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ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010  Solving Unit Commitment Problem...
ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010                                 ...
ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010Vij (iter + 1) = w ∗ Vij (iter ) ...
ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010   Equations (2) and (3) are the ...
ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010Step7:     Generate U-status as i...
ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010                        IX.   CON...
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Solving Unit Commitment Problem Using Chemo-tactic PSO–DE Optimization Algorithm Combined with Lagrange Relaxation


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This paper presents Chemo-tactic PSO-DE
(CPSO-DE) optimization algorithm combined with
Lagrange Relaxation method (LR) for solving Unit
Commitment (UC) problem. The proposed approach
employs Chemo-tactic PSO-DE algorithm for optimal
settings of Lagrange multipliers. It provides high-quality
performance and reaches global solution and is a hybrid
heuristic algorithm based on Bacterial Foraging
Optimization (BFO), Particle Swarm Optimization (PSO)
and Differential Evolution (DE). The feasibility of the
proposed method is demonstrated for 10-unit, 20-unit,
and 40-unit systems respectively. The test results are
compared with those obtained by Lagrangian relaxation
(LR), genetic algorithm (GA), evolutionary programming
(EP), and genetic algorithm based on unit characteristic
classification (GAUC), enhanced adaptive Lagrangian
relaxation (ELR), integer-coded genetic algorithm
(ICGA) and hybrid particle swarm optimization (HPSO)
in terms of solution quality. Simulation results show that
the proposed method can provide a better solution.

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Solving Unit Commitment Problem Using Chemo-tactic PSO–DE Optimization Algorithm Combined with Lagrange Relaxation

  1. 1. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Solving Unit Commitment Problem UsingChemo-tactic PSO–DE Optimization Algorithm Combined with Lagrange Relaxation P.Praveena1, K.Vaisakh2, and S.Rama Mohana Rao3 1 Andhra University/Department of Electrical Engineering, Visakhapatnam, India Email: 2 Andhra University/Department of Electrical Engineering, Visakhapatnam, India 3 Andhra University/Department of Electrical Engineering, Visakhapatnam, India Email: {,}Abstract—This paper presents Chemo-tactic PSO-DE higher dimension problem the problem size increases(CPSO-DE) optimization algorithm combined with rapidly with the number of generators and this requiresLagrange Relaxation method (LR) for solving Unit enormous computation time and large memory space.Commitment (UC) problem. The proposed approach Branch-and-bound and mixed integer linearemploys Chemo-tactic PSO-DE algorithm for optimalsettings of Lagrange multipliers. It provides high-quality programming method also requires large computationperformance and reaches global solution and is a hybrid time and memory space [3], [4]. Lagrange relaxationheuristic algorithm based on Bacterial Foraging for UC problem is advanced than dynamicOptimization (BFO), Particle Swarm Optimization (PSO) programming due to its faster computational time. Theand Differential Evolution (DE). The feasibility of the solution to Lagrange Relaxation for UC problemproposed method is demonstrated for 10-unit, 20-unit, depends on the updating of Lagrange multipliers; henceand 40-unit systems respectively. The test results are it suffers from solution quality problem. This papercompared with those obtained by Lagrangian relaxation proposes a new hybrid heuristic method for solving UC(LR), genetic algorithm (GA), evolutionary programming problem. The proposed method is developed in such(EP), and genetic algorithm based on unit characteristicclassification (GAUC), enhanced adaptive Lagrangian way that a Chemo-tactic PSO-DE optimizationrelaxation (ELR), integer-coded genetic algorithm technique is applied to update Lagrange multipliers and(ICGA) and hybrid