Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner's expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency deviation trajectories in a functional uncertainty set that encodes applicable legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem non-convex. Methodology/results: By exploiting a total unimodularity property of the uncertainty set and an exact linear decision rule reformulation, we prove that this non-convex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. Managerial implications: We find that the prevailing penalties for non-delivery of promised regulation power are too low to incentivize vehicle owners to honor the delivery guarantees given to grid operators.
Citation
Dirk Lauinger, François Vuille, Daniel Kuhn. Reliable frequency regulation through vehicle-to-grid: Encoding legislation with robust constraints. Manufacturing & Service Operations Management, Articles in Advance, 1-17, 2024, https://doi.org/10.1287/msom.2022.0154.