# Battery

Generic battery model

• Library:
• Simscape / Electrical / Specialized Power Systems / Electric Drives / Extra Sources

• ## Description

The Battery block implements a generic dynamic model that represents most popular types of rechargeable batteries.

This figure shows the equivalent circuit that the block models. ### Charge and Discharge Characteristics

The circuit parameters can be modified to represent a specific battery type and its discharge characteristics. A typical discharge curve consists of three sections. The first section represents the exponential voltage drop when the battery is charged. The width of the drop depends on the battery type. The second section represents the charge that can be extracted from the battery until the voltage drops below the battery nominal voltage. Finally, the third section represents the total discharge of the battery, when the voltage drops rapidly.

When the battery current is negative, the battery recharges, following a charge characteristic. The model parameters are derived from the discharge characteristics. The discharging and charging characteristics are assumed to be the same.

The Exp(s) transfer function represents the hysteresis phenomenon for the lead-acid, nickel-cadmium (NiCD), and nickel-metal hydride (NiMH) batteries during the charge and discharge cycles. The exponential voltage increases when a battery is charging, regardless of the battery's state of charge. When the battery is discharging, the exponential voltage decreases immediately. The state of charge (SOC) for a battery is a measure of battery's charge, expressed as a percent of the full charge. The depth of discharge (DOD) is the numerical compliment of the SOC, such that DOD = 100% - SOC.

For example, if the SOC is:

• 100% — The battery is fully charged and the DOD is 0%.

• 75% — The battery is 3/4 charged and the DOD is 25%.

• 50% — The battery is 1/2 charged and the DOD is 50%.

• 0% — The battery is has 0 charge and the DOD is 100%.

### Model Validation

Experimental validation of the model shows a maximum error of 5% (when SOC is between 10% and 100%) for the charge (when the current is 0 through 2 C) and discharge (when the current is 0 through 5 C) dynamics.

### Parameterization

#### Extract Battery Parameters from Data Sheets

This figure shows detailed parameters extracted from the Panasonic NiMH-HHR650D battery data sheet. You can obtain the rated capacity and the internal resistance from the specification tables. The other detailed parameters are derived from the Typical Discharge Characteristics plot.

Parameter

Value

Rated Capacity

`6.5` Ah

Internal Resistance

`2`

Nominal Voltage (a)

`1.18` V

Rated Capacity

`6.5` Ah

Maximum Capacity (b)

`7` Ah (`5.38` h * `1.3` A)

Fully Charged Voltage (c)

`1.39` V

Nominal Discharge Current (d)

`1.3` A

Capacity @ Nominal Voltage (a)

`6.25` Ah

Exponential Voltage (e)

`1.28` V

Exponential Capacity (e)

`1.3` Ah

These parameters are approximate and depend on the precision of the points obtained from the discharge curve.

The discharge curves you obtain from these parameters, which are marked by dotted lines in the following figures, are similar to the data sheet curves. To represent the temperature effects of the lithium-ion (Li-ion) battery type, an additional discharge curve at ambient temperature, which is different from the nominal temperature, and the thermal response parameters are required. Additional discharge curves are not usually provided on the data sheet and may require simple experiments to be obtained. The following examples show parameters extracted from the A123 Li-iron-phosphate ANR26650M1 and the Panasonic Li-cobalt-oxide CGR 18,650 AF battery data sheets.

The A123 ANR26650M1 data sheet specifications include the required discharge curve points and other required parameters. These parameters are derived from the data sheet for the A123 Li-ion temperature-dependent battery model.

