Can Energy Storage Pack Hybridization Improve the Best Theoretically-Achievable Battery State Estimation Accuracy?
Authors: Cleary Timothy , Xu Chu , Fathy Hosam 
Published: February 2020

This article examines the degree to which the creation of a series hybrid ultracapacitor-battery string can improve achievable battery state estimation accuracy. The article is motivated by the existence of fundamental information-theoretic limits on the degree to which one can use input/output current/voltage data to estimate a battery's internal states (e.g., state of charge, state of health, etc.). Previous literature quantifies these limits rigorously using Fisher information theory [1] – [5]. One conclusion of this quantification is that it is particularly difficult to obtain accurate battery state estimates during phase transition processes, such as the phase transition that occurs in lithium iron phosphate electrodes during charge/discharge. The problematic effect, in this context, is the very small dV/dQ slope, or effective electrical elastance, of the battery. Poor battery elastance complicates battery state estimation accuracy by directly contributing to the worsening of the best-achievable battery state estimation accuracy. The literature already shows this through the use of Fisher information analysis which shows the dependence of the best-achievable battery state estimation accuracy and the effective battery elastance.
Building on the above literature, the key conjecture motivating this article is that the creation of hybrid series ultracapacitor-battery strings can improve battery state estimation accuracy substantially by furnishing a significant dV/dQ system behavior. We derive this conclusion analytically, using Fisher information analysis. Then consider estimating the lithium-ion battery state of charge using input current and output battery voltage, where the current measurement is biased and the voltage sensor has zero-mean, random, Gaussian noise. By comparison between the Cramer-Rao lower bound of both the battery-only and ultracapacitor-battery hybrid, we demonstrate improvements in theoretically-achievable initial charge accuracy as well as current bias, and in turn improve the battery SOC estimation.
This conclusion is validated using a Monte Carlo simulation study. Performing least square method to estimate both initial charge in the battery and current sensor bias to achieve point clouds with and without an ultracapacitor in series, as shown in Figure 1a. One can conclude that there is: (i) a dependence between the estimated current bias and initial charge; (ii) a large condition number of the Fisher information metric which is reflected in the thin shape of the cloud ellipse; (iii) significant decrease in the estimation error after adding a series ultracapacitor into the system.
Finally, the article presents an experimental ultracapacitor-battery validation study, as shown in Figure 1b. The full experiment setup includes a system of three parallel 400F ultracapacitors in series with a single 0.6Ah LFP cell. Experimental data is used to solve the optimization problem of minimizing the mean squared error of physical and simulation system outputs with respect to estimated initial charge and current bias. Results show clear improvement on the estimation accuracy.
Figure 1. (a) Monte Carlo simulation results comparison (above) (b) Experiment setup structure (below)
This article answers the title question by providing quantifiable evidence of improved state estimation through theory, simulation and experiment.

Figure 1