240 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007

Bacteria Foraging-Based Solution to Optimize BothReal Power Loss and Voltage Stability Limit

M. Tripathy and S. Mishra, Senior Member, IEEE

AbstractOptimal location and control of a unified power flowcontroller (UPFC) along with transformer taps are tuned with aview to simultaneously optimize the real power losses and voltagestability limit (VSL) of a mesh power network. This issue is formu-lated as a nonlinear equality and inequality constrained optimiza-tion problem with an objective function incorporating both the realpower loss and VSL. A new evolutionary algorithm known as bac-teria foraging is applied for solving the multiobjective multivari-able problem, with the UPFC location, its series injected voltage,and the transformer tap positions as the variables. For a single ob-jective of only real power loss, the same problem is also solved withinterior point successive linearization program (IPSLP) techniqueusing the LINPROG command of MATLAB. A comparison be-tween the two suggests the superiority of the proposed algorithm. Acost effectiveness analysis of UPFC installation vis--vis loss reduc-tion is carried out to establish the benefit of investment in a UPFC.

Index TermsBacteria foraging, continuation power flow, linearprogramming, optimal power flow (OPF).

I. INTRODUCTION

OPTIMAL power flow (OPF) is a static nonlinear programthat intends to schedule the controls of the power systemin such a manner that a certain objective function like realpower loss is optimized with some operating equipment and se-curity requirement, limit constraints forced on the solution. TheOPF problem has been solved from different perspectives, suchas studying the effects of load increase/decrease on voltagestability/power flow solvability, generation rescheduling tominimize the cost of power generation, controls such as taps,shunts, and other modern VAR sources adjustments to minimizereal power losses in the system. The OPF is solved by varietiesof methods, i.e., successive linear programming (SLP) [1], theNewton-based nonlinear programming method [2], and withvarieties of recently proposed interior point methods (IPM)[3][5].

With the advent of flexible ac transmission systems (FACTS)technology, a new possibility of optimizing the power flowwithout resorting to generation rescheduling or topologychanges has arisen. Unified power flow controller (UPFC), themost advanced in the family of these controllers, can providesignificant flexibility in OPF by injecting a controlled seriesand shunt compensation [6].

In deregulated power environment, proper coordination of theUPFC with the existing transformer taps already present in thesystem will not only improve the steady state operating limit of

Manuscript received October 25, 2006; revised September 5, 2006. The workof S. Mishra was supported by AICTE, India under its Young Teachers Awardscheme-2004. Paper no. TPWRS-00694-2005.

The authors are with the Department of Electrical Engineering, Indian Insti-tute of Technology, Delhi, India.

Digital Object Identifier 10.1109/TPWRS.2006.887968

a power system but also see that the system is more secure interms of voltage collapse. In [7], the authors have coordinatedseveral FACTS devices to provide a secured transmission withminimized active power loss. It is well known that the OPF so-lution alone does not reflect upon the above security concerns ofthe system. The continuation power flow (CPF) [8] gives infor-mation regarding how much percentage overloading the systemcan withstand before a possible voltage collapse. In [9], the au-thors have successfully incorporated the CPF problem into anOPF problem so that both the issues can be addressed simul-taneously. In this paper, the maximum percentage overloading

the system can withstand is defined as voltage stabilitylimit (VSL) and incorporated along with the objective of realpower loss minimization, making the problem multiobjective.

The main disadvantage with the classical techniques ofOPF solution lies in the fact that they are highly sensitive tostarting points, owing to a nonmonotonic solution surface. Toeliminate such problems, evolutionary techniques have beenapplied in solving the OPF problem [10], [11]. In [11], theauthors have applied particle swarm optimization (PSO) to theproblem of OPF. Such algorithms, based on food searchingbehavior of species (like birds, etc.), compute both globaland local best positions at each instant of time, to decidethe best direction of search.

