Maximum Cost Saving Approach for Optimal Capacitor Placement in ...

International Journal on Electrical Engineering and Informatics - Volume 7, Number 4, Desember 2015

Maximum Cost Saving Approach for Optimal Capacitor Placement in Radial Distribution Systems using Modified ABC Algorithm N. Gnanasekaran1, S. Chandramohan2, T. D. Sudhakar3, and P. Sathish Kumar4 1

Misrimal Navajee Munoth Jain Engineering College, Chennai-600 097, India 2,4 Anna University, Chennai-600 025, India 3 St. Joseph’s College of Engineering, Chennai-600 103, India

Abstract: This paper proposes an efficient methodology for optimal location and sizing of static shunt capacitors in radial distribution systems to reduce real power loss, improve voltage profile and to maximize total cost saving. The solution methodology has two parts: In part one, the buses to be compensated is identified using loss sensitivity factors. In the second part, modified artificial bee colony algorithm is used to select the optimal size of capacitors to be placed at the candidate buses. In addition the number of candidate buses is selected by searching for maximum cost saving. The results of proposed approach have been presented and compared with previous methods reported in the literature using four test cases. The presented results indicate the efficiency and quality of solution. Keywords: Loss Minimization, Loss Sensitivity Factor, Modified Artificial Bee Colony Algorithm, Optimal Location, Radial Distribution System, Shunt Capacitor 1. Introduction Shunt capacitors placed at the buses of distribution system have major effects like reducing the lagging component of circuit current and I2R real power loss in the system, increasing voltage level at the bus and decreasing kVA loading on the source generators and circuits to relieve an over load condition or release capacity for additional load growth [1]. Studies have indicated that as much as 13% of total power generated is consumed as I 2R losses at the distribution level [2]. The I2R losses can be separated into two parts based on the active and reactive components of branch currents. The losses produced by reactive components of branch currents can be reduced by the installation of shunt capacitors. The problem of placing capacitors in distribution systems involves the determination of the number, type and size of capacitors to be placed on the distribution feeders such that power and energy losses are minimized while taking cost of capacitors in to account. Literature describing capacitor placement algorithms are abundant. All early works of optimal capacitor placement used analytical methods [3]-[6]. Analytical method involves use of calculus to determine the maximum of cost saving function. Duran [7] was the first to use a dynamic programming approach to the capacitor placement problem. The formulation in [7] only considered the energy loss and accounts for discrete capacitor sizes. Fawzi [8] followed the work of [7] but included the released KVA into the savings function. Heuristics are rules of thumb that are developed through intuition, experience and judgment. Heuristics rules produce fast and practical strategies which reduce the exhaustive search space and can lead to a solution that is near optimal with confidence [9],[10]. Several investigations recently applied Artificial Intelligence (AI) techniques to resolve the optimal capacitor selection problem due to the popularity of AI. Sundhararajan and Pahwa [11] used Genetic Algorithm for the optimal selection of capacitors in distribution systems. Salma et al [12], [13] developed an Expert System containing Technical Literature Expertise (TLE) and Human Expertise (HE) for reactive power control of a distribution system. Received: May 11st, 2014. Accepted: November 16th, 2015

DOI: 10.15676/ijeei.2015.7.4.10 665

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Simulated Annealing (SA) is an iterative optimization algorithm which is based on the annealing of solids. Ananthapadmanabha et al [14] used SA to minimize capacitor installation costs. An Artificial Neural Network (ANN) is the connection of artificial neurons which simulates nervous system of a human brain. Santoso and Tan [15] used ANN’s for the optimal control of switched capacitors. The concept of Fuzzy Set Theory (FST) was introduced by Zadeh in 1965 as a formal tool for dealing with uncertainty and soft modeling. Chin [16] used FST to determine nodes for capacitor placement. In this paper, buses to be compensated are identified by Loss Sensitivity Factors and Modified Artificial Bee Colony algorithm (MABC) is used to select the optimal size of capacitors. 2. Distribution Load Flow Distribution load flow plays an important role in getting solution for capacitor placement problem. Generally distribution networks are radial and the R/X ratio is very high. Hence, distribution networks are ill-conditioned and conventional Newton-Raphson (NR) and Fast Decoupled Load Flow (FDLF) methods are inefficient at solving such networks. The distribution load flow algorithm proposed in [17] is used in this paper. 3. Sensitivity Analysis The buses to be compensated are identified using loss sensitivity analysis [18]. It is a systematic procedure to find the buses which have maximum impact on the system real power losses with respect to the reactive power of the bus. The estimation of sensitive buses basically helps in reduction of the search space for the optimization procedure.

