AinShams University, Electric Power and Machines, Cairo, Egypt
Received Date: January 21, 2016; Accepted Date: February 20, 2017; Published Date: February 27, 2017
Citation: Abul’Wafa AR (2017) Novel LossVoltage Sensitivity Factor for Capacitor Placement in Radial Distribution System Using Analytical Approach. J Electr Electron Syst 6:213. doi:10.4172/23320796.1000213
Copyright: © 2017 Abul’Wafa AR. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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An analytical technique is proposed for allocation of shunt capacitor bank in radial distribution system. The objective is formulated to determine the size, number and location of capacitor bank for real and reactive power loss reduction, voltage profile enhancement and annual cost saving. A novel LossVoltage Sensitivity Factor (LVSF), has been incorporated in the technique. The value of LVSF decides the candidate bus location. The achievability of the proposed method (PM) has been demonstrated on IEEE69 bus test system allowing comparing results with latest optimization techniques in literature. Further application of PM on 130 bus relatively large distribution system shows the effectiveness and robustness of the proposed technique. Capacitors allocated (size and location) during light loading condition simulation are forced as fixed capacitors in nominal and heavy loading simulations. This development is essential when allocated capacitors in nominal and heavy loading simulations do not include nodes of fixed capacitors.
Shunt fixed and switchable capacitor bank; Analytical approach; Distribution system; LVSF; Load flow
Placement of capacitor of optimal sizes and at optimal locations not only reduces the power losses, but also improves the voltage stability of the electric power systems. Several metaheuristic techniques have been used by scientists and researchers over the years to address the problems of capacitor placements. They are very effective and powerful in comparison with conventional methods in solving complex nonlinear constrained optimization problems. Authors [1], used Differential Evolution algorithm, Direct Search Algorithm [2], Artificial bee colony algorithm (ABC) [3], Flower Pollination Algorithm [4], Bacteria Foraging (BF) [5], Ant Colony Search Algorithm (ACO) [6], Cuckoo Search Algorithm (CSA) [7], Harmony Search (HS) [8], Plant Growth Simulation Algorithm (PGSA) [9], Teaching Learning Based Optimization (TLBO) [10], Firefly Algorithm (FA) [11], shark smell optimization algorithm [12], Particle Swarm Optimization (PSO) [13,14], Heuristic Algorithm [15], Fuzzy–GA method [16], Simulated Annealing (SA) [17], Genetic Algorithm (GA) [18], Nonlinear Programming [19]. Carpinelli et al. [20] solved the problem of shunt capacitor placement and sizing by approximate power flow method. S Mandal et al. [21] used a new hybrid particle swarm optimization algorithm to determine the best location and size of capacitor units in radial distribution system. The cost of real power losses and cost of capacitors were included in the objective function. However, one of the major difficulties for these methods is the premature convergence.
In this paper a new analytical method has been presented to solve the capacitor allocation problem in distribution system. The objective was formulated to minimize real power loss to its minimum value. A new LossVoltage Sensitivity Factor (LVSF), has been proposed here. LVSF incorporated real power loss and voltage of the system. The proposed technique gives best location and size of capacitor banks simultaneously. The efficacy of the proposed methodology has been tested on IEEE 69 bus distribution system. Three loading conditions (Light, Nominal and Heavy) are also considered here.
A further development of the proposed technique, capacitors allocated (size and location) during light loading condition simulation are forced as fixed capacitors in nominal and heavy loading simulations. This development is when allocated capacitors in nominal and heavy loading simulations do not include nodes of fixed capacitors.
The results of proposed technique applied on IEEE 69 bus distribution system are compared with various algorithms to check its supremacy. Further the proposed technique was applied on relatively large 130 bus real distribution system insuring the effectiveness and robustness of the proposed technique.
The main contributions of this paper can be defined as
• Proposal of a new technique to solve capacitor location problem especially for large scale system.
• Proposal of a new LossVoltage Sensitivity Factor (LVSF), has been incorporated in the technique to decide the candidate bus location.
• The proposed technique outlasts other algorithms in solving the optimal locations and sizing of capacitors in distribution systems. Moreover, it provides a promising and preferable performance over other algorithms in terms of voltage profiles, active and reactive power losses, total cost and net saving.
• Capacitor allocated (size and location) during light loading condition simulation are forced as fixed capacitors in nominal and heavy loading simulations. Capacitors determined in nominal and heavy loading simulations are switchable capacitors.
