ABSTRACT

A simple and efficient method for solving radial distribution networks is

presented. The proposed method involves only the evaluation of a simple

algebraic expression of receiving-end voltages. Computationally, the proposed

method using fuzzy logic is very efficient. The effectiveness of the proposed

method is demonstrated using some examples.

1. INTRODUCTION

Radial distribution systems are

typically spread over large areas and are responsible for a significant portion

of total power losses. Reduction of total power loss in distribution system is

very essential to improve the overall efficiency of power delivery. This can be

achieved by placing the optimal value of capacitors at proper locations in

radial distribution systems. Capacitors are installed at strategic locations to

reduce the losses and to maintain the voltages within the acceptable limits.

Application of shunt capacitors to the

primary distribution feeders is a common practice in most of the countries. The

advantages anticipated include boosting the load level of the feeder

so that additional loads can be carried by the feeder for the same maximum

voltage drop, releasing a certain kVA at the substation that can be used to

feed additional loads along other feeders and reducing power and energy losses

in the feeder.

2. OBJECTIVE

The objective of the capacitor

placement problem is to determine the locations and sizes of the capacitors so

that the power loss is minimized and annual savings are maximized.

Although some of these methods to solve

capacitor allocation problem are efficient, their efficiency relies entirely on

the goodness of the data used. Fuzzy logic provides a remedy for any lack of

uncertainty in the data. Fuzzy logic has the advantage of including heuristics

and representing engineering judgments into the capacitor allocation

optimization process.

3.

General description of Distribution System:

Distribution system is that part of the electric power system which connects the high voltage

transmission network to the low voltage consumer service point.

In any distribution system the power is distributed to

various uses through feeders, distributors and service mains. Feeders are conductors of large current carrying

capacity which carry the current in bulk to the feeding points. Distributors

are conductors from which the current is tapped of for the supply to the

consumer premises.

3.1 Basic Distribution Systems

There are two basic structures for distribution system

namely

(i) Radial distribution system

(ii) Ring main distribution system

(i) Radial distribution system:

If the distributor is connected to the supply

system on one end only then is system is said to be a radial distribution

system. In such a case the end of the distributor nearest to the generating station would be

heavily loaded and the consumers at the distance end of the distributor would

be subjected to large voltage variations as the load varies. The consumer is

dependent upon a single feeder so that a fault on any feeder or distributor

cuts off the supply to the consumers who are on the side of fault away from the

station.

(ii) Ring Main Distribution System:

Ring main employs a feeder which

covers the whole area of supply finally returns to the generating station. The

feeder is closed on itself. This arrangement is similar to two feeders in

parallel on different buses.

3.2

Distribution System

Losses

It has been established that 70% of the total losses occur in the primary and

secondary distribution system, while transmission and sub transmission lines

account for only 30% of the total losses. Distribution losses are 15.5% of the

generation capacity and target level is 7.5%. Therefore the primary and

secondary distribution must be properly planned to ensure losses within the

acceptability limits.

3.2.1

Factors Effecting

Distribution System Losses

1. Inadequate size of conductor,

2. Feeder Length,

3. Location of

Distribution Transformers,

4. Low Voltage,

5. Use of over rated

Distribution transformers,

6. Poor workmanship in fittings,

7. Low Power Factor

3.2.2.

Reduction of line losses:

The losses in Indian power system are on the higher side. So, the government of

India has decided to reduce the line losses and set a target for reduction of

T&D losses by 1% per annum in order to realize an overall reduction of 5%

in the national average.

Methods for the

reduction of line losses:

The following methods are adopted for reduction of distribution losses.

(1) HV distribution system ,

(2) Feeder reconfiguration,

(3) Reinforcement of the feeder

(4) Grading of conductor ,

(5) Construction of new substation,

(6) Reactive power compensation

(7) Installing Voltage regulators.

It is universally acknowledged that the voltage reactive

power control function plays a vital role in the distribution automation. The problem of reactive power compensation can be attempted

by providing static capacitors. The present practice to compensate reactive power component

is to increase reactive power by increasing the terminal voltage of the

generator or by increasing the field current of the synchronous machine

in condenser mode at generating stations. An alternate method for compensating

the reactive power is the use capacitors in distribution systems at customer

points.

There are two methods in capacitor compensation. They are

1. Series compensation. (Capacitors

are placed in series with line)

2. Shunt compensation. (Capacitors

are placed in parallel with load)

The fundamental function of capacitors whether they are in

series or in shunt in a power system is to generate reactive power to improve

power factor and voltage, there by enhancing the system capacity and reducing

losses. In series capacitors the reactive power is proportional to the square

of the load current where as in shunt capacitors it is proportional to the

square of the voltage.

For the capacitor placement problem,

approximate reasoning is employed in this manner:

For

example: It is intuitive that a section in a distribution system with high

losses and low voltage is highly ideal for placement of capacitors; whereas a

low loss section with good voltage is not. Note that the terms, high and

low are linguistic descriptors which cannot be used to define rules in a

conventional ES.