This paper employs a new algorithm from the family of evo-lutionary computation, known as bacteria foraging algorithm(BFA), to solve a combined CPF-OPF problem of real powerloss minimization and VSL maximization of the system. BFAhas been recently proposed [12] and further applied for har-monic estimation problem in power systems [13]. The algorithmis based on the foraging behavior of E. coli bacteria present inhuman intestine. The UPFC location, series injection voltage,and transformer tap positions are simultaneously optimized ascontrol variables, so that the multiple objectives are fulfilled,keeping an eye to all specified constraints. The results so ob-tained show its strength in solving highly nonlinear epistaticproblems. The main objectives of this paper are to optimize thetransformer taps, UPFC location, and its injection voltage for asingle objective of real power loss minimization and then for themultiple objectives of loss minimization and VSL maximiza-tion. For both the cases of single and multiple objectives, theoptimization is carried out in three steps, as given below.

1) Only transformer tap positions are optimized.2) Keeping the optimized transformer tap positions from the

above step fixed, the UPFC variables are optimized.3) Both the transformer taps and UPFC variables are opti-

mized simultaneously.Finally, a cost analysis for installation of UPFC is carried out

to establish the investment in putting a UPFC for the cause.

0885-8950/$20.00 2006 IEEE

TRIPATHY AND MISHRA: BACTERIA FORAGING-BASED SOLUTION TO OPTIMIZE BOTH REAL POWER LOSS AND VSL 241

II. BACTERIA FORAGING OPTIMIZATION: A BRIEF OVERVIEWThe idea of BFA is based on the fact that natural selection

tends to eliminate animals with poor foraging strategies andfavor those having successful foraging strategies. After manygenerations, poor foraging strategies are either eliminated or re-shaped into good ones. The E. coli bacteria that are present inour intestines have a foraging strategy governed by four pro-cesses, namely, chemotaxis, swarming, reproduction, and elim-ination and dispersal [12].

1) Chemotaxis: This process is achieved through swimmingand tumbling. Depending upon the rotation of the flagellain each bacterium, it decides whether it should move in apredefined direction (swimming) or an altogether differentdirection (tumbling), in the entire lifetime of the bacterium.To represent a tumble, a unit length random direction, say,

, is generated; this will be used to define the directionof movement after a tumble. In particular

(1)

where represents the th bacterium at th chemo-tactic, th reproductive, and th elimination and dispersalstep. is the size of the step taken in the random di-rection specified by the tumble. C is termed as the runlength unit.

2) Swarming: It is always desired that the bacterium that hassearched the optimum path of food should try to attractother bacteria so that they reach the desired place morerapidly. Swarming makes the bacteria congregate intogroups and hence move as concentric patterns of groupswith high bacterial density. Mathematically, swarming canbe represented by

(2)

where is the cost function value to beadded to the actual cost function to be minimized to presenta time varying cost function. S is the total number of bac-teria. p is the number of parameters to be optimized thatare present in each bacterium. , , ,and are different coefficients that are to be chosenjudiciously.

3) Reproduction: The least healthy bacteria die, and the otherhealthiest bacteria each split into two bacteria, which areplaced in the same location. This makes the population ofbacteria constant.

4) Elimination and Dispersal: It is possible that in the localenvironment, the life of a population of bacteria changes

Fig. 1. New England power system layout.

Fig. 2. Basic arrangement of UPFC.

either gradually by consumption of nutrients or suddenlydue to some other influence. Events can kill or disperse allthe bacteria in a region. They have the effect of possibly de-stroying the chemotactic progress, but in contrast, they alsoassist it, since dispersal may place bacteria near good foodsources. Elimination and dispersal helps in reducing thebehavior of stagnation (i.e., being trapped in a prematuresolution point or local optima). The detailed mathematicalderivations as well as theoretical aspect of this new conceptare presented in [12] and [13].

III. PROBLEM STATEMENT

Problem: to solve a voltage secure real power loss minimiza-tion of the ten-machine New England power systems [15], con-nected with UPFC by using IPSLP and BFA. Both the sequentialand simultaneous allocation of transformer taps and UPFC arecarried out for comparison,

A. Test System

In this paper, the ten-machine, 39-bus New England powersystem shown in Fig. 1 is considered for study. The system datain detail, including the 12 transformers nominal tap values, aregiven in [15]. The system diagram is shown in Fig. 1.

B. Operating Principle of the UPFC and Its ModelThe UPFC is a unique device in the family of FACTs devices.

It consists of a series and shunt connected converters as depictedin Fig. 2.

