Multi-Objective Optimization For Economic Emission Dispatch Problem In Power Station

With the growing consciousness of environmental protection, traditional economic power dispatch methods can not meet the need for environmental protections. Thus, the economic emission dispatch (EED) problem of thermal power plants has currently become one of hotspots. The EED problem is a complex non-linear constrained multi-objective optimization problem. Conventional optimization approaches, such as weight methods have limitations for solving multi-objectives EED problems. Recently, Pareto-based multi-objective optimization algorithms for solving EED problems have become a new research hotspot. However, the algorithms developed in the previous work still have the problems of premature convergence and being trapped in the local optimum. To tackle the problems above, multi-objective optimization algorithms based on the Pareto optimality are proposed to efficiently solve the EED problems in this paper. The main work of this paper is summarized as follows.1. Marginal models of the EED problem are studied based on the Marginal Analysis (MA) method. The MA method is a quantity analysis method, which is widely used in modern western economics, but it has not been reported that the MA method is used in the research on multi-objective optimization algorithm. Thus, marginal models of the EED problem are studied by using the MA method and the curves of EED marginal models are analyzed, which lay a foundation of the research on optimization algorithms for solving the EED problem in this paper.2. Based on the analysis of the marginal models, a Pareto-based multi-objective marginal analysis optimization algorithm (MMAOA) is developed. A new strategy is proposed for generating a better initial population so as to improve the performance of the MMAOA approach. Furthermore, the load increment is studied to enhance the optimization performance of the proposed approach. The proposed MMAOA algorithm is validated on EED test systems and the simulation results demonstrate that the MMAOA is valid in solving the EED problem and can efficiently find a set of Pareto optimal solutions. The comparison results show that the MMAOA is superior to other approaches such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ), Fuzzy Logic Controller Genetic Algorithm (FCGA), Biogeography-based Optimization (BBO) and Gravitational Search Algorithm (GSA).3. A new multi-objective chaotic marginal analysis optimization algorithm (MCMAOA) is presented based on the MMAOA, in which three chaotic mutation operators based on Logistic, Tent and Sina maps are introduced to improve the global search ability and the capability of escaping from the local optima of the algorithm with the characteristics of the ergodicity, randomicity and regularity of chaos. The proposed MCMAOA is tested on EED test systems and the results are compared with those of MMAOA, chaos optimization algorithm (COA) and other approaches such as GA, NSGA-II, FCGA, PSO, DE and BBO. The simulation results show that the proposed approach has better global searching ability of solving the EED problem and can find a set of Pareto optimal solutions effectively.4. A Pareto multi-objective binary differential evolution algorithm (PMBDE) is proposed to tackle EED problems more efficiently. Besides, a heuristic correction operator is developed for constraints handling which can transfer infeasible solutions into feasible solutions during the optimization process and thus improve the efficiency of the PMBDE. The performance of the proposed PMBDE is verified on EED test systems. The simulation results demonstrate that the PMBDE is valid and can find a set of Pareto optimal solutions of EED problems. The comparison results show that the effectiveness of PMBDE is superior to that of MMAOA, MCMAOA, DE, Pareto DE, Pareto NSDE (Non-dominated Sorting Differential Evolution algorithm), NSGA-II, Pareto Improved Bacterial Foraging Algorithm (Pareto IBFA), PSO, FCGA, BBO, etc.5. For further improving the global search ability of the PMBDE for solving the EED problem, a novel multi-objective marginal analysis differential evolution (MMADE) is proposed based on the marginal analysis method and PMBDE. In the MMADE, a new correction operator is developed based on marginal analysis, called as marginal analysis correction operator, for constraints handling which can transfer infeasible solutions into feasible solutions more effectively, and therefore the performance of MMADE is further enhanced. The effectiveness of the proposed MMADE is tested on the EED test systems. The comparison results demonstrate that the MMADE can effectively find a set of Pareto optimal solutions and outperforms PMBDE, MMAOA, MCMAOA, Pareto DE, Pareto NSDE, NSGA-Ⅱ, Pareto IBFA, PSO, FCGA, BBO, etc., which illustrates the excellent search ability of PMBDE.