Exponential cone-based OPF formulation for monopolar DC electrical networks

Abstract

This paper presents a convex reformulation of the optimal power flow problem for monopolar DC distribution networks with integrated distributed energy resources, including photovoltaic generators, wind turbines, and battery storage systems. The non-convexity introduced by bilinear voltage terms in the power balance and loss equations is addressed using an exponential cone-based transformation. By introducing logarithmic auxiliary variables, the bilinear terms are embedded into the convex domain, enabling the use of efficient conic optimization solvers. The proposed model is implemented using the JuMP modeling framework in Julia and evaluated on benchmark DC feeders ranging from 27 to 123 buses. The results demonstrate that the exponential cone-based formulation achieves highly accurate approximations of the exact nonlinear solution, with relative errors as low as $10^{-5}$, while significantly outperforming standard second-order cone programming relaxations in terms of both accuracy and scalability. The proposed approach offers a reliable and computationally tractable tool for the optimal dispatch and voltage regulation of large-scale DC networks.