روش تجارت کردن با ارزش جانشینی برای مشکل ارسال قدرت حرارتی چندمنظوره

A multiobjective thermal power dispatch problem is solved that has non-commensurable objectives such as operating cost and minimal emissions. Typically, the objectives will conflict in that there is no feasible solution that minimizes them all simultaneously. In such a case, some form of conflict resolution must be adopted to arrive at a solution. In this study, ϵ-constraint method is used to generate non-inferior solutions along with the trade-off function between the conflicting objectives. To access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off (SWT) method and utility approach. The SWT functions are constructed in the functional space and then are transformed into the decision space. So, SWT functions relate the decision maker's preferences to non-inferior solutions. The validity and effectiveness of the method have been proved by analysing a six-generator system.

In the past, it was normal to formulate optimization models concerning minimizing (or maximizing) a single scalar valued objective function. The optimization models and the analysts' perception of a problem become more realistic if many objectives are considered. The power system can also operate most efficiently when optimized with respect to several objectives or criteria under many constraints [1]. Obviously, trade-offs among these objectives are impossible because of their different natures. So, it is stated that objectives are non-commensurable. Generally, the multiobjective problems are solved to find non-inferior (pareto-optimal, non-dominated) solutions. Qualitatively, a non-inferior solution of a multiobjective problem is one where any improvement of one objective function can be achieved only at the expense of another. The most widely used methods of generating such non-inferior solutions are the ϵ-constraint and weighted minimax methods [2]. Methodologies for solving multiobjective problem differ in two major ways: 1. the procedure used to generate non-inferior solutions, and 2. the ways used to interact with the decision makers (DMs) and the type of information made available to the DM such as trade-offs. In almost all decision making problems there are several criteria for judging the possible alternatives. The main concern of the decision maker is to fulfil the conflicting goals while satisfying the constraints of the system. Further, there are two approaches to solve such problems: 1. One assumes that there exists a utility function for the particular problem. Such function is used to obtain the best alternative. 2. The other makes no assumptions regarding the existence of utility function, but provides the DM with a set of simple but effective tools to obtain the best alternative. The SWT method provides the facility to interact with the DM. Apart from heat, power utilities using fossil fuels as a primary energy source, produce particulates and gaseous pollutants. The particulates and the gaseous pollutants such as carbon dioxide (CO2), oxides of sulphur (SOx) and oxides of nitrogen (NOx) cause detrimental effects on human beings. Pollution control agencies restrict the amount of emissions of pollutants depending upon their relative harmfulness to human beings. Therefore, a priority structure can be formed for the multiobjective problem [3] and [4]. In this paper authors formulate classical economic dispatch as a multiobjective optimization problem. Four objectives are considered for minimization. Namely operating cost and impacts on the environment of NOx, SO2 and CO2 emissions. The formulated multiobjective problem adopts a ϵ-constraint form, which allows explicit trade-offs between objective levels for each non-inferior solution [5]. The SWT method is used to find the best alternative among the non-inferior solutions.

In the multiobjective framework it is realized that cost and emission are conflicting objectives and subject to mutual interface. The solution set of the formulated problem is non-inferior due to contradictions among objectives taken and has been obtained through ϵ-constrained technique. The novel formulation as multiobjective optimization problem has made it possible to quantitatively grasp trade-off relations among conflicting objectives. The trade-off approach is effective only for two objectives, as the number of objectives increases, the selection of best solution becomes cumbersome. An interactive method SWT has been applied to identify the best compromise solution for multiobjective power dispatch problem, when conflicting objectives are more than two. The major characteristics and advantages of the SWT method are that the surrogate worth functions, which relate the decision maker's preference to the non-inferior solutions through the trade-off functions, are constructed in the functional space and only then are transformed into the decision space. The proposed method provides interface between the decision maker and the mathematical model through SWT. It also allows explicit trade-off between fuel cost of units with NOx emission, SO2 emission and CO2 emission levels, respectively.