![International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 2, April 2017, pp. 748~753
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i2.pp748-753 748
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Optimal Allocation of Capacitor Bank in Radial Distribution
System using Analytical Approach
Sarfaraz Nawaz1
, M.P. Sharma2
, Abhishek Gupta3
1
Poornima University, Jaipur, India
2
RVPNL Jaipur, India
3
Swami Keshvanand Institute of Technology Management & Gramothan, Jaipur, India
Article Info ABSTRACT
Article history:
Received Jul 13, 2016
Revised Mar 12, 2017
Accepted Mar 26, 2017
In this paper, a novel analytical technique is proposed for optimal allocation
of shunt capacitor bank in radial distribution system. An objective function is
formulated to determine the optimal size, number and location of capacitor
bank for real & reactive power loss reduction, voltage profile enhancement
and annual cost saving. A new constant, Power Voltage Sensitivity Constant
(PVSC), has been proposed here. The value of PVSC constant decides the
candidate bus location and size. The achievability of the proposed method
has been demonstrated on IEEE-69 bus and real distribution system of
Jamawaramgarh, Jaipur city. The obtained results are compared with latest
optimization techniques to show the effectiveness and robustness of the
proposed technique.
Keyword:
Analytical approach
Capacitor bank
Radial distribution network
Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Sarfaraz Nawaz,
Poornima University,
Jaipur, Rajasthan, India.
Email: eesarfaraz1983@gmail.com
1. INTRODUCTION
Complexity of the modern power system is increased due to stressed conditions in a distribution
networks, exponential increment in population and high ongoing demands on power grids are major concern
of the design engineers with every passing day. As per Indian scenario significant part of the system losses
(around 21%) are distribution losses. The power losses can be divided into two parts i.e. active power loss
and reactive power loss. Reactive power loss can be compensated by installation of shunt capacitor units.
Allocation of shunt capacitor units at appropriate location and of optimal size reduces the real power loss and
improves the voltage profile of the system. The researchers suggested many optimization techniques to solve
the problem of optimal allocation of capacitor units in radial distribution system. In [1], Prakash et.al.used
Particle Swarm Optimization algorithm to determine the best location and size of capacitor units in radial
distribution system. Carpinelliet al. [2] solved the problem of shunt capacitor placement and sizing by
approximate power flow method. The cost of real power losses and cost of capacitors were included in the
objective function. Nonlinear Programming [3], Genetic Algorithm (GA) [4], Simulated Annealing (SA) [5],
Cuckoo Search Algorithm [6], Heuristic Algorithm [7], Particle Swarm Optimization (PSO) [8-9], Artificial
Bee Colony(ABC) [10], Firefly Algorithm (FA) [11], Teaching Learning Based Optimization (TLBO) [12],
Plant Growth Simulation Algorithm (PGSA) [13], Harmony Search (HS) [14] Cuckoo Search Algorithm
(CSA) [15], Ant Colony Search Algorithm (ACO) [16], Bacteria Foraging (BF) [17], Flower Pollination
Algorithm[18, 23], Direct Search Algorithm [21], Differential Evolution algorithm [22] are developed to
solve optimal allocation of capacitor problem. However, no author tested their algorithm on real power
distribution system.](https://image.slidesharecdn.com/v2112mar1711811ijeceupdated9march-201016015830/85/Optimal-Allocation-of-Capacitor-Bank-in-Radial-Distribution-System-using-Analytical-Approach-1-320.jpg)
![ ISSN:2088-8708
IJECE Vol. 7, No. 2, April 2017 : 748–753
749
In this paper a new analytical method has been presented to solve the capacitor allocation problem
in distribution system. The objective function was formulated to minimize real power loss to its minimum
value. A new constant, Power Voltage Sensitivity Constant (PVSC), has been proposed here. This constant is
incorporated with real power loss and voltage of the system. In other optimization algorithm the location of
shunt capacitors are determined by loss sensitivity factor (LSF). But, the proposed PVSC gives optimal
location and optimal size of capacitor banks simultaneously. The efficacy of the proposed methodology has
been tested on standard 69 bus and real distribution system of Jamawaramgarh, Jaipur city. Three loading
conditions (Light, Nominal and Heavy) are also considered here. The results of proposed technique are
compared with various algorithms to check its supremacy.
