Dynamic Economic/Environmental Dispatch Problem Considering Prohibited Operating Zones

Abstract

Along with economic dispatch, emission dispatch has become a key problem under market conditions. Thus, the combination of the above problems in one problem called economic emission dispatch (EED) problem became inevitable. However, due to the dynamic nature of today’s network loads, it is required to schedule the thermal unit outputs in real-time according to the variation of power demands during a certain time period. Within this context, this paper presents an elitist technique, the second version of the non-dominated sorting genetic algorithm (NSAGII) for solving the dynamic economic emission dispatch (DEED) problem. Several equality and inequality constraints, such as valve point loading effects, ramp rate limits and prohibited operating zones (POZ), are taken into account. Therefore, the DEED problem is considered as a non-convex optimization problem with multiple local minima with higher-order non-linearities and discontinuities. A fuzzy-based membership function value assignment method is suggested to provide the best compromise solution from the Pareto front. The effectiveness of the proposed approach is verified on the standard power system with ten thermal units.

Strength Pareto Evolutionary Algorithm for the Dynamic Economic Emission Dispatch Problem incorporating Wind Farms and Energy Storage Systems

“…The DEED problem is formulated as an optimization problem, where the objective functions to be minimized are the total fuel cost FT and the total emission ET. These functions are [21]:…”

“…where h loss is the total losses at hour h. It may be calculated using B-loss formula as given in ( 16 [21] is an elitist multi-objective evolutionary algorithm. A brief description of the SPEA is given in this section.…”

Teaching-Learning-Based Optimization Algorithm for the Combined Dynamic Economic Environmental Dispatch Problem

“…In order to find the optimal Pareto solutions, the objective function F T is minimized for various values of δ subject to the constraints ( 5)- (9). Equation (5) describes the power balance constraint where the real power losses t L P at time t are calculated by ( 10) [19].…”

“…Table III depicts the best compromise solution obtained from the resolution of the combined DEEDP. Fuzzy-based method [9] is employed to extract the optimal best compromise solutions. The total cost is 2519909.93$ which is more than the cost obtained for the pure economic dispatch (2472116.66$) and less than the cost obtained for the pure environmental dispatch (2594148.32$).…”

“…Particle swarm optimization (PSO) has also been used to solve power dispatch problems [6][7][8]. Basu [9] has solved the DEEDP by applying the second version of the Non-dominated Sorting Genetic Algorithm (NSGAII) proving that such technique may provide promising results. Another technique based on NGSAII has been developed in [10] to handle the DEEDP incorporating POZ constraints.…”