Optimal Dispatch of DERs and Battery-Based ESS in Distribution Grids While Considering Reactive Power Capabilities and Uncertainties: A Second-Order Cone Programming Formulation

This research proposes an effective energy management dispatch (EMD) using a convex approximation for battery-based energy storage systems (ESS) and renewable sources in medium-voltage distribution networks. By means of the branch flow formulation, the exact nonlinear programming model representing the EMD is transformed into a convex model through a second-order cone programming relaxation. Two contributions are presented in this work. The first involves analyzing battery-based EES and renewable sources, specifically focusing on their operation with a variable power factor. This analysis considers the reactive power control capabilities of the power electronic converters that connect distributed energy resources to the grid. The second contribution involves evaluating a robust operation scenario by incorporating uncertainties in the availability of renewable generation and the expected daily demand profile. Numerical validations are conducted on two radial distribution networks composed of 27 and 33 nodes. These networks were chosen to represent the characteristics of rural and urban networks in the Colombian distribution system. The results are then compared against those obtained with a classical unitary power factor. The main goal of the proposed EMD is to minimize the expected annual grid energy losses and operating costs through a single-objective analysis. A comparison with metaheuristic optimization algorithms, such as the parallel version of the particle swarm optimizer, the vortex search algorithm, and a genetic algorithm, demonstrates the effectiveness of our convex EMD model for both objective functions under study. All numerical simulations, including the robust model, were run using MATLAB’s Yalmip tool.