Optimization problem for in-situ heat generation estimation in lithium-ion batteries

Abstract

Knowledge of the thermal behavior of a lithium-ion battery is a key factor in ensuring its optimum performance. This paper presents a novel and non-intrusive method for accurately estimating the heat generated inside a battery during operation, based solely on surface temperature measurements. The originality of the approach lies in its ability to retrieve the total internal heat sources over time, without any prior assumptions regarding their profile, number, or spatial distribution across the cell thickness by solving an optimization problem with a regularized objective function, where the input is the measured surface temperature, and the output is the time-dependent internal heat generation. This method therefore combines simple and in-situ instrumentation, without requiring other characterization devices such as calorimeters, with a powerful non-iterative estimation method. The results obtained both numerically and experimentally show high accuracy over a wide range of conditions. In numerical tests, the relative error on the total estimated energy remained below 0.03% in most cases where effective thermal properties of the cell are known. To account for uncertainties in these effective properties, an enthalpic formulation was used, and the error in the estimated total enthalpy remained below 0.3% despite significant initial biases in the input thermal properties. Experimental validation using a dummy pouch cell with a controlled heating element confirmed these results, with relative total energy estimation errors not exceeding 8.2% for purely theoretical patterns and as low as 1.6% for a heat generation profile from a real calorimetric experiment, demonstrating the reliability and robustness of the proposed method.