A Nash Equilibrium-Based Strategy for Optimal DG and EVCS Placement and Sizing in Radial Distribution Networks

Distribution System Operators (DSOs) increasingly need planning tools that coordinate utility-influenced assets—such as electric-vehicle charging stations (EVCS) and voltage-support resources—with customer-sited distributed generation (DG). We present a Nash-equilibrium-based Iterative Best Response Algorithm (IBRA-NE) for joint planning of DG and EVCS in radial distribution networks. The framework supports two applicability modes: (i) a DSO-plannable mode that co-optimizes EVCS siting/sizing and utility-controlled reactive support (DG operated as VAR resources or functionally equivalent devices), and (ii) a customer-sited mode that treats DG locations as fixed while optimizing DG reactive set-points/sizes and EVCS siting. The objective minimizes network losses and voltage deviation while incorporating deployment costs and EV charging service penalties, subject to standard operating limits. A backward/forward sweep (BFS) load flow with Monte Carlo simulation (MCS) captures load and generation uncertainty; a Bus Voltage Deviation Index (BVDI) helps identify weak buses. On the EEU 114-bus system, the method reduces base-case losses by up to 57.9% and improves minimum bus voltage from 0.757 p.u. to 0.931 p.u.; performance remains robust under a 20% load increase. The framework explicitly accommodates regulatory contexts where DG siting is customer-driven by treating DG locations as fixed in such cases while optimizing EVCS siting and sizing under DSO planning authority. A mixed scenario with 5 DGs and 3 EVCS demonstrates coordinated benefits and convergence properties relative to PSO, GWO, RFO, and ARFO. Additionally, the proposed algorithm is also tested on the IEEE 69-bus system and results in acceptable performance. The results indicate that game-theoretic coordination, applied in a manner consistent with regulatory roles, provides a practical pathway for DSOs to plan EV infrastructure and reactive support in networks with uncertain DER behavior.