New approach for optimal UPFC placement using hybrid immune algorithm in electric power systems

Electrical Power and Energy Systems 43 (2012) 899–909

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Electrical Power and Energy Systems

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New approach for optimal UPFC placement using hybrid immunealgorithm in electric power systems

Seyed Abbas Taher ⇑, Muhammad Karim AmooshahiDepartment of Electrical Engineering, University of Kashan, Kashan 87317-51167, Iran

a r t i c l e i n f o

Article history:Received 13 August 2010Received in revised form 28 May 2012Accepted 29 May 2012Available online 15 July 2012

Keywords:Optimal locationUnified power flow controller (UPFC)Optimal power flow (OPF)Hybrid immune algorithm (HIA)

0142-0615/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijepes.2012.05.064

⇑ Corresponding author. Tel.: +98 9131614352; faxE-mail address: [email protected] (S.A. Taher)

a b s t r a c t

The unified power flow controller (UPFC) is one of the most promising flexible AC transmission systems(FACTS) devices for the load flow control. Simultaneous optimization of location and parameters forUPFCs is an important issue when a given number of UPFCs is applied to the power system with the pur-pose of increasing system loadability. This paper presents the application of hybrid immune algorithm(HIA) such as immune genetic algorithm (IGA) and immune particle swarm algorithm (IPSO) to find opti-mal location of UPFC to achieve optimal power flow (OPF). The overall cost function, the objective func-tion in the OPF, includes the total active and reactive production cost function of the generators andinstallation cost of UPFCs and hence, should be minimized. The OPF constraints are generators, transmis-sion lines and UPFCs limits. In power system, it may not always be possible to dispatch the contractedpower transactions completely due to congestion of the corresponding transmission corridors. In thisstudy simulations were performed on IEEE 14-bus and IEEE 30-bus test systems for different methods.Under all equality and inequality constraints, the HIA proposed approach minimized the objective func-tion better than other methods such as GA, PSO, and IA; and as far as HIA methods were concerned, theIPSO algorithm gave better minimum cost than IGA method. Results of simulations are encouraging andcould efficiently be employed for power system operations.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

As the number of countries prepared to open their electricitymarket is increased in recent years, the separation of their genera-tion and transmission systems have taken place progressively.Furthermore, this enables every consumer to buy his/her own elec-tricity from any source desired, leading to an increase in the amountof unplanned power exchanges. The increased un-controlledexchanges cause some transmission lines to be overloaded, orcongested. Therefore, power systems need to be managed in orderto utilize the available network efficiently. The introduction ofFACTS devices based on the advance of semiconductor technologyopened up new opportunities for controlling the power flow andextending the loadability of the available power transmission net-work. The UPFC [1,2] is one of the most promising FACTS devicesfor load flow control since it can either simultaneously or selec-tively control the active and reactive power flow along the linesas well as the nodal voltages [3–7]. The outstanding characteristicmentioned above relies on the precondition of prefiguring the UPFClayout [7]. However, on implementation, there is a practicalconcern for finding optimal location. According to the availableliteratures, the location of UPFC tends to be done empirically, if

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not arbitrarily, and the corresponding systematic investigation isnot often enough [8]. The state-of-the-art UPFC analyses primarilyfocus on the application of stability control [8–14] in powersystems.

Some researchers have attempted to solve the optimal locationof UPFCs with respect to different purposes and methods [15,16].In [15], an approach based on the augmented Lagrange multipliermethod is used. Although multi operating conditions can simulta-neously be taken into consideration, the operating condition mustbe pre-assigned. In [16], the genetic algorithm (GA) is used to opti-mize three parameters (location, size and type of FACTS devices) ofmulti-type FACTS devices including TCSC, TCPST, TCVR and SVC. Asensitivity-based approach was developed for finding suitableplacement of UPFC [17]. Ref. [18] proposed an evolutionary-pro-gramming-based load flow algorithm for systems containing uni-fied power flow controllers, and [19] proposed GA for suchapplications. Optimal location and setting of multi-type FACTS de-vices using non-dominated sorting PSO method is also presented in[20]. Application and comparison of computational intelligencetechniques, including GA, PSO, and DE, is introduced in [21], foroptimal location and sizing of UPFC in order to enhance the systemsecurity level.

Recently, a new type of heuristic algorithm, the so-calledimmune algorithm (IA) has been developed and applied in solvingcomplex optimization problems in power systems. The IA method

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Nomenclature

VvR magnitude of UPFC shunt converter voltage sourceVcR magnitude of UPFC series converter voltage sourcehvR phase angle of UPFC shunt converter voltage sourcehcR phase angle of UPFC series converter voltage sourceDPbb power mismatchDX solution vectorJ Jacobian matrixN quantity of antibodiesPij probability that the jth allele comes out at the jth geneEj entropy of the jth geneE(2) information entropy of these two antibodies(AB)ij affinity between the ith antibody and the jth antibodyOPTi total cost to represent the connection between the anti-

gen and antibodyf(x) objective functionPF penalty factorOVL line overload factorVS voltage stability indexSpq complex power flow between buses p and qSmax

pq thermal limit for the line between buses p and q

Nbus number of busesk, l small positive constantsCgpi(Pgi) cost of active power production in $ h�1

Cgqi(Qgi) cost of reactive power production in $ h�1

Sj operating range of the FACTS devices in MVARCt

UPFCjcost of installation of UPFC in $ h�1

CUPFCjcost of installation of UPFC in $/KVAR

a the capital recovery factor (CRF)r the interest raten the capital recovery planSgi;max

operating range of generator in bus iK benefit factor of reactive power productionV1 voltage magnitude of main busPgi active power generations at bus iPspi, Qspi active and reactive powers leaving of UPFCi respectivelyVvrtari target nodal voltage magnitude to be controlled by

shunt branch of UPFC iUPFCnli number of compensated transmission line with UPFCi

UPFCsidei status of install UPFC

z

Shunt converter

Series converterI3 I2

Vdc

+VvR

-

+ VcR -I1Ik

Vk V0Vm

Im

VvR VcR θvR θcR

Fig. 1. UPFC installed in power system.

