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![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 1 An Adaptive Differential Evolution Algorithm for Reactive Power Dispatch Arun.G1 , Chandrasekar.T2 PG Scholar, M.E (PSE), Velammal College of Engineering and Technology, Madurai, India 1 Assistant Professor, M.E ,VelammalCollege of Engineering and Technology, Madurai, India 2 Abstract: Reactive power or VAR management is one of the most crucial tasks required for proper operation and control of a power system. Reactive power management is carried out to reduce losses in a power system, by adjusting the reactive power control variables such as generator voltages transformer tap-setting and other sources of reactive power such as capacitor banks or FACTS devices. VAR management provides better system security improved power transfer capability and overall system operation. VAR management is a complex combinatorial optimization problem involving non-linear functions having multiple local minima and non-linear and discontinuous constraints. In this paper, the VAR management problem is formulated as a non- linear constrained optimization problem with equality and inequality constraints for minimization of real power loss. The problem is solved using Differential evolution (DE), which is a population based search algorithm. For avoiding the time and the effort in tuning the parameters of DE algorithm, an Adaptive DE algorithm with time varying chaotic mutation and crossover is proposed for solving the optimization problem. Effectiveness of the proposed an Adaptive DE algorithm based approach has been demonstrated on the IEEE 57-bus and IEEE 118-bus system are found to be superior to classical DE and its variants Self- adaptive Differential Evolution (SaDE) in terms of convergence behavior and solution quality. Keywords:Adaptive differential Evolution algorithm, Real power loss minimization, VAR management,Voltage deviation. I. INTRODUCTION The main objective of reactive power (VAR) management in a power system is to identify the reactive power control variables settings such as generator voltages, transformer tap settings and other sources of reactive power such as capacitor banks or FACTS devices to reduce losses, system security, power transfer capability and overall system operation. Reactive power management is a sub problem of optimal power flow (OPF) calculation. OPF is an on-linear programming (NLP) problem that is solved find out the optimal control parameters/circumstance to minimize a desired objective function, subject to certain system constraints. It was first introduced by Carpentier [1,2] in 1960s.Reactive power management provides the power system operator a set of control variables to minimize transmission losses and to preserve bus voltage within permissible limits by rescheduling the power flows. In recent years, the issue of reactive power management for various objectives like voltage control and power loss reduction has received much attention. The main objective of VAR management is to improve the voltage profile and minimize real power losses through redistribution of reactive power in the system[3-5]. Through, the conventional optimization techniques like Gradient method, non-linear programming and interior point method can be applied to solve VAR management problem [6-10], but these techniques have several drawbacks, such as insecure convergence properties and excessive numerical iterations: resulting in huge computations and large execution time. Also, these methods are highly complex optimization techniques and insufficient for large-scale system applications [10]. Due to non- differential, non-linear, multi- modal and non- convex nature of the VAR management problem, most of these conventional techniques converge to local optimum[10]. With the advent of Evolutionary computing (EC) techniques like Genetic Algorithm (GA), Evolutionary programming (EP), Differential Evolution (DE) algorithm and Particle swarm optimization (PSO), these techniques have been applied for reactive power dispatch problem [11- 21]. These nature inspired stochastic search based methods are increasingly being proposed for solving power system optimization problems in recent years. The random parallel search capability and non-dependency on nature of the optimization problem has contributed to their popularity for handling various complexoptimization problems. The ease of formulating the equality and inequality constraints and stable convergence behavior also add to their merits. In recent years, Some evolutionary computing based algorithms, their advanced versions and hybrid EC algorithms have been developed and proposed for various optimization problems in power system[22, 23]. The advanced versions and hybrid EC algorithms are claimed to provide better solution for some functions and the problem under considerations, but there is no algorithm available which out performs other algorithms for all the optimization problems. The reason is that, these methods do not converge to the global best solution in every trial run but are able to produce a feasible near solution quit fast and are highly depend on parameter tuning. DE is the simple population based search algorithm, which is highly efficient in handling constrained optimization problems and is supposed to be an improved version of Genetic algorithm. This algorithm can be applied for optimization of a non-smooth, discontinuous and multi- modal function. Differential Evolution algorithm can find near optimal solution regardless the initial parameters, its](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-1-2048.jpg)
![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 2 convergence is fast and it requires a few numbers of parameters. In addition to this, its coding is simple and it can handle integer and discrete optimization [24, 25]. The performance of the Differential Evolution algorithm was compared with various heuristic techniques. It has been observed that DE algorithm is significantly better than that of other heuristic methods like GA, Particle swarm optimization and Evolutionary Algorithm.DE algorithm is found to be robust and able to provide the same results consistently over several trials [26, 27]. In addition to this, DE algorithm has been used to solve high dimensional function optimization [28]. It is found that, it has superior functioning on o set of widely used bench mark functions. Thus, DE algorithm seems to be a promising approach for various engineering optimization problems including reactive power management [29-32]. Differential evolution algorithm has been applied for single objective VAR management problem [18,19].and the results obtained are found to be better than those already reported earlier by using other such techniques. In this paper An Adaptive DE with time varying chaotic mutation and crossover has been proposed for solving the single objective VAR management problem. The problem has been formulated as a non-linear constrained single objective optimization problem, where the real power loss and the bus voltage deviations are to be optimized (minimized) simultaneously. Effectiveness of the proposed an Adaptive DE based approach to solve single objective VAR management problem has been demonstrated and compared on the standard IEEE 57-bus and IEEE 118-bus system[6]. II. PROBLEM FORMULATION AThe optimal VAR management problem is to optimize the steady state performance of a power system in terms of one or more objective functions while satisfying several equality and inequality constraints. The VAR management problemcan be formulated as follows [4]. 