| The economic dispatch model of a power system considering the valve-point effect, the prohibited operating zones (POZs) and the multiple fuel options of generation units is more accurate in comparison with the traditional economic dispatch model. The former model is non-convex, non-continuous, non-differentiable and has a large number of local minima, which complicates its resolving. Thus the former model is usually solved by evolutionary algorithms. Evolutionary algorithms are time consuming and it might have a relatively low accuracy, especially in a large-scale power system. To solve the former model more effectively, the necessary conditions for its optimum solution are proposed and several solution methods, which are fast and accurate, are proposed based on the conditions. To decrease both the fuel cost and the pollution emission during power generation, a new multi-objective optimization method is proposed for the environment/economic dispatch problem. The contributions of this dissertation include the following three parts.The necessary conditions for the local minima of economic dispatch with valve-point effect (EDVPE) problem are proposed and two types of local minima are obtained. In a local minimum in the first type, there is at most one unit which does not locate at the singular points, which include the valve points and the maximum and minimum outputs of units. It is shown that the local minima in the second type could be ignored, which could simplify the process of resolving the EDVPE model. Consequently, it only needs to search the local minima in the first type to find the near global optimum of the EDVPE model. A dimensional steepest decline (DSD) method is proposed to solve the non-smooth economic dispatch problems. The computational load of the method increases approximately at a second-order rate as the increase of the number of units. The simulation results on several test systems, including 2 large-scale power systems, show that DSD can effectively solve the economic dispatch problem considering valve-point effects, POZs, multiple fuel options of a generation unit and the transmission line loss. The simulation results also show that the DSD has a significant advantage in terms of both accuracy and computational load over the best evolutionary algorithms compared, especially on a large-scale power system. Besides, the simulation results also show that the economic dispatch considering the valve-point effect could bring an economic profit of about 2%-9% which is considerable, in comparison with the economic dispatch without considering the valve-point effect.The necessary conditions for the global optimum of the economic dispatch model considering POZs of generation units are proposed. Based on the conditions, a new method, fast λ-iteration (FλI) method, is proposed to solve the model. The simulation results on the 6-,15- and 140-unit systems show that the FλI is accurate and consumes extremely low computational load, and that the FλI has a significant advantage in terms of both accuracy and computational load over the best evolutionary algorithms compared, especially on a large-scale power system with many units having POZs.Based on the KKT conditions for a multi-objective optimization problem, a new method, the multi-objective λ-iteration and Newton method (M0λIN), is proposed to solve the environmental/economic dispatch (EED) problem. There are neither weight coefficients nor penalty coefficients in the method. The solution of the EED problem is a set of Pareto-optimal solutions. A fixed-output unit is chosen in the MOλIN. For an output of the fixed-output unit, a pre-judge scheme is executed to tell whether there exists potential or not to obtain a Pareto-optimal solution, which could decrease the computational load of the MOλIN, especially in a large-scale power system. Besides, a scheme to choose a good fixed-output unit is proposed to improve the efficiency of the MOλIN. It is revealed that in a Pareto-optimum solution, the outputs of the units satisfy an equal difference-ratio incremental cost criterion. The simulation results on 2 test systems show that MOλIN could effectively solve the EED problem, and that MOλIN consumes less time and could obtain more accurate and more evenly distributed Pareto fronts, in comparison with the multi-objective particle swarm optimization method. |
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