Professor.
Prof. Dr. B. E. Kushare graduated in Electrical Engineering from Govt. College of Engineering, Aurangabad and obtained Gold Medal as University Topper in 1989. He completed his ME Electrical Control System from Pune University in 1992 and obtained Ph.D. in Power Quality from Pune University in 2006. He is also a Certified Energy auditor. He Published around 100 International and National Papers. He is also a consultant to various industries in India and abroad. He is working as Professor & Head of Electrical Engg. Dept. at K.K.Wagh Institute of Engg. Education & Research, Nashik, Maharashtra, India.
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