Identification of the dynamic model of second-life lithium-ion cells through Subspace System Identification and similarity transformation

Abstract

When lithium-ion batteries (LiBs) reach the end of their first useful life in electric vehicles (EVs), they can still be used in applications with lower power demands, a process known as second-life. However, to ensure that LiBs – or cells – removed from EVs operate safely, efficiently, and reliably in a second application, various tests and procedures must be applied to study their internal conditions. Some information about the conditions of the lithium-ion cells can be obtained from the parameters of its equivalent circuit model(ECM). However, the tests to obtain blackthe ECM parameters usually require taking the LiBs out of service and testing their cells in laboratory benches with special equipment, which is costly and time-consuming. Therefore, this work proposes a methodology to identify the ECM of lithium-ion cells based on Subspace System Identification (SSI) methods. This procedure can be executed online, while the LiBs are being used in the specified application. SSI methods have been widely adopted to identify the dynamic model of lithium-ion cells, but they return models without a physical meaning, called non-parametric models. This type of model cannot be used to address the internal conditions of a lithium cell, because its parameters do not have any physical meaning. To solve this problem, a novel method for estimating the lithium-ion cell physical parameters, in the ECM format, and from its non-parametric model, is proposed in this work. The procedure is based on similarity transformation techniques and special characteristics of the ECM. To validate the proposed method, nine samples of cells from the same manufacturer were studied. These cells had distinct degradation conditions and were removed from heavy-duty EVs at the end of their first life. The results showed that: (a) a good approximation between the identified model voltage output and the actual cells’ experimental voltage output was achieved, with root mean square error values as small as 2.26 mV; (b) it was possible to identify the ECM of the tested cells and their parameters using the proposed similarity transformation; and (c) the identified parameters can be used to detect the internal conditions of the cells.