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  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022 Particle Swarm Optimization Approach For Economic Load Dispatch: A Review Jaya Sharma1 Amita Mahor2 1 Asst. prof., Electrical Department, SVITS, Indore 2Prof. & Head, Electrical Department NRI,BhopalABSTRACT Particle swarm optimization (PSO ) is an conventional & nonconventional optimizationeffective & reliable evolutionary based approach techniques available in literature are applied to solve.Due to its higher quality solution including such problems. Quadratic linear programming [45],mathematical simplicity, fast convergence & Mathematical linear programming [44], Non linearrobustness it has become popular for many programming[46], dynamic programming [31,26] areoptimization problems. There are various field of the conventional methods. Conventional methodspower system in which PSO is successfully have simple mathematical model and high searchapplied. Economic Load Dispatch(ELD) is one of speed but they are failed to solve such problemimportant tasks which provide an economic because they have the drawbacks of Multiple localcondition for a power system. it is a method of minimum points in the cost function, Algorithmsdetermine the most efficient, low cost & reliable require that characteristics be approximated,operation of a power system by dispatching the however, such approximations are not desirable asavailable electricity generation resources to supply they may lead to suboptimal operation and hencethe load on the system. This paper presents a huge revenue loss over time, Restrictions on thereview of PSO application in Economic Load shape of the fuel-cost curves.Dispatch problems. Other methods based on artificial intelligence have been proposed to solve the I INTRODUCTION economic dispatch problem, these are genetic The efficient optimum economic operation algorithm [32,33], Tabu search[27], particle swarmand planning of electric power generation system optimization [14]. The PSO first introduced byhave always been occupied an important position in kennedy and eberhart is a flexible, robust,the electric power industry. With large population based algorithm. This method solveinterconnection of electric networks, energy crisis in variety of power systems problems due to itsthe world and continuous rise in prices, it is very simplicity, superior convergence characteristics andessential to reduce the running charges of electric high solution quality. Classical PSO approachenergy. The main aim of electric supply utility has suffers from premature convergence, particularlybeen identified as to provide the smooth electrical for complex functions having multiple minima.energy to the consumers. While doing so, it should beensured that the electrical power is generated with II PROBLEM FORMULATIONminimum cost. Hence in order to achieve an The Economic Dispatch problem may beeconomic operation of the system, the total demand formulated as single objective & multi objectivemust be appropriately shared among the units. This problem, however in this case following objectivewill minimize the total generation cost for the system functions can be formulated, ECD with valve pointwith the voltage level maintained at the safe loading effect[36,37,38], ECD with valve pointoperating limits. Major considerations to fulfilling the loading effect & multiple fuel option(ECD-VPL-objectives are Loss minimization. Fuel cost ME)[39,40,41] and EMD & ECED[42,43,25].minimization, Profit maximization (fuel costs/loadtariffs).The main factor controlling the most desirable 1.1 OBJECTIVE FUNCTIONload allocation between various generating units is The primary objective of any ED problemthe total running cost. is to reduce the operational cost of system fulfillingIn electrical power system, there are many the load demand within limit of constraints.optimization problems such as optimal power flow, However due to growing concer ofeconomic dispatch, generation and transmission environment,there are various kinds of objectiveplanning, unit commitment, and forecasting & function formulation can be done as given incontrol. Economic dispatch is one of the major subsequent sections.optimization issue in power system. Its objective is toallocate the demand among committed generator inthe most economical manner, while all physical &operational constraints are satisfied. Many 13 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022 1.1.1 SIMPLIFIED ECONOMIC COST 1.1.3 ECONOMIC COST FUNCTION FUNCTION WITH MULTIPLE FUELS. The Let Fi mean the cost, expressed for The different type of fuels can be used in example in dollars per hour, of producing energy in thermal