AI 中文总结
该研究针对容量市场投标离散性与估值模型连续性的偏差，提出粒度比ρ，分析其对储能资产价值的影响，发现连续授予定价的1兆瓦两小时储能价值比法国格点高4.2%，偏差随ρ非单调变化。
AI 中文摘要
容量市场以离散增量授予备用容量，但估值模型几乎总是将授予数量视为连续变量。我们表明，由此产生的误差的规模依赖性由一个无量纲数组织，即粒度比ρ=Δ/P，其中Δ是授予增量，P是装机功率：能量与备用联合问题是正齐次的，因此在固定市场数据和运行参数下，资产规模仅通过ρ和储能时长影响每兆瓦收入。由此得出三个结构性结果：将连续授予向下舍入到格点总是可行的，因此估值误差为O(ρ)，其上限随资产规模的倒数下降；最大可行授予为Pρ⌊1/ρ⌋，因此最多有一半的连接在结构上不可出售，最坏情况恰好在增量的两倍以下；承诺整个连接会迫使整个产品的净电网位置为零，将部分容量承诺转化为退出能源市场。基于法国日前市场和频率 containment 备用结算价格的943天数据，1兆瓦两小时储能资产按连续授予定价的价值比同一资产在1兆瓦法国格点上的价值高4.2%，且该差异的77%是套利转移而非放弃的容量；偏差并非随规模单调变化，在ρ=0.505时，我们格点上的最大价值为21.5%。因此，投标粒度是具有规模依赖性影响的市场设计变量，所测差距既是建模误差、规模规则，也是聚合价值的上限。
英文摘要
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.
Comments8 pages, 2 figures, 2 tables. Eight numbered results with proofs; 42 solved cases on 943 days of French day-ahead and FCR settlement prices