2.1 objective function 1. Minimization of real power loss (PL) This objective is to minimize the real power loss in transmission lines of a power system by managing reactive power and is expressed as F1=Ploss=∑nl K=1gk[Vi 2 +Vj 2 -2ViVj(δi-δj)] (1) 2.2 Problem constraints (1) Equality constraints The equality constraints represent typical load flow equations as follows PGi-PDi-Vi∑j≠1 Vj(Gijcosθij+ Bijsin θij)= 0 (2) Where θij=(δi– δj) QGi-QDi-Vi∑j≠1 Vj(Gijsin θij- Bijcosθij)= 0 (3) Whereθij=(δi– δj) For i=1,2,3…..NB (2) Inequality constraints The inequality constraints represent the system operating constraints as follows, a. Generation constraints: Generator voltages VG and reactive power outputs QG are restricted by their lower and upper limits as follows: Vi-min ≤Vi ≤ Vi-max (4) QGi-min≤QGi≤QGi-maxiЄ{Npv,N0}(5) b. Transformer constraints: Transformer tap T settings are bounded as follows: Ti-min≤ Ti ≤ Ti-max i Є NT(6) c. Switchable VAR sources constraints: Switchable VAR compensations Qc are restricted by their limits as follows: QCi-min≤QCi≤QCi-maxiЄNC(7) d. Security constraints: These include the constraints of voltages at load buses VL and transmission line loadings SL as follows:as follows: Vli-min ≤ Vli≤Vli-max i = 1,2,……NLB (8) Sli-min≤ Sli-max i = 1,2,……NLB (9) Aggregating the objectives and constraints, the problem can be mathematically formulated as a non-linear constrained multi-objective optimization problemas follows: Minimize [PL(x,u)] (10) Subject to : Equality constraint g(x,u)=0 (11) And Inequality constraint h(x,u) < 0 (12) Here x can be expressed as XT =[VL1…….VNLB,QG1…....QGNG,SL1……Sint] (13) While u can be expressed as UT =[VG1…….VGNG,T1…….TNT,Qc1……..QCNC] (14) I. Adaptive Differential Evolution algorithm has been applied for this multi-objective VAR management problem, which is a combinatorial optimization problem having multi-extremism and non-linear property. In this paper, the reactive power management. III. CLASSICAL DIFFERENTIAL EVOLUTIONARY ALGORITHM A Differential Evolution (DE) is a population based algorithmthat employs crossover, mutation (differential) and selection operators. In differential Evolution, all the solutions have the same probability of being selected as parents. DE employs a greedy selection process that is the best new solution and its parent win the competition](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-2-2048.jpg)
![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 3 providing significant advantage of converging performance over Genetic algorithms, Differential Evolution [18] algorithm works through a simple cycle of the stages as follows 3.1 Initialization At the beginning of DE algorithm implementation, i.e t=0 the problem independent variables are initialized somewhere in their feasible numerical range. Therefore, if the jth variable has its lower and upper bounds as xi andxj respectively, then the jth component of the ith population member may be initialized as: Xij(0)=Xj 1 +rand(0,1)*(Xj u –Xj l ) (15) Where rand(0,1) is a uniformly distributed random numbers between 0and 1. 3.2 Mutation In each generation, a donor vector V(t) is created in order to change the population member vector Xi(t). Generally, the method of creating this donor vector is different in various DE schemes. However, in this paper, DE/rand /1 mutation Strategy is implemented. In this mutation strategy, creation of the donor vector V(t)for the ith member Xi, three parameter vector Xr1,Xr2 and Xr2 are selected randomly from the current population not coinciding with the current member Xi. Next, a scalar number F scales the difference between any two of the three vectors and this scaled difference is added to the third one. Thus, the donor vector V(t) is obtained. The jth component of each vector can be expressed as: Vi,j(t+1)=Xr1,j(t)+F(Xr2,j(t)-Xr3,j(t)) (16) 3.3 Crossover To increase the diversity of the population, crossover operator is carried out in which the donor vector exchanges its components with those of the current member Xi(t). Two types of crossover schemes, namely exponential crossover and binomial crossover can be used by DE algorithm [24,25]. In this paper, binomial crossover scheme is used which is performed on all the D variables and can be expressed as: Ui,j(t)={Vi,j(t) if rand(0,1)< CR Xi,j(t) else (17) 3.4 Selection To keep the population size constant over subsequent generations, the selection process is applied to find out which one of the child and the parent will survive in the next generation, i.e at time t=t+1. Differential Evolution actually adopts the survival of the fittest principle in its selection process. The selection process can be expressed as Xi(t+1)={ Ui(t) iff (Ui(t)≤F(Xi(t)) Xi(t) iff(Xi(t)<F(Ui(t)) (18) Where F(.) is the function to be minimized. So ,if the child Ui(t) yields a better value of the fitness function, it replaces its parents in the next generation: otherwise, the parent Xi(t) is retained in the population. Thus the population either gets better in terms of the fitness function or remains fixed but never degenerates. Hence the population either gets better in terms of the fitness function or remains constant but never deteriorates. 3.4.1 Self-adaptive DE (SaDE) algorithm In Self adaptive DE (SaDE) algorithm, both strategies and their associated parameter are gradually Self-adapted by learning from their previous experiences in generating promising solutions. As a result, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different search/evolution phases. In this algorithm, at each generation, a set of trial vector generation strategies together with their associated parameter values is separately assigned to different individual in current population according to the selection probabilities learned fromthe previous generations [32,34]. 3.4.3 An Adaptive DE algorithm Mutation rate F and crossover rate CR significantly affect the performance of the DE algorithm. The smaller the mutation rate F, longer time will be required for convergence of DE algorithm. While larger values of F allow exploration due to which the algorithm may not converge and skip good optimal solution. The value of F should be small to enough to enable the algorithm to explore tight valleys and large enough to allow global exploration in order to maintain population diversity. A higher CR creates more diversity and better exploration in the new population. In classical DE algorithm, both F and CR are fixed, so a lot of tuning parameters is required to achieve global best results. This problem can be solved by employing time - varying mutation and crossover rates. To improve the performance of classical DE, many hybrids of DE algorithm have been proposed that incorporates chaotic systems in various ways. The most common application of chaos theory in DE algorithm is for its parameter adaptation [36-38]. In addition to this, chaotic sequences have been utilized to initialize DE population diversity [36], to perform local search in the neighborhood of the selected individuals [40] etc. Chaotic sequences with the mutation factor have been integrated in DE algorithm to improve solution quality [38]. In [37], various chaotic sequences in evolutionary algorithms (EAs) were proposed in the place of the randomnumbers. In the present paper, the most commonly used chaotic sequence, known as logistics map has been applied to adapt the DE control parameters. The logistic equation is defined as follows: Y(t)=μ*Y(t-1)*[1-Y(t-1)] (19) Where t is the iteration count and μ is a control parameter 0≤ μ≤4. The behavior of the system represented by [26] significantly changes with the variation in μ. The value of μ controls the variation of the chaotic sequence. The DE variant with time varying F and CR is proposed in this paper. The variation of F chaotically, based on logistic map and time varying crossover rate CR, give rise to the following adaptive differential evolutionary algorithm: The mutation rate factor parameter F1is varied as per Eq.(16) where F1(0) lies between [0,1]. An index „t‟ is the current iteration and F1(t) is the new mutation factor based on the logistic map. F1(t)=μ*Y(t-1)*[1-F1(t-1)] (20) The control parameter μ decides whether mutation rate F1 oscillates between a limited sequences, varies chaotically or](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-3-2048.jpg)