r

Pr+jQr p

Peff(k)+jQeff(k) q Rk+jXk

s Pq+jQq

Ps+jQs

Figure 1. Sample radial distribution system A sample radial distribution system is shown in Figure 1. The real power loss in the kth distribution branch connected between starting bus ‘p’ and ending bus ‘q’ is given by [Ik2]*R[k]. Substituting for Ik in terms of real and reactive powers, we get Plineloss [𝑘] =

2 (P2 eff [k] +Q eff [k] )R[k]

(1)

2

(v[q] )

Where; Ik= Current through kth branch R[k] = Resistance of kth branch Peff[k] = Total active power flow in the branch ‘k’ Qeff[k] = Total reactive power flow in the branch ‘k’ Change in real power loss with respect to change in reactive power of a node is called as Loss Sensitivity Factor. The partial derivative of line loss of the branch with respect to Q eff is the loss sensitivity factor of the ending bus of the branch. For the ending bus ‘q’ of the branch ‘k’, loss sensitivity factor is given by the equation (2).

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∂Plineloss ∂Qeff

|

[q]

=

(2∗Qeff [k] ∗R[k] )

(2)

2

(V[q])

Loss sensitivity factors are calculated from base case load flows and the values are arranged in the descending order for all the buses of the system and are stored as bus position vector ‘bpos’. At these buses given by ‘bpos’ vector, normalized voltage magnitudes are calculated using the base case voltage magnitudes given by (norm[i] = V[i]/0.95). Where, ‘i' represent an element from ‘bpos’ vector. The buses whose nominal voltage magnitude is less than 1.01 are selected as candidate buses for capacitor placement. The candidate buses are stored in‘rank bus’vector. 4. Problem Formulation The objective of capacitor placement in the distribution system is to minimize the cost due to system real power loss and capacitor placement subject to the constraints. Three phase system is considered as balanced and loads are assumed as time invariant. The problem can be mathematically expressed as: Minimize = Cost of Total Energy Loss + Total Capacitor Cost Minimize = K e PL T + ∑NC i=1[K cf + Ci ]

(3) (4)

Where: Total Capacitor Cost = Cost of Capacitors + Capacitor Installation Cost Ke = Energy cost in $ per kW-year PL =Total real power loss in kW T = Design Period [one year] Kcf = Capacitor Installation Cost in $ Ci = Cost of ith capacitor in $ NC= Number of capacitors Subject to the constraints: (i) The voltage magnitude at each bus must be maintained within its limits and is expressed as: V min ≤ |Vi| ≤ V max (5) Where; |Vi| is the voltage magnitude of bus i, V min and V max are minimum and maximum permissible voltages limits, respectively. In order to quantify the violation of limits imposed on bus voltages in a radial distribution system, the voltage deviation index (VDI) is defined as [19] VDI = √∑NVB i=1

(Vi −ViLim )2

(6)

N

Where; Vi = Voltage of ith bus, V(iLim) = The Upper Limit of the ith bus voltage if there is a Upper Limit Violation or Lower Limit if there is a Lower Limit Violation N= Number of buses NVB= Number of buses violating limits (ii) The total reactive power injected is not to exceed the total reactive power demand in radial distribution system: ∑NC i=1 Q ci ≤ Q T

(7)

Where; QT = Total reactive power demand of the system NC = Number of buses compensated Qci= Reactive power injection at bus i

