POWER FLOW OPTIMIZATION USING SEEKEROPTIMIZATION ALGORITHM AND PSO

VIGNESH.PDepartment of Electrical & Electronics Engineering

Anna UniversityVeerammal Engineering College, Dindigul, Tamilnadu

Indiavickymeps@gmail.com

Abstract: - The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operationpoint which minimizes generation cost, loss etc. or maximizes social welfare, loadability etc. whilemaintaining an acceptable system performance in terms of limits on generators’ real and reactive powers,line flow limits, output of various compensating devices etc.

This paper aims to find a solution for the Optimal Power Flow (OPF) problem with securityconstraints by the seeker optimization algorithm (SOA). The major objective is to minimize the overalloperating cost and real power losses while satisfying the power flow equations and system security. TheSOA is based on the concept of simulating the act of human searching, where the search direction is basedon the empirical gradient by evaluating the response to the position changes. To demonstrate itsrobustness, the proposed algorithm was tested on IEEE 30 Bus System and the proposed approach resultswere simulated using MATLAB. The performance of this algorithm is compared with the performance ofPSO.

Key-Words: - global optimization, power system, seeker optimization algorithm

1 IntroductionThe optimal power flow is an inherently non-linear optimization problem with a non-linearobjective function and a set of non-linearequality and inequality constraints. Optimalpower flow is one of the main functions ofpower generation operation and control. Itdetermines the optimal setting of generatingunits[1]. It is therefore of great importance tosolve this problem as quickly and accurately aspossible.

In the past two decades, a wide varietyof optimization techniques have been applied insolving the optimal power flow problem, such aslinear programming, non-linear programming,Newton-based techniques, and interior pointmethods. The optimal power flow problem is ahighly non-linear and a multi-modaloptimization problem which exists more thanone local optimum. Hence, most of thesetechniques are not suitable for such a problem.Recently, genetic algorithm and particle swarmoptimization (PSO) have been proposed forsolving the optimal power flow problem[3].Particle swarm optimization, first introduced by

Eberhart and Kennedy, has been usedextensively in many fields,Including function optimization, neutral networkand system control, etc. Unfortunately, thepremature convergence of particle swarmoptimization algorithm degrades itsperformance.

2 Problem formulationOptimal Power flow (OPF) is allocating loads toplants for minimum cost while meeting thenetwork constraints. It is formulated as anoptimization problem of minimizing the totalfuel cost of all committed plant while meetingthe network (power flow) constraints. Thevariants of the problems are numerous whichmodel the objective and the constraints indifferent ways.

The basic OPF problem can describedmathematically as a minimization of problem ofminimizing the total fuel cost of all committedplants subject to the constraints[1].Minimize (1)

F(Pi) is the fuel cost equation of the‘i’th plant. It is the variation of fuel cost ($ or

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Rs) with generated power (MW).Normally it isexpressed as continuous quadratic equationFi(Pi)=aiPi

2+biPi+ci, Pimin Pi Pi

max (2)The total generation should meet the

total demand and transmission loss. Thetransmission loss can be determined from powerflow.

= D+Pl (3)

3 General reviewsIn 1990, Chowdhury did a survey on economicdispatch methods. In 1999, J.A.Momoh et al.presented a review of some selected OPFtechniques. In last decades, the followingoptimization methods has been used widely.[1]Linear Programming (LP) method, NewtonRaphson (NR) method, Quadratic Programming(QP) method, Nonlinear Programming (NLP)method, Interior Point (IP) method and ArtificialIntelligence (AI) methods.

Even though, excellent advancementshave been made in classical methods, they sufferwith the following disadvantages: In most cases,mathematical formulations have to be simplifiedto get the solutions because of the extremelylimited capability to solve real-world large-scalepower system problems. They are weak inhandling qualitative constraints. They have poorconvergence, may get stuck at local optimum,they can find only a single optimized solution ina single simulation run, they become too slow ifnumber of variables are large and they arecomputationally expensive for solution of a largesystem.

