Optimal Experimental Design for Modeling Battery Degradation

Accurate battery health modeling allows one to make better design decisions, enables health conscious control, and allows for feed-forward State of Health estimation. However, experiments are necessary in order to obtain and validate these models. Unfortunately, battery health experiments are costly in terms of time, person-hours, and equipment. This makes it extremely important to minimize the number of experimental iterations. This paper aims to minimize time and expense of experiments while maximizing information gathered by bridging an important gap between the Optimal Experimental Design (OED) and the battery health experimental/modeling literature. We demonstrate how to apply static OED methods to a battery aging experiment. This allows us to select a set of Constant Current Constant Voltage (CCCV) cycles that maximizes the amount of information gathered in turn allowing us to better identify the health model parameters. The CCCV cycling is carried out in a laboratory using 14 LiFePO4 cells (10 for fitting and 4 for validation). Each of these cells undergoes 429 days of battery health cycling. Results from these experiments include: a model of battery capacity fade based on voltage and current, battery health dependence on voltage, and a lack of power fade under the cycling conditions. The use of OED to coordinate our model form and experiment helped to ensure a fruitful model resulted when processing the collected data. Based on this success we suggest a ∗Address all correspondence to this author. generalized framework for Optimal Battery Health Model Experiments (OBHME), which allows one to apply OED to a variety of related problems. NOMENCLATURE F Fisher Information Matrix [Various] H Battery Capacity [Various] I Battery Current [Amp] I+ CCCV Charge Current Limit [Amp] I− CCCV Discharge Current Limit [Amp] Itrickle CCCV Trickle Current Limit [Amp] P Battery Power [Watt] U Trial Matrix [Various] V Battery Terminal Voltage [Volt] Vmin CCCV Minimum Voltage [Volt] Vmax CCCV Maximum Voltage [Volt] f (·) Experiment Regressor Function [Various] i Model Parameter Index [Index] j Experiment Index [Index] k Trial Index [Index] m Number of Parameters [Unitless] n Number of Trials [Unitless] p Number of Possible Trials [Unitless] q Number of Trials in Experiment [Unitless] t f Duration of Repeated Cycle [Sec] thold CCCV Float Hold Time [Sec] ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference DSCC2012-MOVIC2012 1 Copyright © 2012 by ASME DSCC2012-MOVIC2012-8751 October 17-19, 2012, Fort Lauderdale, Florida, USA u Experiment Regressors [Various] Ξ All Possible Experiments [Set] α Optimized Trial Index [Index] β Model Parameters [Various] λ Trial Time Fraction [Unitless] σ Standard Deviation of Measurement Noise [Various]