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OPTIMAL PLACEMENT OF STATIC VAR COMPENSATORS IN

DISTRIBUTION FEEDERS FOR LOAD BALANCING BY GENETIC

ALGORITHM

M. A. Talebi, A. Kazemi, A. Gholami M. Rajabi

Iran University of Science and Technology Tehran South West Electrical Distribution Company

m_a_taleby@yahoo.com

Abstract:

Unbalanced load is one of the fashionable problems in

distribution systems, which has great unfavorable effects such

as unbalancing in three phase voltages, increase of energy

losses and occupation of feeder capacity. There are two main

sources of unbalanced load, the first ununifored distribution

of the single phase customers and the other, their accidental

and unsimultaneous treatment. For reform load unbalancing

particularly ununiforedness of customers used traditional

methods of customer replacement. But nowadays there is a

novel method that we can balance the load by the reactive

power compensation. Unbalanced load in distribution feeders

has two main features, 1) unbalancing rate is variable

according to the time, 2) it would be dispersion among the

feeder. We can use Static VAR Compensator (SVCs) and so

they will be able to reform this unbalancing according the

specific period of time variation. Therefore if we want to

reform the load unbalancing, according to its dispersion

characteristic, we can use some SVCs among the feeder. In

this paper used an optimal method based on genetic algorithm

for SVCs placement among the feeder for load balancing

during a specific period of time. In addition with this method

a novel algorithm has been used which make a hierarchy of

the priorities in considering the buses. At last, the unbalancetreatment of some real samples of the feeders were studied by

using prepared software which have been done during a week

and effect of SVCs application have been simulated too. The

results of simulation studies show that by using optimally the

SVCs in distribution feeders we can balance the load current

and we are able to decrease considerably unfavorable effects.

Financial analysis shows that this method is optimum from

economical point of view.1-IntroductionUnbalanced loads in distribution system cause many

deficiencies. Actually, amount of load unbalancing

concerned as electrical energy quality index. Ununifored

distribution of the single phase customers among the phases

and accidental and unsimultaneous treatments of the

consumers are the main origins of unbalancing in the low

voltage distribution systems .The main disadvantages of

unbalancing in distribution systems are as follows:

Unbalanced three phase voltage: in spite of balanced

voltage at the beginning of feeder, unbalanced load destroy

voltage profile balancing. The problem disorders in

operation of many consumers, such as induction motor and

reduces their efficiency with heat increment.

Electrical loss increment: it is known that minimum loss in

electrical power transmission requires balanced three phase

currents. Furthermore, in unbalanced state, neutral return

current, intensify the feeder resistive loss in null conductor

and increase copper and iron losses in distribution

transformers.

Network capacity occupancy: in unbalanced load the phase

currents are unequal and one of the amplitudes is bigger

than the others. The maximum capacity of substation or

feeder is based on maximum phase current. Therefore, the

capacity is occupied in spite of free capacity in some

phases.

Null voltages: the return neutral current provides voltage

difference in different points of feeder between earth and

null. This difference depends to neutral current amplitude

and impedance of null conductor which that increases some

phase voltage and decreases others to null.

Accidental and unsimultaneous treatments of consumers

provide dynamic and variable according to the time nature

for load unbalancing. Therefore, load balancing necessitates

a method that determines unbalancing per time and reduces

it to desirable amount. Reactive power compensating is a

suitable process for load balancing that also can improves

load factor.

2-Load balancing with reactive power control [1, 2]

Because one of the unbalanced three phase current

properties is negative and zero component in symmetrical

components, load balancing is based on negative and zero

component elimination. Reactive power compensation

performance is shown with conceptual diagram in fig. 1.

According fig. 1, three phase current and voltage phasors

have measured instantly (on-line) with compensators

sensors and with processing their by compensators

controller, negative and zero components of load current

have determined. Then the compensator has controlled to

inject the same amount of negative and zero components

with 180 degree phase difference to the bus. Its

performance omits and neutralizes the negative and zero

current components and balances the three phase current.

Also the proper control of imaginary part of positive

component, the compensator control and regulate the power

factor of feeder load current. The mentioned procedure can

be applied in specified intervals (e.g. every one hour).

