Modified teaching learning algorithm and double differential evolution algorithm for optimal reactive power dispatch problem: A comparative study

doi:10.1016/j.ins.2014.03.050

Information Sciences

Volume 278, 10 September 2014, Pages 231-249

https://doi.org/10.1016/j.ins.2014.03.050 Get rights and content

Highlights

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A novel hybrid optimization approach for ORPD problem.
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Hybrid MTLA-DDE algorithm has faster converging to better solutions for ORPD problem.
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Hybrid MTLA-DDE algorithm was successfully implemented.

Abstract

One of the major optimization problems in power systems is the optimal reactive power dispatch (ORPD) problem. ORPD problem is a multi-variable problem with non-linear characteristics and has established significant emphasize on secure and economical operation of power systems. Therefore, finding an effective algorithm to solve this problem is absorbing a growing attention among the academics. In this paper, a reliable and effective algorithm is introduced by combining modified teaching learning algorithm (MTLA) and double differential evolution (DDE) algorithm in order to handle the ORPD problem. Moreover, the proposed algorithm is applied to ORPD problem on IEEE 14-bus, IEEE 30-bus and IEEE 118-bus power systems for performance assessment and validation purposes. The obtained results demonstrate the efficiency of the proposed hybrid algorithm and show faster convergence and better solutions in comparison with previously reported algorithms.

Introduction

The optimal power flow (OPF) problem is an principal and powerful tool for operating and planning of power systems first formulated by Carpentier in 1960s [15]. One of the main sub problems of OPF is ORPD problem which includes generator reactive-power outputs, compensators, tap ratios of transformers, and outputs of shunt capacitors/reactors. This sub problem is used to minimize interested objective functions such as transmission losses while satisfying a given set of operating and physical limitations. Since voltage of the generators are inherently continuous variables while the transformer ratios and shunt capacitors are discrete variables, the whole ORPD problem is considered as a non-linear multi-modal optimization problem with a combination of discrete and continuous variables [3], [13], [14], [30].

The evolutionary methods constitute an approach for searching the optimum solutions via some form of the directed random search process, and one of the important characteristics of these methods is that they search for solutions without previous problem knowledge [6], [16], [40], [55], [51], [52], [53], [62], [54], [64], [65]. Previous researches on the ORPD problem have been mostly relied on conventional techniques, such as dynamic programming, linear programming, quadratic programming and interior point methods [4], [20], [32], [37], [44]. However, these techniques generally have major drawbacks such as unsecured convergence of algorithm, and high sensitivity to initial search point, etc. [2].

In recent years, computational intelligence-based techniques have been proposed as an alternative for application of reactive power optimization. Examples of this progress are Wu’s application of an evolutionary programming (EP) method for achieving optimal reactive power dispatch and voltage control [48]. Also, in [29] Lai demonstrated higher ability of EP method in handling non-continuous and non-smooth functions compared to non-linear programming. In [31] Lee introduced the mixture of successive linear programming with simple genetic algorithm (SGA) as a solution for reactive power operational problems. Particle swarm optimization (PSO) algorithm was another approach to solve this problem applied by Yoshida in [66], [69]. A multi-agent based PSO algorithm for the ORPD problem has been offered by Zhao in [67]. A PSO and differential evolution (DE) algorithms based fuzzy adaptive hybrid algorithm has been chose [46], [67], respectively, for handling the ORPD problem. In another reported case, Kannan in [33] offers another method based on comprehensive learning PSO (CLPSO) algorithm. Also, another approaches for solving ORPD problem. Also, approaches for optimization of the above mentioned problem such as seeker optimization algorithm (SOA) and self-adaptive real coded genetic algorithm (SARCGA) are also presented in [12], [43] and, GA is used for solving a stochastic in [21]. In [68] Zhang introduced the mixture of dynamic multi-group self-adaptive differential evolution algorithm (DMSDE), and Khazali used the application of a harmony search algorithm (HSA) for achieving minimum transmission losses and voltage control by reaching a global optimization of a power system [28]. Other approaches for optimization of the above mentioned problem such as imperialist competitive algorithm (ICA) and multi agent-based reinforcement learning (MASRL) approach are also presented in [19], [49]. A modified NSGA-II presented in [24] for multi-objective, and finally, hybrid PSO [23], [69] and quasi-oppositional TLBO (QOTLBO) algorithms are used for solving a stochastic in [34].