2. OBJECTIVE FUNCTION
The objective function of capacitor allocation problem is to minimize the total cost due to energy
loss and reactive power compensation under certain operating constraints.
Mathematically the problem can be written as:
Min. f= Energy loss cost + Reactive power compensation cost
Min. f= Kp*Ploss*t+ Ki * CB + KC * ∑ (1)
where the constants are taken as [19].
The operating constraints are:
1. The voltage of each bus must be maintained between specified limits. Vmin≤V≤Vmax
2. The total reactive power injected is not to exceed the total reactive power demand in radial distribution
system.
3. The reactive power injection at each candidate bus is given by its minimum and maximum compensation
limit.
3. PROPOSED METHODOLOGY
An analytical approach has been presented for capacitor placement problem. The Power Voltage
Sensitivity Constant (PVSC) is proposed to determine the size and location of capacitor units. This constant
takes active power loss and voltage limits of individual buses in account and suggest the optimal location of
the capacitor.
(2)
where,
Prealloss: base case real power loss.
Pcaploss : active power loss after capacitor placement at ith
bus.
Vmax is maximum bus voltage in pu after capacitor placement at ith
bus.
Vmin is minimum bus voltage in pu after capacitor placement at ith
bus.
For optimal placement of capacitor bank the value of PVSC should be minimum.
Computational process for proposed analytical technique is explained below:
Step 1: Run the base case load flow program and calculate real power loss Prealloss.
Step 2: Set any size of capacitor unit and run load flow program.
Step 3: Calculate the real power loss of the system and “PVSC” values for each bus using eq. 2.
Step 4: Now vary the size of capacitor in minute step (10 kVAR) and compute real power loss by running
load flow program.
Step 5: Store the size of capacitor which gives least amount of real power loss.
Step 6: The bus, which has least “PVSC” value, will be the optimal location of capacitor unit.
Step 7: Repeat Steps 4 to 6 to find more location of capacitors.
4. TEST RESULTS AND DISCUSSION
In proposed analytical approach, capacitor units are placed to minimize real power loss and to
enhance voltage profile. A standard system of 69 bus and a real 130 bus distribution system of
Jamwaramgarh, Jaipur are employed to implement the proposed technique. This complete scheme is](https://image.slidesharecdn.com/v2112mar1711811ijeceupdated9march-201016015830/85/Optimal-Allocation-of-Capacitor-Bank-in-Radial-Distribution-System-using-Analytical-Approach-2-320.jpg)
![IJECE ISSN: 2088-8708
Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical … (Sarfaraz Nawaz)
750
developed in MATLAB software. The values of various constant used in equation (1) are: Cost of energy
loss (Kp)= $0.06/kwh, capacitor’s installation cost for single unit (Ki)= $1000, Cost of per kVAr capacitor
bank (Kc)=$3.
Case I: 69 bus system
The standard system of 69 bus has 12.66 kV and 100 MVA base value. The base case real power
loss and minimum bus voltage are 225 kW and 0.9092 pu [20]. To check the effectiveness of proposed
method, three different loading levels i.e. light load (50% decrement in load), nominal load & heavy load
(60% increment in load) are used. The first three candidate buses with optimal size have been determined by
PVSC. The results for three different loading conditions are shown in Table 1. The real power loss at nominal
load level (without compensation) is 225 kW and is reduced to 147 kW after installation of capacitor of total
size 1470 kVAr. The minimum bus voltage is also improved from 0.909 pu to 0.931 pu. The results at light
and heavy loading condition are also given in Table 1.