generating unit, hence fuel cost objective the generator unit i. The total controllable system function can be represented with piecewise production cost such an approach will not be quadratic function reflecting the effect of fuel type workable for nonlinear functions in practical changes. systems. Therefore will be Fi ( Pi )  ai  bi Pi  ci Pi 2 if Pimin ≤ Pi ≤ Pi1 ai  bi Pi  ci Pi 2 if Pi1 ≤ Pi ≤ Pi2 (4) N F   F (P ) i 1 i i (1) - - ai  bi Pi  ci Pi 2 if Pin-1 ≤ Pi ≤ Pimax The fuel input-power output cost function of the ith the nth power level (Fig. 2). unit is given as 2.1.3 EMISSION FUNCTION Fi ( P )  ai  bi P  ci P i i i 2 (2) Different mathematical formulations are used to represent the emission of green house gases in EMD problem. It can be represented in quadratic where F Total generating cost, Fi Cost function of form [42,43],addition of quadratic polynomial with ith generating unit, Pi power of generator, N no. of exponential terms [48,49], or addition of linear generators, ai, bi, ci cost coefficients of generator i. equation with exponential terms [50] of generated power 1.1.2 ECONOMIC COST FUNCTION WITH VALVE POINT LOADING Ei ( Pi )   i   i Pi   i Pi 2 (5) EFFECT The generating units with multi- valve steam turbine exhibit a greater variation in the fuel- Ei ( Pi )   i   i Pi   i Pi 2   i exp(   Pi ) (6) cost function. Since the valve point results in the ripple. To take account for the valve point effect E i ( Pi )   i   i Pi   i Pi 2   1 i exp( 1  Pi ) sinusoidal functions are added to the quadratic cost function. Therefore eq.(2 )should be replaced by   2 exp( 2 i  Pi ) (7) eq.(3 ) where  i ,  i ,  i , 1i , 2i , 1 , 2 are the emission function coefficients.Fi ( Pi )  ai  bi Pi  ci Pi 2  abs (ei sin( f i ( Pi min  Pi ))) (3) 2.2 SYSTEM CONSTRAINTS where ei & fi are the coefficient of unit i Broadly speaking there are two types of considering valve point loading effect. constraints-Equality constraint and Inequality constraints.The inequality constraints are of two types (i) Hard type and, (ii) Soft type. The hard type are those which are definite and specific like the tapping range of an on-load tap changing transformer whereas soft type are those which have some flexibility associated with them like the nodal voltages and phase angles between the nodal voltages, etc. Soft inequality constraints have been very efficiently handled by penalty function Fig. 1. Incremental fuel methods.cost curve for 5 valve steam turbine unit. 2.2.1 EQUALITY AND INEQUALITY CONSTRAINT From observation we can conclude that cost function is not affected by the reactive power demand. So the full attention is given to the real power balance in the system.Different types of constrints are as under Fig. 2. Piecewise 2.2.1.1 Active power balance equation: quadratic and incremental fuel cost function. For power balance equation, equality constraints should be satisfied. The total generated 14 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022 power should be the same as total load demand Zi are the no. of prohibited zones in the ith generator plus the total line loss, curve k is the index of prohibited zones of the ith N L generator Pik is the lower limit of the kth P  P i D  Ploss (8) U i 1 prohibited zone and Pik is the upper limit of the Where PD is the total system demand and kth prohibited zone of the ith generator. Ploss is the total line loss.To calculate system losses , Method based on constant loss formula coefficient III PARTICLE SWARM OPTIMIATION or B coefficient are used. The transmission loss Kennedy and Eberhart [1] developed a equation expressed as: particle swarm optimization (PSO) algorithm based on the behavior of individuals (i.e., particles or N N N agents) of a swarm. Its roots are in zoologists PL   PBij Pj   Boi Pi  Boo (9) i modeling of the movement of individuals (i.e., i 1 j 1 i 1 fishes, birds and insects) within a group. It has been 2.2.1.2 Minimum and maximum power limits: noticed that members of the group seem to share Generator output of each generator should be laid information among them, a fact that leads to between maximum and minimum limits. The increased efficiency of the group. PSO as an corresponding inequality constraints for each optimization tool, provide a population-based generator are search procedure in which individuals called particles change their position (states) with time. In P min  P  P max i i i (10) a PSO system particles fly around in a Where Pimin and Pimax are the minimum and multidimensional search space. maximum output of generator i. During flight each particle adjusts its position 2.2.1.3 Generator ramp rate limits: according to its own experience & the experience Operating