ParameterValue

Nominal voltage (c)

`3.22` V

Rated capacity

`2.3` Ah

Maximum capacity (d)

`2.3` Ah

Fully charged voltage (a)

`3.7` V

Nominal discharge current

`2.3` A

Internal resistance

`10` mΩ

Capacity at nominal voltage (c)

`2.07` Ah

Exponential zone (b)

[`3.4` V, `0.23` Ah]

Nominal ambient temperature

`25`°C

Second ambient temperature

`0`°C

Maximum capacity at 0°C (h)

`2.208` Ah

Initial discharge voltage at 0°C (e)

`3.45` V

Voltage at 90% maximum capacity at 0°C (g)

`2.8` V

Exponential zone at 0°C (f)

[`3.22` V, `0.23` Ah]

Thermal resistance, cell-to-ambient (estimated)

`0.6`

Thermal time constant, cell-to-ambient (estimated)

`1000`

In the figure, the dashed lines show the discharges curves obtained from the simulation at different ambient temperatures. The model performance is very close to the data sheet results. The same approach for parameter extraction is applied to the Panasonic Lithium-Ion CGR18650AF with these specifications. These parameters are extracted for the battery model.

ParameterValue

Nominal voltage (c)

`3.3` V

Rated capacity

`2.05` Ah

Maximum capacity (d)

`2` Ah

Fully charged voltage (a)

`4.2` V

Nominal discharge current

`1.95` A

Internal resistance (estimated)

`16.5` mΩ

Capacity at nominal voltage (c)

`1.81` Ah

Exponential zone (b)

[`3.71` V, 0.6 Ah]

Nominal ambient temperature

`25`°C

Second ambient temperature

`0`°C

Maximum capacity at 0°C (h)

`1.78` Ah

Initial discharge voltage at 0°C (e)

`4` V

Voltage at 90% maximum capacity at 0°C (g)

`3.11` V

Exponential zone at 0°C (f)

[`3.8` V, `0.2` Ah]

Thermal resistance, cell-to-ambient (estimated)

`0.06`

Thermal time constant, cell-to-ambient (estimated)

`1000`

The figure shows a good match between the simulated discharge curves (represented by the dashed lines) and the data sheet curves. The accuracy of the model depends on how precise the selected points from the data sheet discharge curves are. #### Model cells in Series and/or in Parallel

To model a series and/or parallel combination of cells based on the parameters of a single cell, use the parameter transformation shown in the following table can be used. The `Nb_ser` variable corresponds to the number of cells in series, and `Nb_par` corresponds to the number of cells in parallel.

ParameterValue

Nominal voltage

1.18 * Nb_ser

Rated capacity

6.5 * Nb_par

Maximum capacity

7 * Nb_par

Fully charged voltage

1.39 * Nb_ser

Nominal discharge current

1.3 * Nb_par

Internal resistance

0.002 * Nb_ser/Nb_par

Capacity at nominal voltage

6.25 * Nb_par

Exponential zone

1.28 * Nb_ser, 1.3 * Nb_par

### Equations

For the lead-acid battery type, the model uses these equations.

• Discharge Model (i* > 0)

`${f}_{1}\left(it,i*,i,Exp\right)={E}_{0}-K\cdot \frac{Q}{Q-it}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+{\text{Laplace}}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}\cdot 0\right)$`

• Charge Model (i* < 0)

`${f}_{2}\left(it,i*,i,Exp\right)={E}_{0}-K\cdot \frac{Q}{it+0.1\cdot Q}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+{\text{Laplace}}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}\cdot \frac{1}{s}\right)$`

For the lithium-ion battery type, the model uses these equations.

• Discharge Model (i* > 0)

`${f}_{1}\left(it,i*,i\right)={E}_{0}-K\cdot \frac{Q}{Q-it}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+A\cdot \mathrm{exp}\left(-B\cdot it\right)$`

• Charge Model (i* < 0)

`${f}_{2}\left(it,i*,i\right)={E}_{0}-K\cdot \frac{Q}{it+0.1\cdot Q}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+A\cdot \mathrm{exp}\left(-B\cdot it\right)$`

For the nickel-cadmium and nickel-metal-hydride battery types, the model uses these equations.

