Solving network-constrained nonsmooth economic dispatch problems through a gradient-based approach

The Network-Constrained Nonsmooth Economic Dispatch (NCNS-ED) is formulated as a nonsmooth, nonconvex and multimodal optimization problem. Nonsmoothness is generally associated with valve-point loading effects in the cost function of thermal units. Due to nonsmoothness, gradient-based approaches cannot be used directly for solving NCNS-ED problems. Hence, heuristic approaches have been used as the main methodologies for solving this problem. In this paper, we propose a reformulation for the NCNS-ED problem that enable its solution by means of gradient-based approaches. This formulation is based on the definition of an equivalent nonlinear programming problem where the modular terms are eliminated by using artificial variables and inequality constraints. We propose a primal–dual modified log-barrier function approach for solving the reformulated problem, where each inequality constraint is penalized by using a piecewise function that involves the modified barrier functions of Polyak and Jittortrum-Osborne-Meggido. Numerical results involving small-, medium- and large-scale power systems, have shown that the proposed reformulation enables eliminating nonsmoothness in the NCNS-ED problems. The method proposed, which is compared to some methods described the literature, has shown robustness for solving real large-scale NCNS-ED problems with acceptable computation times.