Deterministic Electrochemical Battery State Estimation via Volume-Weighted Lithium Mass Hyperplane Projections: Achieving Zero-Drift SoC and Hard Real-Time BMS on Microcontrollers

Abstract

Precise on-board estimation of State of Charge (SoC) and State of Health (SoH) in lithium-ion battery management systems (BMS) remains a critical bottleneck in electric vehicle range predictability, fast-charging safety, and pack longevity. Conventional BMS firmware is polarized between two inadequate paradigms: empirical Equivalent Circuit Models (ECM) paired with Extended Kalman Filters (EKF), which evaluate rapidly but suffer from cumulative sensor bias drift (2%–6% SoC error over typical drive cycles) and lack physical diffusion dynamics during pulse acceleration; and full Doyle-Fuller-Newman (DFN/P2D) electrochemical models, whose coupled nonlinear differential-algebraic equations (DAEs) require iterative Newton-Raphson solvers and multi-second compute budgets that exceed the memory and compute capacity of automotive microcontrollers (e.g., ARM Cortex-M4/M7, Infineon AURIX TC397). In this paper, we resolve this dichotomy by introducing IdemBattery, a deterministic, zero-heap electrochemical estimator based on an Enhanced Single Particle Model with Thermal and Degradation Coupling (SPM-T) accelerated by algebraic idempotent metric projectors (Π2 = Π). Solid-phase lithium transport is discretized via conservative spherical finite volumes and inverted in closed form using an unconditionally stable O(N) tridiagonal Thomas algorithm. Interfacial charge transfer is evaluated analytically via inverse hyperbolic sine Butler-Volmer kinetics with second-order boundary layer flux extrapolation, completely bypassing nonlinear root-finding. To eliminate numerical discretization truncation leakage, we formulate the Volume-Weighted Lithium Mass Projector (ΠmassL2), which rigorously satisfies exact mass conservation while provably preserving internal spatial concentration gradients: ∂/∂r(ΠmassL2 cs) ≡ ∂cs/∂r. Boundary lattice saturation is resolved simultaneously via an exact O(N) continuous quadratic knapsack projector (Mmass ∩ Mbox). Physical current-sensor zero-offset bias (+80 mA) is rejected via a closed-loop observer (IdemObserver) with terminal voltage innovation feedback. Parametrized with peer-reviewed experimental data from Chen et al. (2020) for NMC-811/Graphite (LG M50) and Safari & Delacourt (2011) for LFP/Graphite, and incorporating Pinson-Bazant SEI degradation, IdemBattery achieves: An average execution latency of 60.49 μs per step on host CPU (σ = 48.34 μs, P99 = 148.91 μs, ≈ 15,000 instruction cycles on automotive MCUs, comfortably fitting within 10–100 ms BMS loop deadlines); Provable machine-precision lithium mass invariance (|ΔQ| / Q0 < 10−14); Total dynamic rejection of sensor bias drift; and Strictly zero dynamic heap memory allocation (0.0 bytes), making it architecturally compatible with safety-critical automotive Electronic Control Units (ECUs).