• Discharge Model (i* > 0)

`${f}_{1}\left(it,i*,i,Exp\right)={E}_{0}-K\cdot \frac{Q}{Q-it}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+{\text{Laplace}}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}\cdot 0\right)$`

• Charge Model (i* < 0)

`${f}_{2}\left(it,i*,i,Exp\right)={E}_{0}-K\cdot \frac{Q}{|it|+0.1\cdot Q}\cdot i*-K\cdot \frac{Q}{Q-it}\cdot it+{\text{Laplace}}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}\cdot \frac{1}{s}\right).$`

In the equations:

• EBatt is the nonlinear voltage, in V.

• E0 is the constant voltage, in V.

• Exp(s) is the exponential zone dynamics, in V.

• Sel(s) represents the battery mode. Sel(s) = `0` during battery discharge, Sel(s) = `1` during battery charging.

• K is the polarization constant, in V/Ah, or polarization resistance, in Ohms.

• i* is the low-frequency current dynamics, in A.

• i is the battery current, in A.

• it is the extracted capacity, in Ah.

• Q is the maximum battery capacity, in Ah.

• A is the exponential voltage, in V.

• B is the exponential capacity, in Ah−1.

#### Temperature Effect Equations

For the lithium-ion battery type, the impact of temperature on the model parameters is represented by these equations.

• Discharge Model (i* > 0)

`${f}_{1}\left(it,i*,i,T,{T}_{a}\right)={E}_{0}\left(T\right)-K\left(T\right)\cdot \frac{Q\left({T}_{a}\right)}{Q\left({T}_{a}\right)-it}\cdot \left(i*+it\right)+A\cdot \mathrm{exp}\left(-B\cdot it\right)-C\cdot it$`

`${V}_{batt}\left(T\right)={f}_{1}\left(it,i*,i,T,{T}_{a}\right)-R\left(T\right)\cdot i$`

• Charge Model (i* < 0)

`${f}_{1}\left(it,i*,i,T,{T}_{a}\right)={E}_{0}\left(T\right)-K\left(T\right)\cdot \frac{Q\left({T}_{a}\right)}{it+0.1\cdot Q\left({T}_{a}\right)}\cdot i*-K\left(T\right)\cdot \frac{Q\left({T}_{a}\right)}{Q\left({T}_{a}\right)-it}\cdot it+A\cdot \mathrm{exp}\left(-B\cdot it\right)-C\cdot it$`

`${V}_{batt}\left(T\right)={f}_{1}\left(it,i*,i,T,{T}_{a}\right)-R\left(T\right)\cdot i,$`

with

`${E}_{0}\left(T\right)={E}_{0}|{}_{{T}_{ref}}+\frac{\partial E}{\partial T}\left(T-{T}_{ref}\right)$`

`$K\left(T\right)=K|{}_{{T}_{ref}}\cdot \mathrm{exp}\left(\alpha \left(\frac{1}{T}-\frac{1}{{T}_{ref}}\right)\right)$`

`$Q\left({T}_{a}\right)=Q|{}_{{T}_{a}}+\frac{\Delta Q}{\Delta T}\cdot \left({T}_{a}-{T}_{ref}\right)$`

`$R\left(T\right)=R|{}_{{T}_{ref}}\cdot \mathrm{exp}\left(\beta \left(\frac{1}{T}-\frac{1}{{T}_{ref}}\right)\right),$`

where:

• Tref is the nominal ambient temperature, in K.

• T is the cell or internal temperature, in K.

• Ta is ambient temperature, in K.

• E/T is the reversible voltage temperature coefficient, in V/K.

• α is the Arrhenius rate constant for the polarization resistance.

• β is the Arrhenius rate constant for the internal resistance.

• ΔQT is the maximum capacity temperature coefficient, in Ah/K.

• C is the nominal discharge curve slope, in V/Ah. For lithium-ion batteries with less pronounced discharge curves (such as lithium iron phosphate batteries), this parameter is set to zero.

The cell or internal temperature, T, at any given time, t, is expressed as:

`$T\left(t\right)={L}^{-1}\left(\frac{{P}_{loss}{R}_{th}+{T}_{a}}{1+s\cdot {t}_{c}}\right),$`

where:

• Rth is thermal resistance, cell to ambient (°C/W).

