Li-Ion Cell

When modeling charge and discharge processes in Li-ion Battery Cells, this report provides the open circuit voltage (OCV), the state of charge (SOC), and the capacity (CAP), where either the SOC or the OCV can be monitored.

The Open Circuit (Cell) Voltage

O C V

is defined as the cell voltage that is approached asymptotically as the cell rests for an infinite period. Empirically, this quantity is measured as the voltage difference between the positive and negative current collectors after the cell is rested for a few hours. For a cell in perfect equilibrium (that is, where the stoichiometry is constant), the

O C V

is computed as:

Figure 1. EQUATION_DISPLAY

O C V = U_{e q, +} (\bar{y}) - U_{e q, -} (\bar{x})

(437)

where

U_{e q, +} (\bar{y})

and

U_{e q, -} (\bar{x})

are the relative galvanic equilibrium potentials of the positive and negative electrode active materials.

\bar{y}

and

\bar{x}

denote their respective (average) stoichiometry (or utilization), given as:

Figure 2. EQUATION_DISPLAY

\bar{y} = \frac{\int_{+} c d V}{c_{s, max, +} V_{+}} = \frac{\bar{c_{+}}}{c_{s, max,+}}

(438)

Figure 3. EQUATION_DISPLAY

\bar{x} = \frac{\int_{-} c d V}{c_{s, max, -} V_{-}} = \frac{\bar{c_{-}}}{c_{s, max, -}}

(439)

where $c$ is the lithium/salt concentration, and $c_{s, \max}$ is the maximum concentration of intercalated lithium in the solid as defined by the Butler-Volmer equation Eqn. (4159).

The SOC is then defined as:

Figure 4. EQUATION_DISPLAY

S O C = {\begin{matrix} 1 & i f & O C V = {O C V}_{s o c = 1} \\ 0 & i f & O C V = {O C V}_{s o c = 0} \end{matrix}

(440)

where $O C V = {O C V}_{s o c = 1}$ is the specified voltage where the battery is fully charged, and $O C V = {O C V}_{s o c = 0}$ is the specified voltage where the battery is considered to be fully discharged (usually the lower cut-off voltage).

Note	Overcharge, as well as deep-discharge, leads to $S O C \notin [0, 1]$ .

The capacity of the battery cell depends on the maximum amount of lithium (ions) that can be transferred from one electrode to the other, in the range $O C V = [O C V_{S O C = 0}, O C V_{S O C = 1}]$ . A lumped model is used within the Li-Ion Cell Report to compute the cell capacity:

Figure 5. EQUATION_DISPLAY

C A P = n_{-} | \binom{1}{S O C = 0} F = (n_{-} |_{S O C = 1} - n_{-} |_{S O C = 0}) F

(441)

where $n_{-}$ is the number of lithium moles that are stored in the negative electrode, and $F$ is Faraday’s constant.

A state table is generated in a new output window on Li-Ion Cell report execution. The state table provides information for:

The conditions to reinitialize the lithium/salt concentration at different values of state of charge $S O C$ .
Estimating the initial conditions for the lithium/salt concentration in both electrodes.

Li-Ion Cell Report Properties


Units	The units of the monitored value. This property is updated automatically when the monitor value is changed.
Voltage at 100% SOC	The voltage at which the battery is fully charged.
Voltage at 0% SOC	The lower cut-off voltage.
Positive Electrode Parts	A list of parts that is used as the source for positive electrodes for this report. Uses the in-place part selector for editing.
Negative Electrode Parts	A list of parts that is used as the source for negative electrodes for this report. Uses the in-place part selector for editing.
Monitor Value	Selects value that the report monitors.
	State of Charge	Monitors the state of charge, $S O C$ in Eqn. (440).
	Open Circuit Potential	Monitors the open circuit voltage, $O C V$ in Eqn. (437).

Li-Ion Cell Report Expert Properties


SOC Step Increment	The state of charge step increment in the state table.
Representation	Selects a representation. Additional selections appear as representations that are added to the simulation.
Smooth Values	Whether to calculate the report using node (interpolated) values of the chosen quantity or cell values.
	Activated	Use node (interpolated) values.
	Deactivated	Use cell values.