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5. Overview of Artificial Bee Colony Algorithm A. Behavior of Honey Bees: A bee colony consists of three groups of bees: employed bees, onlooker bees and scout bees and three actions: searching food source, recruiting bees for the food source and abandoning the food source. The ultimate objective of a bee colony is to forage for food. Initially employed bees will be sent out in search of food source. Employed bees exploit the food source and share the information about the food source with onlooker bees. Onlooker bees wait in the hive for the information employed bees provide. Employed bees share information about food sources by dancing in the dance area and the nature of dance is proportional to the nectar content of food source just exploited by the employed bees. Onlooker bees watch the dance and choose a food source according to the probability proportional to the quality of that food source. Naturally, good food sources attract more onlooker bees. Scout bees search for the new food source. Whenever a scout or onlooker bee finds a food source, it becomes employed bee. Similiarly whenever a food source is exploited compleately, the employed bees associated with it abandon it, and becomes scouts or onlookers. B. Artificial Bee Colony (ABC) algorithm: It is a swarm based meta-heuristic algorithm and simulates the foraging behavior of honey bees. In the ABC algorithm, a food source position represents a possible solution of the problem to be optimized which is represented by a d-dimension real-valued vector. The nectar amount of a food source corresponds to the quality (fitness) of the associated solution. The number of employed bees or the onlookers is equal to the number of the food sources (solutions) in the population. In other words, every food source is associated with only one employed bee. At each cycle at most one scout goes out for searching new food source and the number of employed and onlooker bees are equal. The solutions are initialialized randomly. The employed bees search the solutions space neighbor hood of each food space (eqn-9) and returns to the hive with the fitness value for each solution. The probability P i of selecting a food source ‘i’ by the onlooker is determined using the following expression: Pi =

S

fiti

(8)

N fit ∑n=1 n

Where fiti is the fitness of the solution represented by the food source i and SN is the total number of food sources. Clearly, with this scheme good food sources will get more onlookers than the bad ones. After all on lookers have selected their food sources, each of them determines a food source and computes its fitness. The best food source among all the neighboring food sources determined by the onlookers associated with a particular food source i, along with food source i itself, will be the new location for the food source i. If a solution represented by a particular food source does not improve for a predetermined number of iterations then that food source is abandoned by its associated employed bee and it will become a scout bee i.e., it will search for a new food source stochastically. This tantamount to assigning a randomly generated food source (solution) to the scout bee and changing its state again from scout to employed bee. After the new location of each food source is determined, another iteration of ABC algorithm begins. The whole process is repeated again and again till the termination condition is satisfied. The food source in the neighborhood of a particular food source is determined by altering the value of one randonly chosen solution parameter and keeping other parameters unchanged. This is done by adding to the current value of the chosen parameter the product of uniform variate in [-1, 1] and the difference in values of this parameter for this food source and some other randomly chosen food source.

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Maximum Cost Saving Approach for Optimal Capacitor Placement

Suppose each solution consists of d parameters and let xi= (xi1, xi2 ... xid) be a solution with parameter values xi1, xi2 ... xid. In order to determine a solution vi in the neighborhood of xi, a solution parameter j and another solution xk= (xk1, xk2. . .xkd) are selected randomly. Except for the value of selected parameter j, all other parameter values of vi are same as xi. i.e, vi= (xi1, xi2...xi (j-1), vij, xi (j+1)...xid) The value vi is determined using the following formula: vij= xij+ rij (xij-xkj)

(9)

