Sustaining high inter-satellite link (ISL) throughput under intermittent solar harvesting is a fundamental challenge for LEO mega-constellations. Existing frameworks impose static power ceilings that ignore real-time battery state and comprehensive onboard power budgets, causing eclipse-period energy crises. Learning-based approaches capture battery dynamics but lack equilibrium guarantees and do not scale beyond small constellations. We propose the Hierarchical Battery-Aware Game (HBAG) algorithm, a unified game-theoretic framework for ISL power allocation that operates identically across finite and megaconstellation regimes. For finite constellations, HBAG converges to a unique variational equilibrium; as constellation size grows, the same distributed update rule converges to the mean field equilibrium without algorithm redesign. Comprehensive experiments on Starlink Shell A (172 satellites) show that HBAG achieves 100% energy sustainability rate (87.4 percentage points improvement over SATFLOW), eliminates eclipse-period battery depletion, maintains flow violation ratio below the 10% industry tolerance, and scales linearly to 5,000 satellites with less than 75 ms per-slot runtime.

翻译：在间歇性太阳能量收集条件下维持高星间链路（ISL）吞吐量是低轨巨型星座面临的基础性挑战。现有框架采用忽视实时电池状态和综合星上功率预算的静态功率上限，导致日食期能量危机。基于学习的方法虽能捕捉电池动态特性，但缺乏均衡保证且无法扩展至大型星座。我们提出分层电池感知博弈（HBAG）算法——一种统一的博弈论框架，适用于星间链路功率分配，在有限星座和巨型星座场景中均可同等运行。对于有限星座，HBAG收敛至唯一边际均衡；随着星座规模增长，同一分布式更新规则无需算法重新设计即可收敛至平均场均衡。在Starlink Shell A（172颗卫星）上的综合实验表明：HBAG实现100%能量可持续率（较SATFLOW提升87.4个百分点），消除日食期电池耗尽问题，将流量违规率控制在工业容忍阈值10%以下，并可在单时隙75毫秒运行时间内线性扩展至5000颗卫星。