电池放电的有限时间热力学：功率-效率权衡与优化
Finite-Time Thermodynamics of Battery Discharging: Power-Efficiency Trade-Off and Optimization
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中文总结 AI 辅助
研究电池放电中功率与能量转换效率的权衡，通过分析得出抛物线包络及最大功率效率，制定多阶段恒流放电计划并求解最优策略，量化内阻对运行边界的影响，为电池管理系统调度层建立热力学基线。
中文摘要 AI 辅助
电池放电受输出功率与能量转换效率之间基本权衡的制约，本文证明这种权衡普遍产生抛物线包络\(P\propto\eta(1 - \eta)\)，最大功率时效率为二分之一。制定多阶段恒流放电计划并求解最优策略，量化内阻影响，为电池管理系统调度层建立严格热力学基线。
英文摘要
Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope $P\proptoη(1-η)$. The efficiency at maximum power is exactly one half, mirroring the well-known half-Carnot limit in finite-time thermodynamics. To extend this bound into practical operational rules, we formulate a multistage constant-current discharging (MSCD) schedule subject to simultaneous real-time load demands and a global discharging deadline. Analytical resolution via the Karush--Kuhn--Tucker conditions reveals a remarkably compact optimal policy: $I_{i}^{\star}=\max(I_{i}^{-},I_{0})$. Under this rule, stages limited by external demand run exactly at their minimum required currents, while all remaining stages are elevated to a uniform baseline $I_{0}$ fixed by the deadline constraint. By tracing the dissipation--time Pareto front, we quantify how internal resistance shifts the operational boundaries and sharpens the trade-off corner. This analysis establishes a rigorous thermodynamic baseline for the scheduling layer of battery management systems, offering natural extensions to nonlinear models incorporating temperature and state-of-charge dependencies.