2-1-Load balancing algorithm [1, 2]

Star and delta reactive power compensators are used with

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balancing algorithm. The star compensator is applied to

eliminate the current zero component and control imaginary

part of positive component. The delta type is used for

negative component elimination.

Three phase four wires feeder equipped by both star and delta

compensator is shown in figure 2. The connected load to the

feeder is equal to a composed load and modeled in

compensation node, where:

Vns,Vc

s,Vb

s,Va

s: null and phase voltage at the beginning of

the feeder

GcL,Gb

L,Ga

L: the equal conductance of unbalance load.

BaL,Bb

L,Bc

L: the equal susceptance of unbalance load.

BaY,Bb

Y,Bc

Y: star compensator susceptances.

Bca,Bbc

,Bab: delta compensator susceptances.

The feeder node voltages to derive the equations and

control algorithm are considered as follows:

,VVLar

= ,VaV 2Lbr

= VaVLcr

=

,0VV =r

2

3j

2

1ea 3/2j +== (1)

According to load balance importance in network steady

state behavior, phasor quantities can be used in studies and

analysis. Although feeder's load is compound and time

variant, but they can be modeled by impedance or

admittance load instantly:

)sinj(cosV

IjBGY

)sinj(cosV

IjBGY

)sinj(cosV

IjBGY

ccLc

LcL

cLc

Lc

bbLb

LbL

bLb

Lb

aaLa

LaL

aLa

La

=+=

=+=

=+=

(2)

VL

and IL

are phasor quantities of phase voltage and

current, respectively. Symmetric load current componentsin terms of load admittance are as follows:

( ) ( )[ ]( ) ( )[ ]( ) ( )[ ] 3/BaaBBjGaaGGVI

3/BBBjGGGVI

3/aBBaBjaGGaGVI

Lc

2Lb

La

Lc

2Lb

La

L0

Lc

Lb

La

Lc

Lb

La

L

Lc

Lb

2La

Lc

Lb

2La

L0

+++++=

+++++=

+++++=

+ (3)

Negative and zero current components produce as load

inequality and consequently its admittance in different

phases. Three phase current of compensators in terms of

susceptance are calculated as follows:

( )( )( )V.aBBaBaBjI

V.BaBaBBajIV.BaBBaBjI

aVjBVjBI

VajBVjBI

VjBVjBI

bcbc2

cacac

ab2

abbcbc2

b

cacaab2

aba

Yc

Lc

Yc

Yc

2Yb

Lb

Yb

Yb

Ya

La

Ya

Ya

+=

+=+=

==

==

==

(4)

Symmetric current components of compensators are

calculated as follows:

Fig (1): Conceptual diagram of reactive power compensation.

( )( )

( )

( )( )

cabcab2

cabcab

0

Yc

2Yb

Ya

Y

Yc

Yb

Ya

Y

Yc

Yb

2Ya

Y0

aBBBajVI

BBBjVI

0I3/BaaBBjVI

3/BBBjVI

3/aBBaBjVI

++=

++=

=++=

++=

++=

+

+

(5)

Load balancing by star and delta compensators necessitates

neutralization zero and negative current components:

0III YL =++ (6)

0III 0Y0

L0 =++

(7)

Power factor can be regulated to desirable amount by

positive component control. The following equation should

be satisfied for this reason:

( ) ( )( )PFkIIIkIII

f

YL

f

YL

1costan

ReIm

+++

+++

=

++=++(8)

Where:

PF is desirable amount of power factor.

Considering equation (8) as well as (6), (7) real- imaginary

parts separation, five equations obtained for susceptance

calculation, but another equation is required to satisfy the

equations(compensator's suscepatance).Sixth

equation is

additional condition to set and control the compensators

based on their natural behavior. If the imaginary part just

controlled by star compensator, the sixth equation is as

follows:

0=++

cabcab

BBB (9)

Having solved (6)-(9), the compensators amounts are as

follows:

( )

( )

( )LaLcca

L

c

L

bbc

L

b

L

aab

L

b

fL

a

fL

c

fL

c

Y

c

L

a

fL

c

fL

b

fL

b

Y

b

L

c

fL

b

fL

a

fL

a

Y

a

GGB

GGB

GGB

Gk

Gk

Gk

BB

Gk

Gk

Gk

BB

Gk

Gk

Gk

BB

=

=

=

+

+++=

+

+++=

+

+++=

33

2

33

2

33

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

(10)

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Fig (2): Three phase feeder equipped by star and delta compensator.