Where, rij is a uniformly distributed real random number in the range [-1, 1]. If the resulting value falls outside the acceptable range for parameter j, it is set to the corresponding extreme value in that range. C. Modified Artificial Bee Colony (MABC) algorithm: It is a modified version of Artificial Bee Colony (ABC) algorithm [20]-[23]. In the basic ABC algorithm, greedy selection is applied between the current solutions and the new solutions, the new solutions are produced from the parent solutions as (9), the new solution v i is get only changing one parameter of the parent solution xi, and results in to a slow convergence rate. In modified ABC, the current solution xi and the pervious solution xi-1 are combined to get the new solution vi as vij = xij+ r ij (xij-xkj) if i=1 vij = xi-1j + rij (xij-xkj) if i>1 (10) Where xi−1j is the former neighbor of xij and the better one is selected by greedy selection. Thus, the search range is larger than in the basic ABC algorithm and the convergence rate is improved. The equation (10) is only applied in the exploration of employed bees, and onlooker bees still apply equation (9) for local searching. The combination of the global exploration and local search gets to better balance avoiding the optimization to be got into the local best value. 6. Proposed Algorithm for Capacitor Placement The proposed method is summarized in the following steps: 1. Read the line and load data. 2. Run the load flow program for radial distribution system; determine the active power loss and bus voltages. 3. Calculate loss sensitivity factors and arrange the values in the descending order for all the lines and store the respective end buses of the lines in the bus position vector ‘bpos[i]’. 4. Determine the normalized voltage magnitudes ‘norm[i]’ of the buses. If norm[i] < 1.01, then consider ith bus as candidate bus requiring capacitor placement and form ‘rank bus’ vector. 5. Initialize employed bees and maximum number of cycles. 6. Evaluate fitness for each employed bees. 7. Initialize cycle=1. 8. Generate new population (solution) vij in the neighborhood of xij for employed bees using equation (10) and evaluate them. 9. Apply the greedy selection between xi and vi. 10. Calculate the probability Pi of selecting the solutions xi, by means of their fitness values, using the equation (8). 11. Produce new population vi for the onlookers from the population xi using equation (9), selected based on Pi by applying roulette wheel selection process, and evaluate them. 12. Apply the greedy selection between xi and vi.

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13. Determine the abandoned solution, if exits, and replace it with a new randomly produced

14. 15. 16. 17. 18.

solution xi, for the scout bees using the following equation; xij = minj + ran(0,1) ∗ (maxj − minj ) Store the best solution achieved so for. Increment cycle. If cycle < maximum number of cycles, go to step 8, otherwise go to step 17. Calculate and display VDI, power loss, bus voltages and optimum cost for the global solution. Stop.

7. Simulation Results The proposed method is tested on four different test systems. The minimum and maximum bus voltage limits are fixed at 0.95 and 1.05 respectively. The algorithm of this method was programmed in MATLAB environment and run onto a Pentium IV, 2.1GHz Personal Computer. Constant Ke is chosen as 168 $ per kW- year. Design period T is considered as one year. The capacitor installation cost (Kcf) is taken as 1000 $ per bank. Capacitor bank costs are used from Table-1 [16]. Table-2 shows the costs of available capacitor sizes per year (Ci) derived from Table-1, assuming the life expectancy of capacitor banks as 10 years. The number of candidate nodes are selected such that installation cost is reduced and hence cost saving is maximized. Table 1. Available Capacitor Sizes and Costs Size kVAr Cost $

150 750

300 975

450 1140

600 1320

900 1650

1200 2040

Table 2. Available Capacitor Sizes and Costs/Year Size [kVAr] Cost [$] Cost[$/Year]

150 750 75

300 975 97.5

450 1140 114

600 1320 132

900 1650 165

1200 2040 204

The maintenance and running costs are neglected. The various constants used in the proposed algorithm are: Number of employed bees = 30; Number of onlooker bees = 30; Maximum Number of Cycles = 10. There is no separate allocation for scout bees, in both employed and on looker bee phase each discarded solution due to constraint violation will be handled by scout bees. The test results are shown in tables 4 to 11. For the purpose of comparison, Firefly Algorithm (FA) [28] is coded for this problem and the results are also included for all the test systems. The various control parameters adopted for Firefly Algorithm are: alpha (scaling factor)=0.4; minimum value of beta=0.2; gamma (absorption coefficient)=1; 10 fireflies for 25 generations. A. 10-Bus Test System: The proposed algorithm is tested on 10-bus radial distribution system as shown in figure 2. This is a 23kV system having 10 buses and 9 sections. The data of the system are obtained from [24].