Whereas, the major advantage of the AImethods is that they are relatively versatile forhandling various qualitative constraints. AImethods can find multiple optimal solutions insingle simulation run. So they are quite suitablein solving multi objective optimizationproblems. In most cases, they can find the globaloptimum solution. The main advantages of ANNare: Possesses learning ability, fast, appropriatefor non-linear modeling, etc.Whereas, largedimensionality and the choice of trainingmethodology are some disadvantages of ANN.The advantages of Fuzzy method are: Accuratelyrepresents the operational constraints andfuzzified constraints are softer than traditionalconstraints. The advantages of GA methods are:It only uses the values of the objective functionand less likely to get trapped at a local optimum.Higher computational time is its disadvantage.The advantages of EP are adaptability to change,

ability to generate good enough solutions andrapid convergence. ACO and PSO are the latestentry in the field of optimization. The mainadvantages of ACO are positive feedback forrecovery of good solutions, distributedcomputation, which avoids prematureconvergence. It has been mainly used in findingthe shortest route in transmission network, shortterm generation scheduling and optimal unitcommitment. PSO can be used to solve complexoptimization problems, which are non-linear, nodifferentiable and multi-model. The main meritsof PSO are its fast convergence speed and it canbe realized simply for less parameters needadjusting. PSO has been mainly used to solveBi-objective generation scheduling, optimalreactive power dispatch and to minimize totalcost of power generation.

4 Particle swarm optimizationIt is based on the ideas of social behavior oforganisms such as animal flocking and fishschooling. H.Yoshida proposed a Particle SwarmOptimization (PSO) for reactive power andVoltage/VAR Control (VVC) consideringvoltage security assessment. It determines an on-line VVC strategy with continuous and discretecontrol variables such as AVR operating valuesof generators, tap positions of OLTC oftransformers and the number of reactive powercompensation equipment[6].

Particle swarm optimization (PSO) is apopulation based stochastic optimizationtechnique developed by Dr. Eberhart and Dr.Kennedy in 1995, inspired by social behavior ofbird flocking or fish schooling.

PSO shares many similarities withevolutionary computation techniques such asGenetic Algorithms (GA). The system isinitialized with a population of random solutionsand searches for optima by updating generations.However, unlike GA, PSO has no evolutionoperators such as crossover and mutation. InPSO, the potential solutions, called particles, flythrough the problem space by following thecurrent optimum particles. Each particle keepstrack of its coordinates in the problem spacewhich are associated with the best solution(fitness) it has achieved so far. (The fitness valueis also stored.) [7]This value is called pbest.Another “best” value that is tracked by theparticle swarm optimizer is the best value,obtained so far by any particle in the neighborsof the particle. This location is called lbest.When a particle takes all the population as its

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topological neighbors, the best value is a globalbest and is called gbest.The particle swarmoptimization concept consists of, at each timestep, changing the velocity of (accelerating) eachparticle toward its pbest and lbest locations(local version of PSO). Acceleration is weightedby a random term, with separate randomnumbers being generated for accelerationtoward pbest and lbest locations.

4.1 Implementation of PSO for OPFproblemA swarm consists of a set of particles movingwithin the search space, each representing apotential solution (fitness). In a physical n-dimensional search space, the position andvelocity of each particle are represented as thevectors = (1… ) and = ( 1, … , ),respectively.

Let b e s t = ( b e s t 1, … , b e s t n)and b e s t = ( b e s t 1, … , b e s t ) bethe position of the individual and its neighbor’sbest position so far. Using this information, themodified velocity of each individual can becalculated using the current velocity and thedistance from Pbest and Gbest as shown in

+ 1= + 1r a n d1× ( b e s t − ) + 2r a n d

2× ( P b e s t − ) (4)where is current velocity of individual i atiteration , + 1 modified velocity of individuali at iteration + 1, current position ofindividual i atiteration k, inertiaweightparameter, 1, 2 acceleration factors, r a n d1, r a n d2:random numbers between 0 and 1, b e s t :best position of individual untiliteration , b e s t : best position of the groupuntil iteration .Each individual moves from the current positionto the next one by the modified velocity usingthe following equation:

+ 1= + + 1. (5)The parameters 1and 2are set to constantvalues. Low values allow individual to roam farfrom the target regions before being tuggedback. On the other hand, high values result inabrupt movement towards target regions. Hencethe acceleration constants 1and 2are normallyset as 2.0 whereas r a n d1and r a n d2 arerandom values, and they are uniformlydistributed between zero and one. These valuesare not the same for each iteration because theyare generated randomly every time.