• tc is thermal time constant, cell to ambient (s).

• Ploss is the overall heat generated (W) during the charge or discharge process and is given by

`${P}_{loss}=\left({E}_{0}\left(T\right)-{V}_{batt}\left(T\right)\right)\cdot i+\frac{\partial E}{\partial T}\cdot i\cdot T.$`

#### Aging Effect Equations

For the lithium-ion battery type, the impact of aging (due to cycling) on the battery capacity and internal resistance is represented by these equations:

`$Q\left(n\right)=\left\{\begin{array}{l}{Q}_{BOL}-\epsilon \left(n\right)\cdot \left({Q}_{BOL}-{Q}_{EOL}\right)\begin{array}{ccc}& if& k/2\ne 0\end{array}\\ Q\left(n-1\right)\begin{array}{ccc}\begin{array}{ccc}\begin{array}{ccc}& & \end{array}& & \end{array}& & otherwise\end{array}\end{array}$`
`$R\left(n\right)=\left\{\begin{array}{l}{R}_{BOL}+\epsilon \left(n\right)\cdot \left({R}_{EOL}-{R}_{BOL}\right)\begin{array}{ccc}& if& k/2\ne 0\end{array}\\ R\left(n-1\right)\begin{array}{ccc}\begin{array}{ccc}\begin{array}{ccc}& & \end{array}& & \end{array}& & otherwise\end{array}\end{array},$`

with

`$n=k{T}_{h}\begin{array}{ccc}& \left(k=1,2,3,...\infty \right)& \end{array}$`

where:

• Th is the half-cycle duration, in s. A complete cycle is obtained when the battery is discharged and charged or conversely.

• QBOL is the battery's maximum capacity, in Ah, at the beginning of life (BOL) and at nominal ambient temperature.

• QEOL is the battery's maximum capacity, in Ah, at the end of life (EOL) and at nominal ambient temperature.

• RBOL is the battery's internal resistance, in ohms, at the BOL and at nominal ambient temperature.

• REOL is the battery's internal resistance, in ohms, at the EOL and at nominal ambient temperature.

• ε is the battery aging factor. The aging factor is equal to zero and unity at the BOL and EOL.

The battery aging factor, ξ, is expressed as

`$\epsilon \left(n\right)=\left\{\begin{array}{l}\epsilon \left(n-1\right)+\frac{0.5}{N\left(n-1\right)}\left(2-\frac{DOD\left(n-2\right)+DOD\left(n\right)}{DOD\left(n-1\right)}\right)\begin{array}{ccc}& if& k/2\ne 0\end{array}\\ \epsilon \left(n-1\right)\begin{array}{ccc}\begin{array}{ccc}\begin{array}{ccc}& & \end{array}& & \end{array}& & otherwise\end{array}\end{array},$`

where:

• DD is the battery DOD (%) after a half-cycle duration.

• N is maximum number of cycles and is given by

`$N\left(n\right)=H{\left(\frac{DOD\left(n\right)}{100}\right)}^{-\xi }\cdot \mathrm{exp}\left(-\psi \left(\frac{1}{{T}_{ref}}-\frac{1}{{T}_{a}\left(n\right)}\right)\right)\cdot {\left({I}_{dis_ave}\left(n\right)\right)}^{-{\gamma }_{1}}\cdot {\left({I}_{ch_ave}\left(n\right)\right)}^{-{\gamma }_{2}},$`

where:

• H is the cycle number constant (cycles).

• ξ is the exponent factor for the DOD.

• ψ is the Arrhenius rate constant for the cycle number.

• Idis_ave is the average discharge current in A during a half cycle duration.

• Ich_ave is the average charge current in A during a half cycle duration.

• γ1 is the exponent factor for the discharge current.

• γ2 is the exponent factor for the charge current.

## Limitations and Assumptions

Limitations

• The minimum no-load battery voltage is 0 V and the maximum battery voltage is equal to 2 × E0.