range of all online units is restricted by of neighboring particles, making use of the best their ramp rate limits as follows: position encountered by it & neighbors. The swarm direction of a particle is defined by the set ofmax( P min , P 0  DRi )  P  min( P max , P 0  URi ) i i i i i particles neighboring the particle & its history experience. (11) According to the PSO algorithm, a swarm of The previous operating point of the ith generator is particles that have predefined restrictions starts to Pi0 and URi and DRi are the up and down ramp rate fly on the search space. The performance of each limits respectively. particle is evaluated by the value of the objective 2.2.1.4 Prohibited operating zones: function and considering the minimization A unit with prohibited operating zones has problem, in this case, the particle with lower value discontinuous input-output characteristic as shown has more performance. The best experiences for in fig.(3) each particle in iterations is stored in its memory and called personal best (pbest). The best value of pbest (less value) in iterations determines the global best (gbest).By using the concept of pbest and gbest the velocity of each particle is updated in equation (13) Vik+1 = ωVik + C1 r1 Xipbest − Xik + C2 r2 (Xigbest − Xik ) (13) Where Vik+1 Particle velocity at iteration (k+1) Vik Particle velocity at iteration k r1 , r2 Random number between [0, 1] C1 , C2 Acceleration constant the constraints is described by eq.(12) ω Inertia weight factor  Pi min  Pi  Pi L  After this, particles fly to a new position: Xik+1 = Xik + Vik+1  U  (14) Pi   Pik 1  Pi  PikL  Where (12) Xik+1 Particle position at iteration k+1  U  Xik  PiZi  Pi  Pi max  𝑉𝑖 𝑘 +1 Particle position at iteration k Particle velocity at iteration (k+1) 15 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022 Inertia weight in attempting to increase the rate of illustrated that the fuzzy adaptive particle swarm convergence of the standard PSO algorithm to optimization was a promising optimization method, global optimum, the inertia weight is proposed in which was especially useful for optimization the velocity equation 4.1 is set according to the problems with a dynamic environment. following equation (4.3) Ratnaweera Asanga, Halgamuge Saman K. [5] introduced a novel parameter automation strategy (𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 −𝑖𝑡𝑒𝑟 ) for the particle swarm algorithm and two further 𝜔= 𝜔 𝑚𝑎𝑥 − 𝜔 𝑚𝑖𝑛 × + 𝜔 𝑚𝑖𝑛 (15) 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 extensions to improve its performance after a Where predefined number of generations. Initially, to 𝜔 Inertia weight factor efficiently control the local search and convergence 𝜔 𝑚𝑎𝑥 Maximum value of weighting to the global optimum solution, Time-varying factor acceleration coefficients (TVAC) were introduced 𝜔 𝑚𝑖𝑛 Minimum value of weighting in addition to the time-varying inertia weight factor factor in particle swarm optimization. From the basis of 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 Maximum number of iterations TVAC, two new strategies were discussed to iter Current number of iteration improve the performance of the PSO. First, the concept of Mutation was introduced to the ParticleIV REVIEWS FOR PSO IN ECONOMIC Swarm Optimization along with TVAC (MPSO- DISPATCH PROBLEM TVAC), by adding a small perturbation to a In electrical power system, there are many randomly selected modulus of the velocity vector optimization problems such as optimal power flow, of a random particle by predefined probability. Economic Load Dispatch (ELD), generation and Second, it had introduced a novel particle swarm transmission planning, unit commitment, and concept “Self-organizing Hierarchical Particle forecasting & control. Amongst all optimization Swarm Optimizer with TVAC (HPSO-TVAC).” problems, ELD is important fundamental issue in Under this method, only the “social” part and the power system operation and planning. Its main “cognitive” part of the particle swarm strategy were objective is to allocate the optimal power considered to estimate the new velocity of each generation from different units at the lowest cost particle and particles were reinitialized whenever possible while meeting all system constraints. It is they were stagnated in the search space. a problem of high dimension, non-linear, multiple Chen Guimin et al. [7] gave new idea of constraints and real time specialty. There are Exponential Decreasing Inertia Weight (EDIW), in various conventional and non-conventional which two strategies of natural exponential optimization techniques that have been adopted by functions were proposed. Four different benchmark the researchers