Fig. 2. UPFC equivalent circuit.

900 S.A. Taher, M.K. Amooshahi / Electrical Power and Energy Systems 43 (2012) 899–909

has provided good performance as an optimization algorithm [22–25]. Some science workers used the hybrid IA (HIA) method to solvethe nonlinear and discrete optimization problems, and obtainedbetter solutions [26,27].

This paper proposes an application of HIA including IGA andIPSO methods to solve the optimal location of UPFC problems inpower systems for considering system load-ability, and the overallcost function, and includes the generation costs of power plantsand also the cost of installing UPFC. Therefore, the presented prob-lem becomes a composite objective optimization problem in whichlocation and rated value of UPFC must be optimized and deter-mined simultaneously. Numerical case studies are given to validatethe robustness and effectiveness of the proposed method. Betweentwo introduced HIA methods proposed in this paper, IPSO methodcaused improved escaping of local optima and managed moreeffectively to converge to the nearest global solution.

2. UPFC equivalent circuits and power equations

2.1. UPFC equivalent circuit

The UPFC is a FACTS device, capable of providing active andreactive load flow control between its terminals. It may also pro-vide reactive power compensation to the node to which it is con-nected [1,28]. The device consists of two converters connected bya common DC link as shown in Fig. 1. Coupling transformers pro-vide the connections for these converters and the power systemas follows: one is connected as shunt to the sending end node,the other connects in series the sending and receiving end nodes.

The UPFC cannot generate or absorb active power and hence,the active power in the two converters must be balanced when ac-tive power loss is neglected. This is achieved via the DC link. Theconverters, however, may generate or absorb reactive power. TheUPFC equivalent circuit shown in Fig. 2 is used to derive the stea-dy-state model [29].

The equivalent circuit consists of two ideal voltage sources rep-resenting the fundamental Fourier series component of theswitched voltage waveforms at the AC converter terminals. TheUPFC voltage sources are [29,30]:

VvR ¼ jVvRjðcos hvR þ j sin hvRÞ;VcR ¼ jVcRjðcos hcR þ j sin hcRÞ;

ð1Þ

where VvR (VvR min 6 VvR 6 VvR max) and hvR (0 6 hvR 6 2p) are thecontrollable magnitude and phase angle of the voltage source rep-resenting the shunt converter. The magnitude VcR and phase anglehcR of the voltage source representing the series converter are liewithin the following limits: (VcR min 6 VcR 6 VcR max) (0 6 hcR 6 2p).

2.2. UPFC power equations

The UPFC model described above is converted into two powerinjections in rectangular form for power flow studies. The advan-tage of power injection representation is that the symmetric char-acteristics of admittance matrix will not be destroyed [30]. Byusing the UPFC model illustrated in Fig. 1 and a p-equivalent cir-cuit of the transmission line, the branch embedded with UPFCcan be modeled as shown in Fig. 2. Based on the equivalent circuitshown in this figure the two power injections (Pk,Qk) and ( Pm,Qm)

Antibody #1 1 2 j M-1 MGen 1 Gen 2 … Gen j … Gen M-1 Gen M

j1

Antibody #I

Gen 1 Gen 2 … Gen j … Gen M-1 Gen M jI

Antibody #N

Gen 1 Gen 2 … Gen j … Gen M-1 Gen M jN

diversity

Fig. 3. Data structure of gens with corresponding information entropy for IA.

S.A. Taher, M.K. Amooshahi / Electrical Power and Energy Systems 43 (2012) 899–909 901

of the UPFC can be calculated according to the following equations[30]:

At bus k:

Pk ¼ V2kGkk þ VkVmðGkm cosðhk � hmÞ þ Bkm sinðhk � hmÞÞþ VkVcRðGkm cosðhk � hcRÞ þ Bkm sinðhk � hcRÞÞþ VkVvRðGvR cosðhk � hvRÞ þ BvR sinðhk � hvRÞÞ;

Qk ¼ �V2kBkk þ VkVmðGkm sinðhk � hmÞ � Bkm cosðhk � hmÞÞ

þ VkVcRðGkm sinðhk � hcRÞ � Bkm cosðhk � hcRÞÞþ VkVvRðGvR sinðhk � hvRÞ � BvR cosðhk � hvRÞÞ:

ð2Þ

At bus m:

Pm ¼ V2mGmm þ VmVkðGmk cosðhm � hkÞ þ Bmk sinðhm � hkÞÞþ VmVcRðGmm cosðhm � hcRÞ þ Bmm sinðhm � hcRÞÞ;

Qm ¼ �V2mBmm þ VmVkðGmk sinðhm � hkÞ � Bmk cosðhm � hkÞÞ

þ VmVcRðGmm sinðhm � hcRÞ � Bmk cosðhm � hcRÞÞ:

ð3Þ

Series converter is:

PcR ¼ V2cRGmm þ VcRVkðGkm cosðhcR � hkÞ þ Bkm sinðhcR � hkÞÞ

þ VcRVmðGmm cosðhcR � hmÞ þ Bmm sinðhcR � hmÞÞ;QcR ¼ �V2

cRGmm þ VcRVkðGkm sinðhcR � hkÞ � Bkm cosðhcR � hkÞÞþ VcRVmðGmm sinðhcR � hmÞ � Bmm cosðhcR � hmÞÞ:

ð4Þ

Shunt converter is:

