Optimal Capacitor Placement Using Fuzzy Logic

Published Date: 02 Nov 2017

5.1 INTRODUCTION

The power supplied from electrical distribution system is composed of both active and reactive components. Overhead lines, transformers and loads consume the reactive power. So voltage/VAr control is an essential measure to reduce the power losses through the switching operations of capacitors and load tap changing transformers. Reactive power compensation plays an important role in the planning of an electrical system. A proper control of the reactive power will improve the voltage profile, reduces the system losses and improves the system efficiency. Proper generation and control of reactive power is important for maintaining the network voltages under normal and abnormal conditions and to reduce system losses. The system voltage collapse due to lack of global control of reactive power flow during crucial contingencies is emerging as a serious problem. The aim is principally to provide an appropriate placement and sizing of the compensation devices to ensure a satisfactory voltage profile while minimizing the cost of compensation.

Mainly capacitors are used to develop reactive power near the point of consumption. Series and shunt capacitors in a power system generate reactive power to improve power factor and voltage, thereby enhancing the system capacity and reducing the losses. Due to various limitations in the use of series capacitors, shunt capacitors are widely used in distribution systems. The general capacitor placement problem is formulated as an optimization problem to determine the location of capacitors, the types and size of capacitors to be installed and the control scheme for the capacitors at the buses of radial distribution networks.

Several methods of loss reduction by placing capacitors in distribution systems have been reported over the years. The early approaches to this problem include those using analytical methods, heuristic methods, artificial intelligence methods and those using dynamic programming technique to include the discrete nature of the capacitor size. Baran and Wu [18] have proposed an analytical method based on mixed integer programming to find the optimal size of capacitor to reduce the losses of a radial distribution system. Haque [51] has proposed a method of minimizing the loss associated with the reactive component of branch currents by placing capacitors at proper locations. The method first finds the location of the capacitor in a sequential manner. Once the capacitor locations are determined, the optimal capacitor size at each selected location is determined by optimizing the loss saving equation.

More recently, the use of various non-deterministic methods like tabu search, genetic algorithms, fuzzy expert system and simulated annealing to determine the location and size of capacitor to improve the voltage profile of the system have been reported. Mekhamer et al. [73] have proposed a method to select an optimal location of capacitors using fuzzy logic and its allocation by analytical method. Ng et al. [40] presents a methodology to convert the analytical method stated in Salama and Chikani [28] from crisp solution into fuzzy solution by modeling the parameters using possibility distribution function, thus accounting for the uncertainties in these parameters.

Prasad et al. [102] have presented a genetic approach to determine optimal size of capacitor. The optimal location to install capacitor is determined by taking values of Power Loss Indices randomly. Power loss indices are calculated by compensating the self-reactive power at each bus and run the load flows to determine the total active power losses in each case. Most of the previous studies [30, 31, 45, 57, 64, 124] have presented a method to find the location and size of capacitors using heuristic, genetic, simulated annealing techniques.

In this chapter, a method is proposed to determine the optimal location of capacitors using fuzzy expert system by considering power loss indices and voltage at each bus simultaneously and size of the capacitor by an index based method to obtain good results without violating the voltage constraints. This method has the versatility of being applied to the large distribution systems and having any uncertain data. The proposed method is tested with different radial distribution systems.

The mathematical formulation of the proposed method is explained in Section 5.2. In this Section, the objective function and its constraints are defined. The identification of sensitive bus for capacitor placement using fuzzy logic is described in Section 5.3. Also this Section explains the calculation of Power Loss Index and implementation aspects of Fuzzy Expert System (FES) to identify sensitive bus to place capacitor. The effectiveness of the proposed FES is tested with one example and the results are presented in Section 5.4. The size of the capacitor using Index based method is explained in Section 5.5. In Section 5.6, algorithm to be followed to obtain optimal location and size of capacitor are presented. The effectiveness of the proposed method is tested with different examples of distribution system and the results obtained are compared with the results of existing methods. In Section 5.7, conclusions of the proposed method are presented.

5.2 MATHEMATICAL FORMULATION

The objective function is to maximize the net savings function (F) by placing the proper size of capacitors at suitable locations is formulated as:

… (5.1)

where

F = net savings (`.)

