This paper studies the efficiency of battery storage operations in electricity markets by comparing the social welfare gain achieved by a central planner to that of a decentralized profit-maximizing operator. The problem is formulated in a generalized continuous-time stochastic setting, where the battery follows an adaptive, non-anticipating policy subject to periodicity and other constraints. We quantify the efficiency loss by bounding the ratio of the optimal welfare gain to the gain under profit maximization. First, for linear price functions, we prove that this ratio is tightly bounded by $4/3$. We show that this bound is a structural invariant: it is robust to arbitrary stochastic demand processes and accommodates general convex operational constraints. Second, we demonstrate that the efficiency loss can be unbounded for general convex price functions, implying that convexity alone is insufficient to guarantee market efficiency. Finally, to bridge these regimes, we analyze monomial price functions, where the degree controls the curvature. For specific discrete demand scenarios, we demonstrate that the ratio is bounded by $2$, independent of the degree.

翻译：本文通过比较中央规划者与分散式利润最大化运营商所实现的社会福利增益，研究电池储能在电力市场中的运行效率。该问题在广义连续时间随机框架下建模，其中电池遵循适应性的非预期策略，并受周期性及其他约束限制。我们通过界定最优福利增益与利润最大化下增益之比来量化效率损失。首先，针对线性价格函数，我们证明该比值严格上界为$4/3$。我们表明此上界具有结构不变性：它对任意随机需求过程具有鲁棒性，并能容纳一般凸运行约束。其次，我们证明对于一般凸价格函数，效率损失可能无界，这意味着仅凸性不足以保证市场效率。最后，为衔接这两种情形，我们分析了单项式价格函数，其中次数控制曲率。针对特定离散需求场景，我们证明该比值以$2$为上界，且与次数无关。