PvR ¼ �V2vRGvr þ VvRVkðGvR cosðhvR � hkÞ þ BvR sinðhvR � hkÞÞ;

QvR ¼ V2vRGvR þ VvRVkðGvR sinðhvR � hkÞ � BvR cosðhvR � hkÞÞ:

ð5Þ

where

Ykk ¼ Gkk þ jBkk ¼ Z�1cR þ Z�1

vR ;

Ymm ¼ Gmm þ jBmm ¼ Z�1cR ;

Ykm ¼ Ymk ¼ Gkm þ jBkm ¼ �Z�1cR ;

YvR ¼ GvR þ jBvR ¼ �Z�1vR ;

ð6Þ

and assuming loss-less converter is:

PvR þ PcR ¼ 0: ð7Þ

The UPFC linearized power equations are combined with thelinearized system of equations corresponding to the rest of thenetwork,

½f ðxÞ� ¼ ½J�½DX�; ð8Þ

where

½f ðxÞ� ¼ ½DPk DPm DQk DQ m DPmk DQmk DPbb�T : ð9Þ

DPbb is the power mismatch, DX is the solution vector and J is theJacobian matrix. The power mismatch equations are used as theguiding principle for conducting limit revisions. The mismatch pro-vides an accurate indicator for determining the controllable devicesparameters. The revision criterion of the UPFC is based on its activepower converter mismatch equation.

3. Hybrid immune algorithm

In this section, IA, and two hybrid immune algorithms (HIA)including IGA and IPSO methods are discussed.

3.1. Immune algorithm

The IA has been widely used to solve the optimization problemsby applying the same operation principle of human immune

system. According to [31,32] the capability of IA method for pat-tern recognition and memorization does provide a more efficientway to solve the discrete optimization problem as compared tothe GA. The cost function and limit constraints are representedas antigen inputs, while the solution process is simulated by anti-body production in the feasible space through a genetic operationmechanism. The calculation of affinity between antibodies isembedded within the algorithm to determine the promotion/sup-pression of antibody production. Through the IA computation,the antibody which fits best the antigen is considered as the solu-tion for the optimization problem [23–25,31–37].

3.1.1. The structures of genes and chromosomesAn immune algorithm based decision making procedure [33,34]

is proposed in this study. The population of memory cells is a col-lection of the antibodies (feasible solutions) accessible toward theoptimality, which is the key factor to achieve fast convergence forglobal optimization [33,34]. In this paper, a genetic coding struc-ture of the IA is adopted and the diversity and affinity of the anti-bodies are calculated during the decision making process to findthe optimal solution. The data structure of genes can be depictedas shown in Fig. 3. For a feeder with N possible strategies of phasearrangement involving M object nodes, it will generate N antibod-ies having M genes in the antibody pool. The gene node(i) consistsof a sequence of alternating sign-less integer numbers representingthe candidate connection schemes of n branches connecting node i[33,34].

3.1.2. DiversityThe diversity of feasible strategies in the population is mea-

sured between the antibodies. This will be increased to prevent lo-cal optimization during the searching process of optimal solution.For each evolving generation, the new antibodies are generated tostrengthen the diversity of antibody population in the memory cell[33,34]. With the data structure of genes in Fig. 3, the entropy Ej ofthe jth gene (j = 1,2, . . . ,M) is defined as follows:

Ej ¼ �XN

i¼1

Pij log Pij; ð10Þ

where N is the quantity of antibodies and Pij is the probability thatthe jth allele comes out at the jth gene. If all alleles at the jth geneare the same, the entropy of the jth becomes zero. According to[33,34], the diversity of all genes is calculated as the mean valueof informative entropy as:

E ¼ 1M

XM

j¼1

Ej: ð11Þ


3.1.3. AffinityIf the affinity of some antibodies is the same during immune

process, it will influence the searching efficiency of optimizationfor the planning of phase arrangement. In this paper, the same as[33,34], two types of affinity are calculated for the proposedmethod. One such type is the affinity between antibodies definedas:

ðAbÞij ¼1

1þ Eð2Þ ; ð12Þ

where E(2) is the information entropy of these two antibodies. Itshould be noted that the genes of the ith antibody and the jth anti-body will be the same when E(2) is equal to zero. The affinity be-tween the ith antibody and the jth antibody, (AB)ij, will be withinthe range [0,1].

The other type of the affinity is the one between antibody andthe antigen (i.e. the cost functions).

ðAgÞi ¼1

1þ OPTi; ð13Þ

where OPTi is the total cost representing the connection betweenthe antigen and antibody i. The antigen with the maximum affinity(Ag)i will be the optimal phase arrangement within the feasiblespace.

3.1.4. Computation proceduresThe process to solve the cost function for optimal solution is

simulated by the interaction of antibody and antigen in IA. Duringevolution of genes, the candidates of solution with high affinity areselected and included in the memory cells, which is then used togenerate new candidate solution. The computation procedure istherefore executed as follows [33,34]:

Step (1) Recognition of antigens.Step (2) Production of initial antibody population.Step (3) Calculation of affinity.Step (4) Evaluation and selection.Step (5) Crossover and mutation.Step (6) Decision on optimal strategy.

During this process, the antibody having high affinities with theantigen will be added to the new memory cell, which will be main-tained after applying the operation of crossover, mutation andselection for the population. The search process of optimizationcontinues until no further improvement in relative affinity can beobtained and thus the antibody with the highest affinity in thememory cell will be the optimal strategy for the solution.