1

2

3

4

5

6

7

8

Figure 2. 10-Bus radial distribution system

670

9

10

Maximum Cost Saving Approach for Optimal Capacitor Placement

The loss sensitivity factors are calculated from base case load flows and arranged in the descending order for all the lines of 10-bus system in table-3 and the respective end buses of the lines are arranged in descending order of loss sensitivity factors {4, 6, 5, 9, 10, 8, 7, 2, 3}. The normalized voltage magnitudes are calculated by considering base case voltage magnitudes using the formula Norm[i] = (V[i]/0.95).Then for the buses whose norm[i] value is less than 1.01 were considered as candidate nodes requiring capacitor placement and rank bus vector was formed as {6, 5, 9, 10, 8, 7}. Table 3. Loss Sensitivity Factors and Rank Bus Vector (Candidate Nodes) of 10-Bus Radial Distribution System Loss Sensitivity Factors in Descending Order 0.102933 0.098042 0.086376 0.081138 0.057603 0.038347 0.020795 0.019794 0.002023

Node No. 4 6 5 9 10 8 7 2 3

Base Voltage

Norm[i]={V[i]/0.95}

0.9634 0.9172 0.9480 0.8587 0.8375 0.8890 0.9072 0.9929 0.9874

1.0141 0.9654 0.9978 0.9038 0.8815 0.9357 0.9549 1.0451 1.0393

Rank Bus Vector (Candidate Nodes) --6 5 9 10 8 7 -----

Table 4. Comparison of Capacitor values of 10-Bus Radial Distribution System Fuzzy Reasoning(FR) [24] Bus No. Size[kVAr] 4 1050 5 1050 6 1950 10 900 Total kVAr =4950

PSO [18] Bus No. Size[kVAr] 6 1174 5 1182 9 264 10 566 Total kVAr =3186

Firefly Algorithm(FA) [28] Bus No. Size[kVAr] 6 1200 5 1200 9 300 10 300 Total kVAr =3000

Proposed Bus No. Size[kVAr] 6 1200 5 1200 9 450 10 150 Total kVAr =3000

Table 4 shows the comparison of capacitor values of proposed method compared with the other methods. From the rank vector, the top four buses {6, 5, 9 and 10} are selected as optimal candidate locations. The capacitor ratings of 1200, 1200, 450 and 150 kVAr are placed at the optimal candidate buses 6, 5, 9 and 10 respectively. The voltage profiles of the system before and after capacitor placement for 10-bus system are shown in Figure 3. The minimum voltage, before and after compensation is found as 0.8375 p.u. and 0.8715 p.u. at bus 10. From table-5 it is found that the total real power loss before and after capacitor placement are 783.77kW and 693.93kW respectively. The power loss obtained with the proposed method is less than the Fuzzy Reasoning [24], Particle Swarm Optimization (PSO) [18] and FA [28]. It can also be noted that the VDI is reduced from 0.0526 to 0.0334.

Table 5. Summary of Results of 10-Bus Radial Distribution System Items

Base Case

Real Power Loss (kW) Cost of Energy Loss ($/Year) Net Savings ($/Year) Loss Reduction (%) Cost Saving (%) VDI Time in seconds

783.77 1,31,673 ------0.0526 ----

FR [24] 704.88 ------10.06 ----------

671

Compensated PSO [18] FA [28] 696.21 693.95 ---1,17,586 ---14,087 11.17 11.45 ---10.69 ---0.0331 ---3.98

Proposed 693.93 1,17,577 14,096 11.46 10.70 0.0334 1.52

Bus Voltage (p.u)

N. Gnanasekaran, et al.

1.05 1.00 0.95 0.90 0.85 0.80 0.75 1

2

3

4 5 6 7 8 9 Bus Number Before Placement After Placement

10

Figure 3. Voltage profile before and after capacitor placement for 10-bus system B. 15-BusTest System: The second test case of the proposed method is a 15-bus radial distribution system [29] shown in Figure4. The system voltage rating is 11kV.

1 Substatio n

1 09

2

3 1 11

6

7

8

1 4 4

5

1 5

21 3

Figure 4. 15-Bus radial distribution system Table 6. Comparison of Capacitor values of 15-Bus Radial Distribution System Method Proposed in [25] Bus No. Size[kVAr] 3 805 6 388 Total kVAr =1193

Firefly Algorithm(FA) [28]

PSO[18] Bus No. Size[kVAr] 3 871 6 321 Total kVAr =1192

Bus No. Size[kVAr] 3 900 6 300 Total kVAr =1200

Proposed Method Bus No. Size[kVAr] 3 900 6 300 Total kVAr =1200

Table 7. Summary of Results of 15-Bus Radial Distribution System Items

Base Case

Real Power Loss (kW) Cost of Energy Loss ($/Year) Net Savings ($/Year) Loss Reduction (%) Cost Saving (%) VDI Time in seconds

