  This manuscript presents an algorithm for individual Lithium-ion (Li-ion)
battery cell state of charge (SOC) estimation in a large-scale battery pack
under minimal sensing, where only pack-level voltage and current are measured.
For battery packs consisting of up to thousands of cells in electric vehicle or
stationary energy storage applications, it is desirable to estimate individual
cell SOCs without cell local measurements in order to reduce sensing costs.
Mathematically, pure series connected cells yield dynamics given by ordinary
differential equations under classical full voltage sensing. In contrast,
parallel--series connected battery packs are evidently more challenging because
the dynamics are governed by a nonlinear differential--algebraic equations
(DAE) system. The majority of the conventional studies on SOC estimation for
battery packs benefit from idealizing the pack as a lumped single cell which
ultimately lose track of cell-level conditions and are blind to potential risks
of cell-level over-charge and over-discharge. This work explicitly models a
battery pack with high fidelity cell-by-cell resolution based on the
interconnection of single cell models, and examines the observability of
cell-level state with only pack-level measurements. A DAE-based state observer
with linear output error injection is formulated, where the individual cell SOC
and current can be reconstructed from minimal number of pack sensing. The
mathematically guaranteed asymptotic convergence of differential and algebraic
state estimates is established by considering local Lipschitz continuity
property of system nonlinearities. Simulation results for Graphite/NMC cells
illustrate convergence for cell SOCs, currents, and voltages.