![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 4 stabilizes to a constant value. A very small difference in F1(0) causes the significant difference in its variation pattern. The system at [27] is deterministic and displays chaotic behavior when μ=4 and F(0)€(0,0.25,0.5,0.75,1.0). The mutation parameter F is increased from an initial value F2i to a final value F2f with the iterative progress of the optimization algorithm, as per the dynamics given by [27- 28] by suitable choice of initial and final values of mutation rate. F(t)=[(F2f–F2i)(iter/itermax )+F2i]F1t (21) In the proposed adaptiveDE algorithm, the value of CR is changed iteratively as given below: CR(iter)=(CRmax –Cmin ) (22) IV. IMPLEMENTATION OF ADAPTIVE DE ALGORITHM The proposed Adaptive DE algorithm based approach has been formulated and implemented using matlab. Several trials have been taken with different values of DE key parameters such as differentiation (mutation) constant F, crossover constant CR, size of population NP, and the maximum number of generations (iterations) itermax which is used here as a stopping criteria to find the optimal DE key parameters. The first step in the DE algorithm and Adaptive DE algorithm is creating an initial population. All the independent variables which include generator voltages, transformer tap settings and shunt VAR compensations have to be generated according to [15], where each independent parameter of each individual in the population is assigned a value within its specified feasible region. This creates parent vector of independent variables for the first generation, after finding the independent variables, dependent variables like generator reactive power, and voltages at load buses and line flows were calculated using newton-raphson load flow (NRLF) program. 4.1Computational steps of DE algorithm DE algorithm, SaDE, EPSDE and Adaptive DE have been employed to find the best control variables setting starting from randomly generated initial population. At the end of the each iteration, the best individuals, based on the fitness value, are stored. The computational steps of the proposed DE algorithm are as follows: 1. Generate an initial population randomly within the control variables setting starting from randomly within the control variables lower and upper bounds. 2. For each individual in the population, run NRLF program, to find the operating points. 3. Evaluate the fitness of the individuals. 4. Perform mutation and crossover operation using (16)-(17). 5. Select the individuals for the next generations. 6. Store the best individuals of the current generation. 7.Repeat steps 2-5, till the termination criterion is met. 8.Select the control variables setting corresponding to the overall best individual. 9.If the solution is acceptable, find out the best individual and its objective value. Otherwise, change the settings of DE and repeat the steps 1-8. V. DESCRIPTION OF IEEE TEST BUS SYSTEM The description of the test bus system consists of three buses, namely standard IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus respectively. Each bus is consists of their own generators, transformer tap settings and shunt VAR capacitors with their branches, equality and inequality constraints and base case of control variables and state variables. TABLE 1 description of IEEE test bus system VI. RESULTS AND DISCUSSIONS 6.1 Test Bus system : IEEE 57-bus power system The standard IEEE 57-bus system consists of eighty transmission lines, seven generators (at the buses 1, 2, 3, 6, 8, 9, 12) and fifteen branches under load tap setting transformers branches is taken as test system 1. There reactive power sources are considered at buses 18, 25 and 53. Line data, bus data, variable limits and the initial values of the control variables are considered. The search space of this case systemhas twenty five dimensions, including seven generator voltages, fifteen transformer tap and three reactive power sources. The system loads are given as follows: Pload=12.508 p.u, Qload=3.364p.u. The initial total generations and power losses are: PG=12.7926p.u. ,QG=3.4545p.u. 6.1.1 Comparison results of standard IEEE 57 bus system The Comparison of IEEE 57 bus consists of the results of the non- linear programming methods, particle swarm optimization and chaotic particle swarm optimization results are compared and the better result is obtained from the proposed Adaptive differential algorithmof Ploss=0.2336 p.u TABLE 2: SIMULATION RESULTS OF IEEE 57 BUS TEST SYSTEM description IEEE30 bus IEEE57 bus IEEE 118 bus Buses,NB 30 57 118 Generators,NG 6 7 54 Transformers,NT 4 15 9 Shunts,NQ 9 3 14 Branches,NE 41 80 186 Equality constraints 60 114 236 Inequality constraints 125 245 572 Control variables 19 27 77 State variables 6 20 21 Base case for Ploss,MW 5.660 27.8637 132.4500 Base case for TVD,p.u 0.58217 1.23358 1.439337](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-4-2048.jpg)
![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 9 promising algorithm for solving some more other complex engineering optimization problem for future researchers. ACKNOWLEDGMENT I would especially like to express my extreme gratitude and sincere thanks to: Dr.A. SHUNMUGALATHAM.E,Ph.d, Professor and Head of the Department, Electrical and Electronics Engineering, Velammal College of Engineering and Technology for her enthusiastic and innovative guidance during the entire period of my project. I would like to express my deep sense of gratitude and heartiest thanks to: My guide MR.T.CHANDRASEKAR M.E, Assistant Professor II, Electrical and Electronics Engineering, Velammal College of Engineering and Technology for her constant source of encouragement and for the valuable guidance. Her moral support encouraged me to process through my work successfully. 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[22] Chaturvedi KT, Pandit M, Srivastava I,” Self-organizing hierarchical particle swarm optimization for non-convex economic dispatch”,Roy PK, Ghoshal SP, Thakur SS,” Optimal VAR for improvements in voltage profiles and for real power loss minimization using biogeography based optimization”, IEEE Trans Power Syst 2008;23(3):1079-1087. [23] Pandit M, Srivastava L, Pal K,” Static/dynamic optimal dispatch of energy and reserveusing recurrent differential evolution,” to appear in IET proceedings- GenerTrasmDistri, doi:10.1049/iet- gtd.2013.0127.ISSN1751-8687. [24] Storn R, Price K,” Differential evolution- a simple and efficient heuristic for global optimization over continuous spaces”, Tech Report TR-95-012,ICSI;1995. [25] Storn R, Price K,” Differential evolution- a simple and efficient heuristic for global optimization over continuous spaces”, J global optim 1997;11: 34-359. [26] Vesterstrom J, Thomsen R,” A comparative study of differential evolution, particle swarm optimization and evolutionary algorithm: on numerical benchmark problems,” In; IEEE congress on evolutionary computation:2004. p. 90-987. [27] Das S, Abrham A, Konar A,” particle swarm optimization and differential evolutionary algorithms: technical analysis, applications and hybridization perspectives. <http;//www.softcomputing.net/aciis.pdf>. [28] Yang Zhenyu, Tang KE, Yao Xin,”Differential evolution for high dimensional function optimization‟, In IEEE congress on, Evolutionary computation (CEC2007); p.3523-3530. [29] Vaisakh K, KantaRao P,‟ differential evolution based optimal power dispatch for voltage stability enhancement „, J theorAppl Inform Technol 2008; 638- 646. [30] Balamurugan R, Suramanian S,” Self adaptive differential evolution based power dispatch of generators with valve-point effects and multiple fuel options”. computingSciEng 2007;1:10-17. 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[37] Capnetto R, ForttunaFazzino S, XibiliaMG,‟Chaotic sequences to improve the performance of evolutionary algorithms”, IEEE Trans EvolutComput 2003;7(3):289-304. [38] Coelho R, Mariani VC,” Combining of Chaotic differential evolution and quadratic programming for economic dispatch optimization with valve point effect”, IEEE Trans Power Syst 2006;21(2):989-996.](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-9-2048.jpg)
![International Journal of Research in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 10 [39] He D, Dong G, Wang F, Mao Z,” optimization of dynamic economic dispatch with valve point effect using chaotic sequence based differential evolution algorithms”, Energy Convers Manage 2011;52(2):1026-1032. [40] Pal Kirti, Pandit M, Srivastava L,” Joint energy and reserve dispatch in a multi-area competitive market using time varying differential evolution”, Int J EngSciTechnol (IJEST)2011;3(1):87-10. [41] StandardIEEE 57 Test Bus System. [42] StandardIEEE 118 Test Bus System.](https://image.slidesharecdn.com/vol1issue3p001-160121144600/75/An-Adaptive-Differential-Evolution-Algorithm-for-Reactive-Power-Dispatch-10-2048.jpg)
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An Adaptive Differential Evolution Algorithm for Reactive Power Dispatch
This document summarizes an adaptive differential evolution algorithm for solving the reactive power dispatch problem, which involves minimizing real power losses. The problem is formulated as a non-linear constrained optimization problem. An adaptive differential evolution algorithm is proposed that uses time-varying chaotic mutation and crossover to avoid parameter tuning. The algorithm is applied to the IEEE 57-bus and 118-bus test systems and found to provide superior convergence and solution quality compared to classical differential evolution and self-adaptive differential evolution algorithms.