Plr = Reduction in power losses due to installation of capacitor

= (Power loss before installation of capacitor - Power loss after

installation of capacitor)

Ke = Cost of energy in `./kWh

= Installation cost in `.

= Total number of capacitor buses

QC = total size of capacitor

KC = Capital cost of each capacitor

λ = rate of annual depreciation and interest charges of capacitor

5.2.1 Constraints

The objective function is subjected to the following constraints

The voltage at each bus should lie within the voltage limits.

Vmin.≤Vi≤Vmax. i=1,2, …..no. of buses

The size of the capacitor to be installed at suitable bus is less than the total reactive load of the system.

where nbus= total number of buses

5.3 IDENTIFICATION OF SENSITIVE BUS FOR CAPACITOR PLACEMENT USING FUZZY LOGIC

The fuzzy logic is used to identify the optimal location to place the capacitor in a radial distribution system so as to minimize the losses while keeping the voltage at buses within the limit and also by taking the cost of the capacitors in to account.

The Fuzzy Expert System (FES) contains a set of rules, which are developed from qualitative descriptions. In a FES, rules may be fired with some degree using fuzzy inference, where as in a conventional Expert System, a rule is either fired or not fired. For the capacitor placement problem, rules are defined to determine the suitability of a bus for capacitor placement. Such rules are expressed in the following general form:

If premise (antecedent), THEN conclusion (Consequent)

For determining the suitability of a particular bus for capacitor placement at a particular bus, sets of multiple-antecedent fuzzy rules have been established. The inputs to the rules are the bus voltages in p.u., power loss indices, and the output consequent is the suitability of a bus for capacitor placement.

5.3.1 Procedure to calculate power loss index

The Power Loss Index at ith bus, PLI (i) is the variable which is given to fuzzy expert system to identify suitable location for the capacitor.

Step 1 : Read radial distribution system data

Step 2 : Perform the load flows and calculate the base case active power loss

Step 3 : By compensating the reactive power injections (Qc) at each bus (except

source bus)and run the load flows, and calculate the active power loss in

each case.

Step 4 : Calculate the power loss reduction and power loss indices using the following

equation

… (5.2)

where

X(i) = loss reduction at ith bus

Y = minimum loss reduction

Z = maximum loss reduction

nbus = number of buses

Step 5 : Stop

5.3.2 Implementation aspects of Fuzzy expert system to identify the sensitive bus

The power loss indices and bus voltages are used as the inputs to the fuzzy expert system, which determines the buses which are more suitable for capacitor installation. The power loss indices range varies from 0 to 1, the voltage range varies from 0.9 to 1.1 and the output [Capacitor Suitability Index (CSI)] range varies from 0 to 1. These variables are described by five membership functions of high, high-medium/normal, medium/normal, low-medium/normal and low. The membership functions of power loss indices and CSI are triangular in shape, the voltage is combination of triangular and trapezoidal membership functions. These are graphically shown in Figs. 5.1 to 5.3.

0 0.2 0.4 0.6 0.8 1.0

Power Loss Index

1.0

0.8

0.6

0.4

0.2

0

Degree of Membership

Low-Med

Med

Hi-Med

High

Low

1.0

0.8

0.4

0.2

0.0

Degree of membership

Lo-Norm

Low

Norm

Hi-Norm

High

0.0 0.92 0.94 1.0 1.04 1.06 1.1

Voltage (p.u.)

Fig. 5.1 Power loss index membership function

Fig. 5.2 Voltage membership function

Low-Med

Med

Hi-Med

High

Low

0 0.2 0.4 0.6 0.8 1.0

Capacitor Suitability Index

1.0

0.8

0.6

0.4

0.2

0

Degree of Membership

Fig. 5.3 Capacitor suitability index membership function

For the capacitor placement problem, rules are defined to determine the suitability of a bus for capacitor installation. For determining the suitability for capacitor placement at a particular bus, a set of multiple antecedent fuzzy rules have been established. The rules are summarized in the fuzzy decision matrix in Table 5.1. The consequent of the rules are in the shaded part of the matrix.

And

Voltage

Low

Low-

Normal

Normal

High-Normal

High

Power Loss Index

(PLI)

Low

Low-Med.

Low-Med.

Low

Low

Low

Low-

Med.

Med.

Low-Med.

Low-Med.

Low

Low

Med.

High- Med.

Med.

Low-Med.