• The minimum capacity of the battery is 0 Ah and the maximum capacity is Qmax.

Assumptions

• The internal resistance is assumed to be constant during the charge and discharge cycles and does not vary with the amplitude of the current.

• The parameters of the model are derived from the discharge characteristics. The discharging and charging characteristics are assumed to be the same.

• The capacity of the battery does not change with the amplitude of the current (there is no Peukert effect).

• The self-discharge of the battery is not represented. It can be represented by adding a large resistance in parallel with the battery terminals.

• The battery has no memory effect.

## Ports

### Input

expand all

Input port for the ambient temperature.

#### Dependencies

To enable this port, set Type to `Lithium-Ion` and select Simulate temperature effects.

### Output

expand all

Output vector of signals for the battery temperature, state-of-charge, current, voltage, age, maximum capacity, and the ambient temperature. To demultiplex the signals, you can use a Bus Selector block.

Signal

Definition

Units

Ambient Temperature

Ambient temperature

°C
Cell Temperature

The cell or internal temperature

°C
SOC

Battery SOC, represented as a percentage (between 0 and 100%). The SOC is 100% for a fully charged battery and 0% for an empty battery. The SOC is calculated as:

`$SOC=100\left(1-\frac{1}{Q}{\int }_{0}^{t}i\left(t\right)\text{\hspace{0.17em}}dt\right).$`

%
CurrentBattery currentA
VoltageBattery voltageV
AgeBattery ageEquivalent full cycles
Maximum Capacity Battery maximum capacityAh

#### Dependencies

The port outputs signals for:

• Ambient temperature if Simulate temperature effects is selected.

• Cell or internal temperature if Simulate temperature effects is selected.

• Battery age if Simulate aging effects is selected.

• Battery maximum capacity if Simulate aging effects is selected.

### Conserving

expand all

Specialized electrical conserving port associated with the battery's positive terminal.

Specialized electrical conserving port associated with the battery's negative terminal.

## Parameters

expand all

### Parameters

Battery model. The block provides predetermined charge behavior for four battery types. For the `Lithium-Ion` battery, the block provides models for simulating temperature and aging effects.

#### Dependencies

If this parameter is set to `Lithium-Ion`, these parameters are visible:

Select to model thermal dynamics.

#### Dependencies

To enable this parameter, set Type to `Lithium-Ion`. For more information, see Type.

If Simulate temperature effects is selected:

• The input port Ta is visible. For more information, see Ta.

To model thermal dynamics, the block uses battery-specific temperature parameters.

If you have a license for Simulink Design Optimization™ and empirical battery data, you can:

1. Set this parameter to `no`.

2. Estimate the temperature parameters based on the empirical data by using Simulink Design Optimization.

3. Specify the parameters in the Temperature settings using the estimated values. For more information, see Temperature.

Otherwise, use preset data that the block provides for a lithium-ion battery.

#### Dependencies

To enable this parameter, set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Type and Simulate temperature effects.

If this parameter is set to one of the preset lithium ion batteries, the parameters in the Parameters, Discharge, and Temperature, settings are disabled.

Select to model age-related battery capacity deterioration.

#### Dependencies

To enable this parameter, set Type to `Lithium-Ion`. For more information, see Type.

If this parameter is selected, the Aging settings are visible. For more information, see Aging.

Nominal voltage, Vnom, of the battery, in V. The nominal voltage represents the end of the linear zone of the discharge characteristics.

Rated capacity, Qrated, of the battery, in Ah. The rated capacity is the minimum effective capacity of the battery.

State-of-charge (SOC) of the battery, expressed as a percentage of the maximum potential charge, at the beginning of simulation. An SOC of 100% indicates a fully charged battery and 0% indicates an empty battery.

The specified value does not affect the discharge curve that the block generates if, in the Discharge settings, you click .

Response time of the battery, in s, at 95% of the final value. This value represents the voltage dynamics and can be observed when a current step is applied.

