Optimal Reactive Power Planning By Using Evolutionary Engineering Essay

optimal oxidizable office homework By Using Evolutionary Engineering EssayThis motif presents a orderology for solving Optimal unstable force out Planning (ORPP) problem by utilize Evolutionary programming (EP) Optimization Technique in cast to improve the electric potential stableness and minimize the waiveres in the billet ashes. This study has highly-developed the Evolutionary Programming (EP) Optimization Technique using MATLAB softw ar. The study tested 2 fitness functions namely come in loss minimization and the voltage constancy improvement in source system with dickens different sportsman technique. Comparison in the way outs obtained was made in order to determine the best fitness function and the best mutation technique to be used for solving ORPP and hence the voltage stability is improved. The proposed technique was tested on the IEEE 26 deal reliability test system.KeywordsOptimal Reactive ability Planning (ORPP), Voltage perceptual constancy Improvement, Evolutionary Programming (EP)I. INTRODUCTIONIn general, the problem of optimal unstable post planning (ORPP) can be de dividing lineate as to determine the amount and location of shunt reactive origin compensation devices needed for minimum cost while keeping an adequate voltage profile. The ORPP is one of the most challenging problems since accusing functions, the act cost and the investment cost of new reactive world-beater sources, should be minimized simultaneously 1. transmission loss can be minimised by performing reactive power planning which involves optimisation process. The ORPP is a large-scale nonlinear optimisation problem with a large number of variables and uncertain parameters. Various mathematical optimization algorithms carry way been developed for the ORPP, which in most cases use nonlinear 2, linear 3, or motley integer platformming 4, and decomposition methods 5-8. However, these conventional techniques are known to converge to a local o ptimal re issue rather than the global one for problems such(prenominal) as ORPP which have many local minima.Recently, evolutionary algorithms (EAs) have been used for optimization in particular both the genetic algorithm and evo1ution programming have been used in the ORPP problem. The EA is a powerful optimization technique analogous to the natural selection process in genetics. It is useful especially when other optimization methods fail in finding the optimal solution 1. Evolutionary Programming (EP) optimization technique is recently applied in solving electric power system optimization problems. It is part of the Evolutionary Algorithm (EA) optimization techniques under the artificial intelligence hierarchy. Optimization is an important issue in power system operation and planning particularly in the area of voltage stability studies 9. In this study, EP engine was signly developed to implement the optimisation process considering dickens mutation techniques, each with bo th different objective functions. Comparative studies performed in this study aimed to identify the most suitable mutation technique with the best objective function for minimising transmission loss in power system and also improving the voltage stability. The parameters for this problem are generated reactive power (Qg), injected reactive power (Qinj) and transformer ten-strike (T). Validation on the effectiveness of the proposed technique was conducted on the IEEE-26 reliability test system.Figure 1 The IEEE 26 bus test systemII. OBJECTIVESThe two objective functions of this study areTo obtain the total loss minimizationTo improve the voltage stabilityWhere Total_Loss is total loss minimizationLQNmax is voltage stability improvementIII. BACKGROUND STUDIESA. Optimal Reactive Power Planning (ORPP)Optimal Reactive Power Planning (ORPP) is a sub-problem of Optimal Power Flow solution which has been widely used in power system operation and planning to determine the optimal admit par ameter settings, in order to minimize or maximize the desired objective function while quiting a set of systems constraint. Reactive Power Planning (RPP) involves in optimizing the transformer tap setting, injection of reactive power at generator and load bus so as to fulfill the objective function. Since the OPF approach is commonly concerned with the security and economic operation of the power system, Economic Dispatch (ED) technique is also adopted in RPP scheme. The value of active power generated by the generator is also adjusted in the approach. 