Therefore, compensators susceptances can be set to

neutralize the unbalanced load with on-line measurement ofvoltage-currents phasors, the power factors and load

balanced admittances. Therefore, with current and voltage

phasors sampling each time, compensators susceptances

can be set to load current balancing and power factor

regulating at any node of the feeder.

2-2-Application principles of the compensators [2, 4]

According to the previous parts, feeder load balancing

process can be performed by SVC. Sometimes more than

one SVC is required, so the appropriate load balancing

necessitate a specific performance sequence. Respect to 2-

1, SVC on each bus balance input current of this bus. In

load balancing with reactive power compensation, phase

current unbalancing is measured every 30 minutes or onehour then based on the measured data as well as algorithm,

reactive power injects to balance the currents.

Assume a situation with two SVC installed on a feeder

(figure 3). If compensator No.1 performs faster that No.2,

balancing failed. In figure 3, if compensator No.1 performs

faster, this compensator balances input current of bus No. 1

that consist of buses No. 4,5,7,8,9 and 10 load currents. But

input current of bus No. 6 is unbalanced yet. Then by

performance compensator No. 2, input current of bus No. 6

is balanced (consist of load currents of buses No. 7 and 8).

In fact the required reactive power for balancing load

currents of buses No. 7 and 8 injected to the feeder twice.

But if compensator No. 2 performs faster, this compensator

balances input current of bus No. 6 that consists of loadcurrents of buses No. 7 and 8. Then by performance

compensator No. 1, input current of bus No. 1 is balanced.

In this state, only required reactive power for balancing

load currents of buses No. 4, 5, 9 and 10 injected to the bus

No. 1. Generally, appropriate compensation needs faster

performance in compensator 2 than 1.

In this case, it is simple to distinguish the sequence, but

greater network require classification algorithm.

Classification algorithm is used in radial and multi radial

networks and each bus classified. Connected bus to

substation called No. 1 and classified in zero bunch. The

others classified as follows:

ith bus bunch = bunch of bus that ith bus fed from it + 1.

In other word, bus bunch is the number of branchesbetween ith bus and the bus No. 1. The bus classified

descendingly based on their bunch numbers. The sequence

presents their performance turn. Compensators in higher

rank of classification perform faster than then lower ones.

The algorithm applied on multi radial network (figure 4)

and the results are as follows:

[27 26 25 24 19 18 23 22 17 16 12 8 21 15 11 7 20 14 10 6 13 9 5 4 3 2 1]

Fig (3): Three phase feeder equipped by two compensators.

3-Optimal balancing and compensation in distribution

feeders

Low voltage feeders are the main origin of unbalancing in

power systems and there are the best places to apply

compensation for load balancing. Actually unbalancing in

low voltage feeders has two properties: 1) time variant

intense, 2) inequality dispersion in feeder. Therefore, the

balancing should be performed based on these properties.

The second property necessitates compensator in more than

on point of feeder. Obviously, compensation based on

unbalanced load balancing is a suitable approach, called

perfect-ideal balancing. But, technical-economical

considerations make this unfeasible. So, compensator

application on some feeder buses, called partial or non-

ideal compensation is an applicable approach.

The second choice requires optimal quantity of

compensators as well as their placement. Each

compensation process has three effective components (as

follows), so the most appropriate design is unique way.

1) technical-operational improvement considering feeder

voltage profile and its balancing.

2) Saving with loss reduction and free capacity provision.

3) Compensator application cost

The best compensation choice is a process which optimizes

and coordinates the above issues.

4- Feeder balancing algorithm and optimization

principle [2]

Each optimization process intends to minimize or maximize

definite objective(s). Therefore, objective definition is the

first step in optimize balancing.