Low

Low

High-Med.

High-Med.

High-Med.

Med.

Low-Med.

Low

High

High

High-Med.

Med.

Low-Med.

Low-Med.

Table 5.1 Decision matrix for determining suitable capacitor locations

After the FES receives inputs from the load flow program, several rules may fire with some degree of membership. The fuzzy inference methods such as Mamdani max-min and max-prod implication methods [34] are used to determine the aggregated output from a set of triggered rules.

A final aggregated membership function is achieved by taking the union of all the truncated consequent membership functions of the fired rules. For the capacitor placement problem, resulting capacitor suitability index membership function, s, of bus i for ‘m’ fired rules is

… (5.3)

Where PLI and v are the membership functions of the power loss index and p.u. voltage level respectively.

Once the suitability membership function of a bus is calculated, it must be defuzzified in order to determine the buses suitability ranking. The centroid method of defuzzification is used; this finds the center of area of the membership function. Thus, the capacitor suitability index is determined by:

… (5.4)

5.3.3 Illustration of FES for a sample system

The proposed method is explained with a sample system. Consider a 15 bus system whose single line diagram is shown in Fig. 2.3. The line and load data of this system is given in Appendix – A (Table A.1). After performing the load flows for base case, the total active power loss and minimum voltage is given as 61.7993 kW and 0.9445 p.u.

Considering one bus at a time, every bus is compensated with reactive power injection equivalent to that of self reactive load. Now perform the load flows to determine the active power loss, power loss index and the voltage in each case. These are given in Table 5.2.

Table 5.2 Power Loss Index and voltage

Bus No.

Voltage (p.u.)

PLI

Bus No.

Voltage (p.u.)

PLI

1

1.0000

0

9

0.9697

0.3231

2

0.9730

0.1874

10

0.9686

0.2128

3

0.9599

0.4478

11

0.9532

0.9891

4

0.9551

0.9676

12

0.9491

0.5621

5

0.9542

0.3289

13

0.9478

0.3706

6

0.9600

0.8375

14

0.9529

0.5221

7

0.9578

0.8661

15

0.9537

1.0000

8

0.9587

0.4528

The Capacitor Suitability Indices (CSI) of 15 bus system from FES is given in Table 5.3. The most suitable buses for capacitor placement are selected based on the maximum value of CSI of the system and they are 3, 4, 6, 11 and 15.

Table 5.3 Capacitor suitability indices of 15 bus system

Bus No.

CSI

Bus No.

CSI

1

0.0800

9

0.2574

2

0.2407

10

0.2451

3

0.7500

11

0.7500

4

0.7500

12

0.5719

5

0.3371

13

0.3715

6

0.7500

14

0.5301

7

0.4246

15

0.7500

8

0.4336

5.4 PROCEDURE TO CALCULATE CAPACITOR SIZE USING INDEX BASED METHOD

After knowing the optimal locations to place the capacitor, the size of the capacitor can be calculated by using index based method.

… (5.5)

Where

Vi = Voltage at ith bus.

Ip[k], Iq[k] = real and reactive component of current in kth branch.

Qeffectiveload,I = total reactive load beyond ith bus (including Qload at ith bus)

Qtotal = total reactive load of the given distribution system

… (5.6)

where

Qload[i] = local reactive load at ith bus

5.5 ALGORITHM FOR CAPACITOR PLACEMENT AND SIZING USING FES AND INDEX BASED METHOD

Step 1: Read the system input data

Number of buses, number of branches, resistance and reactance of each branch, from bus and to bus of each branch, active and reactive power of each bus.

Base kV, base kVA, tolerance, etc.

Step 2: Run load flow program and calculate the voltage at each bus and

calculate the active power loss before compensation.

Step 3: Run the load flow program by compensating the reactive load at each

bus, considering one bus at a time, and calculate the loss reduction at

each bus.

Step 4: The power-loss reduction indices and the bus voltages are the inputs to

the fuzzy expert system.

Step 5: The outputs of FES, the capacitor suitability index, CSI are obtained

from which the optimal location for the capacitor placement is selected

by considering the maximum value of it.

Step 6: The index vector is determined at selected buses using Eqn.(5.5).

Step 7: Calculate the size of capacitor at selected buses by multiplying the

reactive load at that bus with index vector at that bus (Eqn. (5.6)).

