Maximum Cost Saving Approach for Optimal Capacitor Placement … · 2016-01-30 · International Journal on Electrical Engineering and Informatics - Volume 7, Number 4, Desember 2015

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. Chandramohan

2, T. D. Sudhakar

3, and P. Sathish Kumar

4

1Misrimal Navajee Munoth Jain Engineering College, Chennai-600 097, India

2,4Anna University, Chennai-600 025, India

3St. 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 I2R 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 16

th, 2015

DOI: 10.15676/ijeei.2015.7.4.10 665

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.

Figure 1. Sample radial distribution system

A sample radial distribution system is shown in Figure 1. The real power loss in the k

th

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] =(Peff

2[k]

+Q eff2

[k])R[k]

(v[q])2 (1)

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 Qeff 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).

p

Rk+jXk

Peff(k)+jQeff(k)

Pq+jQq

q

r

s

Ps+jQs

Pr+jQr

N. Gnanasekaran, et al.

666

∂Plineloss

∂Qeff|

[q]=

(2∗Qeff[k]∗R[k])

(V[q])2 (2)

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 (3)

Minimize = KePLT + ∑ [Kcf + Ci]NCi=1 (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 = √∑(Vi −ViLim )

2

N

NVBi=1 (6)

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:

∑ QciNCi=1 ≤ QT (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 Pi of selecting a food source

‘i’ by the onlooker is determined using the following expression:

Pi = fiti

∑ fitnSNn=1

(8)

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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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 vi

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

solution xi, for the scout bees using the following equation;

xij = minj + ran(0,1) ∗ (maxj − minj)

14. Store the best solution achieved so for.

15. Increment cycle.

16. If cycle < maximum number of cycles, go to step 8, otherwise go to step 17.

17. Calculate and display VDI, power loss, bus voltages and optimum cost for the global

solution.

18. 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 150 300 450 600 900 1200

Cost $ 750 975 1140 1320 1650 2040

Table 2. Available Capacitor Sizes and Costs/Year Size [kVAr] 150 300 450 600 900 1200

Cost [$] 750 975 1140 1320 1650 2040

Cost[$/Year] 75 97.5 114 132 165 204

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].

Figure 2. 10-Bus radial distribution system

8 10 9 7 6 5 4 1 2 3


670

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

Node

No. Base Voltage Norm[i]={V[i]/0.95}

Rank Bus Vector

(Candidate Nodes)

0.102933 4 0.9634 1.0141 ---

0.098042 6 0.9172 0.9654 6

0.086376 5 0.9480 0.9978 5

0.081138 9 0.8587 0.9038 9

0.057603 10 0.8375 0.8815 10

0.038347 8 0.8890 0.9357 8

0.020795 7 0.9072 0.9549 7

0.019794 2 0.9929 1.0451 ---

0.002023 3 0.9874 1.0393 ---

Table 4. Comparison of Capacitor values of 10-Bus Radial Distribution System Fuzzy Reasoning(FR)

[24]

PSO

[18]

Firefly Algorithm(FA)

[28]

Proposed

Bus No. Size[kVAr] Bus No. Size[kVAr] Bus No. Size[kVAr] Bus No. Size[kVAr]

4 1050 6 1174 6 1200 6 1200

5 1050 5 1182 5 1200 5 1200

6 1950 9 264 9 300 9 450

10 900 10 566 10 300 10 150

Total kVAr =4950 Total kVAr =3186 Total kVAr =3000 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 Compensated

FR [24] PSO [18] FA [28] Proposed

Real Power Loss (kW) 783.77 704.88 696.21 693.95 693.93

Cost of Energy Loss ($/Year) 1,31,673 ---- ---- 1,17,586 1,17,577

Net Savings ($/Year) --- ---- ---- 14,087 14,096

Loss Reduction (%) --- 10.06 11.17 11.45 11.46

Cost Saving (%) --- ---- ---- 10.69 10.70

VDI 0.0526 ---- ---- 0.0331 0.0334

Time in seconds ---- ---- ---- 3.98 1.52


671

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.