4. Framework of Approach

Fig:-

Framework of Fuzzy Allocation System

4.1. FES IMPLEMENTATION

The FES contains a set of rules which are

developed from qualitative descriptions. In a FES, rules may be fired with some

degree using fuzzy inferencing; whereas, in a conventional ES, a rule is either

fired or not fired. For the capacitor allocation problem, rules are defined to

determine the suitability of a node for capacitor installation. Such rules are

expressed in the following form:

IF premise (antecedent), THEN conclusion

(consequent)

For determining the suitability

of capacitor placement at a particular node, a set of multiple-antecedent fuzzy

rules have been established. The inputs to the rules are the voltage and power

loss indices, and the output consequent is the suitability of capacitor

placement. The rules are summarized in the fuzzy decision matrix.

4.2 Selection of buses for capacitor placement using fuzzy

By invoking

the instruction fuzzy we got display of the fuzzy inference system (FIS) at the

top of window which shows the inputs, outputs and a central fuzzy rule processor.

In this case, the inputs are

1. Power Loss Index (PLI)

2. Nodal Voltage

The central

fuzzy rule processor contains the rules. The output is capacitor suitability

index (CSI) which indicates the location suitability for capacitor placement.

4.3 The input calculations

1. PLI : The power losses at all buses are calculated

and normalized between 0 and 1 such that, minimum power loss is zero and max

power loss is 1.

The formula is

2. Nodal

Voltage

The

per-unit nodal voltage is calculated from the load flow problem. The voltages

will be generally in range of 0.9 to 1.1.

4.3.1 Assigning of membership

functions

1. PLI The range of

this PLI is between 0 and 1. Triangular membership functions are assigned as

shown below

2. Nodal Voltage

The range of this is between 0.9 and 1.1. The combination of triangular

and trapezoidal membership functions are selected as shown in the figure

3. The Output (CSI)

The range of this is between 0 and 1. Triangular membership functions

are assigned shown below

4.3.2 DECISION MATRIX

4.3.3 RULE BASE

The rules defined in the fuzzy decision matrix are:

1.If

power loss is low and voltage is low then suitability is low- medium

2. If

power loss is low and voltage is low normal then suitability is low medium.

Etc.,

5.

CASE STUDY:

Case

Study Results of 15 Bus System

Capacitor Locations using FUZZY LOGIC

BUS

NO

PLI

VOLTAGE

CSI

NODE

SELECTED

2

0

0.9713

0.0940

———

3

0.3205

0.9567

0.3318

———

4

0.9602

0.9509

0.7500

4

5

0.1742

0.9499

0.2500

———

6

0.8000

0.9582

0.7500

6

7

0.8353

0.9560

0.7500

7

8

0.3267

0.9570

0.3370

———

9

0.1671

0.9680

0.2287

———

10

0.0313

0.9669

0.1972

———

11

0.9865

0.9500

0.7500

11

12

0.4612

0.9458

0.4505

———

13

0.2255

0.9445

0.2500

———

14

0.4119

0.9486

0.4051

———

15

1.0000

0.9484

0.7500

15

Here the candidate buses are selected based

on the CSI value. In this case CSI value is considered to be 0.75. Now the

buses 4,6,7,11,15 are selected as the candidate buses for minimum losses.

Voltage Profiles (before and after

compensation) at the Candidate Buses:

i)

At Bus 4

ii)

At

Bus 6

iii)

At Bus 7

iv)

At

Bus 11

v)

At

Bus 15

6. CONCLUSIONS

By implementing fuzzy logic the

optimal capacitor locations are determined for maximum loss reduction by using

matlab program. For identifying the bus locations for maximum loss reduction

are obtained using MATLAB in distribution systems. The results of the proposed

methods are almost identical and even better results are obtained with these

methods.

7. REFERENCES

1. S. Ghosh

and D. Das :”Method for load-flow solution of radial distribution networks”,

IEE proc-vol. 146,no 6,pp. 641-648, November,1999.

M.H.Haque,”

Capacitor placement in radial distribution systems for loss reduction”

IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5,

September 1999V.K. Mehta, Rohit Mehta “principles

of power systems”, S.Chand & company Ltd, New Delhi,1st edn,1982.S.Rajasekaran,G.A.Vijayalakshmi

pai,”Neural Networks,Fuzzy logic and Genetic algorithms”,PHI

publications,New delhi,2005P.V. Prasad ,

S. Sivanagaraju and

N.Sreenivasulu,” A FUZZY-GENETIC

ALGORITHM FOR OPTIMAL CAPACITOR PLACEMENT IN RADIAL DISTRIBUTION SYSTEMS”, ARPN Journal VOL. 2,

NO. 3, JUNE 2007 IS.M.Amirthavalli,”Fuzzy

logic and neural networks”,scitech publications,Hyderabad,2nd

edn,2007