Research On Modeling Of Lithium-ion Power Battery Based On Fractional Order Theory

At present,Lithium-ion power batteries play an increasingly important role in the field of electric traffic because of their high energy density,high power density and low self-discharge rate.Since the physical debugging is costly and time consuming during the development process of battery application technology,the internal state of the battery in application is not easy to directly measure.Therefore,battery modeling becomes an important means of power system simulation,battery state and parameter estimation and thermal performance analysis.In view of the comprehensive consideration of the physical meaning and complexity of the model,the equivalent circuit model has become the mainstream method of engineering application;among them,the fractional equivalent model has gradually become a research hotspot because it can simulate the capacitance-like and inductance-like characteristics.In this paper,the status quo of battery modeling is reviewed,and the fractional order equivalent circuit model is established,that is compared with the integer order model in both time domain and frequency domain.AC impedance test can obtain rich information of electrode dynamics,which is an important means battery development and battery performance detection.The obtained impedance spectrum complex plane can describe the electrochemical behavior of the battery in the whole frequency band in detail.According to the capacitance-resistance arc based on impedance spectrum,the parallel connection between the fractional-order component CPE and the resistor is selected to simulate the dispersion effect of the electric double layer capacitor and charge transfer process.For the oblique line of the impedance spectrum appearing in low-frequency region,the fractional-order component Warburg impedance is selected to characterize the mass transfer process of Lithium-ion.In this paper,the evolution process of fractional-order model is described.The fractional equivalent circuit model is constructed based on the internal physical-chemical mechanism of the battery to accurately describe the dynamic behavior of the battery.The frequency domain expression of the battery fractional model is derived and the time domain numerical solution of the model is derived based on the fractional differential theory.Based on the battery fractional-order model,the structural composition relationship of 1s internal resistance in the time domain is theoretically revealed.The internal domain 1 s internal resistance includes not only ohmic internal resistance,but also partial charge transfer impedance,partial passivation film impedance and partial diffusion impedance;the approximate equivalent relationship between time domain impedance and frequency domain impedance is derived,and the domain 1s internal resistance is approximately equal to frequency domain impedance of 0.159 Hz,rather than impedance whose frequency is close to 1 Hz or 0.5 Hz.Then,the frequency domain identification method of fractional model parameters is proposed.The particle swarm and differential evolution fusion algorithm are used to identify the model parameters with the minimum error of impedance phase and the modulus as the target.The variation of parameters in different state of charge and temperature is analyzed.Experimental verification shows that the fractional-order model can more accurately simulate the frequency domain characteristics of the battery.Compared with the integer-order model,the fractional-order model can obtain higher precision with fewer components.For existing impedance tests,there are problems such as long test time and special equipment,an electrochemical impedance spectroscopy test method which is easy to implement in engineering is proposed.Finally,in the time domain,the frequency domain model identified by the AC impedance data is verified by the current and voltage data in different frequencies.The model output voltage error is small,and it has better applicability for different frequencies and different amplitudes.According to the time constant of the internal electrochemical reaction in the battery,the RQ model is obtained by simplifying the fractional model structure on a long-term scale,and a fractional-order equivalent circuit model suitable for time domain is established.The Hybrid multi-particle swarm optimization is used to identify the model parameters applying the constant-current pulse data.The model parameters of the single cell and the battery pack are obtained.The accuracy of the fractional-order RQ model is higher than that of the first-order RC model.The identified model parameters are verified under DST and FUDS dynamic conditions and the RQ models all show higher accuracy,that is,the fractional-order model can more accurately describe the battery dynamics.