11ORPP is a nonlinear programming problem which has the following mathematical formulationMaximize or minimizef(x, u) (3)subject tog(x, u) =0 (4)hmin h(x, u) hmax (5)where u is the sender of control variables and x is the vector of dependent variables. f(x, u) is the objective function, while g(x, u) is the nodal power constraints with hmin h(x, u) hmax are the inequality constraints of the dependent and independent variables.B. Evolutionary Programming (EP)EP is one of the popular techniques which oarlock under the Evolutionary Computation in Artificial Intelligence (AI) hierarchy and increasingly applied for solving power system optimization problem in recent years. A new population is formed from an existing population through the use of a mutation operator. This operator produces a new solution by perturbing each component of an existing solution by a random amount. The degree of optimality is measured by the fitness, which can be outlined as the objective function of the problem 12.Through the use of a ranking scheme, the candidate solutions in each population were sorted in hike order according to the number of the best population. The best population form a resultant population is referred as the next generation.The ranking scheme must(prenominal) have more optimal solutions which has a greater chance of survival than the poorer solutions. It is a stochastic optimization strategy, which based on the mechanics of natural selections-mutation, ambition and evolution. This technique stressed on the behavioural linkage between parents and their publication. In general, EP consists of 3 major steps which briefly discussed as follow 12, 13i. InitializationThe initial population of single(a)s consists of (xi, i), i 1, 2, are generated randomly based on its limit, whereby xi denotes the control variable and i is the strategic parameter with respect to xi. The fitness is metrical for each individual based on its objective function, f(xi).ii. Mutationa) First Mutation TechniqueEach parent (xi, i), i=1,, , creates a single offspring (xi, i), where xi and i are given byxi (j) = xi (j) + i (j) Nj (0, 1) (6)i (j) = i (j) exp ( N (0, 1) + Nj (0, 1)) (7)and = ((2(n) ) )-1 (8)= ((2n) )-1 (9)xi (j), xi(j), i(j) and i(j) are the j-th component of the vectors xi, xi, i and i respectively. N(0,1) represents a normally distributed one-dimensional random number with mean zero and standard deviation 1. Nj(0,1) denotes that the random number is generated afresh for each value of j. Subsequently, the fitness is calculated for each offspring.b) Proposed Mutation TechniqueThe proposed mutation rule was inspired by neural network back annexe learning. The following three equations are employed for perturbing the parents to generate their offspringIn these equations, xij k k is the jth variable of an ith individual at the kth generation. The learning rate, , and the momentum rate, , are echt-valued constants that are determined empirically. . denotes an absolute value and N represents the normal distribution. xij k is the amount of change in an individual, which is proportional to the temporal error, and it drives the individual to evolve close to the best individual at the next generation.It may be viewed as a tendency of the other individuals to take after or emulate the best individual in the sure generation. sxij k is the evolution tendency or momentum of previous e volution.It accumulates evolution information and tends to accelerate convergence when the evolution trajectory is moving in a consistent direction 14. The best individual is mutated only by the momentum. This expands the exploitation range and increases the possibility for escaping from local minima. accik in (10) is defined as follows.accik = 1 if the current update has improved cost,0 otherwise. (10)iii. Combination and SelectionIn combination stage, the union of parents and offspring are ranked in ascending or go order according to its fitness and purpose of the optimisation. Hence, the