The gradual decay, with use, of a cell's capacity and increase of its resistance is modeled by enabling the include degradation effects boolean parameter. Enabling this feature adds a state-of-health (soh) output to the model. This signal is 1 when the cell has no decay and 0 when is completely decayed.

The soh output is given by

$\mathrm{soh}={\left(1-\frac{s}{R_s}\right)}^3$

where

The decay of the capacity is

$C\=C_{\max }\mathrm{soh}$

where

The additional series resistance added to a cell is

$R_{\mathrm{sei}}\=\frac{s}{\mathrm{\kappa }}$

with $\mathrm{\kappa }$ a parameter of the model.

The following equations govern the increase in the thickness of the SEI layer ($s$).

$k\=A_e\exp \left(-\frac{E_a}{RT}\right)$

$\frac{\mathrm{ds}}{\mathrm{dt}}\=\{\begin{array}{cc}\frac{kcM}{\left(1\+\frac{ks}{{\mathrm{D}}_{\mathrm{diff}}}\right){\mathrm{\rho }}_{\mathrm{sei}}}& \mathrm{charging}\\ 0& \mathrm{otherwise}\end{array}$

Select the thermal model of the battery from the heat model drop-down list.  The available models are: isothermal, external port, and convection.

	Isothermal
	The isothermal model sets the cell temperature to a constant parameter, $T_{\mathrm{iso}}$.

External Port

The external port model adds a thermal port to the battery model. The temperature of the heat port is the cell temperature. The parameters $m_{\mathrm{cell}}$ and $c_p$ become available and are used in the heat equation $m_{\mathrm{cell}}{c}_p\frac{\mathrm{d}{T}_{\mathrm{cell}}}{\mathrm{d}t}\=P_{\mathrm{cell}}-Q_{\mathrm{cell}}$ $Q_{\mathrm{flow}}\=n_{\mathrm{cell}}{Q}_{\mathrm{cell}}$ $P_{\mathrm{cell}}\=i_{\mathrm{cell}}\left(v_{\mathrm{cell}}-v_{\mathrm{oc}}\right)$ where $P_{\mathrm{cell}}$ is the heat generated in each cell, including chemical reactions and ohmic resistive losses, $Q_{\mathrm{cell}}$ is the heat flow out of each cell, and $Q_{\mathrm{flow}}$ is the heat flow out of the external port.

Convection

The convection model assumes the heat dissipation from each cell is due to uniform convection from the surface to an ambient temperature. The parameters $m_{\mathrm{cell}}$, $c_p$, $A_{\mathrm{cell}}$, $h$, and $T_{\mathrm{amb}}$ become available, as does an output signal port that gives the cell temperature in Kelvin. The heat equation is the same as the heat equation for the external port, with $Q_{\mathrm{cell}}$ given by $Q_{\mathrm{cell}}\=h{A}_{\mathrm{cell}}\left(T_{\mathrm{cell}}-T_{\mathrm{amb}}\right)$

The capacity of a cell can either be a fixed value, $\mathrm{CA}$, or be controlled via an input signal, $C_{\mathrm{in}}$, if the use capacity input box is checked.

A signal output, soc, gives the state-of-charge of the battery, with 0 being fully discharged and 1 being fully charged.

The parameter ${\mathrm{SOC}}_{\min }$ sets the minimum allowable state-of-charge; if the battery is discharged past this level, the simulation is either terminated and an error message is raised, or, if the allow overdischarge parameter is true,  a warning is generated. A similar effect occurs if the battery is fully charged so that the state of charge reaches one; the simulation is terminated unless allow overcharge is true.

The parameter ${\mathrm{SOC}}_0$ assigns the initial state-of charge of the battery.