Step 8: Then placing the calculated size of capacitors at best locations conduct

a load flow study.

Step 9: Print the results.

Step 10: Stop

5.6 FLOW CHART FOR OPTIMAL CAPACITOR PLACEMENT USING FES

Read Distribution System line and load data, base kV and kVA, iteration count (IC) =1and tolerance (ε) = 0.0001

Start

Perform load flows and calculate voltage at each bus, real and reactive power losses

Calculate the loss reduction by running load flow by compensating the reactive load at each bus, considering one bus at a time

Calculate power loss reduction indices, PLI using Eqn. (5.2)

Calculate index vector and size of capacitor using Eqns. (5.5) and (5.6)

Select the optimal locations for the capacitor placement by considering the maximum value of CSI

Obtain Capacitor Suitability Index (CSI) from the FES by providing PLI and bus voltages as inputs to the FES

Stop

Compute voltages, angles, power flows, real and reactive power losses and Print the results

Perform load flow by placing the calculated size of capacitors at best locations

Check for convergence

Yes

No

IC=IC+1

Compute bus voltages, real and reactive power losses

Fig. 5.4 Flow chart for optimal capacitor placement using FES

5.7 ILLUSTRATIVE EXAMPLES

The proposed method is tested with four different radial distribution systems having of 15, 33, 34 and 69 buses.

5.7.1 Example – 1

Consider a 15 bus system whose single line diagram is shown in Fig. 2.3. The line and load data of this system is given in Appendix A (Table A.1). The total real power loss and minimum bus voltage before compensation are 61.7993 kW and 0.9445 p.u.

The optimal locations and the size of the capacitors obtained by the proposed method are given in Table 5.4. In addition, voltage at these buses before and after compensation, loss reduction and net savings due to compensation are also given in the same table. The effect of using the nearest standard size capacitors instead of actual size of the capacitors is presented in Table 5.5 and it is observed that the changes in loss reduction and net savings are marginal. The active power loss reduction due to compensation is from 61.7933 kW to 32.1437 kW i.e., a reduction of 47.98% of the original active power loss.

The voltage profile of the system before and after compensation is given in Table 5.6. The minimum voltage is improved from 0.9445 p.u. to 0.9667 p.u. The voltage regulation is improved from 5.55% to 3. 33%. The line flows of the system is given in Table 5.7.

Table 5.4 Capacitor allocation and loss reduction of 15 bus RDS for calculated

size of capacitor

Bus No.

Without capacitor

With capacitor

Voltage (p.u.)

Voltage (p.u.)

Q-Cap (kVAr)

3

0.9567

0.9734

189.7

4

0.9509

0.9739

349.54

6

0.9582

0.9747

292. 65

11

0.9500

0.9761

284.19

15

0.9484

0.9752

278.95

Total size of capacitor

1,395.03

Without capacitor

With capacitor

Improvement

Ploss (kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

61.7933

57.2967

31.8981

24.5325

29.8952

32.7642

Net Saving (`.)

Without Capacitor

With Capacitor

-----

6, 79, 844/-

Table 5.5 Capacitor allocation and loss reduction of 15 bus system for standard

size of capacitor

Bus No.

Without capacitor

With capacitor

Voltage (p.u.)

Voltage (p.u.)

Q-Cap (kVAr)

3

0.9567

0.9765

200

4

0.9509

0.9740

350

6

0.9582

0.9751

300

11

0.9500

0.9742

275

15

0.9484

0.9748

275

Total size of capacitor

1,400

Without capacitor

With capacitor

Improvement

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

61.7933

57.2967

32.1437

24.9865

29.6496

32.3102

Net Saving (`.)

Without Capacitor

With Capacitor

-----

6,74, 695/-

Table 5.6 Voltage profile before and after compensation of 15 bus RDS

Bus No.

Before compensation

After compensation

Voltage magnitude (p.u.)

Angle (deg.)

Voltage magnitude (p.u.)

Angle (deg.)

