Optimization of Nonlinear Quadratic Economic Dispatch Problem with Transmission Losses: A Scalable Mathematical Modeling Approach

Economic dispatch is a challenging optimization task in power system operation, aiming to determine the least cost generation schedule that meets a specified load demand while respecting physical and operational constraints. In this study, we formulate the economic dispatch problem (EDP) for thermal generation units using a nonlinear quadratic cost function and enforce energy balance, generator capacity, and transmission loss constraints. The model is formulated in the General Algebraic Modeling System (GAMS) and solved using the CONOPT solver. We evaluate two test cases, a three unit and a six-unit system, first neglecting transmission losses and then including a B-matrix loss representation. Our results demonstrate that accounting for losses increases total operating costs by 3.86% in the three-unit case and by 2.21% in the sixunit case. Despite this cost increase, solution times and generator dispatch patterns remain largely unaffected, indicating high computational efficiency. The proposed formulation is readily extensible to larger networks, and the findings emphasize the importance of accurately modeling transmission losses, particularly for units exhibiting low generation to loss ratios, to ensure both economic and reliable system operation.