3.2. Hybrid immune genetic algorithm

To avoid the disadvantage of getting into local optimum solu-tion, IGA method is introduced. Combining IA with GA, optimizedpopulations are vaccinated and immunized. To apply the IGA tofind the optimal solution, lymphocytes and antibodies compo-nents are considered. Lymphocytes recognize invading antigensand produce antibodies to eliminate the antigens. Note that theantigens and the antibodies in the immune system are repre-sented as the objective and feasible solutions, respectively, forthe optimization problem. The calculation strategy of IGA is asfollows [26,38,39]:

Step (1) Definition: antigen and antibody recognition;Antigen 1: object value, Antigen 2: constraints, Antibod-ies: optimal solutions.

Step (2) Initial antibody population production;In the initial step, the antibodies are generated randomlyin the feasible space. The antibody pool is composed ofthese antibodies.

Step (3) Calculating the fitness values (Fs) of all solutions as fol-lows;(This includes the solutions of the previous generationand those generated by present generation.)

MaxFs ¼1

FT þ const; ð14Þ

where FT: objective function, Fs: fitness function, and const: aconstant.Step (4) Antibody evolution process:

(a) Calculating the concentration Cv of antibody v asfollows.

Cv ¼1K

XK

w¼1

ACvw; ð15Þ

where

ACvw ¼1; COL 6 ðAbÞvw 6 COH

0; otherwise

�: ð16Þ

k is the number of antibody w, COL, COH is a predetermined thresholdvalue.

(b) Calculating the expected-breeding ratio Ev defined as:

Ev ¼ðAgÞv

Cv: ð17Þ

Step (5) Generate the next generation offspring population;Allow the antibody population acquired from Step (4)to descend according to the Ev. Select the ahead Ncnumbers for individuals to form the present population.At the same time produce Nm numbers of antibodiesinto the ‘‘Evolutive Memory Cell’’. The Nc and Nm num-bers are predetermined values.

Step (6) Stopping criterion;The search is stopped if the following conditions aresatisfied:1. The values for C(g) and m(g) do not change for sev-

eral generations (for details see in Step (8)).2. When the set number of iterations is achieved.

Step (7) Antibody selection;A roulette selection was implemented based on the

computed affinity for the antibodies. Consequently, anew antibody pool can be formed by spinning thedesigned roulette. The average affinity for a new anti-body generation chosen from Step (4) is higher thanthat the old generation antibody pool.

Step (8) Crossover implementation;Crossover is the primary IGA operator that promotesthe new region exploration in the search space. Theso-called ‘‘selected-window’’ method is used to selecta stated number of genes as a window for the two par-ent antibodies. The window genes for antibodies A andB are then changed. The changed condition is shown inFig. 3. The destruction of important antibody structuresis prevented by adopting this method (the crossoverratio was adjusted by the FS).

Step (9) Mutation implementation;According to the predetermined mutation ratio, muta-tion is a random change in the value for an antibodyposition, as from ‘‘1’’ to ‘‘0’’ or from ‘‘0’’ to ‘‘1’’ (mutationratio determined by the FS).

Step (10) Go to Step (3). It finished a cycle.


3.3. Hybrid immune PSO algorithm

3.3.1. Overview of PSO algorithmPSO is a population-based evolutionary technique which has a

number of key advantages over other optimization techniques.PSO finds the optimal solution using a population of particles. Eachparticle represents a candidate solution to the problem. PSO isbasically developed through simulation of bird flocking in two-dimensional space [40]. Attractive features of the PSO include easeof implementation, the fact that no gradient information is re-quired and its application can be extended in neural network train-ing and minimizing function. The PSO definition is presented by[40–42] as follows:

(1) Each individual particle has the following properties: acurrent position in search space xi, a current velocity vi,and a personal best position in search space Xpbest.

(2) The personal best position Xpbest, corresponds to the posi-tion in search space, where particle i presents the smallesterror as determined by the cost function f, assuming a min-imization task.

(3) The global best position denoted by Xgbest, represents theposition yielding the lowest error among all the Xpbest’s.

Consider a swarm of P particles; with each particle’s positionrepresenting possible solution point in the design problem space.For each particle, Kennedy and Eberhart [40] proposed that its po-sition xi is updated in the following manner:

Viðt þ 1Þ ¼W � ViðtÞ þ c1 � r1ðPbestðtÞ � xiðtÞÞ

þ c2 � r2ðGbestðtÞ � xiðtÞÞ; ð18Þ

xiðt þ 1Þ ¼ xiðtÞ þ Viðt þ 1Þ: ð19ÞHere, subscript t indicates a time increment Xpbest(t) represents thebest ever position of particle i at time t, and Xgbest(t) represents theglobal best position in the swarm at time t. r1 and r2 represent uni-form random numbers between 0 and 1. To allow the product c1r1

or c2r2 to have a mean value of 1, c1 and c2 are assumed constantvalues typically in the range of 2–4. Kennedy and Eberhart proposedthat the cognitive and social scaling parameters c1 and c2 be se-lected such that c1 = c2 = 2. The factor w is the inertia weight. Forlarge w, the search becomes more global, while for smaller one,the search becomes more local. The coefficients c1 and c2 are learn-ing factors, which help particles to accelerate towards better areasof the solution space [42].

3.3.2. IPSO algorithmDuring the calculation, it is important to avoid PSO sinking into

a local optimized solution. The characteristics of a particle are cal-culated by the basic PSO method as mentioned above, in whicheach particle undergoes vaccination and immunization. Each PSOparticle corresponds to an antibody of IA, and each element of par-ticle is equal to each gene of the antibody. The adaptive degrees ofparticles can be improved by vaccination. The higher the adaptivedegree of a particle, the better is the particle. Hence, to avoid trap-ping in a local optimal solution and ensure the search capability ofa near global optimal solution, mutation is employed as it can playan important role in IPSO. The process of IPSO can be described asfollows [27,43–46]:Step (1) An initial particle swarm is randomly generated for

which there is a random initial solution and speed, wherespeed is commutative orders.