242 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007

Fig. 3. UPFC injection model.

It can simultaneously control the real and reactive powers ofthe line and voltage of the bus at which it is connected, by in-jecting proper magnitude of voltage in series and shunt, respec-tively. In this paper, one UPFC, with injection model [6], is con-nected in the system at the suitable location. The UPFC injectionmodel is presented in Fig. 3.

C. Optimal Power Flow (OPF): Problem FormulationThe OPF problem is a static constrained nonlinear optimiza-

tion problem, the solution of which determines the optimal set-tings of control variables in a power network respecting variousconstraints. Hence, the problem is to solve a set of nonlinearequations describing the optimal solution of power system. It isexpressed as

MinimizeSubject to

(3)The objective function is real power loss of the mesh

connected multimachine test system. is a set of non-linear equality constraints to represent power flow, andis a set of nonlinear inequality constraints (i.e., bus voltages,transformer/line MVA limits, etc.). Vector consists of de-pendent variables, and consists of control variables. For theabove problem, the control variables are the transformer tapvalues, and both the magnitude and phase angle of UPFC se-ries injected voltage .D. OPF Formulation Considering Voltage Stability Limit

The same objective of real power loss minimization is aug-mented with maximization of VSL. The VSL can be calculatedthrough CPF, which introduces a load parameter defined as thepercentage increase of generation and load from its base value.The resulting load and generation equation in terms of the loadparameter is as follows:

(4)The load parameter can be increased until the system just

reaches the verge of instability, which is also known as thenotch point of the PV-curve. The maximum value of the loadparameter is termed as VSL. The objective is to

OptimizeSubject to

(5)

The function to be optimized now can be represented as

(6)

whereReal Power Loss

The solution of CPF is carried out with the help of a suitablychosen continuation parameter. With the increase of , a newsolution point is predicted first and then corrected in usual pre-dictor and corrector steps [8]. Since the objective is to maximizethe VSL, so its reciprocal is added to the original cost functionof real power loss so that the overall cost can be minimized.

IV. IMPROVED BACTERIAL FORAGING: THE ALGORITHMThe BF algorithm suggested in [12] and [13] is modified so

as to expedite the convergence. The modifications are discussedbelow.

1) In [13], the author has taken the average value of all thechemotactic cost functions, to decide the health of partic-ular bacteria in that generation, before sorting is carriedout for reproduction. In this paper, instead of the averagevalue, the minimum value of all the chemotactic cost func-tions is retained for deciding the bacteriums health. Thisspeeds up the convergence, because in the average scheme[13], it may not retain the fittest bacterium for the subse-quent generation. On the contrary, in this paper, the globalminimum bacteria among all chemotactic stages passes onto the subsequent stage.

2) For swarming, the distances of all the bacteria in a newchemotactic stage is evaluated from the global optimumbacterium until that point and not the distances of eachbacterium from the rest of the others, as suggested in [12]and [13].

The algorithm is discussed here in brief.

Step 1Initialization

The following variables are initialized.1) Number of bacteria (S) to be used in the search.2) Number of parameters (p) to be optimized.3) Swimming length .4) the number of iterations in a chemotactic loop.

.

5) the number of reproduction.6) the number of elimination and dispersal events.7) the probability of elimination and dispersal.8) Location of each bacterium P(p,S,1), i.e., random numbers

on [01].9) The values of , , , and .

Step 2Iterative algorithm for optimization

This section models the bacterial population chemotaxis,swarming, reproduction, and elimination and dispersal

TRIPATHY AND MISHRA: BACTERIA FORAGING-BASED SOLUTION TO OPTIMIZE BOTH REAL POWER LOSS AND VSL 243

(initially, ). For the algorithm updating,automatically results in updating of P.

1) Elimination-dispersal loop:2) Reproduction loop:3) Chemotaxis loop:

a) For , calculate cost function value foreach bacterium as follows. Compute value of cost function

. Let.

is the location of bacterium corresponding tothe global minimum cost function out of all thegenerations and chemotactic loops until that point(i.e., add on the cell-to-cell attractant effect forswarming behavior).

Let to save this value sincewe may find a better cost via a run.