Following pseudo code summaries the computational process for proposed analytical technique:
While continue decreasing.
Do until a capacitor is allocated
a) Set any size (5 kVAr) of capacitor unit at a bus and run load flow program [22].
Calculate the of the system and LVSF values for each bus.
b) Increment the size of capacitor in 5 kVAr steps and repeat ‘i’ and ‘ii’.
Store the size of capacitor which gives least amount of the system.
Store the bus, which has least LVSF value, will be the best location of capacitor unit.
Repeat steps ‘d’ to ‘e’ to find more locations and sizes of capacitors as multicapacitor compensation.
End do.
Print best capacitor placement.
Print , , power loss reduction % , and annual $ Saving.
Apply this process for Light loading condition to determine best location and size of fixed capacitors. Next apply this process with allocated fixed capacitors, for nominal and peak loading conditions to determine best location and size of switched capacitors.
The variables in the computation algorithm are defined mathematically as follows:
(1)
Where
(2)
The operating constraints are:
• The voltage of each bus must be maintained between specified limits.
(3)
• The total reactive power injected is not to exceed the total reactive power demand in radial distribution system.
• The reactive power injection at each candidate bus is given by its minimum and maximum compensation limit.
The analytical method incorporating a LossVoltage Sensitivity Factor (LVSF), has been proposed to determine the size and location of capacitor units. The LVSF takes the system active power loss with and without capacitors and voltage limits of individual buses with capacitors in account and suggest the best location of the capacitor. The LVSF includes main objectives (power loss reduction and voltage profile enhancement).
(4)
where,
Base case real power loss (kW)
Real power loss after capacitor placement at a bus (kW)
Per unit maximum bus voltage after capacitor placement at a bus
Per unit minimum bus voltage after capacitor placement at a bus
In proposed analytical approach, capacitor units are placed to minimize real power loss and to enhance voltage profile. The technique is employed on the IEEE 69 bus distribution system and on relatively large 130 bus real distribution system.
The implementation of proposed method for the best capacitor placement problem was done using version (9.0.0) R2016 a of MATLAB language on an Intel Core i7 processor running at 2.20 GHz with 7.95 GB RAM.
The values of various constant used in equation (1 to 2) are: Cost of power loss (K_{P}) = $0.06/kwh, Cost of energy loss (K_{e}) = $0.06/kWh , capacitor installation cost for single unit (K_{i}) = $1000, Cost of per kVAr capacitor bank (K_{c}) = $5, maximum loss hours = 1500, discount rate (r) = 0.08, and economic life of investment (years) = 10.
From simulation results, it is learned that capacitor locations during light loading condition simulation may not repeated in nominal and heavy loading simulations. Therefore, in this paper capacitor allocated (size and location) during light loading condition simulation are forced as fixed capacitors in nominal and heavy loading simulations. Capacitors determined in nominal and heavy loading simulations are switchable capacitors. To the author knowledge this approach was not tackled in previous publications. This approach shall be detailed in the following section.
Case 1: 69 bus system
The IEEE 69 bus has 12.66 kV and 100 MVA base values. The base case real power loss and minimum bus voltage are 224.7893 kW and 0.9092 pu [23].
Generally Capacitor bank size, location and control are determined based on reactive load curve usually approximated by a steps ladder function. In this work, three steps functions are used. Thus, calculation of energy losses requires power losses in peak (160 % of nominal load), nominal and light (50% decrement in load) load levels.
Simulation results for the three operating conditions are summarized in Table 1. The voltage profile after compensation compared to base case is shown in Figure 1 for nominal operating condition and in Figure 2 for heavy operating condition.
Light Load (50%)  Nominal Load (100%)  Heavy Load (160%)  

Before Capacitor Placement  Power Loss (kW)  51.6150  224.7893  651.9646 
Min. bus voltage (pu)  0.9567  0.9092  0.8445  
After Capacitor Placement 
Capacitor Size in kVAr and location  175/17 260/50 
1267/61 303/50 
2111/61 357/50 
Total kVAr  435  1570  2468  
Power Loss (kW)  34.6352  145.9182  410.1286  
Min. bus voltage (pu)  0.9680  0.9316  0.8854  
% Loss reduction  32.8969  35.0867  37.0934 
Table 1: Simulation results for 69 bus system after capacitor installation.
