optimal reactive power planning based on improved tabu search algorithm

8/13/2019 Optimal Reactive Power Planning Based on Improved Tabu Search Algorithm

1/4

Optimal Reactive Power Planning Based on

Improved Tabu Search AlgorithmZou yiqin

School of Electronic

EngineeringChangzhou Institute of Technology

Changzhou, China

Abstract:In this paper, an improved Tabu search methodis proposed and applied to reactive power optimizationplanning in power systems .The improvement is donemainly by changing the way that the initial value isgenerated, and by adding sensitivity analysis and expertknowledge to Tabu search process. The minimum sum ofactive power loss and the cost of reactive equipment areused as the objective function of reactive power planning.Three different load operation conditions, namely heavy,normal and light, are considered to decompose the reactivepower planning into three sub-problems. The active powerloss in one year is used to coordinate the three operationconditions. The statistic results of the reactive poweroptimization planning of a power system in a certain areademonstrate that the improved TS algorithm is morestable and reliable and faster than simple TS method infinding global optimal solution.

Keywords: Power system, Reactive power optimization

planning, Tabu search, Decomposition and coordination

algorithm

INTRODUCTION

The purpose of optimal reactive power planning is

to decrease as far as possible the energy loss rate of a

network at reasonable voltage, thus to decrease the

electric power loss in a period of time. Optimal reactive

power planning determines where to add reactive power

compensation equipments and the amount of each place;

the aim of the planning is to minimize the sum of theelectric power waste expenses and the newly invested

compensation equipments in a period of time. The main

control methods include the regulating of the voltage of

generator, the regulating of the tap of OLTC on load

tap-changedtransformer, the inputting and cutting of

the parallel capacitors and reactors etc. How to make

full use of reactive regulate means, improve voltage

quality, reduce total system expenses, and is meaningful

both in theory and in practice. Optimal reactive power

planning is a problem that belongs to complicated mixed

integral non-linear planning.

The artificial intelligence method is applied to

optimal reactive power planning in recent years, and

researchers have already proven that the intelligencealgorithm can overcome the disadvantages of the

tradition optimal algorithms. These intelligence methods

include the genetic algorithm, the evolve optimal

algorithm, the simulated annealing expert system, the

Tabu search algorithm etc... For the intelligence search

algorithms like genetic algorithm, the simulated

annealing algorithm, and the Tabu search algorithm,

there is basically no restrictive assumption like

continuous, the existence of derivative, and single peak

for the search space. They can offset the shortcoming of

tradition mathematic planning because of their abilities

of global optimal search.Some good results are reached

since the intelligence methods are applied in optimal

power planning; these methods can get better results

than mathematical planning in some degree.

THE MATHEMATIC MODEL OF OPTIMAL REACTIVE

POWER PLANNING

A. The mathematic model of optimal reactive power

We take the minimum network energy loss as the

target

( ),VPf L= 1

In the formula, the network energy loss

( )P VL , can get through calculation of power flow.

The power restriction equation, namely the power

flow equation, is shown in formula 2

( )

( )

P V V G B

Q V V G B

i i j i j ij ij ij

j i

i i j i j ij ij ij

j i

NB

= +

=

cos sin

sin cos

2

In formula 2,iii VQP ,, are active power, reactive

power and voltage inputted in the i node respectively,

GijBijij are conductance , susceptance and phase

angle difference between node i and node j respectively.

The variable restriction equation is listed in

formula 3.

max

maxmin

maxmin

max

maxmin

)3(

0

LL

GGG

LLL

cc

TTT

SS

VVV

VVV

QQ

KKK

In formula 3,KTQCVG are control variables toexpress the taps to adjust transformer ratio,

compensation capacity and generator terminal voltagerespectively, VL is the voltage of load node,SL is thepower passing the branches ,they are state variables.

The optimal reactive power planning is to find the

position of tap and the configuration of reactive power

compensation equipments such that the object function

is the minimum when restrict formula 2 and formula 3

are satisfied.