An Adaptive Differential Evolution Algorithm for Reactive Power Dispatch
- 1. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 1 An Adaptive Differential Evolution Algorithm for Reactive Power Dispatch Arun.G1 , Chandrasekar.T2 PG Scholar, M.E (PSE), Velammal College of Engineering and Technology, Madurai, India 1 Assistant Professor, M.E ,VelammalCollege of Engineering and Technology, Madurai, India 2 Abstract: Reactive power or VAR management is one of the most crucial tasks required for proper operation and control of a power system. Reactive power management is carried out to reduce losses in a power system, by adjusting the reactive power control variables such as generator voltages transformer tap-setting and other sources of reactive power such as capacitor banks or FACTS devices. VAR management provides better system security improved power transfer capability and overall system operation. VAR management is a complex combinatorial optimization problem involving non-linear functions having multiple local minima and non-linear and discontinuous constraints. In this paper, the VAR management problem is formulated as a non- linear constrained optimization problem with equality and inequality constraints for minimization of real power loss. The problem is solved using Differential evolution (DE), which is a population based search algorithm. For avoiding the time and the effort in tuning the parameters of DE algorithm, an Adaptive DE algorithm with time varying chaotic mutation and crossover is proposed for solving the optimization problem. Effectiveness of the proposed an Adaptive DE algorithm based approach has been demonstrated on the IEEE 57-bus and IEEE 118-bus system are found to be superior to classical DE and its variants Self- adaptive Differential Evolution (SaDE) in terms of convergence behavior and solution quality. Keywords:Adaptive differential Evolution algorithm, Real power loss minimization, VAR management,Voltage deviation. I. INTRODUCTION The main objective of reactive power (VAR) management in a power system is to identify the reactive power control variables settings such as generator voltages, transformer tap settings and other sources of reactive power such as capacitor banks or FACTS devices to reduce losses, system security, power transfer capability and overall system operation. Reactive power management is a sub problem of optimal power flow (OPF) calculation. OPF is an on-linear programming (NLP) problem that is solved find out the optimal control parameters/circumstance to minimize a desired objective function, subject to certain system constraints. It was first introduced by Carpentier [1,2] in 1960s.Reactive power management provides the power system operator a set of control variables to minimize transmission losses and to preserve bus voltage within permissible limits by rescheduling the power flows. In recent years, the issue of reactive power management for various objectives like voltage control and power loss reduction has received much attention. The main objective of VAR management is to improve the voltage profile and minimize real power losses through redistribution of reactive power in the system[3-5]. Through, the conventional optimization techniques like Gradient method, non-linear programming and interior point method can be applied to solve VAR management problem [6-10], but these techniques have several drawbacks, such as insecure convergence properties and excessive numerical iterations: resulting in huge computations and large execution time. Also, these methods are highly complex optimization techniques and insufficient for large-scale system applications [10]. Due to non- differential, non-linear, multi- modal and non- convex nature of the VAR management problem, most of these conventional techniques converge to local optimum[10]. With the advent of Evolutionary computing (EC) techniques like Genetic Algorithm (GA), Evolutionary programming (EP), Differential Evolution (DE) algorithm and Particle swarm optimization (PSO), these techniques have been applied for reactive power dispatch problem [11- 21]. These nature inspired stochastic search based methods are increasingly being proposed for solving power system optimization problems in recent years. The random parallel search capability and non-dependency on nature of the optimization problem has contributed to their popularity for handling various complexoptimization problems. The ease of formulating the equality and inequality constraints and stable convergence behavior also add to their merits. In recent years, Some evolutionary computing based algorithms, their advanced versions and hybrid EC algorithms have been developed and proposed for various optimization problems in power system[22, 23]. The advanced versions and hybrid EC algorithms are claimed to provide better solution for some functions and the problem under considerations, but there is no algorithm available which out performs other algorithms for all the optimization problems. The reason is that, these methods do not converge to the global best solution in every trial run but are able to produce a feasible near solution quit fast and are highly depend on parameter tuning. DE is the simple population based search algorithm, which is highly efficient in handling constrained optimization problems and is supposed to be an improved version of Genetic algorithm. This algorithm can be applied for optimization of a non-smooth, discontinuous and multi- modal function. Differential Evolution algorithm can find near optimal solution regardless the initial parameters, its
- 2. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 2 convergence is fast and it requires a few numbers of parameters. In addition to this, its coding is simple and it can handle integer and discrete optimization [24, 25]. The performance of the Differential Evolution algorithm was compared with various heuristic techniques. It has been observed that DE algorithm is significantly better than that of other heuristic methods like GA, Particle swarm optimization and Evolutionary Algorithm.DE algorithm is found to be robust and able to provide the same results consistently over several trials [26, 27]. In addition to this, DE algorithm has been used to solve high dimensional function optimization [28]. It is found that, it has superior functioning on o set of widely used bench mark functions. Thus, DE algorithm seems to be a promising approach for various engineering optimization problems including reactive power management [29-32]. Differential evolution algorithm has been applied for single