Optimal Power Flow using Hybrid Teaching Learning Based Optimization Algorithm

GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology (ICIET) - 2016 | July 2016

e-ISSN: 2455-5703

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm 1Dr.

K. Gnanambal 2K. R. Jeyavelumani 3H. Juriya Banu 1 Professor 2Assistant Professor 3P.G Student 1,2,3 Department of Electrical and Electronics Engineering 1,2,3 K.L.N. College of Engineering, Madurai, Tamilnadu, India Abstract

The flow of electric power in an interconnection system is known as power flow. Optimal Power Flow (OPF) refers to load flow that gives maximum system security by minimizing the overload. The main objective of OPF is to reduce the total cost of active power generation and to determine the loss and meet the total demand. This teaching learning algorithm technique is based on the influence of teachers on learners. This algorithm is a population-based method and uses a population of solutions to obtain the global solution. The population is considered as the group of learners or a class of learners. In this project, the Teaching Learning Based Optimization technique along with cross over property of Genetic algorithm is used to solve the optimal power flow problem. The obtained results indicate that the Teaching Learning Based Optimization provides useful and strong high quality solution when solving the optimal power flow problem with different complexities Keyword- optimal power flow-teaching learning based optimization-hybrid teaching learning algorithm-cross over property of genetic algorithm-comparison with other methods-minimization of cost-convergence __________________________________________________________________________________________________

I. INTRODUCTION The Engineers enclose been very flourishing in increasing the effectiveness of boilers, turbines and generators so continuously that all new added to the generating unit plants of a system operates more efficiently than any older unit on the scheme. In operating the system for some load circumstance the role from each plant and from each unit within a plant must be determined so that the rate of the delivered power is a minimum. Any plant may contain dissimilar units such when hydro, thermal, gas etc. These plants have dissimilar attribute which gives different generating cost at any load. So there should be a correct arrangement of plants intended for the minimization of cost of operation. The cost characteristic of the each generating part is also non-linear. So the problem of achieving also difficult.

Power system optimization has evolved with the developments in computing and optimization theory. The optimization has non-convexities, include both binary variables and continues purpose which makes difficulty and complicated to solve. The power system must be able to endure the loss of any generator or transmission element, and system operator must make binary decision to start up and close down generation and transmission resources in response to system events.

A. IEEE-30 Bus System 1) Bus Details No. of Buses

30

No. of Generators

6 (1,2,5,8,11,13)

Transmission lines

41

No. of Load buses

20

No. of individuals

50

Table 1: IEEE 30-Bus Details IEEE 30-Bus System

All rights reserved by www.grdjournals.com

237

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

Fig. 1: Bus Details

II. OPTIMAL POWER FLOW The formulation of minimum cost problem, by including the network, reactive power demand, voltage and current constraints is recognized since an , OPF takes hooked on vindication of losses in the network.

The optimal power flow problem has become an important for operation, control and scheduling of modern power systems. In a number of real world optimization problems, multiple rival objectives make us resolve them simultaneously instead of solving them separately[4].OPF problem is a non-linear, embarrassed optimization problem where many computing objectives are present. The main objective of OPF is to find maximum generation while maintaining acceptable system performance. OPF has been widely used for both operating and planning of power system.The goal of an optimal power flow is to determine the best way to instantaneously operate a power system, usually minimizing the operating cost.Minimize cost function such as operating cost, taking account of realistic equality and inequality constraints[4].

OPF can consider different objectives for the improvement such as transmission loss minimization, voltage stability enhancement and minimization of system operating cost.

A. FUEL COST MINIMIZATION The objective is to minimize the total fuel cost FT of the system. It is modeled as a quadratic function and represented as

Where ai, bi ,ci are the fuel cost coefficients of the ith generator. PGi is real power output of the ith generator and ng is the total number of generators in the system.

III. HYBRID TEACHING LEARNING BASED OPTIMIZATION

ALGORITHM

A. Introduction A book optimization method called teaching-learning-based optimization (TLBO) has been proposed by Rao et al for constrained optimization problem[6].