B The mathematic model of optimal reactive power

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 2010 IEEE

DOI 10.1109/iCECE.2010.961

3945

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 2010 IEEE

DOI 10.1109/iCECE.2010.961

3945


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planning

The object function of optimal reactive power

planning consists of the running expenses C1(Ploss)and investment expenses C2(QC,Ql).We assume thatoptimal reactive power planning is done on the basis

that the active power flow of the planed network is

already allocated well, so the running expenses are the

cost of network energy loss of power system. Investmentis the year value amounted to newly added reactive

compensation equipments. So the optimal reactive

power planning is actually a way to get the minimum of

the object function, while satisfy the equality and the

inequality restriction of system running and investment

limitations, the mathematic model is:

( ) ( )

( )

( )1)1(

)1(,

min

11

2

11

21

+

+

+=

=

+=

==

=

m

m

lii

licii

cilc

l

i

ilossiloss

lcloss

r

rrnnQQ

P

,

CQCQC

TPKC

CCF

lc

QQP

Restriction condition: equality restriction is shown informula 2inequality restriction is shown in formula 4

max

maxmin

maxmin

maxmin

maxmin

)4(

LL

GGG

LLL

GGG

TTT

SS

QQQ

VVV

VVV

KKK

In the formula, Plossi is active power loss , i is load

level,i=1,2,3,,l,Ti is the corresponding loss time, Kispower price of system; Cci and Cli are the investingcoefficient of unit capacitive and the induction reactive

compensation equipment, respectively, nc and nl arethe number of new added capacitive and induction

reactive compensation spot, r is discount rate, m is theequipment economic life; KT and VG are the taps toadjust transformer ratio and generator terminal voltage,

they are control variables;VLQGSL is the voltage ofload node, the generator reactive output power, and the

power passed branching-off respectively, they are state

variables.

The planning problem is a multi-target optimal

problem, and is very hard to solve it directly. Based on

the engineering experience, such problem can be divided

into sub-problems of different loads and solved

separately. We can consider several load modes here,

namely great modes, medium modes and small modes or

heavy modes, normal modes, and light modes.

Great modes model:

1)1(

)1(min

1

11+

++=

=

m

m

cii

ciloss r

rrn

CQTPKFc

Restriction condition: equality restriction is shown

in formula 2 and inequality restriction is shown in

formula 5

max

maxmin

maxmin

maxmin

maxmin)5(

0

LL

GGG

LLL

GGG

TTT

c

SS

VVV

VVV

QQQ

KKK

Q

When load is heavy, the general electric voltage

level is lower, so if capacitive reactive compensation is

not enough under the great modes, new capacity

compensation may be added. The QC in formula 5 iscompensation capacity of node, including the original

compensation and the newly added compensation. Only

the running expense is considered under medium modes,

the object function is

2221 )(min TPKPCF lossloss == Constraint condition is listed in formula 2 and

formula3

Small modes model:

1)1(

)1(min

1

33+

+

+= = mm

lii

liloss r

rrn

CQTPKF

l

Restriction condition: equality restriction is shown

in formula 2, inequality restriction in formula 6

max

maxmin

maxmin

maxmin

maxmin

max

.

0

0

LL

GGG

LLL

GGG

TTT

cc

l

SS

QQQ

VVV

VVV

KKK

QQ

Q

6

The general voltage level is higher while load is

light, if the voltages in some nodes exceed the high

limit, reactance compensation may be added at thesenodes, the quantity of capacity compensate can not

exceed the original compensation quantity.

After decomposing the planning problem, we can

solve the optimal problem of each sub-model, which is

done through the search-based artificial intelligence

algorithm. We propose the improved Tabu search

algorithm based on the traditional one, and solve the

optimizing problem in power systems. .

Improved Tabu search algorithm for reactive

power optimization

A. The disadvantages of simple Tabu search algorithm

The initial solution of TS (Tabu Search) algorithm

is randomly generated. Suppose there is optimizationcomputing of 100 times, and there will be 100 different

initial solutions. TS algorithm is a single-point search

algorithm; its optimal solution depends highly on initial

solution, so the difference between the initial solutions

will lead to the difference in final solution. If the initial

solution is not good, the optimization results might be

far from satisfaction, the value of the object function

may not decrease but increase instead.

B. Step of improved Tabu search algorithm in reactive

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power optimization

(1) read the original data and decode the control

variables: The power system data includes flow

calculation data, the description of control variables and

conditions of various constraints, TS parameters include

Tabu list size, the maximum allowable number of

iterations, and continuous control variables, but

continuous control variables (generator terminal voltage)must be discretized properly before they can be turned

into decimal codes;

(2) generate an initial solution: set the iteration times

to 1, randomly generate a series of random solution

within the restriction of control variables, do the flow

calculation separately and get the value of object

function corresponding to different solutions, pick the

best solution as the initial iteration solution X0 and do

power flow calculation, check if the flow result exceeds

voltage limit, if so, adjust the solution to Xbased on the

sensitivity analysis and the expert knowledge, do flow

calculation again., the value of objective function isf(X),

Set the best solution vector Xopt=f (X);

