State of Charge Estimation of Parallel Connected Battery Cells via Descriptor System Theory

Abstract

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. This paper designs and analyzes an observer with linear output error injection, 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.

Resolving Kirchhoff’s Laws for Parallel Li-Ion Battery Pack State-Estimators

“…The results presented here are in many ways an extension of the recent results of [24] from some of the authors. In [24], an observer was designed for a DAE model of a parallel connected pack but the DAE element of this model introduced severe complexity into the analysis of the model's vector field and the conditions guaranteeing convergence of the observer error. This paper resolves these issues by exploiting the analytic expression for the parallel branch current.…”

“…DAEs models can be significantly more complex than those described by ordinary differential equations (ODEs), so most studies on parallel packs numerically compute solutions to Kirchhoff's laws before projecting the state of the index 1 DAE down into an ODE. Examples of this approach include the iterative scheme of [8], the frequency domain approximations of [7] and the numerical matrix inversion methods of studies like [24] and [6] which was augmented with a thermal model in [18]. In contrast, this work obtains an ODE model by providing an analytical solution to Kirchhoff's laws for n-cells connected parallel.…”

“…In contrast, this work obtains an ODE model by providing an analytical solution to Kirchhoff's laws for n-cells connected parallel. Thus, the main result of this work can be thought of as providing an analytical solution, in terms of the various cell resistances, to the branch current equations defined by Kirchhoff's laws, in place of the numerical solutions in benchmark studies like (20) of [24] and (15) of [6]. This approach follows along a recent direction in battery pack modelling, including the cell merging approach of [12], and generalises similar efforts like [14], [17] by relaxing some of the restrictive modelling assumptions, like the linearity of the open cell voltage [14], as well as providing a more involved model formulation that additionally includes the important state-of-charge dynamics than [17].…”

“…There are two main reasons for this: 1. It is widely assumed that cells in parallel have the same state-of-charge because of this setup's natural selfbalancing [25] but the simulations of [24] suggest this may not always hold; 2. The need to resolve the branch currents makes parallel pack models more complex to analyse.…”

State feedback H ∞ control for a class of affine nonlinear singular systems: Input restricting approach

“…Singular models are the models in which two sets of differential equations and algebraic equations are simultaneously used to describe the dynamics of different systems. These models, including conventional state-space models as a special case, provide a novel analysis and design tool in various real world applications covering several theoretical fields like modern control techniques [12][13][14][15][16][17], as well as a wide range of practical systems including electrical and power systems [18][19][20], robotic and mechanical systems [21,22], biological systems [23][24][25] and chemical processes [26].…”