This research aimed to solve an economic dispatch problem with prohibited operating zones using a hybrid method combining lambda iteration and bee colony optimization with smooth cost function characteristics. The constraints of economic dispatch consisted of load demand, transmission loss, ramp rate limits and prohibited operating zones. To verify the performance of the proposed algorithm, it was operated using a simulation of the MATLAB program and tested with two case studies with certain operating zones involving either three or six generators. The study found that the proposed method could provide better solutions than the others that were tested in terms of a quality solution, and computational and convergence efficiently. It can be concluded that the proposed method was effective in solving the issue of economic dispatch
Słowa kluczowe: Bee Colony Optimization, Lambda Iteration, Economic Dispatch.
W aertykule przedstawiono algorytmy umożliwiające optymalizację ekonomicznego rozsyłu energii. Uwzględniono wzbronione zkakresy mocy wyjściowej.
Keywords: ekonomiczny rozsył energii, iteracja Lambda, algorytmy rojowe.
Reliability, stability, and economic efficiency are very important for the planning and operation of a power generation system. To get profits from the capital invested, efficient economic operation is critical. Operational economics, involving then minimization of power generation and delivery costs, is called Economic Dispatch (ED). The objective of economic dispatch is to minimize the total cost of all generations while satisfying all operating constraints. To solve the problem of economic dispatch, there are two approaches, including classical and meta-heuristic methods. Classical methods, such as lambda iteration and gradient methods are the most common ones applied to solve the continuous ED problem -. These methods require incremental fuel cost curves which are piecewise and linear. Lagrangian relaxation  and dynamic programming  is one of the approaches that are used to solve a non-linear and discontinuous ED problem. Numerical methods can cause problems in complicated and large power systems as they suffer from the complexities of dimensionality and local optimality. Recently, meta-heuristic methods have been used to solve the economic dispatch problem. Such methods include simulated annealing (SA) -, a genetic algorithm (GA) -, an evolutionary program (EP) -, tabu search (TS) , particle swarm optimization (PSO) -, ant colony optimization (ACO) - and bee colony optimization (BCO) -. These methods can obtain a global optimum within a short time and guarantee an optimum solution. However, in these techniques the initial populations are generated randomly. This results in long computation times and a long time to convergence when the generated initial populations are too far from the optimum solution. This problem has been solved by HLBCO - in which the initial population of BCO is modified. However, this method considers a static economic dispatch si [...]
 A. J. Wood and B. F. Wollenberg. “Power Generation Operation and Control," New York: Wiley, 1984.  C. Yasar and S. Fadil. “Solution to Environmental Economic Dispatch Problem by Using First Order Gradient Method," In Proc. of 5th International Conference on Electrical and Electronic, (2007), pp. 1-5.  A.A. El-Keib, H. Ma, and J.L. Hart. “Environmentally Constrained Economic DispatchUsing the LaGrangian Relaxation Method," IEEE Transactions on Power Systems, v 9 (1994), no. 4, pp. 1723-1729.  R.J. Ringlee and D.D. Williams. "Economic dispatch operation considering valve throttling losses, II-distribution of system loads by the method of dynamic programming," IEEE Trans. Power Appar. Syst., (1963), pp.615-620.  K. K. Vishwakarma, H. M. Dubey, M. Pandit and B.K. Panigrahi. “Simulated annealing approach for solving economic load dispatch problems with valve point loading effects," International Journal of Engineering, Science and Technology, 4 (2012), no. 4, pp. 60-72.  I. Ziane, Farid Benhamida, Yacine Salhi and AmelGraa. “Combine Dynamic Economic/Emission Dispatch Using Sinulated Annealing Solution," International Conference on Systems and Control, Sousse, Tunisia, (2015), pp. 302-309.  S. Pratap Singh, Rachna Tyagi and Anubhar Goel. “Genetic Algorithm for Soving the Economic Load Dispatch," International Journal of Electronic and Electrical Engineering, 7 (2014) , no. 5, pp.523-528.  