End of For loopb) For , take the tumbling/swimming

decision Tumble: Generate a random vector

with each element , a randomnumber on [0,1].

Move: let

Fixed step size in the direction of tumble forbacterium is considered.

Compute and then let

Swim:i) Let ; (counter for swim length)

ii) While (have not climbed down toolong) Let If (if doing

better), let and

use this to compute the new

Else, let . This is the end of theWhile statement.

c) Go to next bacterium if (i.e., go to b)to process the next bacterium.

4) If , go to step 3. In this case, continue chemotaxissince the life of the bacteria is not over.

5) Reproductiona) For the given and , and for each , let

be the health ofthe bacterium . Sort bacteria in order of ascendingcost (higher cost means lower health).

b) The bacteria with highest valuesdie and other bacteria with the best value split

Fig. 4. Flowchart of the bacteria foraging algorithm.

(and the copies that are made are placed at the samelocation as their parent)

6) If , go to 2; in this case, we have not reached thenumber of specified reproduction steps, so we start thenext generation in the chemotactic loop.

7) Elimination-dispersal: For , with probability, eliminates and disperses each bacterium (this keeps

the number of bacteria in the population constant). To dothis, if one eliminates a bacterium, simply disperse it to arandom location on the optimization domain.

The flowchart of the improved algorithm is shown in Fig. 4.

V. INTERIOR POINT SUCCESSIVE LINEARIZATIONThe successive linearization program solves the OPF problem

as a succession of linear solutions starting from an initial point.That is to

MinimizeSubject to

(7)

where

, initial values of and ;

, shift about this initial point;

, linear approximation of nonlinear problem.

The basic steps of the IPSLP algorithm are given below.1) Solve the power flow problem.2) Linearize the OPF problem (express it in terms of changes

about the current exact system operating condition).

244 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007

a) The sensitivities of the cost function with respect tothe change in control variables are evaluated by per-turbing around their present value infinitesimally.

b) The changes in values of the monitored constraints areevaluated properly from the power flow.

c) Express the incremental control variables aschanges about the current control variable values.

3) Linearize the incremental network model.4) Solve the linearly constrained OPF by primal-dual interior

point method.5) Update the control variables by , solve the exact non-

linear power flow problem, and evaluate the cost functionfor the updated control variables

6) If the tolerance in changes in control variables has beenreached, then terminate; else, go to step 2 and continue.

In this paper, the real power loss minimization problem is for-mulated by considering a constant real and a variable reactivepower generation profile in the system. The LINPROG com-mand in MATLAB is used to solve the IPSLP. In the IPSLPtechnique, the approach is to minimize the change in loss in-stead of loss itself, as the solution progresses in succession. TheLINPROG command is based on the technique of Linear pro-gramming Interior Point Solver (LIPSOL) algorithm. Startingfrom the last iteration solution, the sensitivities of the real powerloss to the control variables (i.e., the transformer taps and UPFCvariables) are evaluated for them to be used in the LINPROGcommand.

VI. SIMULATION AND RESULTSThe objective function of the real power loss minimiza-

tion problem is formulated by introducing penalty factors forvoltage, transformer MVA, and transmission line limit viola-tions. These penalty factors are added to the total real powerloss in the system

whereReal Power Loss

(8)where , , and are the penalty factors added with thereal power loss , so that a constrained solution is achieved.

and are the maximum and minimum limits of busvoltages [14] for all the buses. Similarly, andare, respectively, the maximum MVA limits of the transformersand lines in the system. The values of andare chosen at double the maximum nominal values of respec-tive quantities. The formulation of penalty factors can be clearlyunderstood with the help of an example. If all the bus voltagesolution so obtained for a particular set of control variable arewithin the and limits, then the value of wouldbe zero; otherwise, it will be either 10 or 20, depending onwhether one or both the upper and lower limits have been vi-olated. Hence, the solution of a minimization problem wouldalways avoid those that violate the limits. The methodology

Fig. 5. Reproduction schemes proposed (Min) versus [13] (average).

adopted for optimization with both the BFA and IPSLP tech-niques are discussed here in brief. With BFA technique, boththe single objective of real power loss minimization (denoted asBFAS) and multiobjective of loss and VSL (denoted as BFAM)were solved. For multiobjective case, the objective function canbe formulated as

