End-to-End Battery Dispatch with Exact Rainflow Degradation via Mixed-Integer Differentiable Predictive Control

Abstract

Optimal dispatch of battery energy storage systems requires balancing energy arbitrage against cycle-induced degradation, which is accurately quantified through rainflow cycle counting. However, rainflow's combinatorial, nondifferentiable algorithm is incompatible with both convex optimization and gradient-based neural network training. We present a self-supervised mixed-integer differentiable predictive control framework that trains neural policies directly on exact rainflow degradation through a novel differentiable rainflow layer combining exact gradients at state-of-charge extrema with dense proxy gradients on incremental changes, enabling stable end-to-end training while preserving true degradation physics. A mixed-integer differentiable architecture enforces power balance, dynamics, and mode exclusivity, with a safety filter guaranteeing constraint satisfaction. We evaluate the framework on 3,650 real battery-day scenarios (a 10-battery fleet over 365 days) spanning three utility regions (SDG&E California, Xcel Energy Colorado, APS Arizona) with diverse time-of-use pricing structures. A single-battery trained policy achieves a 0.35% performance gap on its training distribution with over 200x speedup, while fleet-wide training generalizes across all households and utility regions, achieving a 3.33% performance gap with 564x computational speedup (62 seconds vs. 9.7 hours) and 100% feasibility. The millisecond-scale inference reduces computation by over two orders of magnitude compared to mixed-integer solvers, enabling practical deployment at scale.