61.79 10,380 ------0.0019 ----

Compensated Method Proposed in [25] 32.60 ------47.24 --------

672

PSO [18]

FA [28]

Proposed

32.70 ------47.07 ----------

32.86 5,983 4,397 46.81 42.36 0 5.27

32.86 5,983 4,397 46.81 42.36 0 3.55

Bus Voltage (p.u)

Maximum Cost Saving Approach for Optimal Capacitor Placement

1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91

1

2

3

4

5

6

Before Placement

7

8

9

10

11

12

13

14

15

Bus Number After Placement

Figure 5. Voltage profile before and after capacitor placement for 15-bus system The rank bus vector of 15-bus system contains set of sequence of buses given as {3, 6, 11, 4, 12, 8, 15, 14, 13, 5 and 7}. The top two buses 3 and 6 are selected as optimal candidate locations. From table-6, it is noticed that the amount of kVAr injected at buses 3 and 6 are 900 and 300 kVAr respectively. The voltage profiles of the system before and after capacitor placement for 15-bus system are shown in Figure 5. The minimum voltage, before and after compensation is found as 0.9445 p.u. and 0.9676 p.u. at bus 13. The results of the proposed method are compared with the results of method proposed in [25], PSO method [18] and FA [28]. The base case power loss is 61.79 kW. The power loss after capacitor placement is 32.86 kW which is almost same with other methods as shown in table-7. It is also observed that the VDI is reduced from 0.0019 to 0. C. 34-Bus Test System: The third test case is a 34-bus radial distribution system [10]. The system voltage rating is 11kV. It consists of a main feeder and 4 laterals. The active and reactive loads of the system are 4636.5kW and 2873.5kVAr respectively. The rank bus vector of 34-bus system contains set of sequence of buses given as {19, 22, 20, 21, 23, 24, 25, 26 and 27}. From the rank bus vector, the top three buses {19, 22 and 20} are selected as optimal candidate locations. The capacitor ratings of 900, 900 and 150 kVAr are placed at the optimal candidate buses 19, 22 and 20 respectively as shown in table-8. Table 8. Comparison of Capacitor values of 34-Bus Radial Distribution System Heuristic [10] Size Bus No. [kVAr] 26 1400 11 750 17 300 4 250 Total kVAr =2700

FES [26] Size Bus No. [kVAr] 24 1500 17 750 4 450 --------Total kVAr =2700

PSO [18] Size Bus No. [kVAr] 19 781 22 803 20 479 --------Total kVAr =2063

FA [28] Bus Size No. [kVAr] 19 600 22 900 20 450 --------Total kVAr =1950

Proposed Size Bus No. [kVAr] 19 900 22 900 20 150 --------Total kVAr =1950

Table 9. Summary of Results of 34-Bus Radial Distribution System Items Real Power Loss (kW) Cost of Energy Loss ($/Year) Net Savings ($/Year) Loss Reduction (%) Cost Saving (%) VDI Time in seconds

Base Case 221.72 37,248 ---------0.0027 ----

Heuristic [10] 168.47 -------24.01 ----------

673

FES [26] 168.98 ------23.78 ----------

Compensated PSO FA [18] [28] 168.8 169.04 ----29,103 ---8,145 23.86 23.75 ---21.86 ----0.00014 ----8.32

Proposed 168.92 29,083 8,165 23.81 21.92 0.00017 4.61

Bus Voltage (p.u)

N. Gnanasekaran, et al.

1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Bus Number Before Placement

