1capacitor placement distribution(ga)2003

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Paper accepted fo r presentation at 2003 IEEE Bo logna PowerTech Conference,

June

23-26, Bolog na, Italy

CAPACITOR PLACEMENT IN

DISTRIBUTION SYSTEMS, A NEW

FORMULATION

M. H. Shwehdi, A. Mantawi ,S. Selim A . AkSh ehri, KFUPM and G. K. A -Bassam, Saudi Aramco

Abs t raa - Two formulations of Capacitor Placement Problem

(CPP) are presented. One

is

based on eapscitorsnosses cost

balance. The other is based

on

comprehensive cost evaluation

of

network performance post CP. GA based program is

implemented to solve CPP. Proposed solution technique is

tested on 69411s system reported in literature. In additio n,

impact of capaeitor installation on fault level and network

resonance is investigated.

I Te rm -Ca pac itor Placement, Capacitor Compensated

Distribution Lines, Power System Economics, Genetic

Algorithm,

1 NOMENCLATURE

ACEPS: annual conserved energy, re l ( pcEAR)

ACEQ$: annual conserved energy, reactive ($NE AR )

BRFC: ben efits, released feeder capacity

( /YEAR)

BRGC : benefits, released generation capacity ($N EA R)

BRSC: benefits, released substation capacity ($NE AR )

BRTC: benefits, released transmission Capacity ($/YEAR)

IP: Investment Period (Years)

LD: Load Duration (HoursNear)

SCC: Short Circuit Current (kA)

11. INTRODUCTION

OWER transmitted to the user is composed of two parts:

P

eal power (that is responsible for rotating equipment or

producing heat) and reactive power (also referred to

as

magnetizing power) that

is

responsible for establishing the

magnetic flux in magnetic induction equipment (such as in the

core of a transformer

or

the air gap between stator and rotor of

motors and generators). The physical limit of transmission and

distribution equipment is associated with the total power (real

and reactive) flowing through the electrical system. This

physical limit is commonly referred to as thermal capacity of

the system. Many electrical equipment are rated by their

complex power (for example transformers, bus bars in

switchgears, generators). How ever, the work generated is only

associated with real power (although magnetizing power is

required to transfer power across space). Furthermore, not all

power is utilized, as some is lost as heat in the system's

resistance and inductance. Another constraint imposed on the

transmission distribution equipment

is

voltage drop

attributed to the resistive/inductive nature of the system and

load.

One method of releasing thermal capacity, reducing losses and

improving voltage levels a t equipment terminals is through the

installation of capacitors. However, capacitor cost should be

accurately calculated and weighted against not only the

reduction in losses, but also against other factors related to the

system performance (benefits from improvements and penalties

from deteriorations) and should include all direct as well as

indirect cost of the capacitor. Moreover, impact of the

capacitor installation on increasing the short circuit rating of

the system will have to be considered to determine the need for

new distribution equipment and hence reduction in the

expected revenue from installing the capacitor. In addition,

effect of capacitors on increasing resonance in the system

should also be investigated. Furthermore, performance

improvements such as release of thermal capacity in

generation, distribution and transmission equipment, a s well

as

benefits from reduction in voltage drop should all be included.

On the other hand, capacitor cost does not include equipment

cost only. Rather, it includes cost o f installation, maintenance

as well as cost of space occupied by the equipment. T he latter

is of particular importance since, in distribution systems in

particular, space is at premium.

In order to give full insight into CPP, proposed solution and

results reached, investigation carried by authors is presented

in five sections. Section

I11

provides a comprehensive

definition of the CPP. Section

1V

formulates the objectives

functions to be used in the solution of the CPP problem. In

Section V, the system used to tests the proposed solution is

presented together with the results generated. Section VI

presents the analysis and the results conducted to investigate

the impact

of

the addition of capacitors on the system short

circuit current and resonance.

IU CAPACITOR PLACEMENT PROBLEM

A Definition

CPP is defined as follows: Given an electric network with

predefined permissible locations for capacitor installations and

with defined performance characteristics, load diversity and

growth rate, what are the siz es and locations of capacitors that

can be installed to result in net positive revenue to the

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electrical utility?

load distribution

[SI.

More recent formulations of the CPP make

this assumption unnecessary.

B.