top individuals are selected to be parents for the next generation.The process of mutation, combination and selection are repeated until the stopping cadence is met. In this paper, the stopping criterion is taken to be the convergence of fitness value.IV. METHODOLOGYFigure 3 explained the overall methodology for the evolutionary programming optimization technique to solve ORPP. The produced of fspring vector must satisfy and consider the constraints as at the initialization. The main concept of EP is the mutation process.Then continues with learning near the MATLAB software and tested the IEEE 26-Bus Test form to observe initial values which are total power loss, initial minimum and maximum voltages and the initial line stability index (LQP LQN). These initial values have been taken by considering the unstable transmission lines in the test system (IEEE 26-BUS).The unstable line authority the line stability index value is close to 1.00. The unstable voltage is when the value is not within the range of (0.90V1.10).Figure 3 The hang chart for the EP optimization techniqueThe EP program was developed and the analysis of the result is tested based on objective function of the project such as minimize total loss and the voltage stability improvement. Then, the program has been run for five times for each type of objective function. Finally, this project has been concluded and the account has been written.A. Development of EP for Optimal Reactive Power PlanningThe optimal reactive power planning problems has been tested on the IEEE 26 bus test system.The two objective functions tested areFitness1 = Total_LossFitness2 = LQNmaxTo find the solution of the problem, the parameters d were decided. The parameters wereReactive Power of Generator Bus skirt 1 shows the parameters and size of reactive power of generation bus. There are five generator buses in IEEE 26-bus test system Bus 2, 3, 4, 5 and 26. The size of each bus is as below. gameboard 1 Parameters and size of reactive power of generator busParameterBusSize (MVar)Qg220 to 50Qg330 to 40Qg440 to 35Qg550 to 30Qg26260 to 202. Injected Reactive Power to the BusTable 2 shows the parameters and size of injected reactive power to the bus. It shows that in that location is nine buses have been injected by reactive power. The buses are as below. The unit of the injected reactive power is in MVar.Table 2 P arameters and size of injected reactive power to the busParameterBusSize (MVar)C110 to 9C440 to 9C550 to 9C660 to 9C990 to 9C11110 to 9C12120 to 9C15150 to 9C19190 to 93. Transformer Tap at the Transmission LineTable 3 shows the parameters and size of transformer tap at transmission line. It shows that there is seven transformer tap change at transmission line in IEEE 26-bus test system. The size of each transformer tap is (0.9 to 1.2).Table 3 Parameters and size of transformer tap at the transmission lineParameterLineSize (p.u)T12-30.9 to 1.2T22-130.9 to 1.2T33-130.9 to 1.2T44-80.9 to 1.2T54-120.9 to 1.2T66-190.9 to 1.2T77-90.9 to 1.2The EP process is initialization, mutation, rank and selection and convergence test.4.1.1 InitializationInitial population of size 20 is formed by a set of randomly generated actual value. Each member is tested using equation (12) (17) as below. Equations (12) (16) are the generation constraints. The bus voltage limits in equation (17) are stated in order to avoid any violation to the system operation. The total loss limit in equation (18) is stated in order to avoid the losses greater than the initial values.0MVar Qg2 50MVar (12)0MVar Qg3 40MVar (13)0MVar Qg4 35MVar (14)0MVar Qg5 30MVar (15)0MVar Qg26 20MVar (16)0.90V V 1.10V (17)Total Losses 16 (18)The generated random numbers must be smaller than the initial solution set in order to make sure that fitness will be improved. Only the member that satisfy the constraints are included in the initial population set.4.1.2 MutationMutation is a method to execute the random number to produce offspring. An offspring vector Li is created from each parent vector by adding Gaussian random with zero mean and standard deviation.4.1.3 Rank and SelectionThe offspring populations generated form mutation process is merged with the parent populations. The selection process is to generate a new 20 populations