N. Javidtash, A. Davodi, M. Hakimzadeh and A. Roozb. “Genetic Algorithm for Solving Non-Convex Economic Dispatch Problem," International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering, 8 (2014), no. 5, pp.866-869.  M. Rajkumar, K. Mahadevan and S. Kannan. “Evolutionary Programming Solution For Economic Dispatch Of Units With Ramp Rate Limits," VFSTR J. of STEM, 1 (2015), no. 2, 12-17.  M. F. Zaman, Saber M. Elsayed, Tapabrata Ray, and Ruhul A. Sarker “Evolutionary Algorithms for Dynamic Economic Dispatch Problems," IEEE Transactions on Power Systems, 31 (2016), no. 2, pp.1486-1495.  B. Naama, H. Bouzeboudja, and A. Allali. “Solving the Economic Dispatch Problem by Using Tabu Search Algorithm," TerraGreen 13 International Conference 2013 - Advancements in Renewable Energy and Clean Environment, Energy Procedia 36, (2013), pp. 694-701.  B. Mohammadi-Ivatloo, M. Moradi-Dalvand and A. Rabiee, “Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients", Electric Power Systems Research, Elsevier, (2013), pp. 9-18.  J. Sun, V. Palade, X.J. Wu, W. Fang and Z. Wang. “Solving the Power Economic Dispatch Problem With Generator Constraints by Random Drift Particle Swarm Optimization," IEEE Transactions on Inductrial Informatics, 10 (2014), no. 1, pp. 222-232.  K. Srikanth and V. HariVamsi. “Partical Swarm Optimization Technique for Dynamic Economic Dispatch," Internation Journal of Research in Engineering and Technology, 5 (2016), issue 5, pp. 460-466.  R. Effatnejad, H. Aliyari, H. Tadayyoni, A. Abdollahshirazi. “Novel Optinization Based on the Ant Colont for Economic Dispatch," International Journal on Technical and Physical Problems of Engineering, 5 (2013), issue 15, pp. 75-80.  P. Jamalbhai Vasovala, Chinmay Y. Jani , Vasim H. Ghanchi and P. Harshad Kumar. “Application of Ant colony Optimization technique in Economic Load Dispatch Problem for IEEE-14 Bus System," International Journal for Scientific Research & Development, 2 (2014), issue 02, pp. 990-994.  D. K.Thesia, P. Jangir and Dr. Indrajit N. Trivedi. “Economic Emission Dispatch Problem Solution Using Ant Colny Optimization of Micro-grid in Island Mode," International Journal of Advance Engineering and Research Development, 2 (2015), issue 5, pp.89-95.  P. Lu, J. Zhou, H. Zhang, R. Zhang and C. Wang. “Chaotic differential bee colony optimization algorithm for dynamic economic dispatch problem with valve-point effects," Electrical Power and Energy Systems journal, Elsevier, (2014), 130-143.  H. Shayeghi and A. Ghasemi. “A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch," Energy Conversion and Management 79, (2014), pp. 344-354.  D. Calin Secui. “A new modified bee colony algorithm for the economic dispatch problem," Energy Conversion and Management, Elsevier, (2015), pp.43-62.  W. Khamsen, C. Takeang. “Hybrid of Lamda and Bee Colony Optimization for Solving Economic Dispatch," PRZEGLAD ELEKTROTECHNICZNY, (2016), pp.220-223.  R. Murugan and M. R. Mohan. “Modified artificial bee colony algorithm for solving economic dispatch problem," ARPN Journal of Engineering and Applied Sciences, 7 (2012), no. 10, pp.1353-1366.  D. Karaboga and B. Basturk. “On the performance of artificial bee colony (ABC) algorithm," Applied soft computing, Science Direct, Elsevier, (2008), pp.687-697.  R. Naresh, J. Dubey and J. Sharma. “Two-phase neural network based modeling framework of constrained economic load dispatch," IEE Proc.-Gener., Transm., Distrib., vol. 151, 3 (2004), pp.373-378.  S. Prabakaran and R. Lakshminarayana Rao. “Application of Particie Swarm Optimization Algorithm for solving Power Economic Dispatch with Prohibited operating zones and Ramrate limit Constraints," International Journal of Emerging Technologies and Engineering, 3 (2016), issue 3,March, pp. 19-24.  S. Prabakaran, V. Senthilkumar and G. Baskar. “Economic Dispatch Using Hybrid Particle Swarm Optimization with Prohibited Operating Zones and Ram Rate Limit Constraints," Journal of Electrical Engineering & Teachnology: JEET, 10 (2015), no. 4, pp.1441-1452.  K. Chandram, N. Subrahmanyam, M. Sydulu, “Brent method for dynamic economic dispatch with transmission losses," In: IEEE 2008 Power Engineering Society Transmission Distribution Conference and Exposition Chicago, IL, USA. 21- 24, April, (2008), pp. 1-5.  S. Ganesan and S. Subramanian. “Dynamic Economic Dispatch Based on Simple Algorithm," International Journal of Computer Engineering, 3 (2011), no. 2, pp. 226-232.