(9)

A. Optimization With Only Transformer Taps as ControlVariables (Single Objective of Loss, BFAS)

Bacteria Foraging (Without Swarming): Initially, theswarming effect is excluded from the algorithm so as tostudy the convergence behavior. The values of bacteria number(S) and the chemotactic loops number are chosen in steps,and the algorithm is run for number of times. For a whole cycleof elimination and dispersal loop when the cost function re-mains unchanged, then the algorithm is said to have converged.This occurs when the minimum of cost function values amongall bacteria becomes equal to their average [13]. The speed ofconvergence differs with different combinations of S and . Itwas found that and gives the fastest convergence.A comparison of convergence by taking the average value ofeach bacterium [13] in the chemotactic stage to that of globalminimum for reproduction is presented in Fig. 5. It is foundthat with the proposed scheme, the algorithm converges faster.

Moreover, it is also observed that with the average scheme,the algorithm convergence is very sensitive to the value of S, ,and the run length unit coefficient C. For some combinations ofthese values, the average scheme has a tendency of oscillatingaround the solution point (as in Fig. 5). This phenomenon isavoided when the global minimum bacterium is retained beforereproduction.

Bacteria Foraging (With Swarming): As established above,swarming is included now considering the global minimum. Tochoose the parameters of swarming, the algorithm is run fordifferent values of , , , and . Itwas found that these values when chosen as 2.0, 0.2, 2.0, and

TRIPATHY AND MISHRA: BACTERIA FORAGING-BASED SOLUTION TO OPTIMIZE BOTH REAL POWER LOSS AND VSL 245

Fig. 6. Performance of algorithms.

TABLE IOPTIMIZATION WITH ONLY TRANSFORMER TAPS AS CONTROL VARIABLES

10, respectively, give the fastest convergence. Fig. 6 elucidatesthe relative improvement of convergence when swarming ef-fect is included as compared to without swarming. It is seenthat though the loss minimization is almost the same with boththe techniques, there is a difference in the values of tap posi-tions to which the algorithms have converged. With nominalvalues of taps, the real power loss and VSL were found out tobe 0.4483 and 0.8050 p.u., respectively. With the above opti-mized tap values, the CPF solution is carried out and the VSL iscalculated and presented in Table I. After solving the CPF, thePV-curve for the weakest bus in the solution process is drawnw.r.t. the load parameter . As shown in Fig. 7, the PV-curvefor the weakest bus is similar for both BFAS and IPSLP tech-niques of optimization. It is to be noted that the weakest bus isdefined as that bus that undergoes maximum voltage deviationduring a CPF solution.

Optimization of Both Real Power Loss and VSL With OnlyTransformer Taps as Control Variables (BFAM): With an objec-tive to optimize both real power loss and VSL, the cost functionis modified. The reciprocal of VSL is added to the real power

Fig. 7. PV curve of weakest bus (only taps).

loss. The optimization is carried out only with BFA. The trans-former tap values, along with the corresponding optimized lossand VSL values, are given in Table I. It is seen that the VSLvalue has improved, although the real power loss has increasedmarginally. However, the sum of real power loss and the recip-rocal of VSL has reduced, when the multiobjective function isconsidered. Fig. 7 also depicts the P-V curve of the weakest busfor BFAM. It is seen that, with BFAM, the system can withstandmore loading before a voltage collapse could occur.

B. Sequential Optimization of UPFC Location and ItsInjection Voltage With Above Optimized Tap Values

With the optimized tap positions obtained in previous step,the UPFC variables are then evaluated so that objective functioncould still be reduced. The tap values for each scheme of opti-mization are kept at their corresponding values obtained fromthe previous section. The power injection model as discussedin Section III is used for modeling the UPFC. In both BFA andIPSLP methods, 14 lines (out of a total of 46 lines), containingtransformers or feeding generator powers to the network, areexcluded for connecting the UPFC. The UPFC is connected atthe left-hand-side bus as per line notation given in [15]. For ex-ample, in lines 318 or 1013, the UPFC can be connected atbus 3 or 10, respectively. In the case of BFA, the line at whichUPFC should be connected is decided randomly out of 32 linesselected in the initial stage. So with BFA, the line number inwhich UPFC is to be connected also becomes a control variablealong with the others. On the other hand, the UPFC locationcannot be used as a control variable for IPSLP, as it cannot belinearized through perturbation. Therefore, in IPSLP technique,the UPFC is connected in all the 32 lines, considering one at atime. The best location and the UPFC injection voltage in eachsuccession of linearization are retained.