particle swarm optimization (HPSO) this improves the performance of LR method. Toin terms of solution quality. Simulation results show that illustrate the effectiveness of the proposed method, it isthe proposed method can provide a better solution. tested and compared to the conventional LR [5], GA [5], EP [6], GAUC [7], ELR [8], ICGA [9] and HPSOIndex Terms—Lagrangian Relaxation, Particle Swarm [10] for 10-unit, 20-unit, and 40-unit respectively.Optimization, Differential Evolution, Bacterial Foraging In 2001, Prof. K. M. Passino proposed anOptimization, Unit Commitment optimization technique known as Bacterial Foraging Optimization Algorithm (BFOA) based on the foraging I. INTRODUCTION strategies of the E. Coli bacterium cells [11]. Until date Unit commitment (UC) is used to commit the there have been a few successful applications of thegenerators such that the total production cost over the said algorithm in optimal control engineering,predicted load demand for scheduled time horizon is harmonic estimation [12], transmission loss reductionminimized considering the spinning reserve and [13], machine learning [14] and so on. Experimentationoperational constraints of generator units [1], [2]. Unit with several benchmark functions reveal that BFOAcommitment is a high dimensional, nonlinear, non- possesses a poor convergence behavior over multi-convex, mixed-integer combinatorial optimization modal and rough fitness landscapes as compared toproblem. Priority list method, integer programming, other naturally inspired optimization techniques like thedynamic programming (DP), branch-and-bound Genetic Algorithm (GA), Particle Swarm Optimizationmethods, mixed-integer programming, and Lagrange (PSO) and Differential Evolution (DE). Its performancerelaxation (LR) are a few methods developed up to now is also heavily affected with the growth of search spacefor solving UC problem. dimensionality. In 2007, Kim et al. proposed a hybrid In priority list method, priority of units is determined approach involving GA and BFOA for functionfrom full load average production cost of the unit. The optimization [15]. The proposed algorithmmethod is simple but the quality of solution is low. outperformed both GA and BFOA over a fewPriority list of units is also considered in Dynamic numerical benchmarks and a practical PID tuner designprogramming method. In spite of many advantages problem [16-19].such as ability to maintain solution feasibility, for 50© 2010 ACEEEDOI: 01.ijepe.01.02.10
  2. 2. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 II. NOMENCLATURE objective function can be formulated mathematically as an optimization problem as follows:Pi t : Generation output power of unit i at hour t. T N F ( Pi t , U it ) = ∑∑[ Fi ( Pi t ) + STi t (1 − U it −1 )]U it (1)U it : Status of unit i at hour t (on=1, off=0). t =1 i =1 subject toSTi t : Startup cost of generator i at hour t. (a) Power balance constraint NFi ( Pi t ) : Generator fuel cost function in quadratic Pload − ∑ Pi t U it = 0 t (2)form i =1Fi ( Pi t ) = ai ( Pi t ) 2 + bi Pi t + ci ($/h) (b) Spinning reserve constraint N Pload + R t − ∑ Pi ,maxU it ≤ 0 t tF ( Pi , U ) : Total production cost. i t (3)N : The number of generator units. i =1NS : Swimming length Ns is the maximum (c) Generation limit constraints number of steps taken by each bacterium Pi ,minU it ≤ Pi t ≤ Pi ,maxU it (4) when it moves from low nutrient area to (d) Minimum up and down time constraints high nutrient area. 1 if Ti ,on < Ti ,up ,S : The number of bacteria in the population.  U i = 0 t if Ti ,off < Ti ,down , (5)NC : The number of chemo-tactic steps. T : The number of hours. 