The plots show the voltage and discharge current for a battery with a response time of 30 s. ### Discharge

Select to have the block determine the parameters in the Discharge settings based on the values specified for the parameters in the Parameters settings.

#### Dependencies

Selecting this parameter disables the parameters in the Discharge settings.

Maximum theoretical capacity, Q, when a discontinuity occurs in the battery voltage, in Ah. This value is generally equal to 105% of the rated capacity.

#### Dependencies

To enable this parameter, in the Parameters settings, set Use a preset battery to `no`. For more information, see Use a preset battery.

Minimum allowable battery voltage, in V. This voltage represents the end of the discharge characteristics. At the cut-off voltage, the battery is fully discharged.

Fully charged voltage, Vfull, for a given discharge current. The fully charged voltage is not the no-load voltage.

Nominal discharge current, in A, for which the discharge curve is measured.

For example, a typical discharge current for a 1.5-Ah NiMH battery is 20% of the rated capacity: (0.2 * 1.5 Ah / 1 h = 0.3 A).

Internal resistance of the battery, in ohms. When a preset model is used, a generic value is loaded that corresponds to 1% of the nominal power (nominal voltage multiplied by the battery rated capacity). The resistance is constant during the charge and the discharge cycles and does not vary with the amplitude of the current.

Capacity, Qnom, extracted from the battery until the voltage drops under the nominal voltage. This value should be between Qexp and Qmax.

Voltage, Vexp, and the capacity, Qexp, that correspond to the end of the exponential zone. The voltage should be between Vnom and Vfull. The capacity should be between 0 and Qnom.

#### Display Characteristics

The block can generate a figure of two graphs that show the battery discharge characteristics. The discharge characteristics for these currents are presented in the second graph.

Units used for the x-axis of the plots generated by Plot.

Generate a figure of two graphs that show the battery discharge characteristics. The first graph represents the nominal discharge curve for the specified value for the Nominal Discharge Current parameter. The second graph represents the discharge curves at the specified discharge currents.  #### Dependencies

The discharge currents for the second plot are the specified values for the Discharge current [i1, i2, i3,...] (A) parameter. For more information, see Discharge current [i1, i2, i3,...] (A).

The units for the x-axis of the plots are determined by the specified value, ```Ampere-hour (Ah)``` or `Time`, for the Units parameter. For more information, see Units.

### Temperature

The Temperature settings are visible only if, in the Parameter settings, the Type parameter is set to `Lithium-Ion` and the Simulate temperature effects check box is selected. For more information, see Parameters, Type, and Simulate temperature effects.

The battery provides preset parameter values for common types of lithium-ion batteries. To use the preset parameter values, in the Parameters settings, set the Use a preset battery to parameter to one of the lithium-ion batteries. For more information, see Use a preset battery.

If you use a preset option, the only enabled parameter in the Temperature settings is Initial cell temperature (deg. C). The other parameters in the Temperature settings are disabled because the block provides the values.

Alternatively, if you have a license for Simulink Design Optimization and empirical battery data, you can estimate the temperature parameters for a lithium-ion based. To enable the parameters, In the Parameters settings, set the Use a preset battery to parameter to `no`.

Cell or internal temperature of the battery, in °C at the start of simulation.

#### Dependencies

To enable this parameter, in the Parameter settings, set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

Ambient temperature, in °C, at nominal condition of operation. The block assumes that the parameter values provided in the Parameters settings are obtained at this ambient temperature.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Ambient temperature, in °C, at the second operating condition. This value should be less than the value specified for the Nominal ambient temperature T1 (deg. C) parameter.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

#### Discharge parameters at T2

Maximum battery capacity, in Ah, at the temperature specified for the Second ambient temperature parameter T2 (deg. C).

