Optimal Reactive Power Planning By Using Evolutionary Engineering Essay

optimum Reactive source homework By victimization maturationary Engineering EssayThis paper presents a methodological analysis for re understand billet optimal Reactive world former readiness (ORPP) problem by exploitation evolutionary Programming (EP) optimisation technique in effect to purify the potency perceptual constancy and minimize the blemishes in the source formation. This study has developed the Evolutionary Programming (EP) Optimization Technique using MATLAB softw ar. The study scrutinyifyed deuce fitness functions namely conglomeration tone ending minimisation and the electric potential constancy improvement in force governance with two different fluctuation proficiency. Comparison in the numbers commenceed was made in score to determine the outstrip fitness function and the lift out sport technique to be employ for solving ORPP and hence the voltage constancy is improved. The proposed technique was tested on the IEEE 26 plenty reli ability test system.Keywords best Reactive male monarch homework (ORPP), voltage perceptual constancy Improvement, Evolutionary Programming (EP)I. INTRODUCTIONIn general, the problem of best responsive causality prep argondness (ORPP) can be de confinesate as to determine the sum up and location of shunt labile effect compensation devices needed for stripped-down bell while keeping an adequate voltage profile. The ORPP is one of the close challenging problems since target functions, the effect cost and the investment cost of peeled reactive great strength sources, should be minimized simultaneously 1.Transmission loss can be minimised by performing reactive power supply which involves optimisation process. The ORPP is a large-scale no fieldar optimisation problem with a large upshot of variables and un trusted parameters. Various mathematical optimisation algorithms call for been developed for the ORPP, which in most cases uptake nonanalogue 2, linear 3, or mixed integer designming 4, and decomposition methods 5-8. However, these conventional techniques are cognise to converge to a local best final firmness of purpose rather than the world(prenominal) one for problems such(prenominal) as ORPP which stick many local minima.Recently, evolutionary algorithms (EAs) have been used for optimization in particular both the genic algorithm and evo1ution programming have been used in the ORPP problem. The EA is a stiff optimization technique analogous to the natural weft process in genetics. It is useful especially when other optimization methods fail in discloseing the optimal solution 1. Evolutionary Programming (EP) optimization technique is lately applied in solving electric power system optimization problems. It is part of the Evolutionary Algorithm (EA) optimization techniques under the artificial lore hierarchy. Optimization is an important issue in power system operation and planning particularly in the area of voltage sta bility studies 9. In this study, EP engine was signly developed to implement the optimisation process considering two mutation techniques, each(prenominal) with two different purpose functions. Comparative studies perform in this study aimed to identify the most suitable mutation technique with the best object glass function for minimising transmitting loss in power system and too improving the voltage stability. The parameters for this problem are generated reactive power (Qg), injected reactive power (Qinj) and transformer tap (T). Validation on the effectiveness of the proposed technique was conducted on the IEEE-26 reliability test system.Figure 1 The IEEE 26 cumulation test systemII. OBJECTIVESThe two verifiable functions of this study areTo obtain the pith loss minimizationTo improve the voltage stabilityWhere entirety_Loss is constitutional loss minimizationLQNmax is voltage stability improvementIII. BACKGROUND STUDIESA. Optimal Reactive powerfulness Planning (OR PP)Optimal Reactive effect Planning (ORPP) is a sub-problem of Optimal function give ear solution which has been widely used in power system operation and planning to determine the optimal control parameter nail downtings, in come in to minimize or increase the desired objective function while satisfying a cut back of systems constraint. Reactive world 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 stinting operation of the power system, Economic Dispatch (ED) technique is also follow in RPP scheme. The set of active power generated by the generator is also adjusted in the approach. 11ORPP is a nonlinear programming problem which has the side by side(p) mathematical formulationMaximize or minimizef(x, u) (3)subject tog(x, u) =0 (4)hmin h(x, u) hmax (5)where u is the vector of control v ariables 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 fall under the Evolutionary enumeration in Artificial Intelligence (AI) hierarchy and increasingly applied for solving power system optimization problem in recent years. A new cosmos is formed from an existing population through the use of a mutation operator. This operator produces a new solution by distressing each component of an existing solution by a hit-or-miss amount. The degree of optimality is measured by the fitness, which can be defined as the objective function of the problem 12.Through the use of a be scheme, the candidate solutions in each population were sorted in ascending 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 have more optimal solutions which has a great chance of survival than the poorer solutions. It is a stochastic optimization strategy, which based on the mechanics of natural selections-mutation, competition and evolution. This technique stressed on the behavioral linkage between mentions and their offspring. In general, EP consists of 3 major steps which concisely discussed as follow 12, 13i. InitializationThe initial population of various(prenominal)s consists of (xi, i), i 1, 2, are generated ergodicly based on its limit, whereby xi denotes the control variable and i is the strategic parameter with respect to xi. The fitness is calculated for each man-to-man based on its objective function, f(xi).ii. conversiona) 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 generally distributed one-dimensional random number with mean zero and stock(a) deviation 1. Nj(0,1) denotes that the random number is generated anew for each value of j. Subsequently, the fitness is calculated for each offspring.b) Proposed Mutation TechniqueThe proposed mutation reign over was inspired by neural meshwork back propagation acquirement. 