A Capacity-Constrained Spatial Equilibrium Model for Electric Vehicle Community Charging on Local Street Networks

Abstract Community charging places electric vehicle (EV) chargers in communal spaces such as shopping malls, public parking, and activity centers embedded in local street networks. It creates a spatial equilibrium problem with an access and coupling structure that corridor charging along freeways does not exhibit. Multiple origin–destination pairs and routes converge on the same community charger via overlapping local arterials, so charger waiting times depend on the aggregate inflow from many paths and a single hardware capacity simultaneously constrains feasible flow for many travelers. On the physical network, these features make the generalized link costs non-separable across the links feeding a shared station. We formulate community charging as a capacity-constrained spatial equilibrium with station-level capacity side constraints, and we show it is exactly a Beckmann program with arc-capacity side constraints on a station-expanded network, restricted to range- and access-feasible paths. The capacitated user-equilibrium theory therefore applies, while the community-charging structure lies in the admissible paths and in the queueing origin of the station cost and capacity. We prove the cross-link symmetry that certifies the potential on the physical network, characterize the KKT solution as a generalized user equilibrium with endogenous station prices, and establish uniqueness of equilibrium flows under strict convexity. To solve the program, we develop a primal–dual decomposition: an outer augmented-Lagrangian loop adjusts station-level shadow prices on capacity, and an inner column-generation loop solves parallelizable path-flow subproblems for each OD pair under the current prices. Numerical experiments on a toy network, the Sioux Falls network, and two real-world community-charging networks show that the proposed method consistently attains equilibrium (to the reported tolerances) and outperforms a path-based interaction-ignored algorithm and a link-based interaction-aware Frank–Wolfe algorithm in computational efficiency.