Step (2) The next position (X 0id) of a particle can be calculatedaccording to: the current position (Xid) of that particle,original speed (Vid) of particle, experienced best position

(Pid) of particle and experienced best position (Pgd) ofparticle swarm. The speed of particle is calculatedaccording to Eq. (18). The new solution is then calculatedaccording to Eq. (19).

Step (3) After particles have arrived at new positions, each parti-cle is compared with its experienced best position, Pid. Ifthe new particle is improved, Pid will be replaced by thenew improved particle. Similarly, each particle is com-pared with the experienced best position Pgd of particleswarms, if the new particle is better, Pgd will be replacedby it.

Step (4) The optimized particle swarm is inoculated.Step (5) Immune vaccination, for this there are three main parts:

picking-up vaccine, vaccination, and immune selection.Some characteristic information picked-up from a per-son’s pre-knowledge about the problem to be solved,are regarded as bacterin used to change a certain inte-grant of the particle, aimed at guiding the search process.However, the postvaccinal particle must be checked byimmune selection, which is capable of suppressing deg-radation phenomena. If the fitness of the postvaccinalparticle is smaller than the original one, the originalone will be preserved; otherwise, the postvaccinal parti-cle will be regarded as the new particle and replace theoriginal particle. Therefore, the optimized particle swarmis undergoes immunization and hence, a new particleswarm is generated.

Step (6) The newly generated particle at Step (5) above is
returned to Step (2) and calculations are repeated untilthe optimal solution is found or the maximum iterativenumber is reached.
4. Problem formulation

4.1. Optimization by penalty factor

Constrained optimization (CO) is one of the most commonapplication areas for HIA and its handling is of great importance.A straight forward approach is to convert a CO problem into anon-constrained optimization (NCO) problem by adding penaltyfor violation of constraints. Optimal placement of UPFC consideringobjective function, system loadability and voltage stability is givenby the following equations [47]:

MinLðxÞ ¼ f ðXÞ þ PF� kJ � 1k ð20ÞJ ¼

YLine

OVLLine �YBus

VSBus; ð21Þ

where f(x) is the objective function, PF is the penalty factor, OVL isthe line overload factor for a line, and VS is voltage stabilityindex for a bus. The cost is thus optimized with the followingconstraints:

OVL ¼1 if Spq 6 Smax

pq

exp k 1� Spq

Smaxpq

�� if Spq P Smax

pq

8><>: ; ð22Þ

VS ¼1 if 0:9 6 Vb 6 1:1

expðlj1� VbjÞ otherwise

(; ð23Þ

where Spq is complex power flow between buses p and q, Smaxpq is

thermal limit for the line between buses p and q, Vb is voltage atbus b and k, l are small positive constants both equal to 0.1.

Fig. 4. Capability curve of a generator.


4.2. Objective function

Optimal placement of UPFC is a composite objective optimiza-tion problem. Objective functions are the generation costs of powerplants and installation cost of UPFC as defined below:

f ðXÞ ¼XNg

i¼1

CgpiðPgiÞ þ Cgqi

ðQ giÞ þ

XN

j¼1

CtUPFCj

; ð24Þ

where

CgpiðPgiÞ ¼ ai þ biPgi

þ ciP2gi; ð25Þ

CtUPFCj

¼ ðCUPFCj� Sj � 1000� aÞ=8760; ð26Þ

CUPFCj¼ 0:0003S2

j � 0:2691Sj þ 188:22; ð27Þ

a ¼ rð1þ rÞn

ð1þ rÞn � 1: ð28Þ

Cgpi(Pgi) is the cost of active power production in $ h�1, Cgqi(Qgi) thecost of reactive power production in $ h�1, Sj the operating rangeof the FACTS devices in MVA, Ct

UPFCjthe installation cost of UPFC

Fig. 5. IEEE 14-bu

in $ h�1, CUPFCjthe installation cost of UPFC in $/KVA, a the capital

recovery factor (CRF), r the interest rate, and n is the capital recov-ery plan.

Considering the interest rate r = 0.05, the capital recovery peri-od n = 10 years, the capital recovery factor, a, can be computed, asa = 0.1295.

Capability curve of a generator is usually used to demonstratethe relationship between its active and reactive power outputs. Atypical capability curve of a generator is shown in Fig. 4, fromwhich it can be observed that the active power generation de-creases the reactive power capability of generator. The cost of reac-tive power production can be modeled using opportunity costcalculation [48]. An approximation for cost of reactive power pro-duction is given in the following equation:

CgqiðQ giÞ ¼ Cqpi

ðSgi;maxÞ � Cgpi

ðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2

gi;max� Q 2

gi

qÞ

h i� K; ð29Þ

where Sgi;maxis the operating range of generator in bus i and K is the

benefit factor of reactive power production selected between 0.05and 0.1.

4.3. Gene representation

Some parameters need to be optimized by evolutionary algo-rithms; control variables were selected for this purpose. A geneis represented with the following strings of variables control asfollows:

Gene¼ ½V1 Pg1; . . . ;PgN

Psp1; . . . ;PspN

Q sp1; . . . ;Q spN

Vvrtar1 ; . . . ;

VvrtarN UPFCnl1; . . . ;UPFCnlN UPFCside1; . . . ;UPFCsideN�; ð30Þ

where V1 is the voltage magnitude of reference bus, Pgi the activepower generations at bus i, Pspi, Qspi the active and reactive powersleaving of UPFCi respectively, Vvrtari the target nodal voltage magni-tude to be controlled by shunt branch of UPFCi, UPFCnli the numberof compensated transmission line with UPFCi, UPFCsidei the status of

s test system.

Table 1Generator data of the IEEE 14-bus test system.