Table 1. Results for 69 bus system after capacitor installation
Light Load
(50%)
Nominal Load
(100%)
Heavy Load
(160%)
Before Capacitor Placement Power Loss in kW 53.31 225 643
Min. bus voltage 0.956 0.909 0.845
After
Capacitor Placement
Capacitor Size in kVAr and location
410 (61)
80 (21)
170 (64)
750 (61)
270 (21)
400 (64)
1500 (61)
240 (21)
600 (64)
Total kVAr 660 1420 2340
Power Loss (kW) 36 147 408
Min. bus voltage 0.966 0.931 0.887
% Loss reduction 32.4 34.66 36.54
The results of proposed method is compared with latest optimization technique like Direct Search
Algorithm [21], Differential Evolution algorithm [22], Flower Pollination Algorithm[23].The comparative
analysis is shown in Table 2. It is noticed from table that the proposed approach give maximum loss
reduction on lesser size of capacitor bank and percentage saving in cost is also maximum than other
technique.
Table 2. Comparison of annual loss saving for various techniques at nominal load for 69 bus system
Item Without Capacitor DSA [21]
(2012)
DE [22]
(2103)
FPA [23]
(2016)
Proposed
Total Loss 225 147 151.37 152 147
% Loss Reduction - 34.66 32.7 32.44 34.66
Min. Voltage 0.909 0.93 0.931 0.93 0.931
Optimal Size (Location) in kVAr
- 900 (61)
450 (15)
450 (60)
150 (57)
50 (58)
1000 (61)
150 (60)
100 (59)
1350 (61) 750 (61)
270 (21)
400 (64)
Total kVAr - 1800 1450 1350 1420
Annual Cost ($/year) 118260 85322 88910 84941 84523
Net Saving ($/year) - 32938 29350 33319 33737
% Saving - 27.8% 24.8% 28.17% 28.52%
The bus voltage profile of 69 bus system is also improved due to proposed approach. The improved voltage
profile before and after compensation is shown in Figure 1.](https://image.slidesharecdn.com/v2112mar1711811ijeceupdated9march-201016015830/85/Optimal-Allocation-of-Capacitor-Bank-in-Radial-Distribution-System-using-Analytical-Approach-3-320.jpg)
![IJECE ISSN: 2088-8708
Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical … (Sarfaraz Nawaz)
752
The real power loss is reduced to 208 kW after installation of capacitor of total size 930 kVAr. The
minimum bus voltage is also enhanced from 0.825 pu to 0.872 pu after compensation. There will be 33.3 %
saving in annual cost after shunt compensation. The improved voltage profile after shunt compensation is
shown in Figure 2.
Figure 3. Voltage profile before and after capacitor placement for Jamwaramgarh, Jaipur
5. CONCLUSION
In this paper, the optimal allocation of shunt capacitor in radial distribution system is modeled to
solve the objective of real power loss minimization, voltage profile improvement & energy cost saving. A
power voltage sensitivity constant (PVSC) has been proposed to solve the problem. The effectiveness of
proposed approach has been experienced on 69 bus test system and real distribution system of
Jamawaramgarh village, Jaipur city. The obtained results of 69 bus system are compared with latest
approaches and found superior in terms of percentage loss reduction, voltage profile improvement and annual
cost saving. The proposed approach is also successfully implemented on Jmawaramgarh distribution system.
The annual installation cost of capacitor bank is $117110 whereas the annual cost saving due to energy loss is
$ 58440. Therefore, the cost of shunt capacitor bank will be recovered in 3months of installation.
REFERENCES
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the 6th WSEAS international conference on evolutionary, Lisbon, Portugal, June 16–18, 2005. p. 152–9.