Fig 1: PSO Flow diagram

4.1.1 PSO algorithmThe technique is initialized with a population ofrandom solutions or particles and then searchesthe optima by updating generations. Eachindividual particle I has the three followingproperties: a current position in search space ,a current velocity , and a personal bestposition in search space .

In every iteration, each particle isupdated by the following two best values. Thefirst one is the personal best position which isthe position of the particle in the search space,where it has reached the best solution so far. Thesecond one is the global best solution ∗ whichis the position yielding the best solution amongall the ’s. The pbest and gbest values areupdated at time t using the equations 1 and 2.

Here it is assumed that the swarm hasparticles. Therefore, ∈ 1, …, and assumingthe minimization of the objective function F,

Yi(t+1)=

(6)Y*(t) {y1(t),……,ys(t)}

f(Y*(t))=min{f(y1(t)),……f(ys(t))} (7)After finding the two best values, each

particle updates its velocity and current position.The velocity of the particle is updated accordingto its own previous best position and theprevious best position of its companions whichis given .This new velocity is added to thecurrent position of the particle to obtain its nextposition.

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The acceleration coefficients control the distancemoved by a particle in the iteration. The inertiaweight controls the convergence behavior ofPSO. Initially the inertia weight was consideredas a constant value.

However, experimental results indicatedthat it is better to initially set the inertia weightto larger value and gradually reduce it to getrefined solutions. A new inertia weight which isneither set to a constant value nor set as alinearly decreasing time-varying function is usedin this paper

5 Seeker Optimization AlgorithmThe SOA is based on the concept of simulatingthe act of human searching, where the searchdirection is based on the empirical gradient byevaluating the response to the position changesand the step length is based on uncertaintyreasoning by using a simple Fuzzy rule[2].

SOA operates on a set of solutions calledsearch population. The individual of thispopulation is called seeker.[2] In order to add asocial component for social sharing ofinformation, a neighborhood is defined for eachseeker. In the present simulations, thepopulation is randomly categorized into K=3subpopulations in order to search over severaldifferent domains of the search space and allseekers in the same subpopulation constitute aneighborhood. Assume that the optimizationproblems to be solved are minimizationproblems.The main characteristics features of thisalgorithm are the following;

The algorithm uses search direction andstep length to update the positions of seekers.

The calculations of search direction arebased on a compromise among egotisticbehavior, altruistic behavior and pro-activenessbehavior.

Fuzzy reasoning is used to generate thestep length because the uncertain reasoning ofhuman searching could be the best described bynatural linguistic variables and a simple if elsecontrol rule.

search direction dij(t) and a step lengthαij(t) are computed separately for each seeker ion each dimension j for each time step t whereαij(t≥0 and dij(t)∈{-1,0,1} ).

5.1 Implementation of SOAIn SOA, a search direction dij(t) and a step lengthαij(t) are computed separately for each seeker i

on each dimension j for each time step t whereαij(t≥0 and d ij(t)∈{-1,0,1} ).dij(t)=1 means the i-th seeker goes towards thepositive direction of the coordinate axis on thedimension j.dij(t)=-1 means the seeker goes towards thenegative direction anddij(t)=0 means the seeker stays at the currentposition.For each seeker i (1 ≤ I ≤ s, s is the populationsize), position update on each dimension j (1 ≤ j≤ D) is given by the following:Xij (t+1) = Xij (t)+ αij(t) dij(t) (8)

Since the subpopulations are searchingusing their own informations, they are easy toconverge to a local optimum[2].

In order to avoid this situation the positionsof the worst k=1 seekers of each subpopulationare combined with the best one in each of theother k-1 subpopulations using the followingbinomial crossover operator:

xknj,worst = (9)

where Rj is a uniformly random realnumber within [0, 1], xknj,worst is denoted as thej-th dimension of the n-th worst position in theK-th subpopulation, Xlj,best is the j-th dimensionof the best position in the l-th subpopulationwith n,k,l=1,2,……k-1 and k≠l.