0 or 1, otherwise,pbest : The best previous position of k th (e) Startup cost particles. HSTi , if Ti ,down ≤ Ti ,off ≤ Ti ,cold + Ti ,down  STi t =  (6)gbest : The index of the best particle among all CSTi , if Ti ,off > Ti ,cold + Ti ,down  particles in the group.F : The scale factor IV. OVERVIEW OF PARTICLE SWARMCR : The Cross over probability OPTIMIZATIONC1 ,C 2 : Acceleration constants The Particle Swarm Optimization was introduced byrand, Rand : Random value in the range [0, 1] James Kennedy and Russell C. Eberhart in 1995 [20]. It tPload : Load demand at hour t. is similar to other evolutionary computational techniques those are GA and EP in that PSO initializes t : Spinning reserve at hour t.R a population of individuals randomly. ThesePi ,min : Minimum generation limit of generator i individuals are known as particles and have positions and velocities. In addition, it searches for the optimumPi ,max : Maximum generation limit of generator i by updating generations, and population evolution isTi ,up based on the previous generations. PSO is motivated : Minimum up time of generator i from the simulation of the behavior of social systemsTi ,down : Minimum down time of generator i such as fish schooling and birds flocking. In PSO, each particle flies through the problem space by followingHSTi : The unit’s hot startup cost. the current optimal particles. Each individual adjusts itsCSTi : The unit’s cold startup cost. flying according to its own flying experience and its neighbors flying experience. Based on its own thinkingTi ,cold : The cold start hour. the particle attracts to its best position ( pbest ) theλ ,µt t : Lagrange multipliers particle changes its velocity based on the social- psychological adaptation of knowledge that is theVλ (k ) : Velocity vector of λt in t th hour for k th t particle attracts its previous best position among the bacterial population. group ( gbest ), here so the velocity of the particle isVµ t (k ) : Velocity vector of µt in t th hour for k th updated to new position according to its modified bacterial population. velocity using the information. a) The current velocity III. PROBLEM FORMULATION b) The distance between the current position and From the definition of UC mentioned above, the pbest .objective of UC problem is to minimize the production c) The distance between the current position andcost over the schedule time horizon (e.g., 24h). The gbest . 51© 2010 ACEEEDOI: 01.ijepe.01.02.10
  3. 3. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010Vij (iter + 1) = w ∗ Vij (iter ) solutions. Chemo-tactic process of bacterial foraging + C1 ∗ rand 1 ∗ ( pbest ij − x ij (iter )) (7) describes the movement of an E.coli cell through swimming and tumbling via flagella. It can move in + C 2 ∗ rand 2 ∗ ( gbest i − x ij (iter )) two different ways, it can swim for a definite period ofwhere time or it can tumble and it alternates between thesew = inertia weight factor two modes of operation for the entire lifetime. Forxij (iter ) = current position of i th particle in j th example if θ k denotes the k th bacterium and Ck is the dimension at iteration (iter) size of the step taken in the random direction specifiedVij (iter ) = velocity of i th particle in j th dimension by the tumble. Then the movement of bacterium is represented byat iteration (iter) θk = θk + C k ∗ Delta k Appropriate selection of inertia weight provides a ∆k (11)balance between global and local explorations. The Delta k =updated position of each particle is expressed as ∆k ⋅ ∆k Txij (iter + 1) = xij (iter ) + Vij (iter + 1) (8) where Δ is a unit length vector in the random direction In this article we come up with a hybrid optimizationThe new positions are calculated repeatedly till a pre- technique, which synergistically couples the BFOAspecified maximum number of iterations are reached. with the PSO, DE and Lagrange multipliers method. The proposed algorithm performs local search through V. OVERVIEW OF DIFFERENTIAL the chemo-tactic movement operation of BFOA EVOLUTION OPTIMIZATION whereas the global search over the entire search space Differential Evolution (DE) is a new floating point is accomplished by a PSO-DE operator. In this way itencoded evolutionary algorithm for global optimization balances between exploration and exploitation enjoyingdeveloped by Price and Storn in 1995 [21]. It is similar best of both the other evolutionary computation technique and alsostarts with a population of NP. It is a D-dimensional VII. METHODOLOGYsearch variable vector. A special kind of differential Since UC was introduced, several methods have beenoperator is used to create new offspring from parent used to solve this