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0 20 40 60 80 100 120
0.8
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1
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Voltageinpu
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withcapacitor](https://image.slidesharecdn.com/v2112mar1711811ijeceupdated9march-201016015830/85/Optimal-Allocation-of-Capacitor-Bank-in-Radial-Distribution-System-using-Analytical-Approach-5-320.jpg)
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753
[14] Sirjani R, Mohamed A, Shareef H. Optimal capacitor placement in a radial distribution systems using harmony
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[17] S.M. Tabatabaei, B. Vahidi, Bacterial foraging solution based fuzzy logic decision for optimal capacitor allocation
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[18] A.Y. Abdelaziz, E.S. Ali, S.M. Abd Elazim, “Flower Pollination Algorithm and Loss Sensitivity Factors for
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Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical Approach
- 1. International Journal of Electrical and Computer Engineering (IJECE) Vol. 7, No. 2, April 2017, pp. 748~753 ISSN: 2088-8708, DOI: 10.11591/ijece.v7i2.pp748-753 748 Journal homepage: http://iaesjournal.com/online/index.php/IJECE Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical Approach Sarfaraz Nawaz1 , M.P. Sharma2 , Abhishek Gupta3 1 Poornima University, Jaipur, India 2 RVPNL Jaipur, India 3 Swami Keshvanand Institute of Technology Management & Gramothan, Jaipur, India Article Info ABSTRACT Article history: Received Jul 13, 2016 Revised Mar 12, 2017 Accepted Mar 26, 2017 In this paper, a novel analytical technique is proposed for optimal allocation of shunt capacitor bank in radial distribution system. An objective function is formulated to determine the optimal size, number and location of capacitor bank for real & reactive power loss reduction, voltage profile enhancement and annual cost saving. A new constant, Power Voltage Sensitivity Constant (PVSC), has been proposed here. The value of PVSC constant decides the candidate bus location and size. The achievability of the proposed method has been demonstrated on IEEE-69 bus and real distribution system of Jamawaramgarh, Jaipur city. The obtained results are compared with latest optimization techniques to show the effectiveness and robustness of the proposed technique. Keyword: Analytical approach Capacitor bank Radial distribution network Copyright © 2017 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Sarfaraz Nawaz, Poornima University, Jaipur, Rajasthan, India. Email: eesarfaraz1983@gmail.com 1. INTRODUCTION Complexity of the modern power system is increased due to stressed conditions in a distribution networks, exponential increment in population and high ongoing demands on power grids are major concern of the design engineers with every passing day. As per Indian scenario significant part of the system losses (around 21%) are distribution losses. The power losses can be divided into two parts i.e. active power loss and reactive power loss. Reactive power loss can be compensated by installation of shunt capacitor units. Allocation of shunt capacitor units at appropriate location and of optimal size reduces the real power loss and improves the voltage profile of the system. The researchers suggested many optimization techniques to solve the problem of optimal allocation of capacitor units in radial distribution system. In [1], Prakash et.al.used Particle Swarm Optimization algorithm to determine the best location and size of capacitor units in radial distribution system. Carpinelliet al. [2] solved the problem of shunt capacitor placement and sizing by approximate power flow method. The cost of real power losses and cost of capacitors were included in the objective function. Nonlinear Programming [3], Genetic Algorithm (GA) [4], Simulated Annealing (SA) [5], Cuckoo Search Algorithm [6], Heuristic Algorithm [7], Particle Swarm Optimization (PSO) [8-9], Artificial Bee Colony(ABC) [10], Firefly Algorithm (FA) [11], Teaching Learning Based Optimization (TLBO) [12], Plant Growth Simulation Algorithm (PGSA) [13], Harmony Search (HS) [14] Cuckoo Search Algorithm (CSA) [15], Ant Colony Search Algorithm (ACO) [16], Bacteria Foraging (BF) [17], Flower Pollination Algorithm[18, 23], Direct Search Algorithm [21], Differential Evolution algorithm [22] are developed to solve optimal allocation of capacitor problem. However, no author tested their algorithm on real power distribution system.
