Energy vs Power Relationship for Lithium Ion Cells over a Broad Range of Temperatures and Power Densities

Abstract

We provide an analysis of batteries subject to controlled power operation on both charge and discharge over the temperature range of −30 to 45°C, consistent with vehicle drive events. The method we develop is applied to a high-power lithium ion cell, thereby allowing us to obtain parameters and overall characteristics useful for ͑i͒ representing the battery in vehicle models and ͑ii͒ providing a quantitative means of comparing and classifying battery systems. The current and voltage histories are modeled during the constant power discharge, and Ragone plots ͑energy vs power͒ as well as discharge and charge times are analyzed. The equations employed are based on an equivalent circuit comprising a parallel resistor-capacitor combination in series with a resistor and the open-circuit potential source. The circuit element values are dependent on temperature and independent of the current and potential. Model calculations are compared with experimental data. Good agreement is obtained for temperatures ranging from 0 to 45°C. More work is needed to clarify phenomena below 0°C.

Development of cooling strategy for an air cooled lithium-ion battery pack

“…At given battery pack power each individual battery cell current, I, and voltage, V i , can be expressed using an equivalent circuit model [5,6] as follows…”

Power prediction from a battery state estimator that incorporates diffusion resistance

“…B is used to adjust the dependence of s on V oc . Moreover, in order to accommodate the possibility of different electrode kinetics processes for charge and discharge [29,30], we use two sets of A and B values, A c and B c or A d and B d , (subscript c for charge and d for discharge) for charge and discharge respectively. For example, we may choose a larger A for R diffusion in the discharge power calculation, since diffusion is more prominent in discharge power tests than in charge power tests.…”

Development of efficient air-cooling strategies for lithium-ion battery module based on empirical heat source model

“…As the most commonly used method, various mathematical models have been developed where a thermal model is coupled with first principles electrochemical model [53e55] or even one step further, the local difference in the reaction current and SOC are incorporated [56,57]. Meanwhile, in equivalent circuit model, the voltage and temperature response of the cell is represented as an electric circuit [58]. They are lumped models with relatively few numbers of parameters especially for the purpose of vehicle power management control and battery management system development [59e61].…”