A Modified Harmony Search Algorithm for the
Economic Dispatch Problem
Dinu Călin SECUI, Simona DZITAC, Gabriel BENDEA,
Codruţa BENDEA, Cristina HORA
University of Oradea
University Street, Oradea, 410087, Romania
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Abstract: The paper presents a modified harmony search algorithm (MHS), useful for solving the economic dispatch (ED) problem assuming a non-linear cost function and various technical restrictions. The ED problem is a very important optimization problem for power systems, and technical restrictions must be considered: prohibited operating zones and ramp rate limits of power generating units, as well as transmission line losses. The MHS algorithm is based on harmony search (HS) algorithm, but a new harmony is obtained by inserting some features from artificial bee colony algorithm. The efficiency of MHS algorithm is tested against two systems consisting of 6 and 38 thermal power generating units. Results are compared with those obtained by applying other optimization techniques.
Keywords: economic dispatch; harmony search; transmission losses.
CITE THIS PAPER AS:
Dinu Călin SECUI, Simona DZITAC, Gabriel BENDEA, Codruta BENDEA, Cristina HORA, A Modified Harmony Search Algorithm for the Economic Dispatch Problem, Studies in Informatics and Control, ISSN 1220-1766, vol. 23 (2), pp. 143-152, 2014.
Economic dispatch (ED) is an optimization problem of power systems that aims to determine the output power of thermal power generating units in order to have a minimal fuel cost for the entire system and, in the meantime, to satisfy some technical restrictions while operating the units.
The mathematical model of ED problem is non-linear, where both objective function and restrictions system may be non-linear. Classical methods were used for solving the ED problem: linear programming , non-linear programming , quadratic programming , Lagrangian relaxation algorithm  and dynamic programming . Usually, these methods have got difficulties in finding a global optimum, they being able to offer only a local optimum point. Moreover, classical methods need a calculation of derivatives and some checking on continuity and derivability conditions of functions belonging to optimization model. To cover these drawbacks several artificial intelligence-based optimization techniques were applied. One of the most frequently used methods is based on the particle swarm optimization (PSO) applied in classical, enhanced or hybrid versions: PSO, PSO with time varying acceleration coefficients (PSO-TVAC) [6-8], new PSO (NPSO, NPSO-LSR) [9, 10], improved PSO , distributed Sobol PSO with tabu search algorithm (DSPSO-TSA) . Other methods used for solving ED problems are: evolutionary programming (EPs) , biogeography-based optimization (BBO) , tabu search and multiple tabu search (TS, MTS) , differential evolution (DE) [16, 17], hybrid DE (DEPSO) , artificial bee colony algorithm (ABC) , incremental ABC with local search (IABC-LS) , harmony search (HS) , differential HS (DHS) .
Harmony search is a meta-heuristic algorithm inspired from a musical process of searching for a perfect state of harmony. The HS is an easy to implement algorithm, having good convergence characteristics and may be easily adapt to work with other algorithms [23, 24]. Thus, the HS algorithm or its versions were successfully used for solving mathematical [25-27] and engineering problems with continuous variables: reliability optimization , automatic parameter configuration , design of water distribution networks  etc.
In this paper, the HS classical algorithm is enhanced with some features specific to artificial bee colony algorithm in order to solve the economic dispatch problem. The new algorithm is called modified harmony search (MHS) algorithm. Its results are compared with others obtained by applying different optimization techniques.
- PARIKH, J., D. CHATTOPADHYAY, A Multi-Area Linear Programming Approach for Analysis of Economic Operation of the Indian Power System, IEEE Transaction on Power System, vol. 11(1), 1996, pp. 52-58.
- NANDA, J., L. HARI, M. L. KOTHARI, Economic Emission Load Dispatch with Line Flow Constraints Using a Classical Technique. IEE Proceedings Generation, Transmission and Distribution, Vol. 141(1), 1994, pp. 1-10.
- PAPAGEORGIOU, L., E. FRAGA, A Mixed Integer Quadratic Programming Formulation for the Economic Dispatch of Generators with Prohibited Operating Zones. Electric Power System Research, Vol. 77(10), 2007, pp. 1292-1296.