1

1.0000

0.0000

1.0000

0.0000

2

0.9713

0.0320

0.9835

-0.6516

3

0.9567

0.0493

0.9765

-1.0673

4

0.9509

0.0565

0.9740

-1.2488

5

0.9499

0.0687

0.9730

-1.2372

6

0.9582

0.1894

0.9751

-0.8776

7

0.9560

0.2166

0.9738

-0.9327

8

0.9570

0.2050

0.9738

-0.8625

9

0.9680

0.0720

0.9802

-0.6126

10

0.9669

0.0850

0.9792

-0.5999

11

0.9500

0.1315

0.9742

-1.2571

12

0.9458

0.1824

0.9690

-1.2086

13

0.9445

0.1987

0.9677

-1.1931

14

0.9486

0.0848

0.9717

-1.2218

15

0.9484

0.0869

0.9748

-1.3096

Table 5.7 Line flows of 15 bus system

Bus No.

Before compensation

After compensation

Active power loss (kW)

Reactive power loss (kVAr)

Active power loss (kW)

Reactive power loss (kVAr)

1

37.7019

36.8772

18.2521

17.8528

2

11.2895

11.0426

5.2822

5.1667

3

2.4439

2.3904

1.1573

1.1320

4

0.0554

0.0374

0.0528

0.0356

5

0.4722

0.3185

0.4604

0.3106

6

0.0592

0.0399

0.0577

0.0389

7

5.7680

3.8906

2.8006

1.8890

8

0.3936

0.2655

0.1864

0.1257

9

0.1129

0.0762

0.1091

0.0736

10

2.1763

1.4679

1.0427

0.7033

11

0.6016

0.4058

0.5732

0.3866

12

0.0740

0.0499

0.0705

0.0476

13

0.2049

0.1382

0.1952

0.1317

14

0.4399

0.2967

0.2055

0.1386

The variations of real power loss at each branch and voltage magnitude at each bus with and without compensation are shown in Figs. 5.5 and 5.6 respectively.

Fig. 5.5 Real power loss at each branch of 15 bus RDS with and without

capacitor

Fig. 5.6 Voltages at each bus of 15 bus RDS with and without capacitor

5.7.2 Example – 2

Consider a 34 bus system whose single line diagram is shown in Fig. 5.7. The line and load data of this system is given in Appendix A (Table A.4).The total real power loss and minimum bus voltage before compensation are 221.7210 kW and 0.9417p.u. The capacitor Suitability Index and capacitor sizes (nearest standard size of capacitors to the actual value) at the best suitable buses are given in Table 5.8.

Fig. 5.7 Single line diagram of 34 bus radial distribution system

Table 5.8 CSI and size of capacitor of 34 bus RDS

Bus No.

CSI

Capacitor size (kVAr)

20

0.7500

450

21

0.7500

150

23

0.7500

300

24

0.7500

300

25

0.7500

300

Total size of capacitor

1,500

The summary of results before and after compensation is given in Table 5.9. The comparison of results with existing methods is given in Table 5.10.

Table 5.9 Capacitor allocation and loss reduction for 34 bus system

Bus No.

Without capacitor

With capacitor

Voltage (p.u.)

Voltage (p.u.)

Q-Cap (kVAr)

20

0.9549

0.9684

450

21

0.9520

0.9659

150

23

0.9460

0.9587

300

24

0.9435

0.9555

300

25

0.9423

0.9539

300

Total size of capacitor required

1,500

Without capacitor

With capacitor

Improvement

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

221.7210

65.1093

156.4270

39.8758

65.293

25.2335

Net Saving (`.)

Without Capacitor

With Capacitor

----

16, 05, 926/-

Min. Voltage (p.u.)

0.9417

0.9509

Table 5.10 Comparison of results of 34 bus system with existing methods

Description

Existing method [45]

Existing method [36]

Proposed method

Before compensation

After compensation

Before compensation

After compensation

Before compensation

After compensation

Real power losses (kW)

221.72

168.35

221.72

181.72

221.7210

156.4270

Net saving (`.)

----

12,40,563/-

---

9,65,200/-

----

16,05,926/-

Total size of capacitor required (kVAr)

1550

---

1650

----

1500

---

From Table 5.9 it is observed that, the minimum voltage is improved from 0.9417 p.u. to 0.9509 p.u., total real power loss reduced from 221.7210 kW to 156.4270 kW (i.e., 29.45%) and total reactive power loss reduced from 65.1093 kVAr to 39.8758 kVAr (i.e., 38.76%) due to reactive power compensation. Thus, voltage regulation is improved from 5.83% to 4.91%. From Table 5.10, the size of the capacitor required is 1500 kVAr and the net saving is `.16, 05, 926/- which is comparable with the existing methods.

