The practical Economic Dispatch (ED) problems have non-convex objective functions with complex constraints due to the effects of valve point loadings, multiple fuels, and prohibited zones. This leads to difficulty in finding the global optimal solution of the ED problems. This chapter proposes a new swarm-based Mean-Variance Mapping Optimization (MVMOS) for solving the non-convex ED. The proposed algorithm is a new population-based meta-heuristic optimization technique. Its special feature is a mapping function applied for the mutation. The proposed MVMOS is tested on several test systems and the comparisons of numerical obtained results between MVMOS and other optimization techniques are carried out. The comparisons show that the proposed method is more robust and provides better solution quality than most of the other methods. Therefore, the MVMOS is very favorable for solving non-convex ED problems.
TopIntroduction
The economic dispatch (ED) is one of essential optimization problems in power system operation. Its objective is to allocate the real power output of the thermal generating units at minimum fuel production cost while satisfying all units and system contraints (Xia & Elaiw, 2010).
Traditionally, the cost function objective of the ED problem is the quadratic function approximations and this problem is solved by using mathematical programming methods such as lambda iteration method, Newton’s method, gradient search, dynamic programming (Wollenberg & Wood, 1996), linear programming (Parikh & Chattopadhyay, 1996), non-linear programming (Nanda, Hari, & Kothari, 1994), quadratic programming (Fan & Zhang, 1998), and Maclaurin series-based Lagrangian (MSL) method (Hemamalini & Simon, 2009). Among of them, the linear programming methods have fast computation time with reliable solution. However, they suffers the main disadvantage associated with the piecewise linear cost approximation. The non-linear programming methods suffer problems in convergence and algorithm complexity. The Newton-based algorithms have difficulty in handling a large number of inequality constraints (Al-Sumait, Al-Othman, & Sykulski, 2007). MSL method can directly deal with the non-convex ED problem by using the Maclaurin expansion of non-convex terms in the objective function. Although this method can quickly find a solution for the problem, the obtained solution quality is not high, especially for the large-scale systems. In general, the conventional methods are not capable for solving non-convex ED problems (Dieu, Schegner, & Ongsakul, 2013).