Hierarchical Battery-Aware Game Algorithm for ISL Power Allocation in LEO Mega-Constellations

Abstract

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.

Figures (4)

• Figure 1: Scenario illustration of battery-aware ISL operation in LEO: illuminated satellites harvest solar energy and maintain high-power links, while eclipse-side satellites reduce power or shut down ISLs as state-of-charge decreases.
• Figure 2: Performance comparison across five methods on Starlink Shell A (medium-high traffic, $\theta=0.38$, 10 independent runs). (a) Energy Sustainability Rate (ESR): HBAG and SMFG-adapted achieve 100% (zero depletion events), while SATFLOW-L drops to 12.6% due to eclipse-period battery exhaustion. (b) Energy Efficiency (EE): SMFG-adapted leads at 4.18 Mbit/kJ, followed by HBAG at 3.96 Mbit/kJ (5.3% gap). Error bars represent 95% confidence intervals via bootstrap resampling.
• Figure 3: Battery SOC evolution for a representative satellite over one 90-minute orbital period. Illumination phase (0--55 min): All methods charge the battery via solar harvesting. SATFLOW-L (blue) reaches $C^{B}_{max}$ by $t \approx 54$ min. Eclipse phase (55--90 min): SATFLOW-L continues at static power $P_{max}$, depleting to 0% by $t=89$ min and triggering emergency shutdown (marked by red cross). HBAG (purple) dynamically reduces power via equation \ref{['eq:dynpower']}, maintaining SOC $> C^{B}_{min}$ (10% threshold, red dotted line) throughout, with final SOC $\approx 27\%$ (107.6 kJ). MAAC-IILP (green) and DeepISL (orange) show intermediate behavior. SMFG-adapted (cyan) closely tracks HBAG. Vertical gray line marks eclipse onset. Shaded regions represent 95% confidence bands across 10 independent runs (barely visible due to low variance).
• Figure 4: Combined results for Experiments 3--5. (a) Sensitivity to eclipse fraction: HBAG maintains ESR $\geq 93.4\%$ across all $\theta$, whereas SATFLOW-L drops below 20% for $\theta \geq 0.2$, validating Proposition \ref{['prop:deviation']}. (b) Convergence trajectory: smoothed residual (thick purple) tracks the $\mathcal{O}(1/k)$ reference line (dashed gray), reaching plateau $\approx 0.15$ by $k=200$, validating Theorem \ref{['thm:convergence']}. (c) Scalability: runtime grows linearly from 2.79 ms (172 sats) to 47.42 ms (3168 sats), with fitted slope $1.49 \times 10^{-5}$ ms/sat, confirming $\mathcal{O}(n_t)$ complexity (Proposition \ref{['prop:complexity']}).

Theorems & Definitions (23)

• Remark 1
• Remark 2: Role of hard vs. soft constraint
• Definition 1: Variational Equilibrium facchinei2007vi
• Remark 3: NE under separable strategy sets
• Remark 4
• Definition 2: Exact Potential Game monderer1996potential
• Theorem 1: Exact Potential Game and Unique Variational Equilibrium
• Lemma 1: Strong Concavity of Potential Function
• proof : Proof sketch
• Remark 5: Intuition behind Theorem \ref{['thm:potential']}