Peukert's Law of a Lead-Acid Battery Simulated by a Mathematical Model

Abstract

The Peukert's law is the most widely used empirical equation to represent the rate-dependent capacity of the lead-acid battery (LAB), mainly because it is easy to use, accurate, and applicable to a wide temperature range. In this work, we show that the Peukert behavior can be properly simulated by a mathematical model with only three rate-dependent parameters (specific active surface area, tortuosity exponent of the electrode morphology and the maximum capacity density). In this study, the analysis of the rate-dependent parameters of a flooded LAB provides an interesting case of study to understand the end of discharge (EOD) behavior of the battery at various rates, which constitutes the Peukert behavior of the LAB. Although at high rates, an exhaustion of sulfuric acid may occur in the positive plate as a result of acid transport limitation, the main factor that determines the EOD behavior is the change of the active surface area which is underpinned by the clogging of the pores due to sulfation of the electrodes, preventing the discharge reaction to occur at places where the active material might still be available.