Discovering the precise state of charge (SOC), state of health (SOH), and remaining useful life (RUL) while monitoring depth of discharge (DOD) for Lithium ion (Li-ion) batteries can be computational enormous. Electrical engineers using equivalent circuit models (ECM) or enhanced equivalent circuit models (EECM) have achieved an acceptable level of accuracy modelling the current, voltage, and temperature behaviors to get SOC, SOH, RUL, and DOD. ECM/EECM’s are computationally fast but do not fully account for the electrochemical material that makes up the battery in their mathematical equations or isothermal characteristics that continuously change during charging and discharging or at varying C-rates while cycling. Unfortunately, the number of factors and variables needed to compute the system of differential algebraic equations for the nonlinear physical-based models to achieve this level of precise data is computationally too expensive for real-time systems. In today’s environment, the use of filters has provided a bridge between empirical and physical based models. This paper examines an ECM and a porous electrode pseudo two-dimensional (P2D) model using particle filter (PF) technology for a series, parallel, and series/parallel combination battery switching microcontroller based battery management system (BMS).

Introduction

Reconfigurable battery packs have the advantage of altering the pack topology to adapt to changes in load requirements. The series/parallel battery configuration allows a low cost solution for networks under constraint to meet the energy and power demand placed on an electrical system without adding additional batteries and incurring additional cost. Part of the system is dependent on the fast charging parallel converter which allows the network to balance each cell and accurately estimate the battery SOC. Kim, Qiao, and Qu[1] series cell array negated parallel configurations in their series cell arrays. Physical based models have the advantage of performing comprehensive analysis on the effects of both the solid phase and the liquid phase. Modelling, porous electrode theory coupled with transport phenomena and electrochemical reactions represented by coupled nonlinear partial differential equations (PDE) in one or two dimensions gives physical based models an advantage over equivalent circuit model (ECM) based models. Santhanagopalan[2] and Rahimian[3] have used the single-particle model (SPM) implementing Kalman filtering methods to estimate SOC of Li-Ion cells. An area of concern is the computational complexity of the physical based models.

Experimental Method

State of Charge (SOC)

The SOC, a measure of remaining capacity in the battery, helps to ensure during charging battery cells are not over/under charged and during discharge it is a quick gauge to show how much capacity is remaining capable of supporting the load.

Eq-1

where, Q is the capacity. In battery cells, capacity can be represented as a voltage at specific time.

Fig-1

State of Health (SOH)

The SOH, an indication of where the battery is at in its life cycle, is used to measure capacitance of the used battery relative to the capacitance of a new battery. Using capacity fade analysis to demonstrate the loss of capacity during the life of the cell indicates if the battery is being maximized. This allowed us to monitor the remaining capacitance available in the battery cell at a given time.

Eq-2

where, c is the capacity, α is the deterioration rate multiplier. α varies depending on power density, energy density, and temperature components.

Fig-2

Remaining Useful Life (RUL)

The RUL, an approximation of the cyclability of a battery pack, enables an estimation of the number of duration individual battery cells within the series/parallel battery scheme are useable, thus approximating the life cycle of the entire BMS.

Eq-3

where, β is the cycle deterioration factor.

Fig-3

References

1. Kim, T., et al. “Series-Connected Self-Reconfigurable Multicell Battery.” 26th AAPEC&E, Mar. 2011, IEEE. pp. 1382-1387.
2. Santhanagopalan, S., et al. "Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries." JPS 156.2 (2006): 620-628.
3. Rahimian, S.K., et al. “State of Charge and Loss of Active Material Estimation of a Lithium Ion Cell under Low Earth Orbit Condition Using Kalman Filtering Approaches.” JES (2014): A860-A872.