Battery Modeling
Batteries are electrochemical energy extraction/storage devices that work by using a conducting domain to separate two regions, where the two halves of an overall favorable chemical reaction proceed. By preventing the mixing of reactants and instead forcing the reaction to proceed by mediation of electrical current between the separated reactants, energy can be extracted as a voltage.
In a battery, there is a finite supply of reactant and the system is closed. A battery does not have a steady state condition since its feedstock of reactants progressively depletes until it is consumed. Once consumed, the battery is discharged and it will no longer provide a voltage as its source of electrochemical energy has run out. In a rechargeable battery, the process is reversible and the application of a voltage can return the battery to saturation with feedstock under charging.
The electrochemistry in a battery model usually does not have a steady state, and so it is not appropriate to use a Stationary study with a battery interface.
The maximum achievable voltage in a battery or fuel cell is the difference between the half-cell potentials. The discharge mode is the direction in which the overall reaction is thermodynamically downhill (negative ΔG).
There can be variation in the literature between whether the charge or discharge mode is assumed when an electrode in a battery is referred to as the “anode” or “cathode”. Each electrode can operate in both roles, depending on whether the battery is charging or discharging.
Generic battery models can be set up using the Tertiary Current Distribution interface to describe charge transport coupled to species transport is required.
The Lumped Battery interface and Battery Equivalent Circuit interfaces are general “black box”-approach interfaces, which make use of global equations and parameters, typically fitted to experimental data, for capturing the battery cell dynamic charge-discharge behavior.
The Single Particle Battery interface is a generic interface for modeling intercalation electrode-based batteries. It may be viewed as a semi-lumped version of the Lithium--on and Battery with Binary Electrolyte interfaces described below.
Tailor made Battery Interfaces
Certain common battery types have predefined physics interfaces. Common for all these interfaces is that by the use of concentrated electrolyte theory for the charge and mass transport in the electrolyte, a more accurate electrolyte transport model is achieved, compared to the Nernst–Planck equations described earlier in this chapter.
Lithium-Ion Battery is used for solving problems in batteries where the anode (in discharge mode) is lithium metal intercalated into a material such as graphite, and the cathode (in discharge mode) is lithium ions intercalated into a transition metal oxide. The electrical current through the electrolyte is carried by lithium ions, typically in an organic solution. Because both the anode and cathode materials are typically porous to maximize the active surface area, the Porous Electrode domain node is standard do define each electrode.
The Battery with Binary Electrolyte interface can be used for a range of general battery types involving porous electrodes and current transfer through an ionic conductor. An example is the nickel–metal hydride battery — an early type of rechargeable battery in which the discharge anode is a metal hydride, the discharge cathode is a hydrated nickel oxide, and the current is transferred by high concentration potassium hydroxide in aqueous solution.
The Lead–Acid Battery interface is designed for batteries in which the discharge process is the comproportionation of Pb(0) and Pb(IV) through a sulfuric acid medium.