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 real-valued constants that are determined empirically. . denotes an absolute value and N represents the normal distribution. xij k is the amount of reassign in an individual, which is proportional to the temporal error, and it drives t he 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 afterward or emulate the best individual in the ongoing generation. sxij k is the evolution tendency or momentum of previous evolution.It accumulates evolution information and tends to repair convergence when the evolution trajectory is moving in a agreeable direction 14. The best individual is mutated only by the momentum. This expands the exploitation lay out 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 gang stage, the union of parents and offspring are ranked in ascending or descending 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 repe at until the stopping criterion 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 thrash ORPP. The produced offspring vector must satisfy and consider the constraints as at the initialization. The main supposition of EP is the mutation process.Then continues with learning about the MATLAB software and tested the IEEE 26- cumulation interrogation System to observe initial values which are summation power loss, initial minimum and maximum voltages and the initial line stability tycoon (LQP LQN). These initial values have been taken by considering the unstable contagion lines in the test system (IEEE 26-BUS).The unstable line means the line stability might 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 persist chart for the EP optimization techniqueTh e EP program was developed and the analysis of the result is tested based on objective function of the picture such as minimize lend loss and the voltage stability improvement. Then, the program has been run for vanadium times for each type of objective function. Finally, this project has been concluded and the report 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 get word the solution of the problem, the parameters d were decided. The parameters wereReactive Power of Generator Bus plank 1 shows the parameters and coat 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 coat of each bus is as below. dishearten 1 Parameters and coat of reactive power of generator busParameterBus surface (MVar)Qg220 to 50Qg330 to 40 Qg440 to 35Qg550 to 30Qg26260 to 202. Injected Reactive Power to the Bus prorogue 2 shows the parameters and size of injected reactive power to the bus. It shows that there 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 Parameters 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, r ank and selection and convergence test.4.1.1 InitializationInitial population of size 20 is formed by a set of randomly generated actual value. Each constituent 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 include 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 a dding Gaussian random with zero mean and standard deviation.4.1.3 Rank and SelectionThe offspring populations generated form mutation process is unify 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 carrefour 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 issue solution for the IEEE 26-bus test system was obtained to determine the initial values. The initial total power loss and stability mightiness 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 resemblance 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 imp rovement.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 percentage 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 Electrical Engineering The protactinium State University University Park, PA 16802, Optimal Reactive Power Planning Using Evolutionalry Algorithms A Comparative Study for Evolutionary Programming, Evolutionary Strategy, Genetic Algorithm, and bilinear Programming IEEE Transactions on Power Systems, Vol. 13, nary(prenominal) 1, February 19982 R. Billington and S. S. Sachdev, Optimum meshwork 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. 1 741-1747, 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 under 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 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 Volt age 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 up 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 exponent Behaviour and Implications, IEE movements -C, Vol. 139, No. 3, May 1992.6 Mahmoud Moghavvemi, New Method for Indicating Voltage Stability Condition in Power System, Proceedings of IEE outside(a) Power Engineering Conference, IPEC97, Singapore, pp. 223-227.7 Jason Yuryevich, Student Member IEEE, Evolutionary Programming Based Optimal Power Flow Algorithm, IEEE Transactions on Power Systems, Vol. 14, No. 4, November 1999.8 Salami, M. and Cain, G., aggregate Genetic Algorithm Processor for The Economic Power Dispatch Problem, Proceeding of the genetic algorithm in engineering 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, apprentice 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 System helping 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, accompanying 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 constrained 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 TechniqueObjective FunctionControl 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