objective VAR management problem [18,19].and the results obtained are found to be better than those already reported earlier by using other such techniques. In this paper An Adaptive DE with time varying chaotic mutation and crossover has been proposed for solving the single objective VAR management problem. The problem has been formulated as a non-linear constrained single objective optimization problem, where the real power loss and the bus voltage deviations are to be optimized (minimized) simultaneously. Effectiveness of the proposed an Adaptive DE based approach to solve single objective VAR management problem has been demonstrated and compared on the standard IEEE 57-bus and IEEE 118-bus system[6]. II. PROBLEM FORMULATION AThe optimal VAR management problem is to optimize the steady state performance of a power system in terms of one or more objective functions while satisfying several equality and inequality constraints. The VAR management problemcan be formulated as follows [4]. 2.1 objective function 1. Minimization of real power loss (PL) This objective is to minimize the real power loss in transmission lines of a power system by managing reactive power and is expressed as F1=Ploss=∑nl K=1gk[Vi 2 +Vj 2 -2ViVj(δi-δj)] (1) 2.2 Problem constraints (1) Equality constraints The equality constraints represent typical load flow equations as follows PGi-PDi-Vi∑j≠1 Vj(Gijcosθij+ Bijsin θij)= 0 (2) Where θij=(δi– δj) QGi-QDi-Vi∑j≠1 Vj(Gijsin θij- Bijcosθij)= 0 (3) Whereθij=(δi– δj) For i=1,2,3…..NB (2) Inequality constraints The inequality constraints represent the system operating constraints as follows, a. Generation constraints: Generator voltages VG and reactive power outputs QG are restricted by their lower and upper limits as follows: Vi-min ≤Vi ≤ Vi-max (4) QGi-min≤QGi≤QGi-maxiЄ{Npv,N0}(5) b. Transformer constraints: Transformer tap T settings are bounded as follows: Ti-min≤ Ti ≤ Ti-max i Є NT(6) c. Switchable VAR sources constraints: Switchable VAR compensations Qc are restricted by their limits as follows: QCi-min≤QCi≤QCi-maxiЄNC(7) d. Security constraints: These include the constraints of voltages at load buses VL and transmission line loadings SL as follows:as follows: Vli-min ≤ Vli≤Vli-max i = 1,2,……NLB (8) Sli-min≤ Sli-max i = 1,2,……NLB (9) Aggregating the objectives and constraints, the problem can be mathematically formulated as a non-linear constrained multi-objective optimization problemas follows: Minimize [PL(x,u)] (10) Subject to : Equality constraint g(x,u)=0 (11) And Inequality constraint h(x,u) < 0 (12) Here x can be expressed as XT =[VL1…….VNLB,QG1…....QGNG,SL1……Sint] (13) While u can be expressed as UT =[VG1…….VGNG,T1…….TNT,Qc1……..QCNC] (14) I. Adaptive Differential Evolution algorithm has been applied for this multi-objective VAR management problem, which is a combinatorial optimization problem having multi-extremism and non-linear property. In this paper, the reactive power management. III. CLASSICAL DIFFERENTIAL EVOLUTIONARY ALGORITHM A Differential Evolution (DE) is a population based algorithmthat employs crossover, mutation (differential) and selection operators. In differential Evolution, all the solutions have the same probability of being selected as parents. DE employs a greedy selection process that is the best new solution and its parent win the competition
- 3. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 3 providing significant advantage of converging performance over Genetic algorithms, Differential Evolution [18] algorithm works through a simple cycle of the stages as follows 3.1 Initialization At the beginning of DE algorithm implementation, i.e t=0 the problem independent variables are initialized somewhere in their feasible numerical range. Therefore, if the jth variable has its lower and upper bounds as xi andxj respectively, then the jth component of the ith population member may be initialized as: Xij(0)=Xj 1 +rand(0,1)*(Xj u –Xj l ) (15) Where rand(0,1) is a uniformly distributed random numbers between 0and 1. 3.2 Mutation In each generation, a donor vector V(t) is created in order to change the population member vector Xi(t). Generally, the method of creating this donor vector is different in various DE schemes. However, in this paper, DE/rand /1 mutation Strategy is implemented. In this mutation strategy, creation of the donor vector V(t)for the ith member Xi, three parameter vector Xr1,Xr2 and Xr2 are selected randomly from the current population not coinciding with the current member Xi. Next, a scalar number F scales the difference between any two of the three vectors and this scaled difference is added to the third one. Thus, the donor vector V(t) is obtained. The jth component of each vector can be expressed as: Vi,j(t+1)=Xr1,j(t)+F(Xr2,j(t)-Xr3,j(t)) (16) 3.3 Crossover To increase the diversity of the population, crossover operator is carried out in which the donor vector exchanges its components with those of the current member Xi(t). Two types of crossover schemes, namely exponential crossover and binomial crossover can be used by DE algorithm [24,25]. In this paper, binomial crossover scheme is used which is performed on all the D variables and can be expressed as: Ui,j(t)={Vi,j(t) if rand(0,1)< CR Xi,j(t) else (17) 3.4 Selection To keep the population size constant over subsequent generations, the selection process is applied to find out which one of the child and the parent will survive in the next generation, i.e at time t=t+1. Differential Evolution actually adopts the survival of the fittest principle in its selection process. The selection process can be expressed as Xi(t+1)={ Ui(t) iff (Ui(t)≤F(Xi(t)) Xi(t) iff(Xi(t)<F(Ui(t)) (18) Where F(.) is the function to be minimized. So ,if the child Ui(t) yields a better value of the fitness function, it replaces its parents in the next generation: otherwise, the parent Xi(t) is retained in the population. Thus the population either gets better in terms of the fitness function or remains fixed but never degenerates. Hence the population either gets better in terms of the fitness function or remains constant but never deteriorates. 3.4.1 Self-adaptive DE (SaDE) algorithm In Self adaptive DE (SaDE) algorithm, both strategies and their associated parameter are gradually Self-adapted by learning from their previous experiences in generating promising solutions. As a result, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different search/evolution phases. In this algorithm, at each generation, a set of trial vector generation strategies together with their associated parameter values is separately assigned to different individual in current population according to the selection probabilities learned fromthe previous generations [32,34]. 