Meaning beside (175/17+260/50 kVAr/node) fixed capacitors, (1267/61+303/50 kVAr/node) switched capacitors are required at nominal load operating condition and additional (844/61+54/50 kVAr/node) switched capacitors are required at heavy load operating condition.
The results of proposed method are compared with latest optimization technique like FuzzyGA [16], Direct Search Algorithm [2], PSO [13], Heuristic [15], and Flower Pollination Algorithm [24]. 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 exceeds those in other technique. The bus voltage profile of 69 bus system is also improved due to proposed approach. DE [2] and FPA [24] searched lesser size of capacitor bank, however resulting in lower loss reduction and percentage saving.
Items  Uncompensated  Compensated  

FuzzyGA [16]  DE [2]  PSO [13]  Heuristic [15]  FPA [24]  Proposed Method  
Total losses (kW)  224.8949  156.62  151.3763  152.48  148.48  150.28  145.9182(Base kW losses 224.7893) 
Loss reduction (%)  30.4  32.7  32.2  34 35.2  33.20  35.0867  
Minimum voltage  0.9092  0.9369  0.9311  0.9305  0.9323  0.9316  
Optimal location and size in kVAr (Node/kVAr)  59/100 61/700 64 800 
57/150 58/50 61/1000 60/150 59/100 
46/241 47/365 50/1015 
8/600 58/150 60/1050 
61/1350  61/1267 50/303 

Total kVAr  1600  1450  1621  1800  1350  1570  
Annual cost ($/year)  118,204.8  90119.5  88913.4  88006.5  86441.1  85356.7  
Net saving ($/year)  28085.3  29291.4  30198.3  31763.7  32848.1  39327.5791(Base Annual cost=128130 $/yr.)  
% saving  23.8  24.8  25.6  26.9  27.8  30.69 
Table 2: Comparison of annual loss saving for various techniques at nominal load for 69 bus system.
Case 2: 130 bus system
The system under consideration is 11 kV, 130 bus radial distribution system. The system load is 1911.6 kW and 1423.8 kVAr. The line and load data are given in Appendix and the tree graph of the feeder is shown in Figure 3. The real power loss of the system is 365.1864 kW and minimum bus voltage is 0.9243 pu without compensation. The procedure of proposed approach, as detailed for IEEE 69 bus system is repeated for this relatively large system to determine the best location and size of capacitor bank.
Simulation results for the three operating conditions are summarized in Table 3. The voltage profile after compensation compared to base case is shown in Figure 4 for nominal operating condition and in Figure 5 for heavy operating condition.
Light Load (50%)  Nominal Load (100%)  Heavy Load (160%)  

Before Capacitor Placement  Power Loss (kW)  185.4599  365.9583  979.0706 
Min. bus voltage (pu)  0.9562  0.9242  0.8760  
After Capacitor Placement 
Capacitor Size in kVAr and location  10/5  1085/89 340/20 45/129 40/6 
1670/89 660/19 115/128 65/3 
Total kVAr  10  1510  2510  
Power Loss (kW)  64.0474  241.8028  633.9606  
Min. bus voltage (pu)  0.9682  0.9376  0.8992  
% Loss reduction  65.4656  33.9261  35.3367 
Table 3: Simulation results of the 130 bus distribution system.
Meaning beside (10/5 kVAr/node) fixed capacitors, (1085/89+115/128+65/3 kVAr/node) switched capacitors are required at nominal load operating condition and additional (585/89+320/20+25/6 kVAr/node) switched capacitors are required at heavy load operating condition.
In this paper, an analytical technique is proposed for allocation of shunt capacitor bank in radial distribution system for real and reactive power loss reduction, voltage profile enhancement and annual cost saving. A new LossVoltage Sensitivity Factor (LVSF), has been incorporated in the technique to decide the candidate bus location.
Capacitors allocated (size and location) during light loading condition simulation are forced as fixed capacitors in nominal and heavy loading simulations. This development is when allocated capacitors in nominal and heavy loading simulations do not include nodes of fixed capacitors.
A large scale and small scale distribution systems are used to demonstrate the performance of the new formulation. The proposed algorithm provides an efficient solution since it provides a promising and preferable performance over other algorithms in terms of voltage profiles, active and reactive power losses, total cost and net saving.