Complementarity Reformulations for the Optimal Design of Distributed Energy Systems with Multiphase Optimal Power Flow

Abstract: The design of grid-connected distributed energy systems (DES) has been investigated extensively as an optimisation problem in the past, but most studies do not include nonlinear constraints associated with unbalanced alternating current (AC) power flow in distribution networks. Previous studies that do consider AC power flow use either less complex balanced formulations applicable to transmission networks, or iterative linearisations derived from local power flow solutions and prior knowledge of the design. To address these limitations, this study proposes a new algorithm for obtaining DES design decisions subject to nonlinear power flow models. The use of regularised complementarity reformulations for operational constraints that contain binary variables is proposed. This allows the use of large-scale nonlinear solvers that can find locally optimal solutions, eliminating the need for linearisations and prior knowledge while improving accuracy. DES design models with either multiphase optimal power flow (MOPF), which captures inherent phase imbalances present in distribution networks, or balanced optimal power flow formulations (OPF) are tested using a modified version of the unbalanced IEEE EU low-voltage network. Results are compared with a popular linear DES design framework, which proposes an infeasible operational schedule when tested with MOPF, while the fixed design alone produces the highest annualised costs. Despite the increased complexity, DES with MOPF obtains the best solution, enabling a greater integration of solar capacity and reducing total annualised cost when compared to DES with OPF. The new algorithm achieves a 19% improvement when compared with solving a bi-level model for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within distribution networks.