Solution to unit commitment in power system operation planning using binary coded modified moth flame optimization algorithm (BMMFOA): A flame selection based computational technique
Introduction
The unit commitment problem is considered as one of the key aspects in power system operation. The UC problem presents a highly non-linear, complex, hard-constrained, bounded optimization problem. The hard constraints such as load satisfaction, reserve satisfaction, minimum up and down time makes the UC problem even more complex. The high dimensional at large scale nature of UC accompanied by hard constraints complicates the optimization problem. Thus, the exploration for efficient optimization approaches to solve UC problem is an open challenge for betterment of solution quality improvement.
The earliest optimization approaches employed to solve UC problem include conventional/traditional approaches such as Lagrangian relaxation (LR) [1], branch and bound (BB) [2], priority list method (PLM) [3], dynamic programming (DP), linear programming (LP)[4], multiple integer linear programming (MILP) [5], dynamic programming lagrangian relaxation DPLR [1] etc. The traditional methods are comparatively simpler to model yet suffer from drawbacks such as, high computational time at higher dimensions, local minima trapping, poor convergence etc. To overcome the disadvantages of classical approaches, various evolutionary and heuristic approaches are developed and applied to UCP. The earlier methods include evolutionary programming (EP) [6], evolution strategy (ES) [8], genetic programming (GP) [9], genetic algorithm (GA) [7], differential evolution (DE) [10] etc. In addition, the swarm based approaches such as particle swarm optimization (PSO) [11], artificial bee colony (ABC) [13], grey wolf optimization (GWO) [14], ant colony optimization (ACO) [12], fireworks algorithm (FWA) [15] etc., which use the social behaviour and coordination to arrive at global solution. Other heuristic, meta-heuristic and hybrid approaches can be found in [35], [37], [38], [39], [40], [41], [42], [43], [44], [45], [58] with application to unit commitment problem. The superior exploration and exploitation properties of the swarm based approaches are used to solve UC problem. Later, traditional and heuristic approaches are brought together to design hybrid algorithms to efficiently utilize the advantages of respective approaches.
Recently, many human based intelligence approaches have been developed to efficiently resolve the complex UC problem. The popular approaches include simulated annealing (SA) [18], teaching learning based approach (TLBA), imperialist competitive algorithm (ICA) [16], tabu search (TS) [17], memetic approach (MA) [19] etc. The common aspect of the population based meta-heuristic approaches is the information exchange in both exploration and exploitation processes of the search process. One of the important aspects of meta-heuristic approaches is to maintain proper balance between exploitation and exploration processes. The moth-flame optimization (MFOA) is introduced by Ali Mirjali [46], which mimics the navigation mechanism of moths around artificial flames/lights. The navigation of moths in natural world involves the moon as reference, followed by “traverse navigation” mechanism in which moth navigate in space by maintaining a fixed angle with the direction of moon. However, fooled by artificial lights/flames, moths end up in vicious spirally converging navigation paths. The same is mathematically modelled as an optimization procedure with flame position as a potentially optimal solution. The application of the same to solve UC problem requires mapping of search space to binary search space.
Rest of the paper is structured as follows: Problem formulation for UC is presented in Section 2 along with associated constraints. Section 3 presents an overview of real valued moth-flame optimization algorithm and introduces BMMFOA variants. The application of BMMFOA to solve UC problem is developed in Section 4. Thereafter, Section 5 presents the simulation results, comparison with other approaches. In addition to the simulation solutions quality, the statistical significance of BMMFOA is established in Section 6. Finally, the concluding remarks of the work carried out in this paper and the possible future remarks are summarized in Section 7.
Section snippets
Problem formulation
Leading into the solution procedure, the formulation of objective and constraints of the UC problems are explained before.
Overview of basic MFOA
The new meta-heuristic approach of optimization called MFOA is a nature inspired approach that mimics the navigational properties of moth flies around artificial lights [46]. The navigation of moths around flames (lights) is often referred to a traverse movement. Naturally, the navigation of moths is aided by light emitted by moon with which the moths maintain a constant angle with the source of light moon in nature. In this navigation method, moth-flames navigates in nature by maintaining a
BBMFOA implementation to UC problem
The commitment scheduling of thermal units over the entire scheduling horizon is carried out using Binarization of modified moth flame algorithm. Thereafter, the generation scheduling of committed units to alleviate the system demand is carried out using the Lambda iteration approach through economic dispatch. The complete procedure for commitment and economic dispatch problem using BMMFOA is presented as follows.
