Temperature Estimation in a Battery String under Frugal Sensor Allocation

In electric vehicle applications, batteries are usually packed in modules to satisfy the energy and power demand. To facilitate the thermal management of a battery pack, a model-based observer could be designed to estimate the temperature distribution across the pack. Nevertheless, cost target in industry practice drives the number of temperature sensors in a pack to a number that is not sufficient to yield observability of all the temperature states. This paper focuses on formulating the observer design and sensor deployment strategy that could achieve the optimal observer performance under the frugal sensor allocation. The considered observer performance is the estimation errors induced by model and sensor uncertainty. The observer aims at minimizing the worst-case estimation errors under bounded model and sensor uncertainty. INTRODUCTION Thermal management is an important function of the battery management system (BMS) in electric vehicles (EVs). The electric current applied to the battery pack could be higher than 20 C-rate 1 for hybrid electric vehicles (FHEVs) operated in the Charge Sustaining (CS) mode. The aggressive battery usage may result in excessive temperature rise and a large temperature gradient across the cell, bringing challenges to thermal management. As far as safety is concerned, thermal runaway [1], ∗Address all correspondence to this author. 1C-rate refers to the magnitude of current, defined as the ratio between the current and the capacity of the battery in Ampere hour. which happens under extremely high temperature needs to be prevented. Furthermore, battery degradation is temperature dependent as the capacity and power fade is accelerated at high temperature [2–4]. Hence, the BMS needs to control battery temperature within designed ranges. Model-based temperature estimation [5–7] is a key enabler for effective thermal management, which could provide detailed information about temperature distribution across the battery pack with limited number of temperature sensors. In [8], a thermal model for a one-dimensional battery string of cylindrical cells is constructed based on a single-cell thermal model, which captures the surface and core temperature of the cell, and cell-tocell thermal interaction. Based on the thermal model and measurements of the surface temperatures of a few cells, an observer is designed to estimate all the temperature states in the string. These states include the surface and core temperature of all cells. It is highly desirable that the observer could i) significantly reduce the estimation errors under model uncertainty and ii) converge from erroneous initial estimation errors quickly. Since the thermal dynamics are stable, in an open-loop observer (without output feedback), the estimation error under model uncertainty will be bounded, and the errors caused by erroneous initial guess will die out eventually. However, because the thermal dynamics are slow, the eigenvalues of the model are close to the imaginary axis of the complex plane. The estimation errors could be large under model uncertainty, and the convergence from erroneous initial conditions would be slow. A closed-loop observer could guarantee i) and ii) if the model is fully observable. The numbers of temperature sensors needed for full observability have 1 Copyright © 2014 by ASME Proceedings of the ASME 2014 Dynamic Systems and Control Conference DSCC2014 October 22-24, 2014, San Antonio, TX, USA