Comparison of Kalman filter and H-infinity filter for Battery State of Charge Estimation with a Detailed Validation Method

Correct and reliable determination of the state of charge (SOC) of a lithium-ion battery is essential in today’s applications. The SOC can be determined in different ways; there are simple methods such as integrating the current over time (Coulomb counting) or mathematical filters, in particular the Kalman filter and the H-infinity filter. In addition to the measured values, the latter two also require a battery model in which the behavior of the battery is described under different temperatures, states of charge and currents. The most common variants of the two filter techniques were compared: Extended, Adaptive Extended, Dualextended and, for the Kalman filter, the Unscented Kalman filter. In this paper we present a comparison method in order to objectively evaluate the different methods and thus make a suitable decision for the respective application. In addition, the computing power of the individual methods is evaluated on a digital signal processor. The comparison method uses various criteria and a rating scale. The individual criteria are: Accuracy of estimation, temperature stability, transient behavior, residual charge determination and drift behavior. Each state of charge algorithm undergoes the same test procedures and is evaluated on the basis of the criteria. Three test procedures are used: a test for short-term behavior with low dynamics, a test for short-term behavior and strong dynamics and a test for long-term behavior with different temperatures. Based on the digital signal processor (DSP) implementation, it was shown that the runtimes depend on the number of RC elements in the battery model. In all tests, the Kalman filter managed with fewer processor cycles than its H-Infinity counterpart. The greatest deviations were observed at low temperatures. Overall, both filters ran stably and the tests showed that neither filter was clearly superior to the other.