Optimización multiobjetivo para el despacho económico y ambiental en redes dc: una reformulación convexa a través de una aproximación cónica

Abstract

This work addresses the economic-environmental dispatch problem in a DC power grid with thermoelectric and photovoltaic generation. A multi-objective optimization model is proposed to minimize both fuel costs and CO emissions from thermoelectric plants, considering operational constraints such as power balance, voltage limits, generation bounds, and thermal current limits. Due to the non-convex nature of the original power balance equations, the model is reformulated into a convex structure using a conic relaxation approach based on Second-Order Cone Programming (SOCP), introducing auxiliary variables to linearize quadratic terms. This ensures global optimality and computational tractability. The study involves two test systems: a 6-node DC grid with three generators and three loads, and an 11-node system with additional photovoltaic generators operating under a daily solar profile. The inclusion of renewable generation significantly reduces both costs and emissions. The optimization model is implemented in GAMS Studio, while the convex reformulation is validated in MATLAB using the CVX toolbox. Results confirm the effectiveness of the proposed methodology and highlight the potential of SOCP-based modeling and renewable integration to enhance efficiency and sustainability in DC grids.