to approach the ELD problem. functions i.e. Shere, Rosenbrock, Griewank and Exhaustive literature review in the subject area is Rastrigin were used to evaluate the effects of these given below: strategies on the PSO performance. The results of Kennedy James and Eberhart R. [1] said that the experiments showed that these two new particle swarm optimization is an extremely simple strategies converge faster than linear one during the algorithm that seems to be effective for optimizing early stage of the search process. For most a wide range of functions. PSO method is continuous optimization problems, these two composed of a set of particles called individuals, strategies perform better than the linear one. which are able to follow a certain algorithm to Park Jong-Bae et al. [8] presented a novel and obtain the best solution for an optimization efficient method for solving the economic dispatch problem. These particles explore the search space problems with valve-point effect by integrating the with different velocities and positions. particle swarm optimization with the chaotic Shi Yuhui and Eberhart Russell [2] had sequences. In the ED problems, the inclusion of introduced a parameter inertia weight into the valve point loading effects made the modeling of original particle swarm optimizer. It was concluded the fuel cost functions of generating units more that the PSO with the inertia weight in the range practical. However, this increases the nonlinearity [0.9, 1.2] on average had a better performance with as well as number of local optima in the solution respect to find the global optimum point within a space; also the solution procedure can easily trap in reasonable number of iterations. the local optima in the vicinity of optimal value. Gaing Z.-L. et al. [4] presented an approach in The proposed Improved Particle Swarm which, a fuzzy system was implemented to Optimization (IPSO) combined the PSO algorithm dynamically adapt the inertia weight of the particle with chaotic sequences technique. The application swarm optimization algorithm. Three benchmark of chaotic sequences in PSO was an efficient functions with asymmetric initial range settings strategy to improve the global searching capability were selected as the test functions. The same fuzzy and escape from local minima. To demonstrate the system had been applied to all the three test effectiveness of the proposed method, the functions with different dimensions. The results numerical studies had been performed for two 16 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022different sample systems. The results clearly on the PSO performance and select the best one.showed that the proposed IPSO outperformed other The experimental results showed that for moststate-of-the-art algorithms in solving ED problems continuous optimization problems, the best onewith the valve-point effect. gains an advantage over the linear strategy andAdhinarayanan T. et al. [9] presented an efficient others.and reliable particle swarm optimization algorithm Gao Yue-lin & Duan Yu-hong [12] modifiedfor solving the economic dispatch problems with Random Inertia Weight Particle Swarmsmooth cost functions as well as cubic fuel cost Optimization (REPSO) in which a new particlefunctions. The practical ED problems have non- swarm optimization algorithm with random inertiasmooth cost functions with equality and inequality weight and evolution strategy proposed. Theconstraints that made the problem of finding the proposed random inertia weight was usingglobal optimum difficult using any mathematical simulated annealing idea and the given evolutionapproaches. For such cases, the PSO was applied to strategy was using the fitness variance of particlesthe ED problems with real power of generator in a to improve the global search ability of PSO. Thesystem as state variables. However when the experimented with six benchmark functionsincremental cost of each unit was assumed to be showed that the convergent speed and accuracy ofequal, the complexity involved in this may be REPSO was significantly superior to the one of thereduced by using the incremental cost as state PSO with Linearly Decreasing inertia Weightvariables. The proposed PSO algorithm had been Particle Swarm ( LDW-PSO).tested on 3 generator systems with smooth cost Chaturvedi K.T. et al. [13] proposed to apply afunctions and 3 generator systems, 5 generator novel Self-Organizing Hierarchical Particle Swarmsystems and 26 generator systems with cubic fuel Optimization (SOH_PSO) for the Non-Convexcost function. The results were compared with Economic Dispatch (NCED) to handle the problemgenetic algorithm (GA) and showed better results of premature