based on the objective function of total losses minimization and the voltage stability improvement.All of members were sorted in ascending order to produce the best twenty or the strongest twenty populations for next generation.4.1.4 intersection point testThe stopping criteria in order to obtain the optimal solution are by looking at the difference in maximum fitness and minimum fitness which must less then certain values. If not achieved, the process will be repeated until it converged.WhereTotal_Lossmax- Total_Lossmin LQNmax LQNmin V. RESULTS AND DISCUSSIONAn EP optimization technique has been developed in this study and tested on IEEE 26-bus test system. The objective function is to minimize the total power loss and to improve the voltage stability in power system. The program has been developed to find the optimal value of control variables based on each objective functions. However, before this program was run, load blend solution for the IEEE 26-bus test system was obtained to determine the initial values. The initial total power loss and stabilit y index is 18.986 MW and 0.754 respectively.For each objective function the program was run five times and the results were tabulated in tables according to the objective function. Then the best result for each objective function was selected and tabulated in Table 1 in the Appendix A in order to make a comparison between the two objective functions. According to the result which tabulated in Table 1 in the Appendix A, it was found that EP optimization technique with voltage stability improvement as the objective function give the best result which is total power loss of 14.462 MW and stability index of 0.717. The EP optimization technique with total power loss minimization as the objective function give results 14.987 MW.The EP optimization technique using proposed mutation rule with voltage stability improvement as objective function, the result MW and for the total power loss and stability index respectively.According Table 4, the total power loss and stability index is 15.534 MW and 0.734 respectively. The result after solve the Optimal Reactive Power Planning (ORPP) is 13.019 MW and 0.699. The percentage reduction for total power loss and stability index after solves the ORPP is 16.19 % and 4.77 %.Table 4 Comparison results before and after solves the Optimal Reactive Power PlanningTermsBeforeSolve ORPPAfter Solve ORPPTotal Power Loss (MW)15.53413.019Stability Index, LQNmax0.7340.699VI. CONCLUSIONAn evolutionary programming optimization technique has been developed to optimize the real power of generator bus, the reactive power and transformer tap control variables for minimal total cost of generation, total power loss and voltage stability improvement.In this paper, the total cost minimization is the best objective function for minimization of total cost, total power loss and stability index is reduced. The percentage reduction for the total cost and total power loss is acceptable. The percentage reduction of stability index is the highest. The percent age reduces for the total cost, total power loss and stability index is 7.77 %, 16.19 % and 4.77 % respectively. This is the acceptable and reasonable percentage reduction as compared to other objective functions. Therefore voltage stability improvement may not have to be the objective function in order to improve the voltage stability condition of a power system in solving the OPF.VII. FUTURE DEVELOPMENTFor future development, the other optimization techniques are proposed to be implemented in solving the ORPP in order to minimize the total power system losses and especially to improve the voltage stability in larger power system. Further modification should be included to get more accurate results for example using different mutation rules and selection strategies.VIII. REFERENCES1 Kwang. Y. Lee and Frank F. Yang Department of voltaical Engineering The dada State University University Park, PA 16802, Optimal Reactive Power Planning Using Evolutionalry Algorithms A Comparative St udy for Evolutionary Programming, Evolutionary Strategy, Genetic Algorithm, and Linear Programming IEEE executions on Power Systems, Vol. 13, No. 1, February 19982 R. Billington and S. S. Sachdev, Optimum network VAR planning by