Battery

Generic battery model

Libraries:
Simscape / Electrical / Specialized Power Systems / 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` mΩ
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.

Parameter	Value
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.

Parameter	Value
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.

Parameter	Value
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)

$f_{1} (i t, i *, i, E x p) = E_{0} - K \cdot \frac{Q}{Q - i t} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + {Laplace}^{- 1} (\frac{E x p (s)}{S e l (s)} \cdot 0)$
Charge Model (i* < 0)

$f_{2} (i t, i *, i, E x p) = E_{0} - K \cdot \frac{Q}{i t + 0.1 \cdot Q} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + {Laplace}^{- 1} (\frac{E x p (s)}{S e l (s)} \cdot \frac{1}{s})$

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

Discharge Model (i* > 0)

$f_{1} (i t, i *, i) = E_{0} - K \cdot \frac{Q}{Q - i t} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + A \cdot \exp (- B \cdot i t)$
Charge Model (i* < 0)

$f_{2} (i t, i *, i) = E_{0} - K \cdot \frac{Q}{i t + 0.1 \cdot Q} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + A \cdot \exp (- B \cdot i t)$

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

Discharge Model (i* > 0)

$f_{1} (i t, i *, i, E x p) = E_{0} - K \cdot \frac{Q}{Q - i t} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + {Laplace}^{- 1} (\frac{E x p (s)}{S e l (s)} \cdot 0)$
Charge Model (i* < 0)

$f_{2} (i t, i *, i, E x p) = E_{0} - K \cdot \frac{Q}{| i t | + 0.1 \cdot Q} \cdot i * - K \cdot \frac{Q}{Q - i t} \cdot i t + {Laplace}^{- 1} (\frac{E x p (s)}{S e l (s)} \cdot \frac{1}{s}) .$

In the equations:
- E_Batt 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)

$f_{1} (i t, i *, i, T, T_{a}) = E_{0} (T) - K (T) \cdot \frac{Q (T_{a})}{Q (T_{a}) - i t} \cdot (i * + i t) + A \cdot \exp (- B \cdot i t) - C \cdot i t$

$V_{b a t t} (T) = f_{1} (i t, i *, i, T, T_{a}) - R (T) \cdot i$
Charge Model (i* < 0)

$f_{1} (i t, i *, i, T, T_{a}) = E_{0} (T) - K (T) \cdot \frac{Q (T_{a})}{i t + 0.1 \cdot Q (T_{a})} \cdot i * - K (T) \cdot \frac{Q (T_{a})}{Q (T_{a}) - i t} \cdot i t + A \cdot \exp (- B \cdot i t) - C \cdot i t$

$V_{b a t t} (T) = f_{1} (i t, i *, i, T, T_{a}) - R (T) \cdot i,$

with

$E_{0} (T) = E_{0} |_{T_{r e f}} + \frac{\partial E}{\partial T} (T - T_{r e f})$

$K (T) = K |_{T_{r e f}} \cdot \exp (α (\frac{1}{T} - \frac{1}{T_{r e f}}))$

$Q (T_{a}) = Q |_{T_{a}} + \frac{Δ Q}{Δ T} \cdot (T_{a} - T_{r e f})$

$R (T) = R |_{T_{r e f}} \cdot \exp (β (\frac{1}{T} - \frac{1}{T_{r e f}})),$

where:
- T_ref is the nominal ambient temperature, in K.
- T is the cell or internal temperature, in K.
- T_a 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.
- ΔQ/ΔT 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:

$T (t) = L^{- 1} (\frac{P_{l o s s} R_{t h} + T_{a}}{1 + s \cdot t_{c}}),$

where:
- R_th is thermal resistance, cell to ambient (°C/W).
- t_c is thermal time constant, cell to ambient (s).
- P_loss is the overall heat generated (W) during the charge or discharge process and is given by
  
  $P_{l o s s} = (E_{0} (T) - V_{b a t t} (T)) \cdot i + \frac{\partial E}{\partial T} \cdot i \cdot T .$

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:

$Q (n) = {\begin{cases} Q_{B O L} - ε (n) \cdot (Q_{B O L} - Q_{E O L}) \begin{matrix} i f & k / 2 \neq 0 \end{matrix} \\ Q (n - 1) \begin{matrix} \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & o t h e r w i s e \end{matrix} \end{cases}$

$R (n) = {\begin{cases} R_{B O L} + ε (n) \cdot (R_{E O L} - R_{B O L}) \begin{matrix} i f & k / 2 \neq 0 \end{matrix} \\ R (n - 1) \begin{matrix} \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & o t h e r w i s e \end{matrix} \end{cases},$

with

$n = k T_{h} \begin{matrix} (k = 1, 2, 3, ... \infty) \end{matrix}$

where:

T_h is the half-cycle duration, in s. A complete cycle is obtained when the battery is discharged and charged or conversely.
Q_BOL is the battery's maximum capacity, in Ah, at the beginning of life (BOL) and at nominal ambient temperature.
Q_EOL is the battery's maximum capacity, in Ah, at the end of life (EOL) and at nominal ambient temperature.
R_BOL is the battery's internal resistance, in ohms, at the BOL and at nominal ambient temperature.
R_EOL 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

$ε (n) = {\begin{cases} ε (n - 1) + \frac{0.5}{N (n - 1)} (2 - \frac{D O D (n - 2) + D O D (n)}{D O D (n - 1)}) \begin{matrix} i f & k / 2 \neq 0 \end{matrix} \\ ε (n - 1) \begin{matrix} \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & o t h e r w i s e \end{matrix} \end{cases},$

where:

DD is the battery DOD (%) after a half-cycle duration.
N is maximum number of cycles and is given by
$N (n) = H {(\frac{D O D (n)}{100})}^{- ξ} \cdot \exp (- ψ (\frac{1}{T_{r e f}} - \frac{1}{T_{a} (n)})) \cdot {(I_{d i s_a v e} (n))}^{- γ_{1}} \cdot {(I_{c h_a v e} (n))}^{- γ_{2}},$
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.
- I_{dis_ave} is the average discharge current in A during a half cycle duration.
- I_{ch_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.