- 2. ISSN:2088-8708 IJECE Vol. 7, No. 2, April 2017 : 748–753 749 In this paper a new analytical method has been presented to solve the capacitor allocation problem in distribution system. The objective function was formulated to minimize real power loss to its minimum value. A new constant, Power Voltage Sensitivity Constant (PVSC), has been proposed here. This constant is incorporated with real power loss and voltage of the system. In other optimization algorithm the location of shunt capacitors are determined by loss sensitivity factor (LSF). But, the proposed PVSC gives optimal location and optimal size of capacitor banks simultaneously. The efficacy of the proposed methodology has been tested on standard 69 bus and real distribution system of Jamawaramgarh, Jaipur city. Three loading conditions (Light, Nominal and Heavy) are also considered here. The results of proposed technique are compared with various algorithms to check its supremacy. 2. OBJECTIVE FUNCTION The objective function of capacitor allocation problem is to minimize the total cost due to energy loss and reactive power compensation under certain operating constraints. Mathematically the problem can be written as: Min. f= Energy loss cost + Reactive power compensation cost Min. f= Kp*Ploss*t+ Ki * CB + KC * ∑ (1) where the constants are taken as [19]. The operating constraints are: 1. The voltage of each bus must be maintained between specified limits. Vmin≤V≤Vmax 2. The total reactive power injected is not to exceed the total reactive power demand in radial distribution system. 3. The reactive power injection at each candidate bus is given by its minimum and maximum compensation limit. 3. PROPOSED METHODOLOGY An analytical approach has been presented for capacitor placement problem. The Power Voltage Sensitivity Constant (PVSC) is proposed to determine the size and location of capacitor units. This constant takes active power loss and voltage limits of individual buses in account and suggest the optimal location of the capacitor. (2) where, Prealloss: base case real power loss. Pcaploss : active power loss after capacitor placement at ith bus. Vmax is maximum bus voltage in pu after capacitor placement at ith bus. Vmin is minimum bus voltage in pu after capacitor placement at ith bus. For optimal placement of capacitor bank the value of PVSC should be minimum. Computational process for proposed analytical technique is explained below: Step 1: Run the base case load flow program and calculate real power loss Prealloss. Step 2: Set any size of capacitor unit and run load flow program. Step 3: Calculate the real power loss of the system and “PVSC” values for each bus using eq. 2. Step 4: Now vary the size of capacitor in minute step (10 kVAR) and compute real power loss by running load flow program. Step 5: Store the size of capacitor which gives least amount of real power loss. Step 6: The bus, which has least “PVSC” value, will be the optimal location of capacitor unit. Step 7: Repeat Steps 4 to 6 to find more location of capacitors. 4. TEST RESULTS AND DISCUSSION In proposed analytical approach, capacitor units are placed to minimize real power loss and to enhance voltage profile. A standard system of 69 bus and a real 130 bus distribution system of Jamwaramgarh, Jaipur are employed to implement the proposed technique. This complete scheme is
- 3. IJECE ISSN: 2088-8708 Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical … (Sarfaraz Nawaz) 750 developed in MATLAB software. The values of various constant used in equation (1) are: Cost of energy loss (Kp)= $0.06/kwh, capacitor’s installation cost for single unit (Ki)= $1000, Cost of per kVAr capacitor bank (Kc)=$3. Case I: 69 bus system The standard system of 69 bus has 12.66 kV and 100 MVA base value. The base case real power loss and minimum bus voltage are 225 kW and 0.9092 pu [20]. To check the effectiveness of proposed method, three different loading levels i.e. light load (50% decrement in load), nominal load & heavy load (60% increment in