Research On Lithium-ion Battery Nonlinear System Modeling And Estimation Using Fractional Calculus

The large-scale application of renewable and clean energy such as solar energy,wind energy,etc.,has promoted the development of energy conversion and storage technologies.Lithium-ion battery has become the major energy storage solution in power system energy storage,electrically propelled vehicles,and portable electronics applications due to its superior performance.With its application in various fields being deeper,and continuing to expand,its security and reliability problems become more and more prominent.In this background,studying the modeling and the online state estimation techniques in depth for lithium-ion battery systems is quite significant for managing battery systems effectively,and ensuring that the batteries operate safely,reliably and efficiently.Based on the basic theory of lithium-ion battery,fractional calculus(FOC)theory,swarm intelligence optimization theory,sliding mode control(SMC)technology and observer design theory,researches on the modeling,identification and state estimation of lithium-ion battery systems are conducted in this paper,and the main works are as follows:For the problem of modeling the lithium-ion battery which is a nonlinear system,both the double-layer capacitance and the effect of temperature on parameters are incorporated into the basic P2 D model to construct a lithium-ion battery simulation system.Charge and discharge test simulations of battery are implemented with the constructed battery system,and the battery electrochemical impedance characteristics are analyzed.Based on this,FOC which possesses powerful ability to characterize complex systems is applied to establish fractional order equivalent circuit models in the time domain for lithium-ion batteries: Considering the influences of different conditions on the lithiumion battery,a variable parameter fractional order RC equivalent circuit model related with different working conditions(Wi-FORCECM)is proposed.In the Wi-FORCECM,each sub-model is related with one representative working condition,and the parameter uncertainties,model errors and disturbance effects occur in each typical working case are depicted by uncertainty terms in the sub-model,so that the model fits into the actual application of the battery;Considering the battery behavior characteristics of different scales further,fractional order elements are employed to describe the nonlinear characteristics of the components within the battery system,a double-loop fractional order equivalent circuit model(DFOECM)is presented for lithium-ion battery.In order to obtain the accurate parameters of fractional model of lithium-ion battery,based on the generality of identification issue of fractional order nonlinear system,one transforms the identification problem into an optimization problem,and then a solution framework with optimization for system identification is formed,the system parameters can be obtained by solving this optimization problem.IGAL-ABC and MNIIABC intelligent optimization algorithms for solving high-dimensional complex optimization problems are proposed.The simulations verify that they possess good exploration and exploitation performance,and have the ability to jump out of local extreme points to search the global optimal solutions with robustness.Furthermore,system identification methods based on IGAL-ABC and MNIIABC separately for fractional order nonlinear systems are proposed.Their validity and accuracy are evaluated via identifying fractional order chaotic systems.Finally,the presented identification methods are applied to identify battery system parameters,thus parameter estimation approaches respectively based on IGAL-ABC and MNIIABC intelligent optimization for battery are obtained.The performances of these methods are verified through simulation experiments.And the experimental results show the proposed methods can effectively estimate the parameters of battery model with good accuracy.To estimate battery states online with robustness,and obtain the accurate state of charge(SOC)information,SOC estimation methods respectively based on Wi-FORCECM and DFOECM for lithium-ion batteries are proposed.Firstly,a state estimation approach based on fractional order sliding mode observer for a class of uncertain fractional order nonlinear system is presented.Through combining the Luenberger-type control term and the SMC technique,the proposed fractional order sliding mode observer can compensate system disturbance,model error and parameter uncertainty much better.It provides a theoretical foundation and reference method for the research of battery state estimation.Considering the influence of working and environmental conditions on battery parameters,battery state estimators are designed based on Wi-FORCECM via using SMC technique and linear feedback compensation method.A switching SMC-Luenberger fractional order observer(SW-SMCL-FrCO)are presented.By using the SW-SMCL-FrCO,the SOC can be estimated efficiently with robustness,and good accuracy performance can be obtained.In order to relief the dependence on prior knowledge when determining the observer gain,a new adaptive sliding mode observer based on DFOECM(AdpSMOFOECM)is proposed.A re-initialization adjustment strategy is designed to control the gains of AdpSMO-FOECM,then an adaptive sliding mode observer with gain switching reset(RSW-AdpSMO-FOECM)is obtained,with which the effect of reference observer gain value on the state estimation performance can be controlled properly.Furthermore,estimating the SOC based on RSW-AdpSMO-FOECM can avoid the influence of improper set gain on the convergence speed and accuracy of the observer,and enhance the estimation accuracy.The convergence of the achieved state estimation methods is analyzed by using the Lyapunov stability theory.Effectiveness,accuracy and convergence performance of these SOC estimation methods are tested by comparison simulation experiments.For the health monitoring problem of lithium-ion battery,a SOC and state of health(SOH)joint estimation method is designed based on fractional order equivalent circuit model and SMC theory.For the SOC estimation,in order to deal with the problem that the observer cannot quickly and accurately track the actual value because of the too-large errors between the preset battery state values and the actual state values and other factors,a robustness two phase switching fractional order sliding mode observer(TPS-FrCSMO)based on DFOECM is proposed to estimate battery SOC online accurately.With this approach,the chattering error suppression and the convergence speed performance related to sliding mode gain during the estimation process can be well improved simultaneously.For the SOH estimation,adaptive sliding mode observers are constructed based on the behaviors of capacity and resistance parameters,then the SOH estimation approach based on TPS-FrCSMO and adaptive sliding mode observer is presented,to co-estimate the SOC and SOH iteratively.The convergence of the proposed observers is analyzed by applying the Lyapunov stability theory.In addition,for the remaining useful life(RUL)estimation problem of lithium-ion battery,an adpABC-PF approach with improved state estimation performance is presented.A RUL estimation method based on adpABC-PF and capacity fading model is proposed.Simulation results indicate the proposed health monitoring methods for lithium-ion battery are effective and have good estimation performance.