An Active Distribution Network Model Including Legacy and Modern Equipment: Relaxations and Approximations Under Optimal Management

A distribution management system requires an accurate and computationally efficient model of its distribution network. This paper formulates an active distribution network (ADN) model taking into account legacy equipment and modern equip-ment. Legacy equipment includes mechanically switched capaci-tors and under load tap changer transformers. Modern equipment includes distributed generators in the form of photovoltaic array inverters, battery energy storage systems, and ZIP loads. The full ADN model features nonconvex and intractable equations that need to be relaxed or reformulated for computational efficiency. To address this, we assess a second order cone program relaxation, a convex hull formulation, and linear reformulations. This study explores the impact of equation relaxations and reformulations on ADN models and the impact of modern equipment on ADN management. Results on the IEEE 4-bus test feeder suggest that relaxations and reformulations greatly cut convergence time but optimal solution accuracy decreases by 16% when compared to the original, nonconvex ADN model. Larger IEEE feeder models with relaxations and reformulations converged faster than models with only a relaxation but arrived at the same feasible, but suboptimal, objective value. The true objective value for these larger IEEE feeders is unknown since they did not converge with hueristics within the allotted two hour period, showcasing the need for the relaxed and reformulated ADN models.