(3) Generate a group of test solutions: make singlemovement and exchange movement on X, get a set of

feasible test solution X 1, X 2, ..., XK, and get the

correspondingf(X1),f (X2), ...,f(XK);

(4) Search neighborhood: find the best solution X *

from the test solution, ifX*is not in Tabu table, or ifX*

in the Tabu table, but it meets the release criteria, then

updatesX withX*, if the solutionX*is in the Tabu table,

while X*does not meet the release criteria, then find the

second best solution, and repeat the process;

(5) Update Tabu table: the movement will achieve the

opposite direction of the movement recorded in Tabu

table, if the Tabu table is full, then exclude the first

record from movement;

(6) UpdateXopt: iff(X*)


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simple TS method are illustrated in Figure 1

As can be seen from Figure 1, the objective

function of improved TS method is lower than that of

simple counterpart in the whole iteration process, only

that the objective function of improve TS method

decreases slower, the reason for this is that the objective

function of initial solution is already very lower, so it is

hard to get a fast iteration decrease. Also we can seefrom figure 1 that the optimization result of improved

TS method is always better than that of simple TS

method for any iteration times, furthermore, the

decreasing rate of simple TS method becomes slow after

the iteration time reaches a certain value. Still we can

see from the figure that if the solution quality of both

methods is equal, the iteration time of improved TS

method is less than that of simple TS method; also, it

costs less CPU time, so the improved TS method has

better on-line application prospects

B. The improved coordination method

Improved coordination method also takes into

account three kinds of load modes, in each mode, theallocation of running time, the compensation of

capacitance and reactance, and the annual power loss are

the same as that of the simple TS method, only the

convergence criteria and coordination method aredifferent. We set the coordination times to be 15 , that is,

k max = 15, use the memory strategy to record thelowest energy loss of power network in various modes

during the coordination process and its corresponding

solution, and take the final solution as the coordination

solution in the end. This can not only ensure the

coordination time and reliable convergence, but also can

ensure the optimized results, that is, relatively good

results can be achieved in an acceptable period of time.

The optimized result of using improved coordinationalgorithm in power grid of this region is shown in Table

3.

TABLE 3 OPTIMIZED PLANNING RESULT OF IMPROVED

COORDINATION ALGORITHMGreat modes Medium modes Small modes Annu-

al

opera-

ting

costs

/

Millio-

n yuan

Ann-

ual

inve-

stme-

nt/

Mill-

ion

yua-

n

Ann-

ual

ear-

ning

s/

Mill-

ion

yua-

n

Netw-

ork

ener-

gy

loss/

MW

Vmin/p.

u.

Networ

-k loss

/MW

Vmin/p.u.

Netwo

-rk

energ

y loss

/MW

Vmin/p.u.

PreOp

-timal

Planni

-ng

35.33

930.84

28.906

10.87

23.27

970.89 7649.5 0 0

After

the

optima

-l

planni-

ng

26.58

491.01

21.966

71.00

18.22

631.03

5830.5

213.1

1805

.9

CONCLUSION

Tabu search algorithm and an improved TS method

are applied to Reactive Power Optimization of Power

System and Optimal Reactive Power Planning in this

paper, the improved TS method has a strong ability of

optimal search. The Optimal Reactive Power Planning

takes the minimum sum of the annual cost of power

losses and the investment of reactive power without

compensation as the objective function, takes into

account the large, medium and small load modes, uses

the annual power loss as the coordination factor, adds a

number of coordination guidelines, so as to propose the

improved coordination algorithm. All optimization

calculations use the improved TS method. By doing a lot

of reactive power optimization and optimal planning test,

we can draw a conclusion that:

(1) Compared with simple TS algorithm, theimproved TS algorithm has a unique advantage of

jumping out of the local optimal solution, its

convergence and solution quality are better than that of

the simple TS method. The improved TS method

changes the way the initial solution is generated, uses

sensitive information and expert knowledge to guide the

search process, and gets the stable optimization results,

the decreasing rate of energy loss power network is

satisfactory while the voltage quality remains good.

(2) The improved coordination algorithm, it can take

into account multiple load modes, the result of it is more

accurate and more representational, and the calculation

time is short.

(3) The planning in this paper is done using the

improved coordination algorithm; the optimal search for

each sub-problem is implemented using the improved

Tabu search, so the result of planning is optimal.

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optimal reactive power planning based on improved tabu search algorithm

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