In this paper the objective for optimal compensator

placement is defined based on (2) and (3). But, applied

constraints to provide the technical performance

considering voltage profile and unbalancing. The defined

objective function is as follows:

=

+=

t

1i

RCRCmaxSLi

lossWL CNSCWhCf (11)

Where:

CWL: economical cost of electrical energy loss in Rial/KWh

W: total electrical energy loss in feeder in balanced state

to unbalanced state in Ith time.

t: consumed time of assessment.h: conversion coefficients of achieved economic value to

the present value, considering profit rate and inflation

CSL: economic value of released feeder capacity and

balancing in terms of Rial / KVA.

I II III

IV

V

VI

VII VIII

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Fig (4): Classification algorithm for radial and multi radial networks.

Smax: balanced state feeder's released capacity to theunbalanced state in KVA

CRC: purchase, install and maintenance cost of a

compensator in Rial

Voltage unbalancing index is as follows:

{ }ijcnijbnijanijmax

ijcn

ij

bnij

anijavr

t

1i

n

1jij

avr

ijavr

ijmax

V

V,V,VmaxV3

VVVV

V

VV

n

1

t

1U

=

++=

=

= =

(12)

Where: ijcnij

bnij

an V,V,V are a,b and c phase voltage amplitude to

null in p.u for ith time and jth bus, n is bus amount and tisthe simulation period.

Voltage diversion profile index in kth phase defines as

follows (kcan be a, b or c):

= =

=

t

1i

n

1j

2ij

knk )V1(n

1

t

1VI (13)

Constraints are as follows:

maxc

maxb

maxa

maxVV

VIVI,VIVI,VIVI

UU

(14)

Now, the problem is to maximize (11) under (14)

constraints with appropriate compensation design (their

placement and amount). In this paper, genetic algorithm isused as an optimization process.

4-1-Optimization algorithm [2]

Genetic algorithm is a random-statistical research technique

to access maximum or minimum point of objective

function. According to its simulation capability, it is

efficient in complicate and multipurpose problems. The

principle is based on genetic systems of creatures and the

following calculation process:

-Each answer codifies as variable set, known as a

chromosome.

-Selection of chromosomes as new (basic) population.

-Value function calculation for each chromosome, known

as chromosome fitness.-Genetic operator application with specified probabilities.

-Convergence check and decision making to finish or

continue the algorithm.

In this paper each chromosome consists of a string with the

genes equal to feeder buses. Gene values set as 0, 1 those

represent presence or absence of compensator related bus,

respectively.

5-Load balancing software

MATLAB platform software is provided to simulate

unbalanced load in distribution feeder in specified period,

algorithm application and of compensator optimal

placement determination. The simulation is based on the

measured data at the beginning of the feeder with

unbalanced load flow as well as bus voltage, branch

current, energy loss, occupied capacity and unbalanced

load characteristics calculation. Also, it can simulate star-

delta compensator performance or their combination as

well as their effects on feeder behavior and operation. The

software specifies the optimal placement of reactive power

compensator by genetic algorithm.

6-Simulation study

A low voltage feeder in Tehran South West Electrical

Distribution Company is chosen as an example to apply

simulation. Single diagram of the feeder is shown in

figure(4). The feeder contain 27 buses with 40, 38, 38

participates on phase a, b and c, respectively.

The feeder performance and operation is simulated for 48

hours. Feeder performance is assessed by the software in

the following states:

-Unbalanced load without balancing-Unbalanced load with perfect and ideal balancing

-Unbalanced load with optimal balancing

Table (1): Unbalanced load without balancing

A. unbalanced load without balancing: in this state no

reactive power compensator is installed on buses. The

results for 48 hours are shown in table (1). The occupied

capacity in each phase based on maximum power (kVA) in

168 hour is achieved by simulation. It is the maximumvalue among the three phases as occupied capacity. It can

be seen that, occupied feeder capacity is 3*83.72=251.16

kVA and only 79% used for power transition.