problem. Among those methods, LRchromosomes instead of classical crossover or seems to be the most appropriate one [5], [8]. Thismutation. In each generation to change each population method solves the UC problem by relaxing ormember Xi, a Donor vector vi is created. Three temporarily ignoring the coupling constraints, powerparameter vectors r1, r2, and r3 are chosen in a random balance and spinning reserve requirements, thenfashion from the current population. A scalar number F solving the problem through a dual optimizationscales the difference of any two of the three vectors and procedure. The dual procedure attempts to reach thethe scaled difference is added to the third one. Donor constrained optimum by maximizing the Lagrangevector for j th component of k th population at iter function with respect to the Lagrange multipliers. L( P, U , λ, µ) = F ( Pi t , U it )generation is expressed as T  t N v k , j (iter + 1) = X r1, j (iter ) + ∑ t  Pload − ∑Pi t U it  λ (9) t= 1  i=1  (12) + F ∗ ( X r 2, j (iter ) − X r 3, j (iter )) t  T N + ∑µ  Pload + R − ∑Pi ,maxU it  t tCR is called “Crossover” constant and it appears as a t= 1  i=1 control parameter of DE. The crossover is performed while minimize with respect to the power output andon each of the D variables whenever a randomly picked generating unit status, that isnumber between 0 and 1 is within the CR value. The generating unit status, that istrial vector u k , j is outlined as q ∗ (λ, µ) = max q (λ, µ) λ,µu k , j (iter ) = v k , j (iter ) if rand (0,1) < CR 13) (10) whereu k , j (iter ) = X k , j (iter ) otherwise q (λ, µ) = min L( P,U , λ, µ) (14) t t Pi ,U i VI. OVERVIEW OF CHEMOTACTIC PSO-DE Substitute (1) in (9), the Lagrangian function becomes  Fi ( Pi t ) [  PSO and DE are excellent heuristics like other N  T  L = ∑∑ + STi (1 −U i )] U i  t t−1 t evolutionary algorithms. Practical experiences suggest i= t =  1 1  −λ Pi tU it − µt Pi , maxU it  t (15)that they reach stagnation after certain number ofgenerations as the population is not converged locally, ( ) T + ∑ λ Pload + µt ( Pload + R t ) t t tso they will stop proceeding towards global optimal t=1 52© 2010 ACEEEDOI: 01.ijepe.01.02.10
  4. 4. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Equations (2) and (3) are the coupling constraints If DC i ≤ 0 the unit will be committed if it does not tacross the units. The coupling constraints in the aboveequation are temporarily ignored and then the violate minimum downtime constraint, otherwise theminimum of Lagrangian function is solved for each unit is decommitted if it does not violate the minimumgenerating unit, without regard for what is happening uptime constraint. A step-by-step procedure for theon the other generating units. proposed method is outlined as follows. T [ F ( P t ) + ST t (1 − U t −1 )] t  Ui  N  i imin L( P, U , λ , µ ) = ∑ min ∑  t t t Section -A: i i  (16) t =1  − λ P U i − µ P , maxU i t t  t tPi ,U i i =1  i i  Step1: Compute λt and µ by Chemo-tactic PSO-DE. tTherefore the minimum for each generating unit over Step2: Set the unit status by calculating dual power andall time periods is: T [ F ( P t ) + ST t (1 − U t −1 )] t  obtain on/off decision DC (21). N  i i Ui min q (λ , µ ) = ∑ min ∑  t t t Step3: Calculate the spinning reserve for generated ‘U’ i i  (17) t =1 − λ P U i − µ P , maxU i t t i =1  i i   status at each hour of the population. If excessivesubject to constraints (4) and (5). This problem is spinning reserve is observed decommit the unit withsolved through a two-state dynamic programming high full load average production cost if it does notproblem in two variables for each unit. On the other violate the minimum uptime constraint. Otherwise ifhand, in order to maximize the Lagrange function with the unit violates, the unit with next high full loadrespect to the Lagrange multipliers, the adjustment of average production cost is decommitted. Now set theLagrange multipliers must be done carefully. Most of spinning reserve according to the new status and repeatresearch works use sub-gradient method to achieve this until the spinning reserve satisfies.task. In this paper, we use the Chemo-tactic PSO-DE