Thermodynamics of Lead-Acid Battery Degradation: Application of the Degradation-Entropy Generation Methodology

Abstract

This article details a lead-acid battery degradation model based on irreversible thermodynamics, which is then verified experimentally using commonly measured operational parameters. The model combines thermodynamic first principles with the Degradation-Entropy Generation theorem, to relate instantaneous and cyclic capacity fade (loss of useful charge-holding capacity) in the lead-acid battery to the entropy generated via the underlying dissipative physical processes responsible for battery degradation. Equations relating capacity fade to battery cycling are also formulated and verified. To show robustness of the approach, nonlinear data from uncontrolled and severely abusive battery cycling-including overdischarge-was measured and used to verify formulations. A near 100% agreement between the thermodynamic battery model and measurements is achieved. The model also gives rise to new material and design parameters to characterize all lead-acid batteries.

Methods to Calculate Entropy Generation

“…Subscript indicates evaluation along the phenomenological path, the observable path where the independent states and dissipative process variables are available and measured at each instant. Since the product of temperature and entropy change ( ) in Equation (5) subsumes the heat and flow transfer terms in Equations (2) and (3), Equation (5) is valid for all systems, open and closed [ 7 , 8 , 9 , 10 , 12 ]. Equation (5), which governs the system along an irreversible path, has a pair of unknowns and ; all other terms are observable and can be measured, as shown later.…”

“…To solve, a second independent equation will arise via [ 7 , 8 , 9 , 10 ] applied to Equation (5). Recalling the thermodynamic state principle, all process paths between the same initial and end states must have the same difference between states: = , , etc., whether the path be reversible or irreversible.…”

“…With a specified (most energy systems have rated capacities and specific energies), Equation (9c) measures the actual irreversible entropy generation pertaining to the dissipation of useful energy via compositional changes. From Equation (8c), the Gibbs phenomenological entropy generation [ 7 , 10 ] where . Both and have consistent interpretations in all systems undergoing active compositional reactions (charge, discharge or combinations) and are composed of conjugate pairs involving physically observable and readily measurable system variables dT , dY and dN k .…”

“…DEG methods relate increments of degradation to increments of entropy generation. Instead of a “steady state” assumption, Osara and Bryant [ 7 , 8 , 9 , 10 ] augmented laws of thermodynamics with the thermodynamic potentials to formulate entropy generation. Methods to calculate entropy generation under general conditions for all systems are needed to enable real-time assessment of system transformation.…”

A Unified Treatment of Tribo-Components Degradation Using Thermodynamics Framework: A Review on Adhesive Wear

“…In a tribo-system, degradation is accompanied by material removal [30][31][32][33][34][35]. The same physics is involved when one deals with a deterioration of performance in batteries during charging and discharging [36,37], loss of consistency in grease due to shearing action [38][39][40][41], and accumulation of damage in cyclic fatigue [42][43][44][45]. Therefore, it is hypothesized that the degradation can be characterized using the framework of irreversible thermodynamics.…”