5.2 SOA Flow chart and AlgorithmThe basic form of the proposed SOA

algorithm can only handle continuousvariables. However, both tap position oftransformations and reactive power sourceinstallations are discrete or integer variables inoptimal reactive power dispatch problem. Tohandle integer variables without any effect onthe implementation of SOA, the seekers will stillsearch in a continuous space regardless of thevariable type, and then truncating thecorresponding dimensions of the seekers’ real-value positions into the integers is onlyperformed in evaluating the objective function.The reactive power optimization based on SOAcan be described as follows.Step 1) Read the parameters of power systemand the proposed algorithm, and specify thelower and upper limits of each variable.Step 2) Initialize the positions of the seekers inthe search spaceRandomly and uniformly. Set the time step t=0Step 3) Calculate the fitness values of the initialpositions using the objective function based on

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Fig 2: SOA Flow chartStep 4) Let t=t+1Step 5) Select the neighbors ofeach seeker.Step 6) Determine the search direction and steplength for each seeker, and update his position.Step 7) Calculate t h e f i t n e s s va l u e s o ft h e n e w p o s i tions using the objectivefunction based on the Newton–Raphson powerFlow analysis results. Update the historical bestposition among the population and the historicalbest position of each seeker.Step 8) Go to Step 4 until a stopping criterion issatisfied.

6 Simulation techniques and results

Fig 3: IEEE 30bus Test System

In particle swarm optimization Defaultpopulation size: 24Number of particles used: 20Number of iterations set: 30Initial inertia weight: 0.9 and final inertiaweight: 0.4Pso seed, default=0

=0 for initial positions allrandom

=1 for initial particles as userinput

The table shows, variation of global best valueof the generation for the number of iterations. Inthe end of all iterations the generation of allplants is maximum with reduced losses. And thebus voltages in each bus in the end of iterationare given. This graph depicts the variation ofvoltage in each bus. The bus voltage drops dueto the losses in the bus. This problem derived forwithout considering the constrains andsimulation results are produced in 10 seconds.

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Table 1: PSO output

6.1 Simulation Output of SOASeeker optimization algorithm for optimal powerflow is similar to the Particle swarmoptimization where as it is based on behavior ofhuman searching. Although PSO is easy toimplement, the performance of PSO alsodepends on its parameters and may beinfluenced by premature convergence andstagnation problem. So the disadvantage of PSOalgorithm is overcome and best result foroptimal power flow problem is obtained byseeker optimization algorithm.

Fig 4: SOA voltage variations

Fig 5: SOA voltage variations

Busno

V pu Angledegree

Busno

V pu Angledegree

123456789

101112131415

1.06001.01300.99470.97970.96000.97570.96110.98000.99180.97401.02200.99951.01100.98180.9752

0.0000-4.9686-7.4130-9.1675-14.1797-11.0397-12.9026-11.9201-14.3072-16.0766-14.3072-15.4241-15.4241-16.3934-16.4195

161718192021222324252627282930

0.98100.97040.96180.95720.96050.95970.96460.96000.95190.95990.94110.97410.97380.95310.9410

-15.9998-16.2878-17.0910-17.2733-17.0383-16.6744-16.4171-16.6855-16.7732-16.5460-17.0184-16.1023-11.7559-17.4624-18.4421

Table 2: SOA without capacitorThe figure 4 shows the variation of voltage inaccordance with the number of iterations, andthe figure 5 shows that the variation voltage inaccordance with the angle. As the number ofiterations increases, some voltage on the busdecreases with the increased value of angle.Thebus voltage drop is reduced by addingSTATCOM in the bus and is given in the nexttable. SOA with capacitorWhen we connecting the STATCOM into thebus, it injects the reactive power. Here thecontrolled capacitor is considered to inject thereactive power. Finally the increased bus voltageand the injected reactive power are given. ASTATCOM can compensate for system needsfor reactive power system needs for reactivepower almost instantaneously preventingvariations of voltage.

Bus no Voltage Bus no voltage

1 1.0600 16 1.0471

2 1.0430 17 1.0415

3 1.0254 18 1.0304

4 1.0171 19 1.0277

5 1.0100 20 1.0317

6 1.0148 21 1.0345

7 1.0050 22 1.0350

8 1.0100 23 1.0296

9 1.0530 24 1.0237

10 1.0467 25 1.0204

11 1.0820 26 1.0027

12 1.0599 27 1.0269

13 1.0710 28 1.0128

14 1.0450 29 1.0071

15 1.0402 30 0.9957

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Busno

V pu Angledegree

Busno

V pu Angledegree

123456789

101112131415

1.06001.04301.02001.01081.01001.01011.00231.01001.04021.02311.08201.05031.07101.03301.0263