Like other algorithms Teaching-Learning based optimization is also a stochastic, and population–based evolutionary computer algorithm for crisis solving. It uses a population of solutions to proceed to the global solution.

Teaching Learning-Based Optimization is proposed to obtain global solutions for continuous non-linear functions with a smaller amount computational effort and lofty stability.

The TLBO method is based on the effect of the influence of a teacher scheduled the yield of learners in a class. Here, output is considered in terms of results or grades[6]. The teacher is generally considered as an extremely learned person who

All rights reserved by www.grdjournals.com

238

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

shares his or her knowledge with the learners. The quality of a teacher affects the effect of the learners. It is obvious that a good teacher trains learners such that they can include superior results in conditions of their marks or grades.

B. Overview TLBO is an algorithm specific parameterless, nature inspired metaheuristic method. But many other technique like Genetic algorithm(GA), Differential Evolution(DE) etc their performance are affected by its specific control parameters.

TLBO does not require any specific parameter and it only requires controlling parameter as population size and number of generation for its operation.

Like other algorithm , TLBO is also a stochastic , and population based evolutionary computer algorithm to evolve the optimal solution[10]. It uses a population of solution to proceed to the global solution.

This algorithm is inspired by passing on information surrounded by a classroom environment , where learners first acquire acquaintance as of a teacher (i.e., Teacher Phase) and then from classmate (i.e.,Learner Phase) .Moreover the teacher puts effort to increase the represent of students to a privileged level , at which students will require another teacher of better quality to teach them.In Hybrid-TLBO algorithm the crossover property of genetic algorithm is included with the TLBO algorithm which brings out the optimal solution from the existing solutions[10].

C. TLBO Algorithm Like other population based algorithm , TLBO starts with initialization phase where a randomly generated population of candidate solutions ,are placed in the search phase of the problems consisting of n dimensions where each dimension is limited by an upper and lower bound[1].The process of TLBO is divided into two phases namely they are:  Teacher phase  Learner phase 1) Teacher Phase Teaching earning is an important process where every individuals tries to learn something from other individuals to improve themselves.

The teacher phase is the initial part of the algorithm, in which students improve their knowledge with the help of the teacher who is the most knowledgeable person in the class and who always motivates the students to attain their goal[6].

During this phase, the teacher tries to improve the subject mean performance of the learner depending on his or her capability[13].

Xtotal-kbest.G be the result of the best learner in all the subject who is identified as the teacher for that cycle.

The difference between the result of the teacher and the mean result of the learners in subject is given by the following equation.

Difference_mean j,G =rand(Xj,kbest.G -TF Mean j,G ) (1) Where, Xj,best,G is the result of the best learner in subject j,rand is a random number in the range [0,1].TF is the teaching factor that determines the average to be changed.The value of TF is either 1 or 2. The value of TF is randomly determined by the following equation: TF=round(1+rand(0,1)) (2) This solution was modified and is given by: Xjnew,k,G=Xj,k,G +Difference_meanj,G Here Xjnew,k,G is accepted if it gives the superior result.

2) Learner Phase Learners improve their knowledge in two different ways: one is through the input of the teacher and the other through their interaction with other learners.

A learner learns new information when other learners have more knowledge than him or her.The learning phenomenon in this phase is expressed in equations (4) and (5).

Two learners Xj,p,G, Xj,Q,G are randomly selected ,such thatXj,p,G, ≠ Xj,Q,G. Xjnew,P,G=Xj,P,G+rand(Xj,P,G –Xj,Q,G) (3) If f(Xj,P,G)<f(Xj,Q,G) Xjnew,P,G=Xj,P,G+rand(Xj,Q,G – Xj,P,G) (4) If f(Xj,Q,G) < f(Xj,P,G) Xjnew,P,Q is accepted if it gives superior result.