After Placement

Figure 6. Voltage profile before and after capacitor placement for 34-bus system The voltage profiles of the system before and after capacitor placement for 34-bus system are shown in Figure 6. The minimum voltage, before and after compensation is obtained as 0.9417 p.u. and 0.9492 p.u. at bus 27. It is observed that there is a significant increase in votages of buses from 17 to 27 and a little effect on buses from 13 to 16. This is because, all the three capacitors are placed at the candidate nodes 19, 20 and 22 which are in the same lateral feeder with bus numbers 17 to 27. From table-9 it is found that the total real power loss before and after capacitor placement are 221.72 kW and 168.92 kW respectively. The power loss obtained with the proposed method is less than the FES method [26] and FA method [28]. It is almost same as Heuristic method [10] and PSO method [18]. But the total kVAr requirement is less than all other methods except FA method. It is observed that the VDI is reduced from 0.0027 to 0.00017. D. 85-Bus Test System: The fourth test case of the proposed method is an 85-bus radial distribution system [29]. The system voltage rating is 11kV. The rank bus vector of 85-bus system contains set of sequence of 71 buses given as { 8, 58, 7, 27, 25, 29, 34, 30, 60, 26, 64, 68, 10, 52, 28, 35, 57, 11, 48, 69, 31, 67, 12, 44, 80, 9, 73, 32, 61, 45, 33, 63, 41, 13, 62, 38, 83, 40, 46, 53, 70, 81, 75, 50, 78, 54, 55, 76, 39, 85, 24, 51 , 49, 37, 71, 79, 14, 43, 74, 84, 65, 15, 72, 66, 59, 42, 56, 47, 36, 82 and 77}.The top four buses 8,58,7 and 27 are selected as optimal candidate locations. From table-10 it is noticed that the amount of kVAr injected at buses 8, 58, 7 and 27 are 600, 600, 150 and 900 kVAr respectively. The total kVAr requirement of the system is 2250 which is lesser than the other methods. The voltage profiles of the system before and after capacitor placement for 85-bus system are shown in Figure 7. The minimum voltage, before and after compensation is found as 0.8714 p.u. and 0.9136 p.u. at bus 54. From table-11 it is found that the total real power loss before and after capacitor placement are 315.72kW and 163.22kW respectively. The power loss obtained with the proposed method is slightly less than the PSO [18] and FA [28] methods. It is found that the VDI is reduced from 0.0530 to 0.0187. Table 10. Comparison of Capacitor values of 85-Bus Radial Distribution System PSO[18] Bus No. Size[kVAr] 8 796 58 453 7 314 27 901 Total kVAr =2464

FA [28] Bus No. Size[kVAr] 8 600 58 600 7 600 27 600 Total kVAr =2400

674

Proposed Bus No. Size[kVAr] 8 600 58 600 7 150 27 900 Total kVAr =2250

Maximum Cost Saving Approach for Optimal Capacitor Placement

Table 11. Summary of Results of 85-Bus Radial Distribution System Compensated Items

Base Case

Real Power Loss (kW) Cost of Energy Loss ($/Year) Net Savings ($/Year) Loss Reduction (%) Cost Saving (%) VDI Time in seconds

PSO[18] 163.32 --------48.27 --------

315.72 53,040 -----0.0530 ----

FA [28] 165.29 32,297 20,743 47.64 39.10 0.0203 8.78

Proposed 163.22 28,324 24,716 48.30 46.59 0.0187 7.78

Bus Voltage (p.u)

1.05

1.00 0.95 0.90 0.85 0.80 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85

Bus Number Before Placement

After Placement

Figure 7. Voltage profile before and after capacitor placement for 85-bus system 7. Conclusion A Modified Artificial Bee Colony algorithm based method for optimal capacitor placement in a radial distribution system is proposed. Simulation results show the advantage of this approach over the previous methods. The objective was to minimize the total cost (cost of real power losses, cost of and shunt capacitors to be installed) while satisfying the constraint. Through Modified Artificial Bee Colony method of optimization, the combination of the global exploration and local search gets to better balance avoiding the optimization to be got into the local best value. Compared with previous studies the proposed method utilizes a wider search space which leads to better optimization. Capacitor values have been taken as a discrete variable is an added advantage. The number of candidate nodes for each system is decided to have less number of locations which offers maximum saving in cost of capacitors. The computation time of proposed method is less than the Firefly Algorithm based method. This method is useful for capacitor placement of existing systems and planning for future expansion. Thus, a two-stage methodology of finding optimum nodes and selecting the optimal size of shunt capacitors to minimize total real power loss and maximize cost saving has been presented. The bus voltages are also improved substantially. 8. References [1]. S.F Mekhamer, M.E.El-Hawary, M.M.Mansour, M. A. Moustafa, S. A. Soliman, “State of the art in optimal capacitor allocation for reactive power compensation in distribution feeders” IEEE Proceedings of the 2002 Large Engineering Systems Conference on Power Engineering, pp.61-75 [2]. H.N.Ng, M.M.A.Salama, and A.Y.Chikhani, “Classification of capacitor allocation techniques,” IEEE Trans.Power Delivery, vol.15, no.1, pp.387-392, Jan.2000. [3]. N.M.Neagle, D.R.Samson, “Loss reduction from capacitors installed on primary feeders,” AIEE Trans. vol.75, pp.950-959, Oct.1956.

