Control-oriented modeling, state-of-charge, state-of-health, and parameter estimation of batteries

In this research, we develop a reduced-order Lead-Acid battery model from first principles using linearization and the Ritz discretization method. The model, even with a low-order discretization, accurately predicts the voltage response to a dynamic pulse current input and outputs spatially distributed variables of interest.;As an efficient first principles model, the Ritz model makes an excellent candidate for Battery Management System (BMS) model design. Also, a dynamic averaged model is developed from the Ritz model and realized by an equivalent circuit. The circuit resistances and capacitances depend on electrochemical parameters, linking the equivalent circuit model to the underlying electrochemistry of the first principles model.;Among those built-in functionalities of the BMS in a HEV, the State-Of-Charge (SOC) estimation is crucial. SOC is the overall remaining charge in percentage inside a defined unit (cell, battery, module, or battery pack.). For an electric vehicle, the SOC is similar to the remaining fuel for a vehicle powered by internal combustion engine. State-Of-Charge (SOC) estimation for Valve-Regulated Lead-Acid (VRLA) batteries is complicated by the switched linear nature of the underlying dynamics. A first principles nonlinear model is simplified to provide two switched linear models and linearized to produce charge, discharge, and averaged models. Luenberger and switched SOC estimators are developed based on these models and propogated using experimental data. A design methodology based on Linear Matrix Inequalities (LMIs) is used in the switched SOC estimator design to obtain a switched Luenberger observer with guaranteed exponential stability. The results show that estimation errors are halved by including switching in the observer design.;To fully utilize a Lead-Acid cell also requires real-time estimates of its State-Of- Power (SOP) and State-Of-Health (SOH) to efficiently allocate power and energy amongst the cells in a pack. SOP and SOH are inversely and directly proportional to cell resistance and capacity, respectively. In this research, the Least Squares Method estimates the coefficients of a second order transfer function using experimental voltage and current data from new, aged, and dead Valve Regulated Lead-Acid batteries. The coefficients are explicitly related to the cell ohmic resistance, capacity, charge transfer resistance, and double layer time constant using a fundamental model of the cell. The ohmic resistance estimate increases monotonically with age, providing an estimate of SOP. The capacity estimate decreases monotonically with age, matching the actual capacity loss for aged cells. Finally, the voltage estimate error can be used as a SOH/SOP estimator and quantify the reliability of the parameter estimates. The first pulse after a long rest period shows the highest estimation error.;In battery systems, the parameters often vary with SOC, SOH, and operating conditions. Accurate and fast battery parameter measurement methods are desirable in many applications. Solid phase diffusivity Ds is one of the first parameters to be measured in a new Lithium-Ion cell design because it dominates the electrochemical kinetics. Amongst the D s measurement methods, the Galvanostatic Intermittent Titration Technique (GITT) is easy to implement and univerally accepted as the standard for diffusivity measurement. The accuracy of GITT, however, has not been reported, because there is no direct measurement method of Ds. In this research, we develop a Least Squares Galvanostatic Intermittent Titration Technique (LS-GITT) that uses all of the voltage data from a GITT test to optimally tune the diffusivity in a reduced order solid phase diffusion model. The accuracy of the GITT and LS-GITT are evaluated using voltage predication error RMS. Based on experimental results from a NCM half cell, LS-GITT is more accurate than GITT, sometimes by several orders of magnitude. LS-GITT gives results accurate to 1 mV RMS from 15% - 100% SOC while GITT provides that level of accuracy over less than half that range. Neither technique provides accurate Ds measurements below 10% SOC. (Abstract shortened by UMI.).