0.0000-5.3525-7.5318-9.2848-14.1692-11.0627-12.8655-11.8168-14.0508-15.6455-14.0508-15.0935-15.0935-15.9691-15.9809

161718192021222324252627282930

1.03151.02021.01281.00801.01101.01021.01471.01061.00331.01251.00001.02401.00911.00761.0000

-15.5967-15.8422-16.5781-16.7371-16.5223-16.1952-15.9655-16.2084-16.3066-16.1605-16.7794-15.7112-11.7434-17.0359-18.0205

S dataBus

Vsh pu Thstdegree

Qsh pu

2630

1.00141.0020

-16.7872-18.0321

-0.0137-0.0202

Table 3: SOA with capacitor

7 ConclusionSOA is a novel heuristic stochastic optimizationalgorithm based on simulating the act of humansearching. The algorithm has the additionaladvantage of being easy to understand, simple toimplement so that it can be used for a widevariety of design and optimization tasks. In thispaper, a SOA-based reactive power optimizationapproach is proposed, and the benefits of SOAfor optimal reactive power dispatch problem arestudied. The simulation results show that SOAhas better performance in balancing globalsearch ability and convergence speed than otheralgorithms. So, it is believed that the proposedSOA approach is capable of quickly andeffectively solving reactive power dispatchproblem and will become a promising candidatefor the OPF problems.GA is used for optimal placement of FACTSdevices that GA based reactive power dispatchalgorithm is able to minimize the power loss inthe system. Overall performance of the SOA-GAalgorithm and its advantages were discussed andthe algorithm shows that it is easy to implementand also produces good results for optimalpower flow problem than other algorithms.

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[2] “Seeker optimization algorithm for optimalreactive power dispatch” Chaohua Dai, WeirongChen, Member, IEEE, Yunfang Zhu, and XuexiaZhang IEEE transactions on power systemsvol24 no 3 aug 2009[3]Q. H. Wu, Y. J. Cao, and J. Y. Wen, “Optimalreactive power dispatch using an adaptive geneticalgorithm,” Int. J. Elect. Power Energy Syst., vol.20, pp. 563–569, Aug. 1998.[4]G. A. Bakare, G. Krost, G. K.Venayagamoorthy, and U. O. Aliyu,“Comparative application of differentialevolution and particle swarm techniques toreactive power and voltage control,” in Proc.Int. Conf. Intelligent Systems Applications toPower Systems, 2007, pp. 1–6.[5]Stephane Gerbex, Rachid Cherkaoui,andAlain J.Germond. (2001). ‘Optimal Locationof Multi-type FACTS Devices in a PowerSystem by Means of Genetic Algorithm’, IEEETrans on Power System, Vol.16, No.3, pp.658-667.[6]L. dos Santos Coelho and B. M. Herrera,“Fuzzy identification based on a chaotic particleswarm optimization approach applied to anonlinear yo-yo motion system,” IEEE Trans.Ind. Electron., vol. 54, no. 6, pp.3234–3245,2007.[7]Enhanced Particle Swarm OptimizationApproach for Solving the Non-Convex OptimalPower Flow by M. R. AlRashidi, M. F. AlHajri,and M. E. El-Hawary World Academy ofScience, Engineering and Technology 62 2010.[8]Zhao B. Guo C.X. and Cao Y.J.(2005) ’Amultiagent based particle swarm optimizationapproach for optimal reactive power dispatch’,IEEE Trans on power system, May,Vol.20.No.2,pp.1070-1078.[8]G. Cai, Z. Ren, and T. Yu, “Optimal reactivepower dispatch based on modified particle swarmoptimization considering voltage stability,” inProc. IEEE Power Eng. Soc. General Meeting,2007, pp. 1–5.[9]M. Fozdar, C. M. Arora, and V. R. Gottipati,“Recent trends in intel- ligent techniques topower systems,” in Proc. 42nd Int. UniversitiesPower Engineering Conf., 2007, pp. 580–591.[10]L. dos Santos Coelho and B. M. Herrera,“Fuzzy identification based on a chaotic particleswarm optimization approach applied to anonlinear yo-yo motion system,” IEEE Trans.Ind. Electron., vol. 54, no. 6, pp. 3234–3245,2007.

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