Examples

Ni-MH Battery Model

A 200 V, 6.5 Ah Ni-MH battery model during charge and discharge process.

Open Model

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 Q_max.

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

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Ta — Ambient temperature
Simulink^® signal | scalar

Input port for the ambient temperature.

Dependencies

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

Output

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m — Battery temperature, state-of-charge, current, voltage, age, maximum capacity, and ambient temperature
Simulink signal | vector

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: $S O C = 100 (1 - \frac{1}{Q} \int_{0}^{t} i (t) d t) .$	%
Current	Battery current	A
Voltage	Battery voltage	V
Age	Battery age	Equivalent full cycles
Maximum Capacity	Battery maximum capacity	Ah

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

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+ — Positive terminal
specialized electrical

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

- — Negative terminal
specialized electrical

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

Parameters

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Parameters

Type — Battery model
`Lithium-Ion` (default) | `Lead-Acid` | `Nickel-Cadmium` | `Nickel-Metal-Hydride`

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:

Simulate temperature effects. For more information, see Simulate temperature effects.
Simulate aging effects. For more information, see Simulate aging effects.

Simulate temperature effects — Thermal dynamics
off (default) | on

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:

Temperature settings are visible. For more information, see Temperature.
The input port Ta is visible. For more information, see Ta.

Use a preset battery — Parameterization
`no` (default) | `3.3V 2.3Ah (LiFePO4)` | `3.6V 2050mAh (LiCoO2)` | `3.6V 2.0Ah` | `3.6V 3.6Ah (LiNiO2)` | `3.6V 4.5Ah` | `3.6V 48Ah (LiNiO2)` | `3.7V 4.4Ah` | `7.4V 5.4Ah (LiCoO2)` | `11.1V 6600mAh (LiCoO2)` | `12.8V 40Ah (LiFeMgPO4)`

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:

Set this parameter to no.
Estimate the temperature parameters based on the empirical data by using Simulink Design Optimization.
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.

Simulate aging effects — Model age-related battery capacity deterioration
off (default) | on

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 (V) — Nominal voltage
`7.2` (default) | positive scalar

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

Rated capacity (Ah) — Rated capacity
`5.4` (default) | positive scalar

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

Initial state-of-charge (%) — Initial SOC
`100` (default)

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 Plot.

Battery response time (s) — Response time
`30` (default) | nonnegative scalar

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

Determined from the nominal parameters of the battery — Discharge parameter determination
on (default) | off

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 capacity (Ah) — Maximum amp-hour capacity
`5.4` (default) | positive scalar

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.

Cut-off Voltage (V) — Cut-off voltage
`5.4` (default) | positive scalar

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 (V) — Fully charged voltage
`8.3807` (default) | positive scalar

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

Nominal discharge current (A) — Nominal discharge current
`2.3478` (default) | positive scalar

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 (Ohms) — Internal resistance
`0.013333` (default) | positive scalar

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 (Ah) at nominal voltage — Amp-hour capacity at nominal voltage
`4.8835` (default) | positive scalar

Capacity, Q_nom, extracted from the battery until the voltage drops under the nominal voltage. This value should be between Q_exp and Q_max.

Exponential zone [Voltage (V), Capacity (Ah)] — Exponential zone voltage and capacity
`[7.7788 0.2653]` (default) | nonnegative vector

Voltage, V_exp, and the capacity, Q_exp, that correspond to the end of the exponential zone. The voltage should be between V_nom and V_full. The capacity should be between 0 and Qnom.

Display Characteristics

Discharge current [i1, i2, i3,...] (A) — Discharge characteristic plot currents
`[6.5 13 32.5]` (default)

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 — Discharge characteristic plot x-axis units
`Time` (default) | `Ampere-hour`

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

Plot — Plot discharge characteristics

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.

Initial cell temperature (deg. C) — Initial battery temperature
`20` (default) | scalar

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.

Nominal ambient temperature T1 (deg. C) — Nominal ambient temperature
`20` (default) | scalar

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.

Second ambient temperature T2 (deg. C) — Second ambient temperature
`-30` (default) | scalar

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 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 capacity (Ah) — Maximum amp-hour capacity
`4.8` (default) | positive scalar

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.

Initial discharge voltage (V) — Initial discharge voltage
`7.1` (default) | positive scalar

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

Dependencies

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.

Voltage at 90% maximum capacity (V) — 90% maximum capacity voltage
`5.655` (default) | positive scalar

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

Dependencies

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.

Exponential zone [Voltage (V), Capacity (Ah)] — Exponential zone voltage and capacity
`[6.58 1]` (default) | positive vector

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 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

Thermal resistance, cell-to-ambient (deg. C/W) — Thermal resistance
`0.6` (default) | positive scalar

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

Thermal time constant, cell-to-ambient (s) — Thermal time constant
`2000` (default) | positive scalar

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

Heat loss difference [charge vs. discharge] (W) — Heat loss difference
`0` (default) | scalar

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:

$Δ P = \frac{t_{c} (θ_{2} - θ_{1})}{R_{t h}}$

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.

Initial battery age (Equivalent full cycles) — Initial battery age
`0` (default) | nonnegative scalar

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.