3.4.3 An Adaptive DE algorithm Mutation rate F and crossover rate CR significantly affect the performance of the DE algorithm. The smaller the mutation rate F, longer time will be required for convergence of DE algorithm. While larger values of F allow exploration due to which the algorithm may not converge and skip good optimal solution. The value of F should be small to enough to enable the algorithm to explore tight valleys and large enough to allow global exploration in order to maintain population diversity. A higher CR creates more diversity and better exploration in the new population. In classical DE algorithm, both F and CR are fixed, so a lot of tuning parameters is required to achieve global best results. This problem can be solved by employing time - varying mutation and crossover rates. To improve the performance of classical DE, many hybrids of DE algorithm have been proposed that incorporates chaotic systems in various ways. The most common application of chaos theory in DE algorithm is for its parameter adaptation [36-38]. In addition to this, chaotic sequences have been utilized to initialize DE population diversity [36], to perform local search in the neighborhood of the selected individuals [40] etc. Chaotic sequences with the mutation factor have been integrated in DE algorithm to improve solution quality [38]. In [37], various chaotic sequences in evolutionary algorithms (EAs) were proposed in the place of the randomnumbers. In the present paper, the most commonly used chaotic sequence, known as logistics map has been applied to adapt the DE control parameters. The logistic equation is defined as follows: Y(t)=μ*Y(t-1)*[1-Y(t-1)] (19) Where t is the iteration count and μ is a control parameter 0≤ μ≤4. The behavior of the system represented by [26] significantly changes with the variation in μ. The value of μ controls the variation of the chaotic sequence. The DE variant with time varying F and CR is proposed in this paper. The variation of F chaotically, based on logistic map and time varying crossover rate CR, give rise to the following adaptive differential evolutionary algorithm: The mutation rate factor parameter F1is varied as per Eq.(16) where F1(0) lies between [0,1]. An index „t‟ is the current iteration and F1(t) is the new mutation factor based on the logistic map. F1(t)=μ*Y(t-1)*[1-F1(t-1)] (20) The control parameter μ decides whether mutation rate F1 oscillates between a limited sequences, varies chaotically or
- 4. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 4 stabilizes to a constant value. A very small difference in F1(0) causes the significant difference in its variation pattern. The system at [27] is deterministic and displays chaotic behavior when μ=4 and F(0)€(0,0.25,0.5,0.75,1.0). The mutation parameter F is increased from an initial value F2i to a final value F2f with the iterative progress of the optimization algorithm, as per the dynamics given by [27- 28] by suitable choice of initial and final values of mutation rate. F(t)=[(F2f–F2i)(iter/itermax )+F2i]F1t (21) In the proposed adaptiveDE algorithm, the value of CR is changed iteratively as given below: CR(iter)=(CRmax –Cmin ) (22) IV. IMPLEMENTATION OF ADAPTIVE DE ALGORITHM The proposed Adaptive DE algorithm based approach has been formulated and implemented using matlab. Several trials have been taken with different values of DE key parameters such as differentiation (mutation) constant F, crossover constant CR, size of population NP, and the maximum number of generations (iterations) itermax which is used here as a stopping criteria to find the optimal DE key parameters. The first step in the DE algorithm and Adaptive DE algorithm is creating an initial population. All the independent variables which include generator voltages, transformer tap settings and shunt VAR compensations have to be generated according to [15], where each independent parameter of each individual in the population is assigned a value within its specified feasible region. This creates parent vector of independent variables for the first generation, after finding the independent variables, dependent variables like generator reactive power, and voltages at load buses and line flows were calculated using newton-raphson load flow (NRLF) program. 4.1Computational steps of DE algorithm DE algorithm, SaDE, EPSDE and Adaptive DE have been employed to find the best control variables setting starting from randomly generated initial population. At the end of the each iteration, the best individuals, based on the fitness value, are stored. The computational steps of the proposed DE algorithm are as follows: 1. Generate an initial population randomly within the control variables setting starting from randomly within the control variables lower and upper bounds. 2. For each individual in the population, run NRLF program, to find the operating points. 3. Evaluate the fitness of the individuals. 4. Perform mutation and crossover operation using (16)-(17). 5. Select the individuals for the next generations. 6. Store the best individuals of the current generation. 7.Repeat steps 2-5, till the termination criterion is met. 8.Select the control variables setting corresponding to the overall best individual. 9.If the solution is acceptable, find out the best individual and its objective value. Otherwise, change the settings of DE and repeat the steps 1-8. V. DESCRIPTION OF IEEE TEST BUS SYSTEM The description of the test bus system consists of three buses, namely standard IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus respectively. Each bus is consists of their own generators, transformer tap settings and shunt VAR capacitors with their branches, equality and inequality constraints and base case of control variables and state variables. TABLE 1 description of IEEE test bus system VI. RESULTS AND DISCUSSIONS 6.1 Test Bus system : IEEE 57-bus power system The standard IEEE 57-bus system consists of eighty transmission lines, seven generators (at the buses 1, 2, 3, 6, 8, 9, 12) and fifteen branches under load tap setting transformers branches is taken as test system 1. There reactive power sources are considered at buses 18, 25 and 53. Line data, bus data, variable limits and the initial values of the control variables are considered. The search space of this case systemhas twenty five dimensions, including seven generator voltages, fifteen transformer tap and three reactive power sources. The system loads are given as follows: Pload=12.508 p.u, Qload=3.364p.u. The initial total generations and power losses are: PG=12.7926p.u. ,QG=3.4545p.u. 6.1.1 Comparison results of standard IEEE 57 bus system The Comparison of IEEE 57 bus consists of the results of the non- linear programming methods, particle swarm optimization and chaotic particle swarm optimization results are compared and the better result is obtained from the proposed Adaptive differential algorithmof Ploss=0.2336 p.u TABLE 2: SIMULATION RESULTS OF IEEE 57 BUS TEST SYSTEM description IEEE30 bus IEEE57 bus IEEE 118 bus Buses,NB 30 57 118 Generators,NG 6 7 54 Transformers,NT 4 15 9 Shunts,NQ 9 3 14 Branches,NE 41 80 186 Equality constraints 60 114 236 Inequality constraints 125 245 572 Control variables 19 27 77 State variables 6 20 21 Base case for Ploss,MW 5.660 27.8637 132.4500 Base case for TVD,p.u 0.58217 1.23358 1.439337