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type parameter to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Discharge voltage at the second ambient temperature, in V, when the discharge current is first applied.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Discharge voltage at the second ambient temperature when 90% of the maximum capacity is used, in V.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Discharge voltage, in V, and the capacity, in Ah, that correspond to the end of the exponential zone, at the second ambient temperature.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

#### Thermal response and Heat loss

Total thermal resistance, in °C/W, between the cell and ambient points of measurement. It is assumed the cell temperature is equivalent to the average internal temperature of the battery.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Temperature response time constant, in s, between the cell and ambient points of measurement. You can obtain this value from the ambient temperature step response while the battery is in idle mode.

#### Dependencies

This parameter is visible if, in the Parameter settings, you set Type to `Lithium-Ion` and select Simulate temperature effects. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled if, in the Parameters settings, you set Use a preset battery to `no`. For more information, see Use a preset battery.

Power loss difference between charge and discharge, in W, when the battery is charged and discharged at the same C-rate and ambient temperature.

To determine the power loss difference ΔP, use this equation:

`$\Delta P=\frac{{t}_{c}\left({\theta }_{2}-{\theta }_{1}\right)}{{R}_{th}}$`

where θ1 and θ2 are the rates of change of the battery internal temperature (°C/s) during discharge and charge.

#### Dependencies

This parameter is visible only if, in the Parameter settings, the Type parameter is set to `Lithium-Ion` and the Simulate temperature effects check box is selected. For more information, see Parameters, Type, and Simulate temperature effects.

This parameter is enabled only if, in the Parameters settings, the Use a preset battery parameter is set to `no`. For more information, see Use a preset battery.

### Aging

The Aging settings visible if, in the Parameters settings, you set the  Type parameter to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Battery age or equivalent full cycles at the beginning of the simulation. A full cycle is defined as a complete discharge and charge to 100% DOD and 100% SOC at a nominal ambient temperature and nominal discharge and charge current. Default is `0`.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Simulation time step of the aging model, in s.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

#### Aging characteristics at ambient temperature Ta1

First ambient temperature , Ta1, during the aging performance test, in °C.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Maximum capacity at EOL at ambient temperature Ta1, in Ah.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Internal resistance at EOL at ambient temperature Ta1, in ohms.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Nominal and maximum charge current, in A.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Nominal and maximum discharge current in A.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Number of cycles at 100% depth of discharge, at nominal charge current and discharge current, and at the first ambient temperature, Ta1.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Number of cycles at 25% depth of discharge, at nominal charge current and discharge current, and at the first ambient temperature, Ta1.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Number of cycles at 100% DOD, at nominal charge current, at maximum discharge current, and at the first ambient temperature, Ta1.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Number of cycles at 100% depth of discharge, at maximum charge current, at nominal charge current and discharge current, and at the first ambient temperature, Ta1.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

#### Aging characteristics at ambient temperature Ta2

Second ambient temperature,bTa2, in °C, during the aging performance test.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

Number of cycles at 100% DOD, at nominal charge and discharge currents, and at the second ambient temperature, Ta2.

#### Dependencies

To enable this parameter, in the Parameters settings, set Type to `Lithium-Ion` and select Simulate aging effects. For more information, see Type and Simulate aging effects.

 Omar N., M. A. Monem, Y. Firouz, J. Salminen, J. Smekens, O. Hegazy, H. Gaulous, G. Mulder, P. Van den Bossche, T. Coosemans, and J. Van Mierlo. “Lithium iron phosphate based battery — Assessment of the aging parameters and development of cycle life model.” Applied Energy, Vol. 113, January 2014, pp. 1575–1585.

 Saw, L.H., K. Somasundaram, Y. Ye, and A.A.O. Tay, “Electro-thermal analysis of Lithium Iron Phosphate battery for electric vehicles.” Journal of Power Sources. Vol. 249, pp. 231–238.

 Tremblay, O., L.A. Dessaint, "Experimental Validation of a Battery Dynamic Model for EV Applications." World Electric Vehicle Journal. Vol. 3, May 13–16, 2009.

 Zhu, C., X. Li, L. Song, and L. Xiang, “Development of a theoretically based thermal model for lithium ion battery pack.” Journal of Power Sources. Vol. 223, pp. 155–164.