Metaheuristic approaches for Non-Convex Economic Dispatch Problem

The operation of the power utilities is controlled tightly to achieve the most efficient use of its capability. Economic dispatch (ED) is one of the power system energy management tools that is used to allocate required power generation to a number of generating units to meet the active load demand. The Economic Dispatch problem is a large-scale nonlinear constrained optimization problem. The operation cost of the power utilities depends on the fuel cost of the generating units. By optimizing the objective functions that depend on the fuel cost, the Economic Dispatch results in fuel cost savings. The most difficult problem is the non-linearity (non-convexity) of the power system which reflects in any design of the cost objective functions. One bigger source of complexity is the power system governing physical constraints (spinning reserve, transmission losses, prohibited operation zones, ramp rate limit, valve point loading effect, and multi fuel options). The proper schedule of the spinning reserve let the power system be robust to the unexpected outages of the generating units or incorrect load allocation among the units. The Prohibited zones are caused by physical operation limitations due to faults in the machines its self or the associated auxiliaries. The ramp rate limits are caused by the restrictions in the generation of the power. Some generating units have multi steam valves which opened sequentially to follow the required increase in generation for the generating unit this introduces another mathematical difficulty by adding further ripple non smoothness to the cost function. Taking the valve point effect and multiple fuels will increase the number of local minimums, which make the ED more difficult (searching for global optimum). This non-linearity causes the non-smoothness of the cost functions or the discontinuity of the cost functions, which poses a difficulty in the optimization. The difficulty of the ED problem arises from the nonlinearity impeded in the power system parameters, in addition to the large amount of calculations needed in iterating the system parameters. This makes ED problem a large scale nonlinear constrained optimization problem. In this project two metaheuristics are proposed and developed to solve the Convex and Non-Convex Economic Dispatch problem. The first algorithm is based on the harmony search algorithm (HSA) (Geem et al., 2001) and the second algorithm is based on the non-linear threshold accepting algorithm (Nahas and Nourelfath, 2015).