Selective power: A joint planning and operation framework for phased vehicle-to-grid deployment

Large-scale deployment of Vehicle-to-Grid (V2G) technology is widely recognized as a key enabler for integrating electric-vehicle (EV) fleets into future power systems, yet the prohibitive upfront cost of bi-directional infrastructure, the uncertain behavioral response of EV users, and the operational risk borne by the platform render a network-wide, one-shot rollout economically infeasible. Motivated by this gap, we examine a pragmatic “phased zonal activation” paradigm in which a V2G service platform decides (i) in which geographical zones to invest fixed activation capital and (ii) how to operate the resulting hybrid charging network in real time through dynamic retail prices and V2G compensations. The problem is cast as a mixed-integer nonlinear programme that simultaneously embeds (a) binary activation variables with fixed costs, (b) a behavioral demand model that endogenously partitions the potential EV population into conventional and V2G participants, and (c) DC-power-flow constraints that secure the distribution grid. To overcome the pronounced non-convexity of the formulation we first linearize all complementarity equilibrium constraints by using tight big-M bounds and binary auxiliaries, obtaining a purely linear constraint set. The remaining nonlinearities, confined to the bilinear terms in the objective, are tackled by a bespoke Spatial Branch-and-Bound algorithm. Core ingredients of the solver include McCormick envelope relaxations, optimization-based bound tightening, Reformulation–Linearization cuts, and three primal heuristics that construct feasible solutions from each node’s LP relaxation. The algorithm provably converges to a ϵ -global optimum and, at intermediate nodes, supplies matching lower and upper bounds that certify solution quality. A case study calibrated on a stylized ten-zone urban grid demonstrates the value of selective deployment: relative to an all-or-nothing benchmark, optimal zonal activation increases platform profit by over 10.7%. The results further reveal a non-monotone diffusion pattern—core urban zones are activated en bloc owing to network synergies, after which coverage expands radially as activation costs fall. Finally, sensitivity analyses on infrastructure cost and user compensation elasticity confirm the robustness of the phased strategy and highlight equity implications for peripheral districts. • Propose a phased V2G deployment strategy co-optimized with grid-aware operations. • Capture user behavior and infrastructure economics in a unified MINLP framework. • Reveal how network topology shapes optimal V2G diffusion and spatial flexibility. • Develop a spatial branch-and-bound solver tailored for bilinear MINLP with binary variables.