The variations of real power loss at each branch and voltages at each bus for with and without compensation are shown in Figs. 5.8 and 5.9 respectively.

Fig. 5.8 Real power loss at each branch of 34 bus RDS with and without

capacitor

Fig. 5.9 Voltages at each bus of 34 bus RDS with and without capacitor

5.7.3 Example – 3

Consider a 33 bus system whose single line diagram is shown in Fig. 2.5. The line and load data of this system is given in Appendix - A (Table A.2). The CSI and size of capacitor is given in Table 5.11. The summary of results before and after compensation is given in Table 5.12. From results it is observed that, the minimum voltage is improved from 0.9131 p.u. to 0.9237 p.u. The improvement in voltage regulation is 1.06%. Also, the total real power loss reduces from 202.5022 kW to 145.0658 kW (i.e., 28.36%) and reactive power loss reduces from 135.1286 kVAr to 96.956 kVAr (i.e., 28.25%) after capacitor placement. The net saving is `.14,57,428/-. The variation of real power loss at each branch and voltages at each bus with and without capacitor are shown in Figs. 5.10 and 5.11 respectively.

Table 5.11 CSI and size of capacitor for 33 bus system

Bus No.

CSI

Capacitor size (kVAr)

30

0.9180

1050

Table 5.12 Capacitor allocation and loss reduction for 33 bus system

Description

Without capacitor

With capacitor

Min. Voltage

0.9131

0.9237

Voltage regulation (%)

8.69

7.63

Total real power loss(kW)

202.5022

145.0658

Total reactive power loss(kVAr)

135.1286

96.956

Improvement in real power loss (kW)

157.4364

Improvement in reactive power loss (kVAr)

38.1726

Total capacitor size at bus 30

1050

Net saving (`.)

-----

14,57,428/-

Fig. 5.10 Real power loss at each branch of 33 bus RDS with and without

capacitor

Fig. 5.11 Voltages at each bus of 33 bus RDS with and without capacitor

5.7.4 Example – 4

Consider a 69 bus system whose single line diagram is shown in Fig. 2.6. The line and load data of this system is given in Appendix - A (Table A.3). The CSI and size of capacitor (nearest standard size of capacitor to the actual value) is given in Table 5.13. The summary of results before and after compensation is given in Table 5.14. From results it is observed that, the minimum voltage is improved from 0.9123 p.u. to 0.9341 p.u. The improvement in voltage regulation is 2.18%. Also, the total real power loss reduces from 224.9457 kW to 152.0469 kW (i.e., 32.40%) and reactive power loss reduces from 102.1397 kVAr to 70.485 kVAr (i.e., 30.99%) after capacitor placement. The net saving is `. 20, 65, 298/-.The variation of real power loss at each branch and voltages at each bus with and without capacitor are shown in Figs. 5.12 and 5.13 respectively.

Table 5.13 CSI and size of capacitor for 69 bus system

Bus No.

CSI

Capacitor size (kVAr)

61

0.9200

1350

Table 5.14 Capacitor allocation and loss reduction for 69 bus system

Description

Without capacitor

With capacitor

Min. Voltage

0.9123

0.9341

Voltage regulation (%)

8.77

6.59

Total real power loss(kW)

224.9457

152.0469

Total reactive power loss(kVAr)

102.1397

70.485

Improvement in real power loss (kW)

72.8988

Improvement in reactive power loss (kVAr)

31.6547

Total capacitor size at bus 61

1350

Net saving (`.)

-----

20,65,298/-

Fig. 5.12 Real power loss at each branch of 69 bus RDS with and without

capacitor

Fig. 5.13 Voltages at each bus of 69 bus RDS with and without capacitor

5.8 CONCLUSIONS

A method has been proposed to determine most sensitive buses to place capacitors using fuzzy logic and its size is calculated using index based method in radial distribution systems. The FES considers loss reduction and voltage profile improvement simultaneously while deciding which buses are the most ideal for placement of capacitor. Hence, a good compromise of loss reduction, voltage profile improvement and net saving is achieved when compared to existing methods. The proposed method has been tested on four distribution systems consisting of 15, 33, 34 and 69 buses. It has been noticed that losses are reduced and voltage profile is improved.