D. Need for Teaching Learning Based Optimization Technique Does not require algorithm specific controlling parameters.Only common controlling parameters like:  Population size  Number of generation.

All rights reserved by www.grdjournals.com

239

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

E. Hybrid-TLBO Algorithm In Hybrid-TLBO the TLBO algorithm is implemented in which crossover property of genetic algorithm is included.The aim of implementing crossover property is that to bring out optimal solution for the problem.

Crossover is an extremely significant operative for the GA. It is responsible for the structure recombination (information exchange between mating chromosomes) and the junction speediness of the GA and is usually applied with high probability (0.6â&#x20AC;&#x201C;0.9). The chromosomes of the two parents selected are shared to structure recent chromosomes that inherit segments of information stored in parent chromosomes. Until at this time, many cross schemes, such as single point, multipoint, or uniform crossover have been proposed in the literature. While crossover is the main genetic operator exploiting the information included in the present production, it does not produce new information.

The crossover operator, used with a specified probability, interactions genetic in sequence by splitting two chromosomes at a accidental site and joining the first part of one chromosome with second part of another chromosome.

The crossover probability pc controls the rate at which solutions are subjected to crossover. The higher value of pc, the quicker are the new solutions introduced into the population. As pc increases, however, solutions can be disrupted faster

Fig. 2: Flow Chart

All rights reserved by www.grdjournals.com

240

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

IV. COMPARISON OF TLBO WITH OTHER ALGORITHMS Like GA, PSO, ABC, HS, etc., TLBO is a population based technique which implements a group of solution to proceed for the optimal solution. Many optimization methods require algorithm parameters that affect the performance of the algorithm[2] .

GA requires crossover probability, mutuation rate, and selection method; PSO requires learning factors , variation of weight , and greatest value of velocity[2]; ABC requires number of employed bees, onlooker bees and value of limit : HS requires harmony remembrance reflection rate , pitch adjusting rate, and number of improvisations.

Like GA which uses collection , intersect and mutation stage and ABC which uses employed , onlooker and scout bees phase . TLBO uses the mean value of the population to update the solution. TLBO equipment miserliness to accept the good result like ABC.

V. RESULT ANALYSIS The optimal power flow(OPF) using Hybrid-TLBO algorithm has been carried out for IEEE 30-bus system.The system consists of 30 buses,6 generators,41 lines and slack bus as bus1.The OPF solution has been attempted for minimizing generating cost and losses while keeping voltage profile,real power and reactive power within given limits.

A. Result Analysis of Optimal Power Flow PARAMETERS VALUES PG1(MW) 210.4 PG3(MW) 36.08 PG5(MW) 30.95 PG8(MW) 12.45 PG11(MW) 5.70 PG13(MW) 0 FUEL COST($/hr) 823.212 LOSS(MW) 12.794 Table 2: Result for OPF of IEEE-30 bus system using MATPOWER

B. Result of Optimal Power Flow Using TLBO Algorithm and Hybrid-TLBO Algorithm PARAMETERS PG1 (MW) PG3 (MW) PG5 (MW) PG8 (MW) PG11 (MW) PG13 (MW) FUEL COST($/hr) LOSSES(MW) CONVERGENCE RATE (SECONDS)

VALUES 176.94 49.02 21.53 21.81 12.20 11.41 802.45 9.525 35.986577

Table 3: Result for OPF of IEEE-30 bus system using TLBO algorithm:

1) Convergence Characteristics of Ieee-30 Bus System Using TLBO Algorithm

Fig. 4: convergence characteristics for IEEE 30-bus system using TLBO algorithm

All rights reserved by www.grdjournals.com

241

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

The convergence characteristics of TLBO is shown in fig 8.1. The curve convergence starts from 10th iteration with minimum fuel cost of 802.4 ($/hr).