The optimization with BFA is carried out for both BFAM andBFAS. Table II presents the values of UPFC location, its injec-tion voltage, and the corresponding real power loss and VSLvalues for IPSLP, BFAS, and BFAM separately. It is seen thatwhen more nonlinear equipment like UPFC is inducted into thesystem, the IPSLP falls prey of a local minima, but the BFA

246 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007

TABLE IIOPTIMIZED VALUES OF UPFC LOCATION AND INJECTION

VOLTAGE WITH TRANSFORMER TAP VALUES FIXED

Fig. 8. PV curve of weakest bus (sequential UPFC).

has successfully converged. Moreover, with IPSLP optimizedUPFC variables, the VSL calculated was much lower. That is,with IPSLP, though the system real power loss could be reduced,it would be at the cost of decreasing the security margin of thesystem. It is also seen that, even though with BFAM the losscould not be reduced considerably, it has best succeeded in re-ducing the combined objective of loss minimization and VSLmaximization.

Fig. 8 depicts the PV-curves of the weakest bus for all thethree cases of IPSLP, BFAS, and BFAM. It is found that withBFAM, the UPFC parameters can be so optimized that thesystem could be loaded beyond double ( is more than 1),its nominal loading before a voltage collapse could occur.It is depicted from Fig. 8 that the other two techniques haveachieved lower magnitude of VSL.

C. Simultaneous Optimization of UPFC Location, Its InjectionVoltage Along With Taps

Simultaneous optimization of UPFC location and its variablesalong with the transformer taps could still reduce the overall

cost function. For optimizing with the BFAS, the numbers ofvariables now become 15, i.e., 12 transformer tap positions, andthree UPFC variables. With IPSLP, this becomes 14, as the lo-cation of UPFC cannot be taken. The optimization algorithm re-mains the same. It is seen that the loss could still be reduced withsimultaneous optimization with both BFAS and IPSLP tech-niques, but the later again fails to minimize the loss as success-fully as the BFAS. Moreover, it is seen that with the BFAM, theVSL has improved considerably, though at the cost of deterio-rated loss reduction. For all the optimized transformer tap andUPFC variables, the corresponding loss and the VSL values aregiven in Table III. Fig. 9 shows the P-V curves of the weakestbus for all the three optimization schemes. The magnitude ofbus voltages (with simultaneous optimization), obtained withthe three schemes of optimization, is shown in Fig. 10. It is seenthat all the bus voltages remain within the limits, and the gener-ator buses maintain their specified voltages when the optimizedvariables are used.

D. Cost Benefits Analysis for Implementing a UPFCfor Loss Reduction

For comprehending the economic benefit of investing in acostly device like the UPFC, a straightforward calculation interms of reduction in cost of generation due to reduced loss inthe system can be compared vis--vis the investment cost ofUPFC, assuming it is to be delivering service for a certain pe-riod of time [16]. So for a cost benefit analysis, the optimizedUPFC parameters only with one objective of real power lossminimization are considered. For any of the schemes, the re-duction in generation cost is evaluated [17], by considering asmuch reduction in generation of the slack bus as there was re-duction in loss of the system. The cost of generation isevaluated as follows:

(10)

The values of and for the tenth (slack) generator is chosenas per [17]. The savings in generation cost owing to loss re-duction after installation of UPFC can be estimated by findingthe differential generation cost for two different generationscheduling, i.e., before and after incorporation of UPFC (trans-former taps being optimized), considering the total loss reduc-tion has been translated only to the slack generator. Five percentof the UPFC MVA rating is considered as its switching loss andadded to the actual real power loss of the system. The invest-ment cost of UPFC is evaluated with the help of the followingempirical formula [14], [16]:

(11)where is the cost of UPFC in $/Kvar, and is theoperating range of the UPFC in Mvar. The coefficients , ,and are taken as 188.2, 0.2691, and 0.0003, respectively[16]. Taking the average running duration of the UPFC to befive years, the cost of UPFC is evaluated in terms of $/h, sothat it can be compared with . Table IV below gives the com-parative figures of investing in UPFC with both simultaneousand sequential BFAS schemes, denoted as X and Y, respectively.