Among the above mentioned methods, the performance of TLA method has been continuously confirmed by successful application in various cases such as constrained mechanical design optimization problems [38], reserve constrained dynamic economic dispatch [35], optimization of multi-pass turning operations [60], optimal power flow problems with non-smooth cost functions [18], and continuous non-linear large scale problems [39]. TLA method was introduced by Rao, Savsani and Vakharia in 2011. In general, TLA and DE algorithms have a more capability for global searching at the beginning of the run and a local search near the end of the run. Therefore, by solving problems with more local optima, TLA and DE algorithms can also explore local optima at the end of each run. However, the reactive power optimization problem has the mentioned properties in itself. For these reasons, there is a significant need for reliable global approach for handling power system optimization problems.

The rest of the presented article is categorized in four major parts, described as follows: Section 2 explains the typical formulation of an ORPD problem, Section 3 is dedicated to discussing the standard structure of the proposed algorithms, Section 4 of the paper covers optimization results and conducts comparison and performance analysis of the applied approaches used to solve the case studies of ORPD problem on IEEE 14-bus, IEEE 30-bus and IEEE 118-bus systems and last section of this article presents the conclusion of the implementation for the proposed hybrid algorithm.

Section snippets

Problem formulation

In general view, ORPD problem is used to optimize the active power loss in the transmission network while satisfying equality and inequality constraints at the same time [49].

The ORPD problem can be mathematically formulated as follows: $Min J (x, u) = P_{loss} = \sum_{k \in NTL} g_{k} (V_{i}^{2} + V_{j}^{2} - 2 V_{i} V_{j} \cos δ_{ij})$ $Subject to : g (x, u) = 0$ $h (x, u) ⩽ 0$ In the above equation, P_loss is the active power loss function of the transmission network, g_k is the conductance of branch k, V_i and V_j are the voltages of ith and jth bus respectively, NTL

TLA algorithm

The TLA method is a novel algorithm which is recently introduced in [38]. TLA method uses certain population of solutions to achieve the global solution as well as any other nature-inspired algorithm [11], [47]. The backbone of TLA method is based on the simulation of a classical learning process consisting of two stages: (i) learning through teacher (also known as teacher phase) and (ii) learning through interacting with the other learners (known as learner phase). In this optimization

Numerical results of optimization in performance comparison

For the purpose of verifying the performance and efficiency of the proposed hybrid MTLA-DDE algorithm, tests are carried out on IEEE 14-bus, IEEE 30-bus and IEEE 118-bus power systems. The platform for implementation of hybrid MTLA-DDE algorithm is MATLAB 7.6 and the simulation conducted on a Pentium IV E5200 PC 2 GB RAM. Iterations for all the test systems are limited to maximum number of 100 for all power systems.

In the simulation runs, initial population size for DDE is specified as 100 for

Conclusions

In this article, novel MTLA, DDE and hybrid MTLA-DDE approaches has been purposed as a novel solution for solving ORPD problem. The performance of proposed algorithms has been assessed by testing on IEEE 14-bus, IEEE 30-bus and IEEE 118-bus systems and comparison of gathered results with other methods reported in the references. The results obtained by simulation runs endorse the ability of MTLA-DDE to balance global search ability and convergence rate effectively than other reported

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Modified teaching learning algorithm and double differential evolution algorithm for optimal reactive power dispatch problem: A comparative study

Highlights

Abstract

Introduction

Section snippets

Problem formulation

TLA algorithm

Numerical results of optimization in performance comparison

Conclusions

Int. J. Electr. Power Energy Syst.

Electr. Power Syst. Res.

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Optimal load flow with steady-state security

IEEE Trans. Power Appar. Syst.