Capacity Subsidy Design for Battery Energy Storage Under Availability Opportunity Costs

The transition toward sustainable power systems with high shares of renewable energy requires flexible resources that can support both resource adequacy and broader sustainability goals. Battery energy storage is an important enabler of this transition, but capacity-linked subsidies may alter its operation when payments require peak-period availability. Reserving energy for this obligation sacrifices spot market arbitrage value, and so the subsidy needed to induce capacity commitment depends on an endogenous availability opportunity cost. This study aims to characterize that trade-off and derive a practical rule for subsidy calibration. We formulate an annual unified capacity commitment model in which storage selects one committed capacity across seasonal representative days while optimizing hourly dispatch subject to peak-period energy reservation constraints. The model is reduced to a one-dimensional problem that balances linear subsidy revenue against a convex, piecewise affine opportunity cost function, yielding forward commitment thresholds and an inverse rule from a target commitment to the minimum subsidy required to induce it. In a representative system calibrated for Gansu, commitment remains zero below 0.300s0, reaches 46.3% of maximum capacity at 0.325s0, and becomes full at 0.550s0. The average opportunity cost threshold is 0.424s0. A target of 0.50Dmax requires 0.525s0 but implements 0.780Dmax; at high subsidies, normalized throughput falls from 2.001 to 1.298, and the spot revenue share declines from 1.000 to 0.265. These results show that effective capacity subsidy design must account for opportunity cost thresholds, staged commitment, over-procurement, and reduced spot market participation.