General Solution Algorithm

The solution algorithm for the capacitor Placement Problem has

the following general structure:

Furthermore, many of the CP t(:chniques assumed constant

voltage profile along the feeder. This allows for development

of closed form eauations for c;alculation of

loss

reduction

IMo deling of Network

2Calcualtion of network performance (precapacitors, at each

load level)

3-Initialization o f capacitors (locations and sizes)

Kalculation of network performance (post-capacitors,

objective function)

5Comparison of system performance (pre- and posG

without the need to execute load Ilow calculations for every set

of proposed capacitor attributes (sizes and locations). Since

the reactive power output from a capacitor is dependent on the

square of th e voltage, assuming a constant voltage system will

lead to incorrect calculation of the system performance (which

will eventually lead to selection of the wrong solution to the

CPP [6] .

capa citors ) Moreover, capacitor sizes were commo nly treated

as

&Alteration of capacitors attributes (locations, sizes or

continuous variables when they are in fact discrete and

the

switching times, collectively or individually) to increase the

difference in favor of an increase in the objective function

based

on

the

VAR

rating,

The ca paci torsizes were then rounded to the nearest standard

alue

7Aepetition of steps

4, 5

satisfied (mismatch between

network

performance in two

the majority o f the literature, cap.acitor cost is treated as linear

consecutive iterations is less than a pre-set minimum or total function

of two 3oo-kvAR

hanks is the same

as

the cost of a single

600

kVAR bank. This

umber of iterations is exeed ed).

cost

thereof is controlled by two t:lements, fixed value

for

each

unit and a variable

6

until

a

convergence criteria is sizes

upon

completion

ofthe prol,lem solution.

worse,

in

no offset.

This meSIIIS

he

formulation would almost always bias a solution toward

C. Differences in Methods

placement of several hanks

as

opposed to a smaller number of

Implementation of the solution algorithm varies in the

larger banks

L61

following forms:

In addition,

a

radial feeder with no laterals is also used in much

lRepresentation o f t h e objective function where one or of the literature. This is done becm se it is much more difficult

of the rewards, penalties or constraints are ignored for either

to

derive

equations for power

losses

laterals are

perceived insignificant contib,,tion

or

lack of theoretical considered.

[61.

Finally, in the rnethods that apply switched

formulation to or to improve convergence rate and

capacitors, the solution algorithm assumed that relative

reduce execution time).

positions of the switched and Fixed capacitors are known

2Contrihuters

to

cost/benefit

elements

of

Assumption ha s also been made to the relative switching times

3Mathematical representation of network (constant Of the

switched

capacitors f61

impedance, constant load, three phase, single phase)

4Initial capacitor attributes (locations and sizes, pre-set or free

function

IV. 11 CPP SOLUTIOk FORMULATION

A. Objec tive Function

Tw o main formulations of the obj'ective function were reported

in the literature. Th e first is hasecl on cost (a nd not saving)

as

shown in I ) . The second is based on savings resulting from

location policy )

5-Types of capacitors (switched, fixed)

Wptimization method for altering capacitors attributes

7Crite ria for stopping the search

D implifying Assumptions

In their effort to simplify the solution to the CPP, early pioneers

of the CPP have either ignored some of the terms in the

objective function or made assumptions that simplified the

formulation of the problem and the solution thereof.

For

instance, early papers assumed a uniformly distributed

load

along radial feeders. This configuration greatly simplified the

problem where it was converted to

a

calculus problem with

closed form solutions developed based on the gradient of the

objective function. However, error has resulted when this

assumption was applied to nonqadial feeders with non-uniform

cost reduction from decreased losses taking into consideration

capacitor cost as shown in (2).

Fitnes s-l= System Losses +Capac:itor Cost

Fitness-2 =C os t of Los s Reducticsn Capacitor Cost

Where Cost of Loss Reduction =(Original -Modified) System

Power Losses Cost.

(1)

(2)

The new formulation presented hy the authors (referred to as

Fitness-3) eliminates the need for

all

the abov e simplifications

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and assumptions, mo re accurately reflects the net reven ue from

the solution an d is based on comprehensive cost evaluation of

network performance pre- and po st- capacitor placement.

Fitness-3 =N et Revenue =Bene fits- Cost (3)

Benefits

=

Demand Reduction +Energy Reduction

Demand Reduction= BRGC+BRTC+BRSC+BWC

Energy Reduction

=

ACEP$+ACEQ$

Cost

=

Direct Cost + Indirect Cost

(3 ontd.)

=( TotalCapacitor-Cost +Total-Switchgear_Cost

)flP

Subject to the following performance constraints

Power Mismatch

1capacitor placement distribution(ga)2003

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