convergence. The performance furtherand computation efficiency than genetic algorithm. improves when time-varying accelerationAl Rashidi M. R. et al. [20] presented a PSO coefficients were included.algorithm to solve an Economic-Emission Dispatch Kuo Cheng-Chien et al. [14] proposed a newproblem (EED). This problem had been getting approach and coding scheme for solving economicmore attention recently due to the deregulation of dispatch problems in power systems throughthe power industry and strict environmental Simulated Annealing Particle Swarm Optimizationregulations. It was formulated as a highly nonlinear (SA-PSO). This novel coding scheme couldconstrained multi-objective optimization problem effectively prevent obtaining infeasible solutionswith conflicting objective functions. PSO algorithm through the application of stochastic searchwas used to solve the formulated problem on two methods, thereby dramatically improving searchstandard test systems, namely the 30-bus and 14- efficiency and solution quality. Many nonlinearbus systems. Results obtained show that PSO characteristics of power generators and theiralgorithm outperformed most previously proposed operational constraints such as generationalgorithms used to solve the same EED problem. limitations, ramp rate limits, prohibited operatingThese algorithms included evolutionary algorithm, zones, transmission loss and nonlinear coststochastic search technique, linear programming, functions were all considered for practicaland adaptive hopfield neural network. PSO was operation. The effectiveness and feasibility of theable to find the pareto optimal solution set for the proposed method were demonstrated by fourmulti-objective problem. system case studies and compared with previousSai H. Ling et al. [10] introduced new hybrid literature in terms of solution quality andparticle swarm optimization that incorporates a computational efficiency. The experiment showedwavelet theory based mutation operation for encouraging results, suggesting that the proposedsolving economic load dispatch. It applied a approach was capable of efficiently determiningwavelet theory to enhance PSO in exploring higher quality solutions addressing economicsolution spaces more effectively for better dispatch problems.solutions. The results showed that the proposed Wilasinee Sugsakarn et al. [15] presented anmethod had performed significantly better, in terms effective method for solving economic dispatchof the s olution quality and solution stability, than problem (EDP) with non-smooth cost functionsome other hybrid PSOs and standard PSO. using a hybrid method that integrates Particle Chongpeng Huang et al. [11] modified the Swarm Optimization with Sequential Quadraticconcept of Decreasing Inertia Weight (DIW) by Programming (PSO-SQP). PSO was the mainintroducing some non-linear strategies on the optimizer to find the optimal global region whileexisting Linear DIW (LDIW). Then a power SQP was used as a fine tuning to determine thefunction was designed to unify them. Four optimal solution at the final stage. The proposedbenchmark functions sphere, rastrigrin, rosenbrock hybrid PSO-SQP method was applied to solve EDPand Shaffer’s were used to evaluate these strategies of a test system with ten generator units. 17 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022Ahmed Y. Saber et al. [16] presented a novel decreasing exponential method. In this methodmodified Bacterial Foraging Technique (BFT) to merely used an iteration to make an inertia weightsolve economic load dispatch problems. BFT was and it was fast and had highly accurate resultsalready used for optimization problems, and rather than other strategies.performance of basic BFT for small problems with Peng Chen et al. [21] introduced the floating pointmoderate dimension and searching space was representation to the Genetic Particle Swarmsatisfactory. Search space and complexity grow Optimization (GPSO). GPSO was derived from theexponentially in scalable ELD problems, and the Standard Particle Swarm Optimization (SPSO) andbasic BFT is not suitable to solve the high incorporated with the genetic reproductiondimensional ELD problems, as cells move mechanisms, namely crossover and mutation. Arandomly in basic BFT and swarming was not modified heuristic crossover was introduced, whichsufficiently achieved by cell-to-cell attraction and was derived from the differential evolution andrepelling effects for ELD. However, chemo taxis, genetic algorithm along with the mechanism ofswimming, reproduction and elimination-dispersal GPSO.steps of BFT were very promising. On the other Bhattacharya A. et al. [47] presented a novelhand, particles move toward