Bid Lattices and the Value of Flexibility:A Granularity Ratio for Capacity Markets

Abstract

Capacity markets award reserve in discrete increments, yet valuation models almost always treat the awarded quantity as continuous. We show that the size dependence of the resulting error is organised by one dimensionless number, the granularity ratio rho = delta/P of award increment to installed power: the joint energy-and-reserve problem is positively homogeneous, so, at fixed market data and operating parameters, asset size enters per-megawatt revenue only through rho and storage duration. Three structural results follow. Rounding a continuous award down to the lattice is always feasible, so the valuation error is O(rho) and its upper bound falls as the inverse of asset size. The largest feasible award is P rho floor(1/rho), so up to half of a connection can be structurally unsellable, worst just below twice the increment. Pledging the whole connection forces a zero net grid position for the entire product, converting a partial capacity commitment into exclusion from the energy market. On 943 days of French day-ahead and frequency containment reserve settlement prices, a 1 MW two-hour battery priced with a continuous award is worth 4.2% more than the same asset on the 1 MW French lattice, and 77% of that difference is displaced arbitrage rather than foregone capacity. The bias is not monotone in size: the largest value on our grid is 21.5% at rho = 0.505. Bid granularity is therefore a market-design variable with a size-dependent incidence, and the measured gap is at once a modelling error, a sizing rule, and a ceiling on aggregation value.