- BARD, J. F., Short-term Scheduling of Thermal-Electric Generators using Lagrangian Relaxation, Operations Research, Vol. 36(5), 1988, pp. 756-766.
- TRAVERS, D., R. KAYE, Dynamic Dispatch by Constructive Dynamic Programming. IEEE Transaction on Power System, Vol. 13(1), 1998. pp. 72-78.
- GAING, Z.-L., Particle Swarm Optimization to Solving the Economic Dispatch Considering the Generator Constraints, IEEE Transaction on Power System, Vol. 18(3), 2003, pp. 1187-1195.
- CHATURVEDI, K. T., M. PANDIT, L. SRIVASTAVA, Particle Swarm Optimization with Time Varying Acceleration Coefficients for Non-Convex Economic Power Dispatch, Electrical Power and Energy Systems, Vol. 31(6), 2009, pp. 249-257.
- SECUI, D. C., I. FELEA, S. DZITAC, L. POPPER, A Swarm Intelligence Approach to the Power Dispatch Problem, International Journal of Computers Communications & Control, Vol. 5(3), 2010, pp. 375-384.
- SELVAKUMAR, A. I., K. THANUSHKODI, A New Particle Swarm Optimization Solution to Non-Convex Economic Dispatch Problems, IEEE Transaction on Power System, Vol. 22(1), 2007, pp. 42-51.
- NIKNAM, T., H. D. MOJARRAD, H. Z. MEYMAND, A New Particle Swarm Optimization for Non-Convex Economic Dispatch, European Transactions on Electrical Power, Vol. 21(1), 2011, pp. 656-679.
- PARK, J.-B., Y.-W. JEONG, J.-R. SHIN, K. Y. LEE, An Improved Particle Swarm Optimization for Non-Convex Economic Dispatch Problems, IEEE Transaction on Power System, Vol. 25(1), 2010, pp. 155-166.
- KHAMSAWANG, S., S. JIRIWIBHAKORN, DSPSO-TSA for Economic Dispatch Problem with Non-Smooth and Non-continuous Cost Functions. Energy Conversion and Management, Vol. 51(2), 2010, pp. 365-75.
- SINHA, N., R. CHAKRABARTI, P. K. CHATTOPADHYAY, Evolutionary Programming Techniques for Economic Load Dispatch, IEEE Transactions on Evolutionary Computation, Vol. 7(1), 2003, pp. 83-94.
- BHATTACHARYA, A., P. K. CHATTOPADHYAY, Biogeography-based Optimization for Different Economic Load Dispatch Problems, Power Systems, Vol. 25(2), 2010, pp. 1064-1077.
- POTHIYA, S., I. NGAMROO, W. KONGPRAWECHNON, Application of Multiple Tabu Search Algorithm to Solve Dynamic Economic Dispatch Considering Generator Constraints, Energy Conversion and Management, Vol. 49(4), 2008, pp. 506-516.
- NOMAN, N., H. IBA, Differential Evolution for Economic Load Dispatch Problems, Electric Power System Research, Vol. 78(3), 2008, pp. 1322-1331.
- PEREZ-GUERRERO, R. E. J. R. CEDENIO-MALDONADO, Economic Power Dispatch with Non-smooth Cost Functions using Differential Evolution, Proceedings of the 37th Annual North American, Power Symposium, Ames, Iowa, 2005, pp. 183-190.
- SAYAH, S., A. HAMOUDA, A Hybrid Differential Evolution Algorithm based on Particle Swarm Optimization for Non-convex Economic Dispatch Problems, Applied Soft Computing, Vol. 13(4), 2013, pp. 1608-1619.
- HEMAMALINI, S., S. P. SIMON, Artificial Bee Colony Algorithm for Economic Load Dispatch Problem with Non-smooth Cost Functions, Electric Power Components and Systems, Vol. 38(7), 2010, pp. 786-803.