promising locations particle swarm optimizer combined with roulettedepending on best values from memory and selection operator to solve the economic loadknowledge in particle swarm optimization. dispatch problem of thermal generators of a powerTherefore, best cell (or particle) biased velocity system. Several factors such as quadratic cost(vector) was added to the random velocity of BFT functions with valve point loading, transmissionto reduce randomness in movement (evolution) and Loss, generator ramp rate limits and prohibitedto increase swarming in the proposed method to operating zone are considered in the computationsolve ELD. Finally, a data set from a benchmark models. This new approach provided a newsystem was used to show the effectiveness of the mechanism to restrain the predominating of superproposed method. (global best) particles in early stage and canRen Zihui et al. [17] modified the basic structure effectively avoid the premature convergenceof the original PSO algorithm. It proposed that the problem and speed up the convergence property.particle’s position have relationship with the one Ming-Tang T. sai et al. [23] presented anparticle’s and the whole swarm’s perceive extent in Improved Particles Swarm Optimization (IPSO)the processing of this time and last time, and where integration of random particles and fine-presents the inertial weight based on simulated tuning mechanism have been added in traditionalannealing temperature. So New Particle Swarm PSO to solve the economic dispatch problemsOptimization algorithm (NPSO) was proposed. It with carbon tax consideration. This economiccannot improve the one particle’s and the whole dispatch problem had a non-convex cost functionswarm’s perceivable extent and improve the and nonlinear emission cost function with linearsearching efficient but also increase variety of and nonlinear constraints that it was difficult toparticles and overcome the defect of sinking the find the compromised solution using mathematicallocal optimal efficiently. At the same time the approaches, the proposed method used to solve thisconvergence condition given for this new problem. By considering the emissions, the carbonalgorithm. The algorithm of PSO and NPSO and was embedded in the economic dispatch problem.LPSO were tested with four well-known Many nonlinear characteristics of generating unitsbenchmark functions. The experiments showed that could be handled properly with a reasonable time.the convergence speed of NPSO was significantly Wanga Yongqiang et al. [22] proposed a Hybridsuperior to PSO and LPSO. The convergence Particle Swarm Optimization combined Simulatedaccuracy was increased. Annealing method (HPSAO) to solve economicYadmellat P. et al. [18] proposed a new Fuzzy load dispatch. The Simulated Annealing (SA)tuned Inertia Weight Particle Swarm Optimization algorithm was used to help PSO to jump out the(FIPSO), which remarkably outperformed the local optimum. Furthermore, a feasibility-basedstandard PSO, previous fuzzy as well as adaptive rule was introduced to deal with the constraints.based PSO methods. Different benchmark Finally, HPSAO was tested on three Gorgesfunctions with asymmetric initial range settings hydroelectric plants. The results were analyzed andwere used to validate the proposed algorithm and compared with other methods, which show thecompare its performance with those of the other feasibility and effectiveness of HPSAO method intuned parameter PSO algorithms. Numerical results terms of solution quality and computation time.indicate that FIPSO was competitive due to its Park Jong-Bae et al. [28] presented an efficientability to increase search space diversity as well as approach for solving economic dispatch problemsfinding the functions’ global optima and a better with non-convex cost functions using an Improvedconvergence performance. Particle Swarm Optimization (IPSO). Although theEmemipour Jafar et al. [19] proposed a new PSO approaches had several advantages suitable tostrategy to calculate inertia weight based on heavily constrained non-convex optimization 18 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022problems, they still had the drawbacks such as local industry. In this changed scenario, the scarcity ofoptimal trapping due to premature convergence energy resources, the ever increasing power(i.e., exploration problem), insufficient capability generation cost, environmental concerns, everto find nearby extreme points (i.e., exploitation growing demand for electrical energy necessitateproblem) and lack of efficient mechanism to treat optimal economic dispatch. The conventionalthe constraints (i.e., constraint handling problem). optimization methods