Piecewise Linear Approximation of Battery Open-Circuit Voltage Characteristics Using Dynamic Programming

An open-circuit voltage (OCV) model, which represents OCV as a function of state of charge (SOC), is essential for estimating the state of a battery. Typically, the OCV-SOC characteristic is approximated using empirical functions, such as polynomials or lookup tables, and stored in a battery management system (BMS). However, polynomial approximations have several limitations: they are sensitive to floating-point errors, can be noninvertible, and require a high-precision computing system for numerical inverse lookups (determining the SOC for a given OCV). Moreover, many OCV models fail to maintain the monotonicity of the OCV-SOC relationship, especially in resource-constrained environments. While table-based (or piecewise linear) approaches have been explored, existing methods often fall short of preserving the accuracy of the OCV-SOC curve with a minimal number of breakpoints. This article introduces a novel dynamic programming approach to model the OCV-SOC characteristic as piecewise line segments. Compared to existing piecewise models, the proposed approach is more resource-efficient in systematically reducing the required table breakpoints while maintaining optimal accuracy. Experimental validation across various lithium-ion chemistries at four ambient temperatures consistently demonstrated a root mean square error below 5 mV. Additionally, differential feature extraction and segmented correlation analysis highlight the model’s effectiveness in estimating the battery’s state of health (SOH).