Figure 4. 15-Bus radial distribution system

Table 6. Comparison of Capacitor values of 15-Bus Radial Distribution System Method Proposed

in [25] PSO[18]

Firefly Algorithm(FA) [28] Proposed Method

Bus No. Size[kVAr] Bus No. Size[kVAr] Bus No. Size[kVAr] Bus No. Size[kVAr]

3 805 3 871 3 900 3 900

6 388 6 321 6 300 6 300

Total kVAr =1193 Total kVAr =1192 Total kVAr =1200 Total kVAr =1200


Items Base Case

Compensated

Method Proposed

in [25] PSO [18] FA [28] Proposed

Real Power Loss (kW) 61.79 32.60 32.70 32.86 32.86

Cost of Energy Loss ($/Year) 10,380 ---- ---- 5,983 5,983

Net Savings ($/Year) --- ---- ---- 4,397 4,397

Loss Reduction (%) --- 47.24 47.07 46.81 46.81

Cost Saving (%) --- --- ---- 42.36 42.36

VDI 0.0019 --- ---- 0 0

Time in seconds ---- ---- ---- 5.27 3.55

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1 2 3 4 5 6 7 8 9 10B

us

Vol

tage

(p.u

)Bus Number

Before Placement After Placement

1 2 4 3 5

6

7 8

9

1

0

1

1 1

2 1

3

1

4

Substatio

n 1

5


672


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] FES [26] PSO [18] FA [28] Proposed

Bus No. Size

[kVAr] Bus No.

Size

[kVAr] Bus No.

Size

[kVAr]

Bus

No.

Size

[kVAr] Bus No.

Size

[kVAr]

26 1400 24 1500 19 781 19 600 19 900

11 750 17 750 22 803 22 900 22 900

17 300 4 450 20 479 20 450 20 150

4 250 ----- ----- ----- ----- ----- ----- ----- -----

Total kVAr =2700 Total kVAr =2700 Total kVAr =2063 Total kVAr =1950 Total kVAr =1950


Items Base Case

Compensated

Heuristic [10]

FES [26]

PSO [18]

FA [28]

Proposed

Real Power Loss (kW) 221.72 168.47 168.98 168.8 169.04 168.92

Cost of Energy Loss ($/Year) 37,248 ----- ---- ----- 29,103 29,083

Net Savings ($/Year) ---- ---- ---- ---- 8,145 8,165

Loss Reduction (%) ---- 24.01 23.78 23.86 23.75 23.81

Cost Saving (%) ---- ---- ---- ---- 21.86 21.92

VDI 0.0027 ---- ---- ----- 0.00014 0.00017

Time in seconds ---- ---- ---- ----- 8.32 4.61

0.910.920.930.940.950.960.970.980.991.001.01

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15B

us V

olta

ge (p

.u)

Bus NumberBefore Placement After Placement


673


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] FA [28] Proposed

Bus No. Size[kVAr] Bus No. Size[kVAr] Bus No. Size[kVAr]

8 796 8 600 8 600

58 453 58 600 58 600

7 314 7 600 7 150

27 901 27 600 27 900

Total kVAr =2464 Total kVAr =2400 Total kVAr =2250

0.910.920.930.940.950.960.970.980.991.001.01

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

Bu

s V

olt

ag

e (p

.u)

Bus NumberBefore Placement After Placement


674


Items Base Case Compensated

PSO[18] FA [28] Proposed

Real Power Loss (kW) 315.72 163.32 165.29 163.22

Cost of Energy Loss ($/Year) 53,040 ----- 32,297 28,324

Net Savings ($/Year) --- ----- 20,743 24,716

Loss Reduction (%) --- 48.27 47.64 48.30

Cost Saving (%) -- -- 39.10 46.59

VDI 0.0530 ---- 0.0203 0.0187

Time in seconds ---- ---- 8.78 7.78


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

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0.80

0.85

0.90

0.95

1.00

1.05

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

Bu

s V

olt

age (

p.u

)

Bus Number

Before Placement After Placement


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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.


677

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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