Phase-specific energy storage configuration for a power grid integrated with unbalanced traction loads via two-stage distributionally robust optimization

In remote mountainous areas, unbalanced railway traction loads and renewable energy sources are often connected to weak grids through points of common coupling (PCCs). This integration can cause severe voltage deviations, three-phase voltage unbalance, and renewable energy curtailment. Existing energy storage configuration methods generally assume balanced grid conditions or deterministic renewable generation. Therefore, they cannot adequately address the combined effects of unbalanced traction loads and renewable energy uncertainty. To overcome these limitations, this paper develops a two-stage distributionally robust optimization model for phase-specific energy storage system (ESS) configuration in three-phase coupled power grids. The model jointly optimizes the ESS capacity, rated power, and operation strategy for each phase. It also considers three-phase voltage deviation, voltage unbalance, and uncertainty in the probability distribution of renewable generation scenarios. An ambiguity set is constructed using norm-1 and norm-inf constraints to characterize the distributional uncertainty. The nonlinear three-phase power flow equations and distributionally robust optimization model are then reformulated into a tractable mixed-integer optimization problem. The proposed method is validated on a mountainous railway power grid. Compared with the case without ESS configuration, the proposed model reduces voltage unbalance and voltage deviation by 29.05% and 31.30%, respectively. It also decreases the renewable energy curtailment rate by 15.72 percentage points. The results demonstrate that the proposed phase-specific ESS configuration method can improve three-phase voltage quality and promote renewable energy utilization. It provides an effective ESS configuration approach for power grids along mountainous railways.