Time-domain fitting of battery electrochemical impedance models

Electrochemical impedance spectroscopy (EIS) is an effective technique for diagnosing the behaviour of electrochemical devices such as batteries and fuel cells, usually by fitting data to an equivalent circuit model (ECM). The common approach in the laboratory is to measure the impedance spectrum of a cell in the frequency domain using a single sine sweep signal, then fit the ECM parameters in the frequency domain. This paper focuses instead on estimation of the ECM parameters directly from time-domain data. This may be advantageous for parameter estimation in practical applications such as automotive systems including battery-powered vehicles, where the data may be heavily corrupted by noise. The proposed methodology is based on the simplified refined instrumental variable for continuous-time fractional systems method ('srivcf'), provided by the Crone toolbox [1,2], combined with gradient-based optimisation to estimate the order of the fractional term in the ECM. The approach was tested first on synthetic data and then on real data measured from a 26650 lithium-ion iron phosphate cell with low-cost equipment. The resulting Nyquist plots from the time-domain fitted models match the impedance spectrum closely (much more accurately than when a Randles model is assumed), and the fitted parameters as separately determined through a laboratory potentiostat with frequency domain fitting match to within 13%

Time-domain fitting of battery electrochemical impedance models

Electrochemical impedance spectroscopy (EIS) is an effective technique for diagnosing the behaviour of electrochemical devices such as batteries and fuel cells, usually by fitting data to an equivalent circuit model (ECM). The common approach in the laboratory is to measure the impedance spectrum of a cell in the frequency domain using a single sine sweep signal, then fit the ECM parameters in the frequency domain. This paper focuses instead on estimation of the ECM parameters directly from time-domain data. This may be advantageous for parameter estimation in practical applications such as automotive systems including battery-powered vehicles, where the data may be heavily corrupted by noise. The proposed methodology is based on the simplified refined instrumental variable for continuous-time fractional systems method ('srivcf'), provided by the Crone toolbox [1,2], combined with gradient-based optimisation to estimate the order of the fractional term in the ECM. The approach was tested first on synthetic data and then on real data measured from a 26650 lithium-ion iron phosphate cell with low-cost equipment. The resulting Nyquist plots from the time-domain fitted models match the impedance spectrum closely (much more accurately than when a Randles model is assumed), and the fitted parameters as separately determined through a laboratory potentiostat with frequency domain fitting match to within 13%

Identifiability of Generalized Randles Circuit Models

The Randles circuit (including a parallel resistor and capacitor in series with another resistor) and its generalized topology have widely been employed in electrochemical energy storage systems, such as batteries, fuel cells, and supercapacitors, also in biomedical engineering, for example, to model the electrode–tissue interface in electroencephalography and baroreceptor dynamics. This paper studies identifiability of generalized Randles circuit models, that is, whether the model parameters can be estimated uniquely from the input–output data. It is shown that generalized Randles circuit models are structurally locally identifiable. The condition that makes the model structure globally identifiable is then discussed. Finally, the estimation accuracy with respect to noise-free, noisy, zero-mean, and nonzero-mean data is evaluated through extensive simulations. The existing tradeoff between the estimation of Warburg term and other parameters by using zero- and nonzero-mean data is fully discussed

Bayesian inference in non-Markovian state-space models with applications to battery fractional order systems

Battery impedance spectroscopy models are given by fractional order (FO) differential equations. In the discrete-time domain, they give rise to state-space models where the latent process is not Markovian. Parameter estimation for these models is therefore challenging, especially for non-commensurate FO models. In this paper, we propose a Bayesian approach to identify the parameters of generic FO systems. The computational challenge is tackled with particle Markov Chain Monte Carlo methods, with an implementation specifically designed for the non-Markovian setting. Two examples are provided. In a first example, the approach is applied to identify a battery commensurate FO model with a single constant phase element (CPE) by using real data. We compare the proposed approach to an instrumental variable method. Then we consider a non-commensurate FO model with more than one CPE and synthetic datasets, investigating how the proposed method enables the study of various effects on parameter identification, such as the data length, the magnitude of the input signal, the choice of prior, and the measurement noise