Determination of the lead-acid battery's dynamic response using Butler-Volmer equation for advanced battery management systems in automotive applications

Micro-hybrid vehicles (μH) are currently starting to dominate the European market and seize constantly growing share of other leading markets in the world. On the one hand, the additional functionality of μH reduces the CO2 emissions and improves the fuel economy, but, on the other hand, the additional stress imposed on the lead-acid battery reduces significantly its expected service life in comparison to conventional vehicles. Because of that μH require highly accurate battery state detection solutions. They are necessary to ensure the vehicle reliability requirements, prolong service life and reduce warranty costs. This paper presents an electrical model based on Butler-Volmer equation. The main novelty of the presented approach is its ability to predict accurately dynamic response of a battery considering a wide range of discharge current rates, state-of-charges and temperatures. Presented approach is fully implementable and adaptable in state-of-the-art low-cost platforms. Additionally, shown results indicate that it is applicable as a supporting tool for state-of-charge and state-of-health estimation and scalable for the different battery technologies and sizes. Validation using both static pulses and dynamic driving profile resulted in average absolute error of 124 mV regarding cranking current rate of 800 A respectively.