are not able to solve suchThis work proposed an improved PSO framework problems due to local optimum solutionemploying chaotic sequences combined with the convergence. In the past decade, Met heuristicconventional linearly decreasing inertia weights optimization techniques especially Imperialistand adopting a crossover operation scheme to Competitive Algorithm (ICA) has gained anincrease both exploration and exploitation incredible recognition as the solution algorithm forcapability of the PSO. In addition, an effective such type of ED problems. The application of ICAconstraint handling framework was employed for in ED problem which is considered as the mostconsidering equality and inequality constraints. The complex optimization problem has beenproposed IPSO was applied to three different non- summarized in this paper.convex ED problems with valve-point effects, Vo Ngoc. Dieu. et al. [54] proposed newlyprohibited operating zones, ramp rate limits as well improved particle swarm optimization(NIPSO) foras transmission network losses, and multi-fuels solving economic load dispatch problem with valvewith valve-point effects. point loading effect. The proposed NIPSO is basedMeng K. et al. [29] proposed the Quantum- on the PSO with timevarying accelerationinspired Particle Swarm Optimization (QPSO) coeficient (PSO-TVAC) with more improvedwhich has stronger search ability and quicker including the use of sigmoid function with randomconvergence speed, not only because of the variation for inertia weight fctor, pseudo-gradiantintroduction of quantum computing theory, but also for guidance of particles,a and quadraticdue to two special implementations: self-adaptive programming for obtaing initial condition with newprobability selection and chaotic sequences improvement the search ability of the NIPSOmutation. The proposed approach was tested with method has been considerably enhanced infive standard benchmark functions and three power comparison with the PSO-TVAC method. Thesystem cases consisting of 3, 13, and 40 thermal proposed NIPSO has been tested on 13 unit &40units. Comparisons with similar approaches units system & obtained better optimal solutionincluding the Evolutionary Programming (EP), than the many other methods.genetic algorithm, Immune Algorithm (IA), and Sishaj P. Simon et al. [52] discussed dynamicother versions of particle swarm optimization were economic load dispatch using Artificial Beegiven. The promising results was illustrated the Colony algorithm for generating units with valve-efficiency of the proposed method and showed that point loading effect. The feasibility of the proposedit could be used as a reliable tool for solving ELD method is validated with 10 & 5 units test systemsproblems. for a period of 24 hours. In addition, the effects ofVu PhanTu et al. [30] presented a novel Weight- control parameters on the performance of ArtificialImproved Particle Swarm Optimization (WIPSO) Bee Colony (ABC) algorithm for Dynamicmethod for computing Optimal Power Flow (OPF) Economic Dispatch (DED) problem are studied.and ELD problems. To evaluate the accuracy, Results obtained with the proposed approach areconvergence speed and applicability of the compared with other techniques.proposed method, the OPF results of IEEE 30 bus Omaranpour H. et al. [51] presented a localsystem by WIPSO are compared with traditional extremum escape approach to Particle Swarmparticle swarm optimization, genetic algorithm, Optimization (PSO) method. Here previous worstDifferential Evolution (DE) and Ant Colony position of the particles are also considered in heOptimization (ACO) methods. Further solutions velocity update equation which makes theof ELD problem of IEEE 13 & 40 units test system convergence of algorithm faster & capable tohave also being determined by the proposed escape from local minimum. For manyalgorithm and results are compared with Classical optimization problems where other PSO variantsEvolutionary Programming (CEP), Improved Fast are stuck in local optimal solution, but the proposedEvolutionary Programming (IFEP) and various method has been tested on standard bench markimproved particle swarm optimization methods. functions and gave superior results.The tested results indicated that the proposed M. Vanitha et al. [55] explians a new optimizationmethod is more efficient than existing one in terms technique efficient hybrid simulated annealingof total fuel costs, total losses and computational algorithm(EHSA)for both convex & nonconvextimes. ELD problem. The mutation operator of differentailChahkandi H. Nejad et al. [53] introduced a evolution is used in particle swarm optimization tohighly vibrant and competitive market which improve its performance & it ishybridized withaltered revolutionized many aspects of the power simulated annealing to get EHSA technique. 19 | P a g e
  • Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January-February 2013, pp.013-022V CONCLUSION 5. Asanga Ratnaweera, Saman K. Due to deregulation of the power industry Halgamuge “Self-Organizing Hierarchicaland strict environment regulations, highly non- Particle Swarm Optimizer With Time-linear constraints, multi objective problem with Varying Acceleration Coefficients” IEEEconflicting objective functions are involved in ELD Trans. on evolutionary computation,vol.problem. 8,no.3, June 2004 In practical ELD problem it is necessary 6. Gao Yue-lin , Duan Yu-hong “A Newto consider valve point loading, prohibited zones Particle Swarm Optimization Algorithmwith ramp rate limit as well as transmission with Random Inertia Weight andnetwork losses and multi-fuels with valve point Evolution Strategy” Internationaleffects. The complexity further increases when Conference on Computationaldimensionality of power system increases. The Intelligence and Security Workshopsbasic PSO is insufficient to address the problem of 2007.practical ELD. The global optimal solution and 7. Guimin Chen, Xinbo Huang, Jianyuan Jiaglobal search ability, premature convergence and and Zhengfeng Min “ Natural Exponentialconvergence speed, and stuck in local optima are Inertia Weight Strategy in Particle Swarmcertain major issues for PSO. In this review, it is Optimization” 6th World Confress onshown that many new algorithms are developed to Intelligent Control and Automation, Junesolve this problem of PSO. 21 - 23, 2006, Dalian, China. By adopting dynamic inertia weight, fuzzy 8. Jong-Bae Park, Yun-Won Jeong, Hyun-tuned inertia weight, PSO with wavelet theory, SA- Houng Kim and Joong-Rin Shin “AnPSO, GPSO and QPSO with chaotic sequence, we Improved Particle Swarm Optimizationcan get better global optimum solution and global for Economic Dispatch with Valve-Pointsearch ability. To improve the ability of PSO for Effect” International Journal ofpremature convergence and convergence speed we Innovations in Energy Systems and Power,can apply DIW PSO, SOH-PSO and PSO Vol. 1, no. 1 (November 2006)combined with roulette selection on operator. In 9. T.Adhinarayanan, Maheswarapu Syduluaddition to that local optima problem is solved by “Particle Swarm Optimisation forapplying NPSO and HPSO. Economic Dispatch with Cubic Fuel Cost In this paper it is reviewed that ELD for Function”, TENCON 2006, IEEE regionvalve point loading, PSO with chaotic sequence conference.can be applied. For large ELD problem weight 10. Sai H. Ling, Herbert H. C. Iu, Kit Y. Chanimproved PSO can be applied. For more practical and Shu K. Ki “Economic Load Dispatch:problem, another PSO with chaotic sequence A New Hybrid Particle Swarmcombined with DIW and crossover scheme Optimization Approach”sept.11 2007.(improved PSO) can be applied. So it can be 11. Huang Chongpeng, Zhang Yuling, Jiangconcluded that PSO can be applied to large Dingguo, Xu Baoguo “On Some Non-dimension ELD problem as well as complex linear Decreasing Inertia Weightproblem of ELD. If PSO is applied with another Strategies in Particle Swarmevolutionary programming technique it can provide Optimization” Proceedings of the 26thmuch better results. Chinese Control Conference July 26-31, 2007, Zhangjiajie, Hunan, China.REFERENCES 12. Gao Yue-lin, Duan Yu-hong “A New 1. J. Kennedy and R.Eberhart, “Particle Particle Swarm Optimization Algorithm swarm optimization,” in Proc. IEEE Int. with Random Inertia Weight and Conf. Neural Networks, 1995, pp. 1942– Evolution Strategy” 2007 International 1948. Conference on Computational Intelligence 2. Yuhui Shi and Russell Eberhart “A and Security Workshops. modified particle swarm optimizer” 0- 13. K.T.Chaturvedi, Manjaree Pandit “Self- 7803-4869-9198 0.0001998 IEEE. Organizing Hierarchical Particle Swarm 3. Yuhui Shi and Russell C. Eberhart “Fuzzy Optimization for Nonconvex Economic Adaptive Particle Swarm Optimization” Dispatch” IEEE transactions on power Evolutionary computation, 2001 system,vol.23,august 2008. proceeding of the 2001 congres on vol.1 14. Cheng-Chien Ku “A Novel Coding page no. 101-106. Scheme for Practical Economic Dispatch 4. Z.-L. Gaing, “Particle Swarm Modified Particle Swarm Approach” IEEE Optimization to solving the economic transactions on power dispatch considering generator system,vol.23,no.4,nov.2008 constraints,” IEEE Trans. Power Syst., 15. Wilasinee Sugsakarn and Parnjit vol. 18, no. 3, pp. 1718–1727, Aug. 2003 Damrongkulkamjorn “Economic Dispatch 20 | P a g e
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