Step4: If less spinning reserve than required is observedoptimization to adjust the Lagrange multipliers and commit the unit with less full load average cost if itimprove the performance of Lagrange relaxation does not violate the minimum downtime constraint.method. Otherwise if it violates, the unit with next less full load This is solved as a dynamic programming problem in average production cost is committed. Now set theone variable with two possible unit states ( U i = 0 or t spinning reserve according to the new status and repeat until the spinning reserve satisfies.1). Step5: Economic dispatch for the generated U-status is U= carried out by Lagrangian multiplier method. 1 Section-B: U=0 Step1: Randomly generate λt , µ , Vλt , and Vµ with t t t=0 t= t=2 t=3 1 Fig. 1 Unit on/off statusThe dynamic programming part must take into account in the range for initialized bacterium. Generate unit-all the start up costs as well as the minimum up and status U as in section-A and calculate pbest for U, λtdown time for the generating units. , µt , cost and fit (J and JF) and gbest for U, λt , µt , J tAt U =0 state the value of function to minimize is i and JF. t Step2: Starting of the chemo-tactic loop (it=it+1)zero. At U i =1 state the function to be minimized is Step3: For each bacteria (k=k+1) JFlast = JF (k )min[ Fi ( Pi t ) − λt Pi t ] . The minimum of this functionis found by taking the first derivative Step4: Calculate Vλt , Vµ t and check for maximum d [ Fi ( Pi t ) −λ Pi t ] = 0 t and minimum velocity limits.dPi t (18) Vλt ( k ) = Vλt ( k ) Pi t ,opt is obtained from (19) + C1 * Rand * ( pbestλt ( k ) − λt (k )) (22)The dual power λt − bi + C 2 * Rand * ( gbestλt − λt ( k ))Pi t ,opt = (19) Vµt (k ) =Vµt (k ) 2c i + C1 * Rand * ( pbestµt ( k ) − µt ( k )) (23)if Pi t ,opt < Pi ,min , then Pi = Pi , min t + C 2 * Rand * ( gbestµt − µt (k ))if Pi t ,opt > Pi ,max , then Pi t = Pi ,max (20) Step5: Move to new position λ ( k ) =λ (k ) +C λ ∗Vλ ( k ) t t tif Pi , min ≤ Pi t ,opt ≤ Pi ,max , then Pi = Pi t t , opt (24) µt (k ) = µt (k ) +C µ ∗Vµt ( k )The dual power obtained from (20) is substituted inon/off decision criterion DC where C λ and C µ are chemo-tactic step sizeDC it = [ Fi ( Pi t ) + STi t (1 − U it −1 ) − λt Pi t − µ t Pi , max ] (21) Step6: Handle limits λmin ≤λ ≤λmax t k µmin ≤µt ≤µmax (25) k 53© 2010 ACEEEDOI: 01.ijepe.01.02.10
  5. 5. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010Step7: Generate U-status as in section-A TABLE IStep8: Compute cost and fit – J and JF UNIT STATUS FOR 40-UNIT SYSTEMStep9: Swimming Peri 40-Unit Status9a) swim-count=0 od 1-409b) while (swim-count<Ns) and JF (k ) > JFlast 1 1111111100000000000000000000000000000000 i. swim-count = swim-count + 1 2 1111111100000000000000000000000000000000 JFlast = JF (k ) 3 1111111100000000000100000000000000000000 ii. 4 1111111100000001011100000000000000000000 λt ( k ) = λt ( k ) + C λ ∗Vλt ( k ) iii. 5 1111111100000011111100000000000000000000 µt ( k ) = µt ( k ) + C µ ∗Vµt ( k ) 6 1111111100011111111100000000000000000000 iv. Handle limits 7 1111111100111111111100000000000000000000Step10: Generate unit-status U as in section-A 8 1111111111111111111100000000000000000000Step11: Compute cost and fit - J and JF 9 1111111111111111111111111000000000000000Step12: Differential Evolution 10 1111111111111111111111111111111100000000While(rand<CR) 11 1111111111111111111111111111111111110000 12 1111111111111111111111111111111111111111λdef t (k ) = λt (k ) + F ∗ (λt (r2 ) − λt (r3 )) 13 1111111111111111111111111111111100000000 14 1111111111111111111111111000000000000000 µ def t (k ) = µ t (k ) + F ∗ ( µ t (r2 ) − µ t (r3 )) (26) 15 1111111111111111111100000000000000000000 i. Handle limits 16 1111111111111111111100000000000000000000Step13: Generate unit status – U def as in section-A 17 1111111111111111111100000000000000000000 18 1111111111111111111100000000000000000000Step14: Compute cost and fit – J def , JFdef 19 1111111111111111111100000000000000000000 20 1111111111111111111111111000111111110000Step15: 21 1111111111111111111111111000000000000000if ( JFdef > JF ) then 22 1111111111000000111111111000000000000000JF = JFdef , J = J def , U = U def , λ = λ def , µ = µ def 23 1111111100000000001100000000000000000000 24 1111111100000000000000000000000000000000Step16: Update best location pbest and gbest for JF, J, U, λ, µStep17: if k<S, go to step3 otherwise perform step18. TABLE II COMPARISON OF COSTStep18: If iter < N c then go to step2 otherwise stop. Total Cost ($) VIII. RESULTS AND DISCUSSIONS No. of Units 10 20 40 LR [5] 565825 1130660 2258503 The 10-unit system data and load demands are taken GA [5] 565825 1126243 2251911from [5]. The 20 and 40 unit’s data are obtained byduplicating the ten unit case, and the load demands are EP [6] 564551 1125494 2249093adjusted in proportion to the system size. In the GAUC [7] 563977 1125516 2249715simulation, the reserve is assumed to be 10% of the ELR [8] 563977 1123297 2244237load demand. The control parameters chosen for these ICGA [9] 566404 1127244 2254123units are CR=0.7, F=0.1 or 0.2, C1=0.5, C2=0.5, C λ and HPSO [10] 563942 --- ---Cµ =random number between 0.1 and 1. The unit Proposed method CPSO-DE 563977 1123297 2243363status obtained through Chemo-tactic PSO-DE for 40unit system is shown in Table I. From simulation it is 2450000observed that setting up of maximum and minimumbounds for λ and µ, such that λ max = 30 , 2400000 Total Cost λ min = 12 , µ max = 15 and µ min = 2 , leads 2350000the system to high-quality convergence.The proposed 2300000method provides best production cost when compared 2250000to literature as in Table II with a reasonablecomputation time per iteration of 0.72s for 10-unit 2200000 1 131 261 391 521 651 781 911system, 2.1s for 20-unit system and 5.7s for 40-unit Iterationssystem. The convergence characteristics for theproposed method (40-unit system) are as shown infigure2. Fig. 2. Cost convergence characteristics for 40-unit system 54© 2010 ACEEEDOI: 01.ijepe.01.02.10
  6. 6. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 IX. CONCLUSION [14] Kim.D.H, Abraham.A, Cho.J.H, A hybrid genetic algorithm and bacterial foraging approach for global Unit commitment problem is solved with a new optimization, Information Sciences, Vol. 177 (18), 3918-methodology Chemo-tactic PSO-DE Optimization 3937, (2007).algorithm. PSO and DE are incorporated in chemo- [15] Yao.X, Liu.Y, Lin.G, “Evolutionary programming madetactic algorithm to update Lagrange multipliers so that faster”, IEEE Transactions on Evolutionarythey are suitable for high dimensional combinatorial Computation, vol 3, No 2, 82-102, (1999).optimization problem. Results show that as the [16] Hao.Z, F.Guo.G.H, Huang.H, “A Particle Swarm Optimization Algorithm with Differential Evolution”, indimension of the problem increases it generates good IEEE Int.Conf. Systems, man and Cybernetics, Aug.unit status with lower production cost. Hence it can be 2007, Vol. 2, pp. 1031-1035concluded that the proposed method provide lower [17] Kennedy.J, Eberhart.R, “Particle swarm optimization”,production cost than those of LR, GA, EP,GAUC and In Proceedings of IEEE International Conference onELR methods for 40-unit system and also the problem Neural Networks, (1995) 1942-1948.can be extended for 60-unit, 80-unit and 100-units as in [18] Storn.R., Price.K, “Differential evolution – A Simplethis method better costs are obtained as the dimension and Efficient Heuristic for Global Optimization over(number of generators) of the problem increases. Continuous Spaces”, Journal of Global Optimization, 11(4) 341–359, (1997). REFERENCES BIOGRAPHIES[1] A.J. Wood, B.F. Wollenberg, Power Generation P.Praveena received the B.E degree Operation and Control, 2nd ed., New York: John Wiley in Electrical and Electronics & Sons, Inc., 1996. Engineering from Andhra University,[2] J.A. 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University, Visakhapatnam, AP,[12] Tripathy.M, Mishra.S, Lai.L.L and Zhang.Q.P, India. “Transmission Loss Reduction Based on FACTS and His research interests include load flow solutions and Bacteria Foraging Algorithm”. PPSN, 222-231, (2006). optimal operation of power system.[13] Kim.D.H, Cho.C.H, “Bacterial Foraging Based Neural Network Fuzzy Learning”. IICAI 2005, 2030-2036. 55© 2010 ACEEEDOI: 01.ijepe.01.02.10