Gi No. bus ai bi ci Pmingi

(pu) Pmaxgi

(pu) Qmingi

(pu) Qmaxgi

(pu)

G1 1 100 15 0.02 0.3 2 �0.5 0.5G2 2 100 10 0.01 0.2 2.7 �0.8 1G3 3 100 30 0.05 0.2 2 �0.8 0.8G4 6 100 20 0.03 0.4 2 �0.7 0.7G5 8 100 30 0.05 0.2 2.5 �0.8 0.8

Table 2Results of the IEEE 14-bus test system.

Variable Case 1 Case 2 Case 3

GA PSO IA IGA IPSO

Pg1 0.6963 0.3738 0.8291 0.5028 0.6924 0.2912 0.6057Qg1 0.1961 0.1888 0.0548 �0.0576 �0.4492 0.1811 �0.1300Pg2 2.7000 2.2278 2.0379 1.3293 1.5164 1.6766 1.9011Qg2 �0.2626 �0.2678 �0.026 0.4941 0.8493 0.2529 0.4666Pg3 0.6937 0.6759 0.6481 0.2787 0.4220 0.5100 0.2387Qg3 0.7999 0.7543 0.6900 0.4124 0.3950 0.3859 0.4428Pg4 0.4000 0.4033 0.5658 0.8702 0.8529 1.0000 0.6102Qg4 0.2115 0.2326 0.2144 0.1980 0.1696 0.0072 0.4098Pg5 0.2000 0.9510 0.5773 0.7167 0.2564 0.2188 0.3811Qg5 0.0000 0.0000 0.0000 0.3723 0.2936 0.3651 0.2915Costgen_p ($/h) 8860.1 10229.6 9613 8059.9 7462.1 7551.7 7037.2Costgen_Q ($/h) 112.1 107.4 86.063 31.693 43.208 25.08 36.89Cost_UPFC ($/h) . . .. . .. . .. . . .. . .. . .. 24.639 609.36 166.41 25.30 47.96UPFC p Send . . .. . .. . .. . . .. . .. . .. 0.3349 �0.4812 0.1458 �0.4122 0.1458

Rec. . . .. . .. . .. . . .. . .. . .. �0.3349 0.4812 �0.1458 0.4122 �0.1458UPFC Q Send . . .. . .. . .. . . .. . .. . .. 0.3121 �0.1342 0.2419 �0.1238 0.2419

Rec. . . .. . .. . .. . . .. . .. . .. �0.2107 0.1142 �0.1931 0.0943 �0.1931Ploss 0.1575 0.0992 0.1247 0.0980 0.0962 0.0765 0.1108

Total cost ($/h) 8972.2 10337 9723.7 8700.98 7671.7 7612.6 7122

Table 3Results of complex power line in IEEE 14-bus system.

Line Case 1 Case 2 Case 3 (based on IPSO method) Line limit

Send Rec. Send Rec. Send Rec.

1–2 0.1960 0.2392 0.1723 0.2234 0.2469 0.2482 11–5 0.5863 0.5671 0.3860 0.3790 0.4154 0.4060 0.62–3 0.9155 0.9054 0.7897 0.7796 0.7960 0.7693 12–4 0.8385 0.8089 0.5766 0.5602 0.5357 0.5193 12–5 0.6938 0.6734 0.4897 0.4774 0.4604 0.4477 0.63–4 0.2171 0.2408 0.3020 0.3184 0.3339 0.3349 1.24–5 0.6366 0.6419 0.3970 0.3990 0.3350 0.3361 0.44–7 0.2915 0.2936 0.2375 0.2513 0.1418 0.1430 14–9 0.2096 0.2175 0.0869 0.1250 0.0425 0.0416 0.55–6 0.4672 0.4660 0.3270 0.3204 0.4265 0.4393 0.5

6–11 0.1755 0.1917 0.1071 0.1584 0.3496 0.3385 1.26–12 0.1584 0.1464 0.1469 0.1383 0.1439 0.1409 16–13 0.3385 0.3337 0.2989 0.2985 0.3882 0.3758 0.8

7–8 0.2109 0.2000 0.9573 0.9510 0.4599 0.4798 1.27–9 0.5025 0.5082 0.7525 0.7518 0.3240 0.3172 0.8

9–10 0.0752 0.0506 0.1658 0.1343 0.1958 0.1949 19–14 0.1417 0.1347 0.1989 0.1818 0.0908 0.1838 1.2

10–11 0.1395 0.1228 0.1357 0.1031 0.2851 0.1971 112–13 0.0401 0.0761 0.0294 0.0786 0.0534 0.0643 1.513–14 0.1327 0.1432 0.0939 0.1250 0.2311 0.3233 0.4


install UPFC; 0 corresponds to the status that UPFC is installed insending end of transmission line, 1 corresponds to the is status thatUPFC is installed in receiving end of transmission line, and N is thenumber of UPFC’s.

The parameter initializations of the applied methods are givenin Appendix A.

5. Simulation results

The effectiveness of the proposed approach for optimal locationof UPFC is illustrated using IEEE 14-bus and 30-bus system. Thesimulation studies were carried out on Pentium 4 (Core 2 Quad)2.83 GHz system (personal computer) in MATLAB 7.8 environment.

Table 4Parameters of UPFC in IEEE 14-bus system.

Control parameters of UPFC Series source Shunt source

VcR (pu) hcR (deg) VvR (pu) hvR (deg)

GA �0.0736 �36.7565 0.9540 �5.3705PSO 0.0869 52.2231 1 0.2040IA 0.0103 8.8236 1.0454 2.4522e�004IGA 0.0149 76.9712 1 �0.0048IPSO 0.0994 �22.7980 1.0302 �0.2235

Fig. 6. IEEE 30-bus test system.

Table 5Generator data of the IEEE 30-bus test system.

