  This manuscript presents an algorithm for individual Lithium-ion (Li-ion)
battery cell state of charge (SOC) estimation when multiple cells are connected
in parallel, using only terminal voltage and total current measurements. For
battery packs consisting of thousands of cells, it is desirable to estimate
individual SOCs by only monitoring the total current in order to reduce sensing
cost. Mathematically, series connected cells yield dynamics given by ordinary
differential equations under classical full voltage sensing. In contrast,
parallel connected cells are evidently more challenging because the dynamics
are governed by a nonlinear descriptor system, including differential equations
and algebraic equations arising from voltage and current balance across cells.
An observer with linear output error injection is formulated, where the
individual cell SOCs and local currents are locally observable from the total
current and voltage measurements. The asymptotic convergence of differential
and algebraic states is established by considering local Lipschitz continuity
property of system nonlinearities. Simulation results on LiNiMnCoO$_2$/Graphite
(NMC) cells illustrate convergence for SOCs, local currents, and terminal
voltage.