PARAMETERS VALUES PG1(MW) 166.78 PG3(MW) 49.93 PG5(MW) 23.31 PG8(MW) 27.94 PG11(MW) 12.10 PG13(MW) 12.07 FUEL COST($/hr) 803.43 LOSSES(MW) 8.75 CONVERGENCE RATE (SECONDS) 32.483190 Table 4: Result for OPF of IEEE 30-bus system using Hybrid-TLBO algorithm:

2) Convergence Characteristics of IEEE 30-Bus System Using Hybrid-TLBO Algorithm

Fig. 5: convergence characteristics for IEEE 30-bus system using HYBRID-TLBO algorithm

The convergence characteristics of HYBRID- TLBO is shown in fig 8.1.The curve convergence starts from 9th iteration with minimum fuel cost of 803.43($/hr).

C. Comparison with Other Algorithm METHODS FUEL COST($/hr) GENETIC ALGORITHM 803.699 TLBO ALGORITHM 802.45 HYBRID-TLBO ALGORITHM 803.43 Table 5: Comparison table

LOSSES(MW) 9.5177 9.525 8.75

VI. CONCLUSION In this project work, the application of Hybrid Teaching Learning algorithm has been developed, which is the combination of teaching learning based optimization algorithm and the cross over property of Genetic algorithm. The new Suggested algorithm has been applied to the test case of IEEE 30-bus system. The result has been compared with the Genetic algorithm and proves the applicability of this technique as a tool for solving the optimization problem to find the total fuel cost of generating units with minimum losses. The algorithm has accurately and reliably converged to the global optimum solution.

REFERENCES [1] Taher Niknam, Faranak Golestaneh, and Mokhtar Sha Sadeghi “θ -Multiobjective Teaching–Learning-Based Optimization for Dynamic Economic Emission Dispatch”, IEEE systems Journal., vol. 6, no. 2,pp. 341-351,June 2012

All rights reserved by www.grdjournals.com

242

Optimal Power Flow using Hybrid Teaching Learning based Optimization Algorithm (GRDJE / CONFERENCE / ICIET - 2016 /038)

[2] Gajendra Shu and Kuldeep Swarnkar, “Optimization of Economic Load Dispatch Problem using Genetic Algorithm”, International Journal of Science, Engineering and Technology Research (IJSETR)., vol. 3, pp. 2673-2679,Oct 2014.

[3] Dharamjit and D.K.Tanti, “Load Flow Analysis on IEEE 30 bus system”, International Journal of Scientific and Research Publications., vol. 2, pp 1-6, Nov 2012.

[4] Viktor A. Levi and Dusko P. Nedic, “Application of the Optimal Power Flow Model in Power System Education”, IEEE Transactions on power systems., vol.16, no.4, pp 572-580, Nov 2001.

[5] B.Bommirani and K.Thenmalar “Optimization Technique For Economic Dispatch In Power System Operation”, International journal of computer.,vol. 2, pp. 153-158,June 2013.

[6] Deyu Tang, Jie Zhao and Huan Li “An Improved TLBO algorithm with Memetic method for Global Optimization”, IJACT., vol.5, no.9, May 2013.

[7] T.Govindaraj and M.Vidhya, “Optimal Economic Dispatch for Power Generation using Genetic Algorithm”, International Journal of Innovative Research in Electrical, Electronics, Instrumentation and Control Engineering., vol. 2, no.1, pp. 808814, Jan.2014.

[8] A.Farag, S.Baiyat, and T.C Cheng, “Economic Load Dispatch Multiobjective optimization Procedures using Linear Programming Techniques”, IEEE Trans. power syst., vol. 10, no. 2,pp.731-738,May 1995.

[9] K.Lee, Y.Park and J.Ortiz, “A united approach to optimal real and reactive power dispatch”, IEEE Trans. Power App. Syst., vol. PAS-104, no.5, pp. 1147-1153,May 1985.

[10] H.R.E.H.Bouchekara,M.A.Abido and M.Boucherma “Optimal Power flow using Teaching learning based optimization”, pp.

49-59, March 2014.

All rights reserved by www.grdjournals.com

243