load) are used. The first three candidate buses with optimal size have been determined by PVSC. The results for three different loading conditions are shown in Table 1. The real power loss at nominal load level (without compensation) is 225 kW and is reduced to 147 kW after installation of capacitor of total size 1470 kVAr. The minimum bus voltage is also improved from 0.909 pu to 0.931 pu. The results at light and heavy loading condition are also given in Table 1. Table 1. Results for 69 bus system after capacitor installation Light Load (50%) Nominal Load (100%) Heavy Load (160%) Before Capacitor Placement Power Loss in kW 53.31 225 643 Min. bus voltage 0.956 0.909 0.845 After Capacitor Placement Capacitor Size in kVAr and location 410 (61) 80 (21) 170 (64) 750 (61) 270 (21) 400 (64) 1500 (61) 240 (21) 600 (64) Total kVAr 660 1420 2340 Power Loss (kW) 36 147 408 Min. bus voltage 0.966 0.931 0.887 % Loss reduction 32.4 34.66 36.54 The results of proposed method is compared with latest optimization technique like Direct Search Algorithm [21], Differential Evolution algorithm [22], Flower Pollination Algorithm[23].The comparative analysis is shown in Table 2. It is noticed from table that the proposed approach give maximum loss reduction on lesser size of capacitor bank and percentage saving in cost is also maximum than other technique. Table 2. Comparison of annual loss saving for various techniques at nominal load for 69 bus system Item Without Capacitor DSA [21] (2012) DE [22] (2103) FPA [23] (2016) Proposed Total Loss 225 147 151.37 152 147 % Loss Reduction - 34.66 32.7 32.44 34.66 Min. Voltage 0.909 0.93 0.931 0.93 0.931 Optimal Size (Location) in kVAr - 900 (61) 450 (15) 450 (60) 150 (57) 50 (58) 1000 (61) 150 (60) 100 (59) 1350 (61) 750 (61) 270 (21) 400 (64) Total kVAr - 1800 1450 1350 1420 Annual Cost ($/year) 118260 85322 88910 84941 84523 Net Saving ($/year) - 32938 29350 33319 33737 % Saving - 27.8% 24.8% 28.17% 28.52% The bus voltage profile of 69 bus system is also improved due to proposed approach. The improved voltage profile before and after compensation is shown in Figure 1.
- 4. ISSN:2088-8708 IJECE Vol. 7, No. 2, April 2017 : 748–753 751 Figure 1. Voltage profile before and after capacitor placement for 69 bus system Case II: 130 bus Jamwaramgarh (Jaipur) system The system under consideration, as shown in figure 2, is 11 kV, 130 bus radial distribution system of Jamwaramgarh area, Jaipur city. The system load is 1878 kW and 1415 kVAr. The line and load data are given in appendix. The real power loss of the system is 335 kW and minimum bus voltage is 0.825 pu without compensation. The proposed approach is applied to determine the optimal location and size of capacitor bank. According to PVSC value, first five candidate buses are selected for allocation of capacitor units. Table 3 shows the result of jamwaramgarh system after compensation. Figure 2. 130 bus Radial Distribution system, Jamwaramgarh, Jaipur Table 3. Results of Jamwaramgarh (Jaipur) system Item Without Capacitor With capacitor Total Loss 335 208 % Loss Reduction - 38% Min. bus Voltage 0.825 0.872 Optimal Size (Location) in kVAr - 290 (53) 140 (77) 140 (114) 150 (120) 210 (126) Total kVAr - 930 Annual Cost ($/year) 175550 117110 Net Saving ($/year) - 58440 % Saving - 33.3 % 1 13 9 12 141556 16 17 18 19 57 20 21 22 26 27 23 24 25 28 29 31 32 30 33 34 36 38 42 45 48 35 37 39 40 41 44 43 46 4713 10 11 8 4 2 3 5 6 7 51 54 58 59 60 63 62 61 64 65 67 69 70 66 68 717273 78 79 77 76 74 80 75 81 8382 84 85 86 95 89 97 112 113 93 96 94 5053102105106107 99 98 49 100 92 9091 87 88 101103 104 108 109110111 114 115 117 116 118 121 122 119 120 123 124126128129130 125127