Gi No. bus ai bi ci Pmingi

(pu) Pmaxgi

(pu) Qmingi

(pu) Qmaxgi

(pu)

G1 1 18 2 0.0037 0.5 3.6 �0.4 1.5G2 2 16 1 0.0175 0.2 1.4 �0.4 0.6G3 5 14 1 0.0625 0.15 1 �0.4 0.4G4 8 12 3.25 0.0083 0.10 1 �0.1 0.4G5 11 13 3 0.025 0.10 1 �0.6 0.24G6 13 13 3 0.025 0.12 1 �0.6 0.24


Table 6Optimal allocation of UPFC in the IEEE30-bus test system.

Optimization method UPFC1 location UPFC2 location

Line Near bus Line Near bus

GA 2–6 2 6–28 6PSO 6–8 6 22–24 24IA 6–28 28 6–10 6IGA 2–6 6 22–24 22IPSO 2–6 6 22–24 22

Table 8Results of complex power line in IEEE 30-bus system.

Line Optimization method based on IPSO Line limit

Send Rec.

1–2 1.2999 1.2475 1.31–3 0.8361 0.7910 1.32–4 0.5136 0.5002 0.653–4 0.7505 0.7414 1.32–5 0.9125 0.8695 1.32–6 1.55e�4 1.55e�4 0.654–6 0.7817 0.7795 0.95–7 0.1322 0.1317 0.76–7 0.4991 0.4882 1.36–8 0.1731 0.1724 0.326–9 0.1227 0.1252 0.65

6–10 0.1456 0.1476 0.329–11 0.5461 0.5586 0.659–10 0.6054 0.6070 0.654–12 0.3810 0.3691 0.65

12–13 0.3757 0.3805 0.6512–14 0.1285 0.1260 0.3212–15 0.2998 0.2924 0.3212–16 0.1138 0.1126 0.3214–15 0.0244 0.0243 0.1616–17 0.0618 0.0619 0.1615–18 0.0893 0.0885 0.1618–19 0.0400 0.0400 0.1619–20 0.1339 0.1351 0.3210–20 0.1762 0.1712 0.3210–17 0.1491 0.1473 0.3210–21 0.3196 0.3135 0.3210–22 0.1556 0.1528 0.3221–22 0.0278 0.0278 0.3215–23 0.0917 0.0907 0.16


5.1. IEEE 14-bus system

This system, as shown in Fig. 5, has been used to test the effec-tiveness of the proposed approach. The test system data can befound in [49]. System data and results are based on a 100 MVAand bus 1 is the reference bus. In order to verify the proposed ap-proach and illustrate the impacts of UPFC, three cases for test sys-tems were investigated:

Case 1: OPF without UPFC, with line limits ignored.Case 2: OPF without UPFC.Case 3: optimal location of one UPFC.

For evaluation of the proposed approach, system load is as-sumed to increase to 75%. We used the total active and reactiveproduction cost function of the generators and cost of installationof UPFC as the objective function for testing the system and findingthe optimal location of UPFC. Generator data are given in Table 1.The data for the UPFC are:

22–24 0.1370 0.1342 0.1623–24 0.0417 0.0416 0.1624–25 0.0428 0.0422 0.1625–26 0.0690 0.0670 0.1625–27 0.0303 0.0304 0.1628–27 0.2619 0.2542 0.6527–29 0.1047 0.1012 0.1627–30 0.1191 0.1129 0.1629–30 0.0606 0.0594 0.16

8–28 0.0732 0.0729 0.326–28 0.1983 0.1966 0.32

XcR ¼ 0:1; XvR ¼ 0:1; 0:001 6 VcR 6 0:2; 0:9 6 VvR 6 1:1;0 6 hcR 6 2p; 0 6 hvR 6 2p:

There are three cases to be discussed. The results are shown inTables 2–4. As can be observed from Tables 2 and 3, when line lim-its are relaxed, the results for case 1 are the same as those for thetraditional economic dispatch indicating a total active and reactivepower generation cost of 8972.2 $/h. For this case, lines 2–5 and 4–5 would carry more than their limits; the most expensive genera-tor G5 produced its minimum limits. The cheaper generator G2produced its maximum limits and most of the load is served byG2 without utilizing UPFC. Considering the limits (see results ofcase 2), the line 4–5 carry its maximum thermal limits, which pres-ent a congestive condition.

This condition will prevent loads to be served from generatorsobtained from the cheapest combination of generator outputs as

Table 7Results of the IEEE 30-bus test system.

Variable Optimization method

GA PSO

Pg1 (pu) 1.6211 1.8043Qg1 (pu) �0.2077 0.4334Pg2 (pu) 0.9335 1.0079Qg2 (pu) 0.0356 �0.0187Pg3 (pu) 0.9078 0.5927Qg3 (pu) 0.0037 0.0078Pg4 (pu) 0.6855 0.6732Qg4 (pu) 0.0425 0.1357Pg5 (pu) 0.2223 0.3148Qg5 (pu) 0.1671 0.0611Pg6 (pu) 0.3011 0.2890Qg6 (pu) 0.1584 0.0547Ploss 0.1368 0.1475

Total cost ($/h) 1954.36 1891.01

in case 1. Note that the most expensive generator G5 whichproduced 20 MW in case 1 produces 95.1 MW here and a cheapergenerator G2 is dispatched back. This dispatch of generatorscontributes an increase to the total active and reactive power pro-duction cost of generators (increased from 8972.2 $/h to 10337 $/h).

