Stochastic economic emission load dispatch
ABSTRACT The economic emission load dispatch (EELD) problem is a multiple non-commensurable objective problem that minimizes both cost and emission together. In the paper a stochastic EELD problem is formulated with consideration of the uncertainties in the system production cost and nature of the load demand, which is random. In addition, risk is considered as another conflicting objective to be minimized because of the random load and uncertain system production cost. The weighted minimax technique is used to simulate the trade-off relation between the conflicting objectives in the non-inferior domain. Once the trade-off has been obtained, fuzzy set theory helps the power system operator to choose the optimal operating point over the trade-off curve and adjust the generation levels in the most economic manner associated with minimum emission and risk. The validity of the method is demonstrated by analysing a sample system comprising six generators.
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ABSTRACT: Co-allocation of energy and reserve is an efficient approach in market clearance. Many different factors contribute to this problem while accounting for system security and credible contingencies may increase the allocated spinning reserve and the total costs, load flexibility as a result of Demand Side Programs may contribute with a positive effect on the total amount and cost of spinning reserve as well as the dispatched energy. This paper presents the integration of Time of Use Program in the securityconstrained energy and reserve Co-allocation market and the effect that TOUP has on the total costs and amount of reserve services are studied in an actual unit commitment market clearing problem. Differential Evolution Algorithm is utilized for an efficient 24-hour unit commitment approach which accounts for both system security and load elasticity. The effectiveness of proposed method is evaluated by application of the algorithm on IEEE 24 bus reliability test system. The results of the algorithm are compared in various cases with other approaches for the unit commitment problem and it is shown that considering TOU program has a noticeable positive effect on the obtained optimum solution.Science International (Lahore). 12/2014; 26(5):1931-1940.
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ABSTRACT: This paper presents a fuzzy goal programming (FGP) procedure for solving multilevel programming problems (MLPPs) having chance constraints in large hierarchical decision organizations. In the proposed approach, first the chance constraints of a problem are converted into their respective deterministic equivalent in the decision making context. Then, the objective functions of decision makers (DMs) located at different hierarchical levels are converted into fuzzy goals by introducing an imprecise aspiration level to each of them to make decision in an uncertain environment. In the model formulation, the concept of tolerance membership functions in fuzzy sets for measuring the degree of satisfaction of DMs with regard to achieving the aspired levels of fuzzy goals as well as degree of optimality of the decision vectors controlled by upper-level DMs on the basis of their order of hierarchy in the organizational system. In the solution process, minimization of under deviational variables associated with membership goals defined for the membership functions are considered for achieving the highest membership value (unity) of each of the fuzzy goals to the extent possible on the basis of their weights of importance in the decision making horizon. To illustrate the effectiveness of the proposed approach, a numerical example is solved.International Journal of Advanced Computer Research. 03/2014; 3(1):193-200.
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ABSTRACT: A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch (EED) problem. Furthermore, the polynomial functions of both objective functions are aggregated into a single objective function using the weighted sum approach. This thus reduces the problem to a standard polynomial optimization problem which was formulated as a hierarchy of semi-definite relaxation problems. The resulting SDP problem was then solved at different degrees of approximation. The performance of the proposed approach was evaluated by conducting experiments on the standard 6-unit and the 13-unit IEEE test systems. The results obtained were compared with those reported in the literature and indicated that SDP has inherently good convergence property and provides better exploration of the Pareto front.Applied Energy 09/2014; 134:446–455. · 5.26 Impact Factor