- 5. IJECE ISSN: 2088-8708 Optimal Allocation of Capacitor Bank in Radial Distribution System using Analytical … (Sarfaraz Nawaz) 752 The real power loss is reduced to 208 kW after installation of capacitor of total size 930 kVAr. The minimum bus voltage is also enhanced from 0.825 pu to 0.872 pu after compensation. There will be 33.3 % saving in annual cost after shunt compensation. The improved voltage profile after shunt compensation is shown in Figure 2. Figure 3. Voltage profile before and after capacitor placement for Jamwaramgarh, Jaipur 5. CONCLUSION In this paper, the optimal allocation of shunt capacitor in radial distribution system is modeled to solve the objective of real power loss minimization, voltage profile improvement & energy cost saving. A power voltage sensitivity constant (PVSC) has been proposed to solve the problem. The effectiveness of proposed approach has been experienced on 69 bus test system and real distribution system of Jamawaramgarh village, Jaipur city. The obtained results of 69 bus system are compared with latest approaches and found superior in terms of percentage loss reduction, voltage profile improvement and annual cost saving. The proposed approach is also successfully implemented on Jmawaramgarh distribution system. The annual installation cost of capacitor bank is $117110 whereas the annual cost saving due to energy loss is $ 58440. Therefore, the cost of shunt capacitor bank will be recovered in 3months of installation. REFERENCES [1] Prakash K, Sydulu M. Particle swarm optimization based capacitor placement on radial distribution systems. In: Proceedings of IEEE power engineering society general meeting, Tampa, June 2007. p. 1–5. [2] G. Carpinelli, P. Varilone, V. Di Vito, and A. Abur, “Capacitor placement in three-phase distribution systems with nonlinear and unbalanced loads”, Proc. Inst. Elect. Eng., Gen., Transm. Distrib., vol. 152, no. 1, pp. 47–52, 2005. [3] S. Nojavan, M. Jalali, K. Zare, Optimal allocation of capacitors in radial/ mesh distribution systems using mixed integer nonlinear programming approach, Int. J. Electric Power Syst. Res. 107 (2014) 119–124. [4] Swarup KS. Genetic algorithm for optimal capacitor allocation in radial distribution systems. In: Proceedings of the 6th WSEAS international conference on evolutionary, Lisbon, Portugal, June 16–18, 2005. p. 152–9. [5] H.D. Chiang, J.C. Wang, O. Cockings, H.D. Shin, Optimal capacitor placements in distribution systems: part 1: a new formulation and the overall problem, IEEE Trans. Power Deliv. 5 (2) (1990) 634–642. [6] Das P, Banerjee S. Placement of capacitor in a radial distribution system using loss sensitivity factor and cuckoo search algorithm. Int J Sci Res Manage, 2013; 2: 751–7. [7] Hamouda A, Sayah S. Optimal capacitors sizing in distribution feeders usingheuristics search based node stability indices. Int J Electr Power Energy Syst 2013; 46: 56–64. [8] Amanifar O, Golshan MEH. Optimal distributed generation placement and sizing for loss and THD reduction and voltage profile improvement in distribution systems using particle swarm optimization and sensitivity analysis. Int J Tech Phys Probl Eng, 2011; 3(2): 47–53. [9] Prakash K. Sydulu M. Particle swarm optimization based capacitor placement on radial distribution systems. IEEE power engineering society general meeting, 2007, 24–28 June 2007. p. 1–5. [10] M.M. Legha, M. Tavakoli, F. Ostovar, M.A. Hashemabadi, Capacitor placement in radial distribution system for improve network efficiency using artificial bee colony, Int. J. Eng. Res. Appl. 3 (6) (2013) 228–233. [11] P. Das, S. Banerjee, Optimal sizing and placement of capacitor in a radial distribution system using loss sensitivity factor and firefly algorithm, Int. J. Eng. Comput. Sci. 3 (4) (2014) 5346–5352. [12] S. Sultana, P.K. Roy, Optimal capacitor placement in radial distribution systems using teaching learning based optimization, Int. J. Electr. Power Energy Syst. 54 (2014) 387–398. [13] R.S. Rao, S.V.L. Narasimham, M. Ramakingaraju, Optimal capacitor placement in a radial distribution system using plant growth simulation algorithm, Int. J. Electr. Power Energy Syst. 33 (2011) 1133–1139. 0 20 40 60 80 100 120 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 Bus Number Voltageinpu Without capacitor withcapacitor
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