IA IGA IPSO

1.6337 1.5743 2.0287�0.3624 �0.0948 0.6594

0.7572 0.9058 0.57420.1861 0.1280 �0.03290.7212 0. 4386 052720.0251 0.0757 0.00900.7238 0.8272 0.65990.0065 0.0382 0.34280.4100 0.4892 0.53740.1553 0.1904 0.15220.4189 0.4325 0.36390.1369 0.1670 0.11110.1303 0.1332 0.1569

1780.05 1743.88 1687.43

Table 9Parameters of UPFC in IEEE 30-bus system.

Control parameters of UPFC Series source (UPFC1) Shunt source (UPFC1) Series source (UPFC2) Shunt source (UPFC2)

VcR (pu) hcR (deg) VvR (pu) hvR (deg) VcR (pu) hcR (deg) VvR (pu) hvR (deg)

GA 0.0232 0 1.0468 0 0.0181 78.0963 1.0423 0.0438PSO 0.0133 76.0067 1.0841 0.0034 0.00154 76.0067 0.983 �0.0316IA 0.00067 0 1.0501 0 0.0176 79.4317 1.0231 �0.0142IGA 0.0180 86.1679 1.0193 �0.0015 0.0240 86.1679 1.0534 0.0033IPSO 0.00089 0 1.0522 0 0.0133 0 1.0193 0.00245


Case 3 contains the results of UPFC optimal location with fiveevolutionary algorithms, GA, PSO, IA, IGA and IPSO in the sameiteration (No. of iteration = 100). In the GA algorithm UPFC is allo-cated between buses 4 and 5 and near bus 5, in the PSO and IAtechniques UPFC is allocated between buses 4 and 7 and nearbus 4, in the IGA technique UPFC is allocated between buses 3and 4 and near bus 4 and in the IPSO technique UPFC is allocatedbetween buses 5 and 6 and near bus 5. However, a cheaper dis-patch is obtained with IPSO algorithm (see results of case3) wherethe total cost has been reduced by 3215 $/h. In the GA, PSO, IA, IGAtechniques the total cost has been reduced by 613.3, 1636.02,2665.3, 2724.4 $/h, respectively. It could also be mentioned thatin comparing the two HIA methods, the total cost in applied IPSOmethod were reduced by 490.6 $/h. The complex power line andcontrol parameters of UPFC are shown in Tables 3 and 4.

5.2. IEEE 30-bus system

In this section, the proposed method was tested on IEEE 30-bustest system. Fig. 6 shows the 30-bus IEEE test system and the busdata and line data are taken from Refs. [50,51]. For evaluation ofproposed method, system load is assumed to be increased by60%. We used the total active and reactive production cost functionof the generators and cost of installation of UPFC as the objectivefunction. Generator data are given in Table 5. The data for the UPFCare:

XcR ¼ 0:1; XvR ¼ 0:1; 0:001 6 VcR 6 0:2; 0:9 6 VvR 6 1:1;0 6 hcR 6 2p; 0 6 hvR 6 2p:

As above, the results of optimal location of UPFC’s with five evo-lutionary algorithms mentioned above in the same iteration arecompared. The results are shown in Tables 6–9. In the five evolu-tionary algorithm applied, two UPFC were required, whose optimallocations are shown in Table 6. In this case, a cheaper dispatch isobtained with IPSO algorithm where the total cost has been re-duced at least by 3.24% compared with the other methods investi-gated in this paper (Table 7). It is worth mentioning that incomparing both HIA methods, the total cost in applied IPSO meth-od was reduced by 56.45 $/h. The complex power line and controlparameters of UPFC are shown in Tables 8 and 9.

6. Conclusion

This paper presents the applications of HIA to find the optimallocation of UPFCs for obtaining minimum total active and reactivepower production cost of generators and minimizing the installa-tion cost of UPFCs. The UPFC can provide control of voltage magni-tude, voltage phase angle and impedance. Therefore, it was utilizedeffectively in this paper to increase power transfer capability of theexisting power transmission lines, and reduce operational andinvestment costs. UPFC also offers a mechanism that may help tra-ditional congestion mitigation methods and in some cases may

prevent generators to run in out of-merit order, and thus may pre-vent load shedding or curtailment that is normally required tomaintain system security.

In this study, simulations were performed on IEEE 14-bus and30-bus test system. Optimizations were carried out on the controlparameters including the location of the UPFCs and their settings.Results show that utilizing UPFC may reduce generation costs. IPSOand IGA as HIA methods, give minimum cost of power productionand installation of UPFC compared with other methods such as GA,PSO, and IA. The optimal solutions found by the IPSO were betterthan those found by IGA method. IPSO added immunity and en-hanced global optimization ability, so the combinative algorithmseems to be more accurate and reliable.

Appendix A

In this appendix, the parameters used in the simulations carriedout on different algorithms are presented.

For GA method:Crossover fraction = 0.3Mutation rate = 0.2For PSO method:C1 = 1, C2 = 3, C = 1W = 0.6 � (0.6 � iteration number)/No. of generation;

For IA method:Replacement rate = 0.2Cloning rate = 0.1Mutation rate = 0.2 � (0.2 � iteration number)/No. ofgenerationSuppression threshold = 1e�9Percentile amount of clones to be re-selected = 0.7Pruning threshold = 1For IGA method:Crossover fraction = 0.5Cloning rate = 0.2Mutation rate = 0.1Suppression threshold = 1e�9Percentile amount of clones to be re-selected = 0.6Pruning threshold = 1For IPSO method:C1 = 0.6, C2 = 3.4,C = 1W = 1 � (1 � iteration number)/No. of generation

Replacement rate = 0.6Cloning rate = 0.1Mutation rate = 0.6 � (0.6 � iteration number)/No. ofgenerationSuppression threshold = 1e�9Percentile amount of clones to be re-selected = 0.6Pruning threshold = 1Population size and No. of generation for all above meth-ods were 80 and 100, respectively.


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New approach for optimal UPFC placement using hybrid immune algorithm in electric power systems