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Renewable energy generation, vehicle electrification, and smart grids rely critically on energy storage devices for enhancement of operations, reliability, and efficiency. Battery systems consist of many battery cells, which have different characteristics even when they are new, and change with time and operating conditions due to a variety of factors such as aging, operational conditions, and chemical property variations. Their effective management requires high fidelity models. This paper aims to develop identification algorithms that capture individualized characteristics of each battery cell and produce updated models in real time. It is shown that typical battery models may not be identifiable, unique battery model features require modified input/output expressions, and standard least-squares methods will encounter identification bias. This paper devises modified model structures and identification algorithms to resolve these issues. System identifiability, algorithm convergence, identification bias, and bias correction mechanisms are rigorously established. A typical battery model structure is used to illustrate utilities of the methods.