Taylor-series based Convex Approximation Method for Optimization of Active Distribution Networks

In the context of active distribution networks, innovative solution techniques based on reformulating the original non-convex AC Optimal Power Flow (AC-OPF) problem have received increasing attention. However, their accuracy is often sensitive to the objective function and grid size. This paper first investigates the performance of a selection of state-of-the-art convex approximations and relaxations of the AC-OPF problem for a range of engineering and economic objective functions in distribution grids. Then, it proposes a novel convex approximation based on the Taylor expansion, which is applicable to a wide range of objective functions as it yields high-quality solutions with small AC-violations. The performance is evaluated via optimality gaps and power mismatches on several active grids varying in size and the penetration of active energy storage systems.