- 5. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 5 Fig.1 Diagram of IEEE 57 bus test system Fig.2 Convergence Results of IEEE 57 bus test system 6.2 Test system 2: IEEE 118 test bus system To test the proposed Adaptive differential evolutionary algorithm in solving optimal reactive power dispatch problems of larger power systems, a standard IEEE 118-bus test system is considered as test system 2. The search space of this case system has seventy seven dimensions, i.e., the fifty four generator buses,sixty four load buses, one hundred and eighty six transmission lines, nine transformer taps and fourteen reactive power sources. The system line data, bus data, variable limits and the initial values of control variables are taken. The maximum and minimum limits of reactive power sources, bus voltages and transformer tap- setting limits are taken. The system loads are given as follows: Pload=42.4200p.u, Qload=14.3800p.u. The initial total Variable Initial setting A-DE GENERATOR VOLTAGE V1,p.u 1.0400 1.0975 V2,p.u 1.0100 1.0828 V3,p.u 0.9850 1.0687 V6,p.u 0.9800 1.0762 V8,p.u 1.0050 1.0969 V9,p.u 0.9800 1.0645 V12,p.u 1.0150 1.0758 TRANSFORMER TAP RATIO T4-18 0.9810 1.0623 T4-18 1.0100 0.9749 T21-20 1.0080 1.0337 T24-26 0.9990 0.9840 T7-29 0.9840 0.9501 T34-32 0.9590 0.9794 T11-41 0.9740 1.0429 T15-45 0..9880 0.9136 T14-46 0.9700 0.9535 T10-51 0.9860 0.9328 T13-49 0.9790 1.0887 T11-43 0.9730 0.9998 T40-56 1.0100 1.0000 T39-57 0.9830 1.0085 T9-55 0.9800 1.0202 CAPACITOR BANK QC-18,p.u 0.0 0.0040 QC-25,p.u 0.0 0.0258 QC-53,p.u 0.0 0.0259 Ploss,p.u NR* 0.2366 TVD,p.u NR* NR* CPU time NR* NR*
- 6. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 6 generations and power losses are as follows: PG=43.7536 p.u., QG=8.8192p.u.,Ploss=1.25751p.u., Qloss=-7.6511 p.u. 6.2.1 Comparison results of standard IEEE 118 bus system The Comparison of IEEE 118 bus consists of the results of the non- linear programming methods, particle swarm optimization and chaotic particle swarm optimization results are compared and the better result is obtained from the proposed Adaptive differential algorithmof Ploss=125.7MW. Thus the proposed algorithm has smoothly converged and the graph is displayed in fig. 4. Then result and comparison table is given table 4 and 5 respectively with their generator voltage, transformer tap settings and shunt VARs (capacitor banks) with their initial and final values in p.u. and the losses values of IEEE 118 test bus system is achieved better than the classical Differential Evolutionary Algorithm. TABLE3: COMPARISION RESULTOF IEEE57 TEST BUS SYSTEM Variable A-DE NLP CGA L-SaDE PSO-w PSO-d CLPSO GENERATOR VOLTAGE V1,p.u 1.0975 1.06 0.9686 1.0600 1.06 1.06 1.0541 V2,p.u 1.0828 1.06 1.0493 1.0574 1.0578 1.0586 1.0529 V3,p.u 1.0687 1.0538 1.0567 1.0438 1.04378 1.0464 0.0337 V6,p.u 1.0762 1.06 0.9877 1.0364 1.0356 1.0415 0.0313 V8,p.u 1.0969 1.06 1.0223 1.0537 1.0546 1.06 1.0496 V9,p.u 1.0645 1.06 0.9918 1.0366 1.0369 1.0423 1.0302 V12,p.u 1.0758 1.06 1.0044 1.0323 1.0334 1.0371 1.0342 TRANSFORMER TAP RATIO T4-18 1.0623 0.91 0.92 0.94 0.90 0.98 0.99 T4-18 0.9749 1.06 0.92 1.00 1.02 0.98 0.98 T21-20 1.0337 0.93 0.97 1.01 1.01 1.01 0.99 T24-26 0.9840 1.08 0.90 1.01 1.01 1.01 1.01 T7-29 0.9501 1.00 0.91 0.97 0.97 0.98 0.99 T34-32 0.9794 1.09 1.1 0.97 0.97 0.97 0.93 T11-41 1.0429 0.92 0.94 0.9 0.90 0.90 0.91 T15-45 0.9136 0.91 0.95 0.97 0.97 0.97 0.97 T14-46 0.9535 0.98 1.03 0.96 0.95 0.96 0.95 T10-51 0.9328 0.98 1.09 0.96 0.96 0.97 0.98 T13-49 1.0887 0.98 0.90 0.92 0.92 0.93 0.95 T11-43 0.9998 0.98 0.90 0.96 0.96 0.97 0.95 T40-56 1.0000 0.98 1.00 1.00 1.00 0.99 1.00 T39-57 1.0085 1.08 0.96 0.96 0.96 0.96 0.96 T9-55 1.0202 1.03 1.00 0.97 0.98 0.98 0.97 CAPACITOR BANK QC-18,p.u 0.0040 0.08352 0.084 0.08112 0.05136 0.9984 0.09888 QC-25,p.u 0.0258 0.00864 0.00816 0.05808 0.05904 0.05904 0.05424 QC-53,p.u 0.0259 0.1104 0.05376 0.06192 0.06288 0.06288 0.0.6288 Ploss,p.u 0.2366 0.259023 0.2524411 0.2426739 0.2427052 0.2428022 0.2451520 TVD,p.u NR* NR* NR* NR* NR* NR* NR* CPUtime ,s NR* NR* 321.4872 408.97 353.08 404.63 423.30 Fig.3 Diagram of IEEE 118 bus test system
- 7. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 7 Fig.4 Convergence Characteristics of IEEE 118 bus test system TABLE 4 RESULTS OF IEEE 118 BUS TEST SYSTEM Variable Initial setting ADE Variable Initial setting ADE Variable Initial setting ADE Generator voltage Transformer tap setting V1,p.u 0.9550 1.0442 V65,p.u 1.0050 1.0698 T8 1.0150 0.9788 V4,p.u 0.9980 1.0439 V66,p.u 1.0500 1.0309 T32 1.0150 0.9895 V6,p.u 0.9900 1.0569 V69,p.u 1.0350 1.0785 T36 0.9680 0.9780 V8,p.u 1.0150 1.0259 V70,p.u 0.9840 1.0460 T51 0.9620 0.9966 V10,p.u 1.0500 1.0400 V72,p.u 0.9800 1.0585 T93 0.9690 0.9643 V12,p.u 0.9900 1.0400 V73,p.u 0.9910 1.0314 T95 0.9840 0.9933 V15,p.u 0.9700 1.0617 V74,p.u 0.9580 1.0579 T102 1.0050 1.0245 V18,p.u 0.9730 1.0420 V76,p.u 0.9430 1.0523 T107 1.0030 0.9642 V19,p.u 0.9620 1.0482 V77,p.u 1.0060 1.0568 T117 0.9970 1.0071 V24,p.u 0.9920 1.0195 V80,p.u 1.0400 1.0470 Capacitor banks V25,p.u 1.0500 1.0469 V85,p.u 0.9850 1.0626 QC-5,p.u 0.0 0.0256 V26,p.u 1.0150 1.0325 V87,p.u 1.0150 1.0334 QC-34,p.u 0.0 0.0427 V27,p.u 0.9680 1.0751 V89,p.u 1.0050 1.0663 QC-37,p.u 0.0 0.0211 V31,p.u 0.9670 1.0668 V90,p.u 0.9850 1.0365 QC-44,p.u 0.0 0.0211 V32,p.u 0.9630 1.0404 V91,p.u 0.9800 1.0534 QC-45,p.u 0.0 0.0247 V34,p.u 0.9840 1.0425 V92,p.u 0.9900 1.0463 QC-46,p.u 0.0 0.0061 V36,p.u 0.9800 1.0498 V99,p.u 1.0100 1.0821 QC-48,p.u 0.0 0.0344 V40,p.u 0.9700 1.0634 V100,p.u 1.0170 1.0725 QC-74,p.u 0.0 0.0255 V42,p.u 0.9850 1.0677 V103,p.u 1.0100 1.0461 QC-79,p.u 0.0 0.0255 V46,p.u 1.0050 1.0509 V104,p.u 0.9710 1.0613 QC-82,p.u 0.0 0.0193 V49,p.u 1.0250 1.0546 V105,p.u 0.9650 1.0490 QC-83.p.u 0.0 0.0166 V54,p.u 