Fractional Equivalent Circuit Research Articles

A Finite Memory Approach Applied to Verified Pseudo State Estimation of Fractional Models of Lithium-Ion Batteries

Fractional equivalent circuit models have been used in numerous publications to represent long-term memory phenomena of the charging/discharging behavior of Lithium-ion batteries. However, despite the fact that fractional models allow for capturing (infinite horizon) memory properties, the same feature also complicates the numerical evaluation. This is especially critical in cases, in which state estimation procedures are implemented that need to be executed in real time. For this type of applications, it is necessary that the execution time in each time step is bounded a-priori and that it does not grow over time. For that purpose, classical simulation approaches exploit, for example, Grünwald-Letnikov schemes with a finite length of previous state information. However, truncating the memory window without considering the arising errors may lead to wrong state estimates. This is especially critical if interval observers are designed which are meant to include the sets of reachable states with certainty.

Quantification of Lithium Plating in Lithium-Ion Batteries Based on Impedance Spectrum and Artificial Neural Network

Accurate evaluation of the health status of lithium-ion batteries must be deemed as of great significance, insofar as the utility and safety of batteries are of concern. Lithium plating, in particular, is notoriously known to be a chemical reaction that can cause deterioration in, or even fatal hazards to, the health of lithium-ion batteries. Electrochemical impedance spectroscopy (EIS), which has distinct advantages such as being fast and non-destructive over its competitors, suffices in detecting lithium plating and thus has been attracting increasing attention in the field of battery management, but its ability of assessing quantitatively the degree of lithium plating remains largely unexplored hitherto. On this point, this work seeks to narrow that gap by proposing an EIS-based method that can quantify the degree of lithium plating. The core conception is to eventually circumvent the reliance on state-of-health measurement, and use instead the impedance spectrum to acquire an estimate on battery capacity loss. To do so, the effects of solid electrolyte interphase formation and lithium plating on battery capacity must be first decoupled, so that the mass of lithium plating can be quantified. Then, based on an impedance spectrum measurement, the parameters of the fractional equivalent circuit model (ECM) of the battery can be identified. These fractional ECM parameters are received as inputs by an artificial neural network, which is tasked with establishing a correspondence between the model parameters and the mass of lithium plating. The empirical part of the work revolves around the data collected from an aging experiment, and the validity of the proposed method is truthfully attested by dismantling the batteries, which is otherwise not needed during the actual uptake of the method.

Fractional equivalent circuit model and parameter identification of reactance components in high-frequency operation

PurposeThe purpose of this paper is to find a simpler model for the reactance components in the high-frequency range on the premise of ensuring the accuracy.Design/methodology/approachIn this paper, based on the fractional calculus theory and the traditional integer-order model, a reactance model suitable for high frequency is constructed, and the mutation cross differential evolution algorithm is used to identify the parameters in the model.FindingsBy comparing the integer-order model, high-frequency fractional-order model and the actual impedance characteristic curve of inductance and capacitance, it is verified that the proposed model can more accurately reflect the high-frequency characteristics of inductance and capacitance. The simulation and experimental results show that the oscillator constructed based on the proposed model can analyze the frequency and output waveform of the oscillator more accurately.Originality/valueThe model proposed in this paper has a simple structure and contains only two parameters to be identified. At the same time, the model has high precision. The fitting errors of impedance curve and phase-frequency characteristic curve are less than 5%. Therefore, the proposed model is helpful to improve the simplicity and accuracy of circuit system analysis and design.

Estimation for Battery State of Charge Based on Temperature Effect and Fractional Extended Kalman Filter

The electric vehicle has become an important development direction of the automobile industry, and the lithium-ion power battery is the main energy source of electric vehicles. The accuracy of state of charge (SOC) estimation directly affects the performance of the vehicle. In this paper, the first order fractional equivalent circuit model of a lithium iron phosphate battery was established. Battery capacity tests with different charging and discharging rates and open circuit voltage tests were carried out under different ambient temperatures. The conversion coefficient of charging and discharging capacity and the simplified open circuit voltage model considering the hysteresis characteristics of the battery were proposed. The parameters of the first order fractional equivalent circuit model were identified by using a particle swarm optimization algorithm with dynamic inertia weight. Finally, the recursive formula of a fractional extended Kalman filter was derived, and the battery SOC was estimated under continuous Dynamic Stress Test (DST) conditions. The results show that the estimation method has high accuracy and strong robustness.

A Simplified Fractional Order Equivalent Circuit Model and Adaptive Online Parameter Identification Method for Lithium-Ion Batteries

In order to improve the battery management system performance and enhance the adaptability of the system, a fractional order equivalent circuit model of lithium-ion battery based on electrochemical test was established. The parameters of the fractional order equivalent circuit model are identified by the least squares parameter identification method. The least squares parameter identification method needs to rely on the harsh test conditions of the laboratory, and the parameter identification result is static; it cannot adapt to the characteristics of the lithium battery under dynamic conditions. Taking into account the dynamic changes of lithium batteries, a parameter adaptive online estimation algorithm for fractional equivalent circuit model is proposed. Based on the theory of fractional order calculus and indirect Lyapunov method, the stability and convergence of the estimator are analyzed. Finally, simulation experiments show that this method can continuously estimate the parameters of the fractional order equivalent circuit under UDDS conditions.

Modeling Study for Li-ion Batteries Considering High-frequency Inductance Characteristics Based on Electrochemical Impedance Spectroscopy

As a non-destructive test method, electrochemical impedance spectroscopy (EIS) has been widely used in the analysis and diagnosis of Li-ion batteries in recent years. But the study of the high-frequency characteristics of Li-ion batteries is still not enough and the performance of Li-ion batteries at high frequency is not the same with that of the pure capacitance or pure inductance. Based on EIS, a fractional equivalent circuit model considering high-frequency inductance characteristics is established in frequencies from 10mHz to 10kHz in this paper. Then the model is verified and the parameters of the circuit are explored by using differential evolution (DE) algorithm and fractional-order numerical operations. Compared with the traditional equivalent circuit model, a fractional-order model based on EIS can not only describe the characteristics of the battery more comprehensively but also reduce the number of parameters because each component can simulate a certain physicochemical process of Li-ion batteries. The dominant process of the battery reaction is diverse in different frequency bands and therefore the structure of the developed model can be simplified accordingly. For the high-frequency inductive analysis of the battery, results show that the battery's 'inductance-like' phenomenon has a certain relationship with the frequency. This discovery might be implemented in a power electronic circuit to improve understanding of how batteries react to working condition of high-frequency.

Fractional Order Equivalent Circuit Model and SOC Estimation of Supercapacitors for Use in HESS

Supercapacitors are an important part of the hybrid energy storage system for electric vehicles (EVs.) They not only protect the battery, but also improve the starting performance, acceleration performance, and regenerative braking performance of the EVs. Accurate modeling and state of charge (SOC) estimation of supercapacitors are essential for reliability, resilience, and safety in hybrid energy storage system operations. In this paper, a fractional order dynamic equivalent circuit model of the supercapacitor is proposed. Through the parameter identification and the experimental analysis, it is proved that the fractional equivalent circuit has better precision. Furthermore, the SOC estimation method of particle filter and Kalman filter is investigated, and a method of estimating supercapacitor SOC is proposed by combining the particle filter and the fractional Kalman filter. The validation results prove that the proposed method has better accuracy and real-time performance based on the fractional order.