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[23]. R. Srinivasa Rao, “Capacitor placement in radial distribution system for loss reduction using artificial bee colony algorithm,” World Academy of Science, Engineering and Technology 68, 2010, pp.288-292. [24]. Ching-Tzong Su and Chih-Cheng Tsai, “A New Fuzzy- Reasoning Approach to Optimum Capacitor Allocation for Primary distribution Systems,” proceedings of IEEE International Conference on Industrial Technology, 1996, pp.237-241. [25]. M.H.Haque, “Capacitor Placement in Radial Distribution Systems for Loss Reduction,” IEE Proceedings, Generation, Transmission and Distribution, Vol.146, issue: 5, pp.501505, Sep.1999. [26]. H.N.Ng, M.M.A. Salama and A.Y.Chikhani, “Capacitor Allocation by Approximate Reasoning: Fuzzy Capacitor Placement,” IEEE Trans. Power Delivery, vol. 15, no.1, pp. 393-398, Jan. 2000. [27]. M. E Baran and F. F. Wu, “Optimal Sizing of Capacitors Placed on a Radial Distribution System,” IEEE Trans. Power Delivery, vol. no.1, pp.1105-1117, Jan. 1989. [28]. X. S Yang, “Firefly Algorithm, Stochastic Test Functions and Design Optimisation,” Int. J. Bio-Inspired Computation, vol. 2, no. 2, pp.78-84. March 2010. [29]. D.Das, D. P. Kothari, and A. Kalam, “Simple and efficient method for load flow solution of radial distribution networks,” Electrical Power & Energy Systems, vol. 17. no.5, pp 335-346, 1995. N. Gnanasekaran received B.E degree in Electrical and Electronics Engineering from Annamalai University, India, in 1998 and M.E degree in Power System Engineering from Anna University, Chennai, India, in 2005. Presently he is an Associate Professor in Department of Electrical and Electronics Engineering, Misrimal Navajee Munoth Jain Engineering College, Chennai, India. He is a Research Scholar of Anna University, Chennai, India. His areas of interest include Electrical Machines, Electric Power Distribution Systems and Power System Operation and Control.

S. Chandramohan was born in 1969 and received his B.E in Electrical and Electronics Engineering and M.E [Power Systems] from Madurai Kamaraj University, Madurai, India, in 1991 and 1992 respectively. He received his Ph.D in Power System from Anna University, Chennai, India. He is currently working as Professor in Electrical and Electronics Engineering Department, College of Engineering, Guindy, Anna University, Chennai, India. He is the Director for Anna University - Ryerson University Urban Energy Centre .He has published number of technical papers in international and national journals and conferences. His areas of interests are Deregulation in Power System and Renewable Energy Management Systems.

T. D. Sudhakar received the B.E. degree in Electrical and Electronics Engineering from Madras University, Chennai, India, in 2001, M.E. and Ph.D. degree in Power System Engineering from Anna University, Chennai, India, in 2004 and 2012, respectively. He is currently working as a Professor in St. Joseph's College of Engineering, Chennai, India. He has published more than 50 research papers in referred journals and conference proceedings in the area of power system and power electronics. His research interests are in the field of network reconfiguration, capacitor placements and grid connected network. He has received many state level awards for his research activities.

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P. Sathish kumar received B.E degree from Thiagarajar College of Engineering, Madurai, India, in 2011. He was a post graduate student of Power System Engineering, College of Engineering, Guindy, Anna University, Chennai, India. His areas of interest include Electric Power Distribution System Automation and Power System Operation and Control.

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