0.9550 1.0366 V107,p.u 0.9520 1.0420 QC-105,p.u 0.0 0.0308 V55,p.u 0.9520 1.0647 V110,p.u 0.9730 1.0531 QC-107,p.u 0.0 0.0338 V56,p.u 0.9540 1.0499 V111,p.u 0.9800 1.0679 QC-110,p.u 0.0 0.2571 V59,p.u 0.9850 1.0442 V112,p.u 0.9750 1.0583 Ploss,MW NR* 125.7512 V61,p.u 0.9950 1.0527 V113,p.u 0.9930 1.0803 TVD,p.u NR* NR* V62,p.u 0.9980 1.0373 V116,p.u 1.0050 1.0412 CPU,s NR* NR* TABLE5 COMPARISION RESULTS OF IEEE118 BUS TESTSYSTEMS Variable ADE OGSA GSA CLPSO PSO Variable ADE GSA GSA CLPSO PSO Generator voltage Generator voltage V1,p.u 1.0442 1.0350 0.9600 1.0332 1.0853 V91,p.u 1.0534 1.0297 1.0032 1.0288 0.9615 V4,p.u 1.0439 1.0554 0.9620 1.0550 1.0420 V92,p.u 1.0463 1.0353 1.0927 0.9760 0.9568 V6,p.u 1.0569 1.0301 0.9729 0.9754 1.0805 V99,p.u 1.0821 1.0395 1.0433 1.0880 0.9540 V8,p.u 1.0259 1.0175 1.0570 0.9669 0.9683 V100,p.u 1.0725 1.0275 1.0786 0.9617 0.9584 Variable ADE OGSA GSA CLPSO PSO Variable ADE GSA GSA CLPSO PSO Generator voltage Generator voltage V10,p.u 1.0400 1.0250 1.0885 0.9811 1.0756 V103,p.u 1.0461 1.0158 1.0266 0.9611 1.0162
- 8. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 8 V12,p.u 1.0400 1.0410 0.9630 1.0092 1.0225 V104,p.u 1.0613 1.0165 0.9808 1.0125 1.0992 V15,p.u 1.0617 0.9973 1.0127 0.9787 1.0786 V105,p.u 1.0490 1.0197 1.0163 1.0684 0.9694 V18,p.u 1.0420 1.0047 1.0069 1.0799 1.0498 V107,p.u 1.0420 1.0408 0.9987 0.9769 0.9656 V19,p.u 1.0482 0.9899 1.0003 1.0805 1.0776 V110,p.u 1.0531 1.0288 1.0218 1.0414 1.0873 V24,p.u 1.0195 1.0287 1.0105 1.0286 1.0827 V111,p.u 1.0679 1.0194 0.9852 0.9790 1.0375 V25,p.u 1.0469 1.0600 1.0102 1.0307 0.9564 V112,p.u 1.0583 1.0132 0.9500 0.9764 1.0920 V26,p.u 1.0325 1.0855 1.0401 0.9877 1.0809 V113,p.u 1.0803 1.0386 0.9764 0.9721 1.0753 V27,p.u 1.0751 1.0081 0.9809 1.0157 1.0874 V116,p.u 1.0412 0.9724 1.0372 1.0330 0.9594 V31,p.u 1.0668 0.9948 0.9500 0.9615 0.9608 Transformer tap ratio V32,p.u 1.0404 0.9993 0.9552 0.9851 1.1000 T8 0.9788 0.9568 1.0659 1.0045 1.0112 V34,p.u 1.0425 0.9958 0.9910 0.0157 0.9611 T32 0.9895 1.0409 0.9534 1.0609 1.0906 V36,p.u 1.0498 0.9835 1.0091 1.0849 1.0367 T36 0.9780 0.9963 0.9328 1.0008 1.0033 V40,p.u 1.0634 0.9981 0.9505 0.9830 1.0914 T51 0.9966 0.9775 1.0884 1.0093 1.0000 V42,p.u 1.0677 1.0068 0.9500 1.0516 0.9701 T93 0.9643 0.9960 1.0579 0.9922 1.0080 V46,p.u 1.0509 1.0355 0.9814 0.9754 1.0390 T95 0.9933 0.9956 0.9493 1.0074 1.0326 V49,p.u 1.0546 1.0333 1.0444 0.9838 1.0836 T102 1.0245 0.9882 0.9975 1.0611 0.9443 V54,p.u 1.0366 0.9911 1.0379 0.9637 0.9764 T107 0.9642 0.9251 0.9887 0.9307 0.9067 V55,p.u 1.0647 0.9914 0.9907 0.9716 1.0103 T117 1.0071 1.0661 0.9801 0.9578 0.9673 V56,p.u 1.0499 0.9920 1.0333 1.0250 0.9536 Capacitor banks V59,p.u 1.0442 0.9909 1.0099 1.0003 0.9672 QC-5,p.u 0.0256 -0.3319 0.00 0.0000 0.0000 V61,p.u 1.0527 1.0747 1.0925 1.0771 1.0938 QC-34,p.u 0.0427 0.0480 7.46 11.7135 9.3639 V62,p.u 1.0373 1.0753 1.0393 1.0480 1.0978 QC-37,p.u 0.0211 -0.2490 0.00 0.0000 0.0000 V65,p.u 1.0698 0.9814 0.9998 0.9684 1.0892 QC-44,p.u 0.0211 0.0328 6.07 9.8932 9.3078 V66,p.u 1.0309 1.0487 1.0355 0.9648 1.0861 QC-45,p.u 0.0247 0.0383 3.33 9.4169 8.6428 V69,p.u 1.0785 1.0490 1.1000 0.9574 0.9665 QC-46,p.u 0.0061 0.0545 6.51 2.6719 8.9462 V70,p.u 1.0460 1.0395 1.0992 0.9765 1.0783 QC-48,p.u 0.0344 0.0181 4.47 2.8546 11.8092 V72,p.u 1.0585 0.9900 1.0014 1.0243 0.9506 QC-74,p.u 0.0255 0.0509 9.72 0.5471 4.6132 V73,p.u 1.0314 1.0547 1.0111 0.9651 0.9722 QC-79,p.u 0.0255 0.1104 14.25 14.8532 10.5923 V74,p.u 1.0579 1.0167 1.0476 1.0733 0.9713 QC-82,p.u 0.0193 0.0965 17.49 19.4270 16.4544 V76,p.u 1.0523 0.9972 1.0211 1.0302 0.9602 QC-83.p.u 0.0166 0.0263 4.28 6.9824 9.6325 V77,p.u 1.0568 1.0071 1.0187 1.0275 1.0781 QC-105,p.u 0.0308 0.0442 12.04 9.0291 8.9513 V80,p.u 1.0470 1.0066 1.0462 0.9857 1.0788 QC-107,p.u 0.0338 0.0085 2.26 4.9926 5.0426 V85,p.u 1.0626 0.9893 1.0491 0.9836 0.9568 QC-110,p.u 0.2571 0.0144 2.94 2.2086 5.5319 V87,p.u 1.0334 0.9693 1.0426 1.0882 0.9642 Ploss,MW 125.7512 126.99 127.7603 130.96 131.99 V89,p.u 1.0663 1.0527 1.0955 0.9895 0.9748 TVD,p.u NR* 1.1829 NR* NR* NR* V90,p.u 1.0365 1.0290 1.0417 0.9905 1.0248 CPU,s NR* 1152.3 1198.658 1472 1215 VII.CONCLUSION In this paper, one recently developed Adaptive differential evolutionary algorithm has been successfully implemented to solve ORPD problem of power systems for minimization of active power losses benefits arisen are presented. The ORPD problem is formulated as a nonlinear optimization problem with equality and inequality constraints of the power network. In this study, the minimization of active power loss are considered and the Ploss=2.633MW for IEEE 57 bus and Ploss=125.7512 MW for IEEE 118 bus. The proposed ADE is tested on IEEE 57, and IEEE 118 bus power system to demonstrate its effective ness. From the simulation work, it is observed that the proposed ADE yields the optimal settings of the control variables of the test power system. The simulation result also indicates the robustness and superiority of the proposed approach to solve the ORPD problem of power system. The proposed ADE algorithm may be recommended as a very
- 9. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 9 promising algorithm for solving some more other complex engineering optimization problem for future researchers. ACKNOWLEDGMENT I would especially like to express my extreme gratitude and sincere thanks to: Dr.A. SHUNMUGALATHAM.E,Ph.d, Professor and Head of the Department, Electrical and Electronics Engineering, Velammal College of Engineering and Technology for her enthusiastic and innovative guidance during the entire period of my project. I would like to express my deep sense of gratitude and heartiest thanks to: My guide MR.T.CHANDRASEKAR M.E, Assistant Professor II, Electrical and Electronics Engineering, Velammal College of Engineering and Technology for her constant source of encouragement and for the valuable guidance. Her moral support encouraged me to process through my work successfully. 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- 10. International Journal ofResearch in Advanced Technology - IJORAT Vol. 1, Issue 3, DECEMBER 2015 All Rights Reserved © 2015 IJORAT Page 10 [39] He D, Dong G, Wang F, Mao Z,” optimization of dynamic economic dispatch with valve point effect using chaotic sequence based differential evolution algorithms”, Energy Convers Manage 2011;52(2):1026-1032. [40] Pal Kirti, Pandit M, Srivastava L,” Joint energy and reserve dispatch in a multi-area competitive market using time varying differential evolution”, Int J EngSciTechnol (IJEST)2011;3(1):87-10. [41] StandardIEEE 57 Test Bus System. [42] StandardIEEE 118 Test Bus System.