- ÖZYÖN, S. D. AYDIN, Incremental Artificial Bee Colony with Local Search to Economic Dispatch Problem with Ramp Rate Limits and Prohibited Operating Zones, Energy Conversion and Management, Vol. 65, 2013, pp. 397-407.
- ARUL, R., G. RAVI, S. VELUSAMI, Non-Convex Economic Dispatch with Heuristic Load Patterns, Valve Point Loading Effect, Prohibited Operating Zones, Ramp-Rate Limits and Spinning Reserve Constraints using Harmony Search Algorithm, Electrical Engineering, Vol. 95(1), 2012, pp. 53-61.
- WANG, L., L.-P. LI, An Effective Differential Harmony Search Algorithm for the Solving Non-Convex Economic Load Dispatch Problems, Electrical Power and Energy Systems, Vol. 44(1), 2013, pp. 832-843.
- GEEM, Z. W., J. H. KIM, G. V. LOGANATHAN, A New Heuristic Optimization Algorithm: Harmony Search, Simulation, vol. 76(2), 2001, pp. 60-68.
- LEE, K. S., Z. W. GEEM, A New Meta-Heuristic Algorithm for Continuous Engineering Optimization: Harmony Search Theory and Practice, Computer methods in applied mechanics and engineering, Vol. 194(36-38), 2005, pp. 3902-3933.
- ZOU, D., L. GAO, J. WU, S. LI, Novel Global Harmony Search Algorithm for Unconstrained Problems, Neurocomputing, Vol. 73(16-18), 2010, pp. 3308-3318.
- WU, B., C. QIAN, W. NI, S. FAN, Hybrid Harmony Search and Artificial Bee Colony Algorithm for Global Optimization Problems, Computers and Mathematics with Applications, Vol. 64(8), 2012, pp. 2621-2634.
- OMRAN, M. G. H. M. MAHDAVI, Global-Best Harmony Search, Applied Mathematics and Computation, Vol. 198(2), 2008, pp. 643-656.
- ZOU, D., L. GAO, S. LI, J. WU, An Effective Global Harmony Search Algorithm for Reliability Problems, Expert Systems with Applications, Vol. 38(4), 2011, pp. 4642-4648.
- VERA-PEREZ, O. L., A. MESEJO-CHIONG, A. JAUME-I-CAPO, M. GONZALEZ-HIDALGO, Automatic Parameter Configuration: A Case Study on a Rehabilitation Oriented Human Limb Tracking Algorithm, Studies in Informatics and Control, vol. 23 (1), 2014, pp. 87-96.
- GEEM, Z. W., Optimal Cost Design of Water Distribution Networks using Harmony Search, Eng. Optimization, Vol. 38(3). 2006, pp. 259-280.
- KARABOGA, D. B. BASTURK, A Powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm, Journal of Global Optimization, Vol. 39(3), 2007, pp. 459-471.
- AKAY, B., D. KARABOGA, A Modified Artificial Bee Colony Algorithm for Real-Parameter Optimization, Information Sciences, Vol. 192(1), 2012, pp. 120-142.
- KRISHNAVENI, V., G. ARUMUGAM, A Novel Enhanced Bio-Inspired Harmony Search Algorithm for Clustering, Proceedings of the International Conference Recent Advances in Computing and Software Systems (RACSS), Chennai, 2012, pp. 7-12.
- GAING, Z.-L., Closure to Discussion of Particle Swarm Optimization to Solving the Economic Dispatch Considering the Generator Constraints. IEEE Tr. on Power Systems, Vol. 19(4), 2004, pp. 2122-2123.
- SYDULU, M., A Very Fast and Effective Non-Iterative Lamda Logic based Algorithm for Economic Dispatch of Thermal Units, Proceedings of the IEEE Region 10 Conference TENCON, Cheju Island, Vol. 2, 1999, pp. 1434-1437.
- BHATTACHARYA, A., P. K. CHATTOPADHYAY, Hybrid Differential Evolution with Biogeography-based Optimization for Solution of Economic Load Dispatch, IEEE Trans. on Power Systems, vol. 25(4), 2010, pp. 1955-1964.