TRIPATHY AND MISHRA: BACTERIA FORAGING-BASED SOLUTION TO OPTIMIZE BOTH REAL POWER LOSS AND VSL 247

TABLE IIISIMULTANEOUSLY OPTIMIZED VALUES OF UPFC AND TRANSFORMER TAPS

Fig. 9. PV curve of weakest bus (simultaneous UPFC and taps).

From Table IV, at the particular operating conditions, it is foundthat the actual MVA capacity of the series part of the UPFC forthe two schemes, required for only reducing transmission loss,are 8.55 and 4.22 MVA, respectively. However, the operatingconditions can change, which may require different MVA injec-tion for the same cause. Moreover, the UPFC can also be usedfor many other application such as improving VSL, regulatingthe real and reactive power flow in the transmission line, and im-proving stability of a power system. To accommodate such extrafeatures along with the loss reduction, the MVA capacity has tobe increased. Therefore, in this paper, to evaluate the cost effec-tiveness of UPFC, we have considered the rating as 15 MVA.The IPSLP scheme was found to be still more cost ineffective,as the loss reduction is poorer as compared to BFA, whereas theUPFC injection requirements are almost comparable. From theresults, the simultaneous scheme (X, shown bold in Table IV)proves to be more beneficial, as compared to the sequential (Y)scheme. In this paper, 100 MVA is considered as the base valuefor carrying out the simulation work.

VII. CONCLUSIONSIn any power system, it can be inferred that optimizing control

variables for any one objective of real power loss or VSL may

Fig. 10. Voltage profiles of all the buses at nominal load.

TABLE IVSAVING IN COST OF GENERATION (F ) VERSUS UPFC COST (F )

deteriorate the other. Therefore, the new evolutionary technique,bacteria foraging, is used for allocating, transformer taps, andUPFC with a view to minimize the real power loss and improvethe VSL of the system simultaneously. For single objective ofreal power loss, the BFA technique succeeds in better loss mini-mization as compared to conventional IPSLP technique, partic-ularly after the UPFC is introduced into the system. It can be de-duced that the IPSLP becomes more prone to local optimality,when variables of highly nonlinear devices like the UPFC aretaken into consideration. The results of the multiobjective so-lution show that the BFAM technique has provided the bettersolution as compared to the IPSLP. In BFAM case, it is seenthat even though a marginal price is paid for the loss, the system

248 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007

VSL has improved. Finally, an economic viability study of in-stalling the UPFC is carried out, which clarifies the fact that thesimultaneous scheme of optimizing both UPFC variables andtransformer taps together is more beneficial compared to the se-quential scheme. This is because of the fact that more systemreal power loss reduction is achieved with the former scheme,with the same UPFC MVA rating.

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M. Tripathy is pursuing the Ph.D. degree (part-time) in the Department of Elec-trical Engineering at Indian Institute of Technology, Delhi, India.

He is with the University College of Engineering Burla, Orissa, India. Hisfield of interest is intelligent control application to power system dynamics.

S. Mishra (SM04) received the B.E. degree fromUniversity College of Engineering, Burla, Orissa,India, in 1990 and the M.E. and Ph.D. degrees fromRegional Engineering College, Rourkela, Orissa,India, in 1992 and 2000, respectively.

In 1992, he joined the Department of Electrical En-gineering, University College of Engineering, Burla,as a Lecturer and subsequently became a Reader in2001. Presently, he is an Assistant Professor with theDepartment of Electrical Engineering, Indian Insti-tute of Technology, Delhi, India. His interests are in

soft computing applications to power system control and power quality.Dr. Mishra has been honored with many prestigious awards, such as INSA

Young Scientist Medal-2002, INAE Young Engineers Award-2002, recognitionas DST Young Scientist 20012002, and the Carrier Award for young teachersby AICTE.