B. unbalance loads with ideal and perfect compensation:Reactive power compensators are installed at all the

unbalanced buses. The results for 168 hour period are

shown in table (2). It can be seen current-voltage

unbalancing is eliminated. The voltage diversion profile is

reduced and balanced in each phase. Comparing A state,

resistive loss reduced 54% and 50% of the occupied

Phase A Phase B Phase C Null

Energy Losses (kWh) 58.34 184.67 127.93 36.11

Occupied Capacity(kVA) 45.97 83.72 65.66 -

Voltage Index (VI) 4.9e-4 1.0e-2 5.8e-3 -

Unbalancing indexUv

4.78 %

Table (2): Unbalanced load with perfect and ideal balancing

Phase A Phase B Phase C Null

Energy Losses (kWh) 62.31 62.31 127.93 0

Occupied Capacity(kVA) 41.55 41.55 41.55 -

Voltage Index (VI) 1.6e-3 1.6e-3 1.6e-3 -Unbalancing indexU

v 0

Table (3): Unbalanced load with optimal balancingPhase A Phase B Phase C Null

Energy Losses (kWh) 61.87 74.14 70.06 3.43

Occupied Capacity(kVA) 41.85 41.85 41.85 -

Voltage Index (VI) 1.4e-3 2.0e-3 1.9e-3 -

Unbalancing indexUv

0.40 %

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capacity released.

C. unbalanced load with optimal compensation:According to the optimal calculations of genetic algorithm,

three buses (No. 4, 6, 8) are recommended for optimal

installation. The results are shown in table (3). Feeder

resistive loss reduced 48.5% and occupied feeder capacity

released 50% comparing state A.

Figure (5): Profile of three phase voltages at the 12th bus of feeder

Having compared state c and b, in spite of using 3 buses

instead 15, no significant changes happened in feeder loss

reduction or occupied capacity, 89.8% and 99.3% of state

b, respectively. Also, the compensators reduced 0.80. But,

voltage diversion profile, unbalancing characteristics and

feeder current improved significantly than state A.

It can be seen, optimal compensation effects significantly

on voltage, loss and capacity release performance of low

voltage feeders. Time profile situation of three phase

currents at the beginning of feeder and time profile

situation of three phase voltages at the 12th

bus are shown

in figures 5 and 6 as an example for A, B and C states in 48

hours.

7-Concluion

The simulation results using the software for typical feeders

represent the optimal efficiency in unbalanced load

modification, energy loss reduction, network capacity

emptying and voltage profile improvement. The followings

results are achieved:

-Unbalanced load and its power factor can be modified

desirably by reactive power compensation.

-Genetic algorithm is an effective way to optimal placement

of compensators in distribution feeders. Load balancing

with a few compensators, modify unbalancing.

-The optimal amount of reactive power compensators are

achieve 3 or 4. Note that more that apply no significant

difference in addition to cost increment.

Figure (6): Profile of three phase currents at the beginning of feeder

References:

[1] M. R. Aghamohammadi; M.A. Talebi and M. Rajabi,

2004, "Optimal load balancing by reactive power

compensation in distribution feeders", International Power

Systems conference, Tehran.

[2] M.A. Talebi, 2003, "Optimal placement of reactive power

compensators for load balancing and power factor

correction by genetic algorithm", B. S. Thesis, Power and

Water Institute of Technology.

[3] S. Y. Lee and C. J. Wu., 2000, Reactive power

compensation and load balancing for unbalanced three

phase four wire system by an SVC, IEE Proc. Electr.Power, Vol. 147, No. 6, pp 563-570.

[4] Jen-Hung Chen; Wei-Jen Lee; Mo-Shing Chen, 1999,

Using a static VAR compensator to balance a

distribution system, Industry Applications, IEEE

Transactions on Power Systems , Vol. 35 , pp 298 304.

[5] Singh, B.; Saxena, A.; Kothari, D.P,1998, Power factor

correction and load balancing in three-phase distribution

systems, 1998 IEEE Region 10 International Conference

on Global Connectivity in Energy, Computer,

Perfect and ideal balancing

Optimal compensation

Unbalanced load without balancing

Perfect balancing

Optimal compensation

Unbalanced load without balancing

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Communication and Control , Volume: 2.