nonlinear programming IEEE Trans. on Power Appar. and Syst., Vol. PAS-92, pp. 63 T. Heydt and W. M. Grady, Optimal Var siting using linear load flow formulation, IEEE Trans. on Power Appar. and Syst., pp. 1214-1222. Vol. PAS-102, No. 5, May 1983.3 K. Aoki, M. Fan, and A. Nishkori, Optimal Var planning by approximation method for recursive mixed integer linear planning, IEEE Trans. on Power Syst.,Vol. PWRS-3, No. 4, pp. 1741-1747, November 1988.4 K. Y. Lee, Y. M. Park, and J. L. Oritz, A united approach to optimal real and reactive power dispatch, IEEE Trans. on Power Appar. and Syst., Vol. PAS-104, pp. 1147-1153, May 1985. SI K. Y. Lee, J. L. Ortiz, Y. M. Park, andL. G. Pond, An optimization technique for reactive power planning of subtransmission network u nder normal operation, IEEE Trans. on Power Syst., Vol. PWRS-1, pp. 153-159, May 1986.6 M. K. Mangoli, K. Y. Lee, and Y. M. Park, Operational real and reactive power control using linear programming, Electric Power Systems Research,7 M. K. Mangoli, K. Y. Lee, andY. M. Park, Optimal long-term reactive power planning using decomposition techniques, Electric Power System Research, Vol. 26,Rana Mukerji, Wendell Neugebauer, Richard P. Ludorf and Armand Catelli, Evaluation of Wheeling and Non-Utility Generation (NUG) Options using Optimal Power Flows, IEEE Transaction on Power Systems, Vol. 7, No. 1, February 1992.3 Kessel and Glavitsch Estimating the Voltage Stability of a Power System, IEEE Transaction on Power Delivery, Vol. PWRD-1, NO. 3, July 1986, pp 346-352.4 Jason Yuryevich and Kit Po Wong, Evolutionary Programming Based Optimal Power Flow Algorithm, IEEE Transaction on Power Systems, Vol. 14, No. 4, November 1999, pp 1245-1250.5 A.M. Chebbo, M.R. Irving. M.J.H Collapse Proximity Indicator Behaviour and Implications, IEE Proceedings -C, Vol. 139, No. 3, May 1992.6 Mahmoud Moghavvemi, New Method for Indicating Voltage Stability checker in Power System, Proceedings of IEE International Power Engineering Conference, IPEC97, Singapore, pp. 223-227.7 Jason Yuryevich, Student Member IEEE, Evolutionary Programming Based Optimal Power Flow Algorithm, IEEE minutes on Power Systems, Vol. 14, No. 4, November 1999.8 Salami, M. and Cain, G., Multiple Genetic Algorithm Processor for The Economic Power Dispatch Problem, Proceeding of the genetic algorithm in applied science systems Innovations and Applications, Conference Publication No. 414, IEE, 1995, pp 188-193.9 I Musirin and T K Abdul Rahman, On-Line Voltage Stability Index for Voltage Collapse Prediction in Power System, presented at Brunei International Conference on Engineering and Technology 2001 (BICET2001), Brunei. October 2001.10 Toro, V.D., Electric Power System, Prentice Hall, Englewood Cliffs, New Jersey, 1992.11 Whats Evolutionary Programming, http//www.faqs.org/faqs/ai-faq/genetic/part2/section-3.html.12 Leandro Nunes de Castro and Fernando Jose Von Zuben, Artificial Immune SystemPart 1- Basic Theory and Applications, Technical report TR-DCA 01/99. 1999.13 Slobodan Pajic, Dr Kevin A. Clements, Dr. Paul W. Davis and Dr Alexander E. Emanuel, Sequential Quadratic Programming Base Contingency Constraint Optimal Power Flow, Degree of Master of Science in Electrical and Computer Engineering, Worcester Polytechnic Institute, April, 29 2003.14 Fogel , D.B. A comparison of evolutionary programming and genetic algorithms on selected encumber optimization problems, Simulation, June,1995,pp.397-404.15 Yao, X., Liu, Y. and Lin, G., (1999) Evolutionary programming made faster, IEEE Trans. Evolutionary Computation. vol. 3, no. 2, pp. 82-102.16 Miller, R.H. and Malinnowski, J.H., Power System Operation, McGraw-Hill, Inc., 1994.Appendix ATable 1 Results of EP Optimization Technique fair game Fun ctionControl Variables/ Parameters of OPFTotal Cost($/h)Total Power Loss(MW)Stability Index, LQNmaxTime Taken(s)Real Power of Generator Bus (MW)Injected Reactive Power (Mvar)Transformer Tap (p.u)Pg2Pg3Pg4Pg5Pg26C1C4C5C6C9C11C12C15C19T1T2T3T4T5T6T7Total Power Loss Minimization163.12281.14146.07147.9492.115.954.790.395.395.231.404.235.433.830.960.991.040.960.960.960.9115449.112.1320.76711843Voltage Stability Improvement110.35287.28128.95163.4297.141.241.282.361.052.580.764.502.192.390.941.000.961.111.050.900.9815523.114.4610.7136358