Step 1: Initialize the parameters of UC problem and BMMFOA.
Step 2: initialize the
Numerical results and discussion
The proposed variants of BMMFOA are simulated using various test systems from 10 unit to 100 unit size. The simulation setup is prepared in MATLAB platform and executed on 3.6 GHz Intel core i7 processor working on Microsoft Windows 8 operating system. The simulation set up is executed for 30 identical trails for carrying out statistical analysis. The operation cost characteristics and operation constraints of thermal units are listed in Table 1 [1]. The parameters of the moth-flame algorithm
Statistical analysis
Apart from the commonly used performance metrics such as minimum, mean and worst fitness value, standard deviation, execution time etc., the aggregated/overall performance comparison of proposed approaches can be carried out using standard non-parametric statistical analysis [55]. The commonly used tests include Friedman test, Wilcoxon pairwise test, Quade test etc., and are also used for analysing the statistical significance of the optimization algorithms in solving UC problem [56], [57]. The
Conclusion
Different variants of Moth-Flame optimization algorithms namely Modified moth-flame optimization algorithm(s) (MMFOA) and their binary coded modified moth-flame optimization algorithm (BMMFOA) variants for UC problem are examined in this paper. The MMOFA variants differ from the basic MFOA with respect to the flame update procedure employed as a function of iteration count of search process. This paper discussed five variants (including basic MFOA) of flame update/selection mechanism. The same
Srikanth Reddy K received his B. Tech. degree in electrical engineering from Jawaharlal Nehru Technological University, Kakinada (JNTUK), India in 2012 and M. Tech. degree in Renewable Energy from MNIT Jaipur, India in 2015. He is now working towards his Ph.D. in Electrical Engineering from Indian Institute of Technology Delhi (IITD), India. His research interests include resource scheduling in smart grids, energy storage and electric vehicle applications in power systems, clean technologies,
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Srikanth Reddy K received his B. Tech. degree in electrical engineering from Jawaharlal Nehru Technological University, Kakinada (JNTUK), India in 2012 and M. Tech. degree in Renewable Energy from MNIT Jaipur, India in 2015. He is now working towards his Ph.D. in Electrical Engineering from Indian Institute of Technology Delhi (IITD), India. His research interests include resource scheduling in smart grids, energy storage and electric vehicle applications in power systems, clean technologies, deregulated electricity markets.
Lokesh Kumar Panwar received his B. Tech. degree in electrical engineering from Rajasthan Technical University (RTU), Rajasthan, India, in 2012 and M. Tech. degree in Renewable Energy from MNIT Jaipur, India in 2015. His research interests include smart grid, plug-in electric vehicle, optimization, micro-grid, renewable energy systems and optimization of electric vehicle charging under uncertainty subjected to its mobility in electric network and renewable energy scheduling.
BK Panigrahi received the Ph.D. degree in power system from Sambalpur University, Sambalpur, India, in 2004. Since 2005, he has been an Associate Professor with the Department of Electrical Engineering, Indian Institute of Technology (IIT), New Delhi, India. Prior to joining IIT, he was a Lecturer with the University College of Engineering, Sambalpur, India, for 13 years. His research interests include intelligent control of flexible ac transmission system devices, digital signal processing, power quality assessment, and application of soft computing techniques to power system.
Rajesh Kumar received the B.Tech. (Hons.) degree from National Institute of Technology (NIT), Kurukshetra, India, in 1994, the M.E. (Hons.) degree from Malaviya National Institute of Technology (MNIT), Jaipur, India, in 1997, and the Ph.D. degree from the University of Rajasthan, India, in 2005. Since 1995, he has been a Faculty Member in the Department of Electrical Engineering, MNIT, Jaipur, where he is serving as an Associate Professor. He was Post Doctorate Research Fellow in the Department of Electrical and Computer Engineering at the National University of Singapore (NUS), Singapore, from 2009 to 2011. His research interests include theory and practice of intelligent systems, computational intelligence and applications to power system, electrical machines and drives.