Battery (Table-Based)

Tabulated battery model

Libraries:
Simscape / Electrical / Sources
Simscape / Battery / Cells

Description

The Battery (Table-Based) block represents a high-fidelity battery model. The block calculates open-circuit voltage as a function of charge level and optional temperature using lookup tables and includes several modeling options:

Self-discharge
Battery fade
Charge dynamics
Calendar aging

Note

For all the table-based parameters, the Battery (Table-Based) block supports linear interpolation only. For extrapolation, set the Extrapolation method for all tables parameter to either Nearest, Linear, or Error.

For rows and columns, it follows the row-column convention, whereas rows are indexed first and, subsequently, columns.

The plot shows a battery whose performance varies with temperature and state of charge changes, as typically found on a datasheet.

Use this block to parameterize batteries with complex open-circuit voltage behavior from datasheets or experimental results. For a simpler representation of a battery, see the Battery block.

The Battery (Table-Based) block has two optional ports that you can expose by setting the corresponding parameters. The extra physical signal port, SOC, outputs the internal state of charge. Use this functionality to change the load behavior as a function of state of charge, without the complexity of building a charge state estimator. To expose the SOC port, in the Main setting, set the Expose SOC measurement port parameter to Yes.

To expose the thermal port, in the Thermal setting, set the Thermal port parameter to Model. The thermal port represents the battery thermal mass.

You can also choose different built-in parameterizations for this block. For more information, see the Predefined Parameterization section.

The battery equivalent circuit is made up of the fundamental battery model, the self-discharge resistance R_SD, the charge dynamics model, and the series resistance R₀.

Battery Model

The block calculates the open-circuit voltage, or the voltage across the fundamental battery model by interpolation:

$v_{0} = v_{0} (SOC, T)$

Where:

v₀ is the open-circuit voltage of the battery. Specify the grid of lookup values using the Open-circuit voltage, V0(SOC,T) parameter if tabulating parameters over temperature, or Open-circuit voltage, V0(SOC) otherwise.
SOC is the ratio of current charge to nominal battery capacity specified in the Cell capacity, AH parameter along with the effects of the temperature dependent fade percentage change in cell capacity, δ_AH(n, Tfade), specified in the Percentage change in cell capacity, dAH(N, Tfade) parameter. Specify the SOC breakpoints using the Vector of state-of-charge values, SOC parameter. The block estimates the nominal battery capacity based on the number of cycles and the temperature of the battery by interpolating the specified temperature dependent fade characteristic and the Cell capacity, AH parameter.
SOC represents the normalized data with respect to q_nom.
For the lookup-table based fade characteristic option,

$q_{n o m} (T, n) = (1 + \frac{δ_{A H} (n, T_{f a d e})}{100}) * A H A h .$
For the equation-based fade characteristic option,

$q_{n o m} (T, n) = (1 + \frac{δ_{A H}}{100} \sqrt{\frac{n}{N}}) * A H A h .$
Finally, SOC is obtained from the following equation.

$S O C (t) = \frac{1}{q_{n o m} (T, n)} \int (i (t) - \frac{V_{o p e n} (T, n, t)}{R_{S D} (T, n)}) d t$
Where:
- q_nom is the cell capacity of the battery. Specify this value using the Cell capacity, AH parameter.
- N is the reference number of discharge cycles over which you specify percent change of several battery parameters. Set this value using the Number of discharge cycles, N parameter.
- n is the present number of cycles of the battery.
- δ_AH is the percentage change in cell capacity of the battery after N discharge cycles.
T is the battery temperature. Specify the T breakpoints using the Vector of temperatures, T parameter if tabulating the parameters over temperature.

The block also models the series resistance R₀ as a function of state of charge and optional temperature. Specify the grid of lookup values for the series resistance using the Terminal resistance, R0(SOC,T) parameter if tabulating the parameters over temperature, or Terminal resistance, R0(SOC) otherwise.

Modeling Self-Discharge

When the battery terminals are open-circuit, it is still possible for internal currents to discharge the battery. This behavior is called self-discharge. To enable this effect, set the Self-discharge parameter to Enabled.

The block models these internal currents with a temperature-dependent resistance R_SD(T) across the terminals of the fundamental battery model. You can specify the lookup values for this resistance using the Self-discharge resistance, Rleak(T) parameter if tabulating the parameters over temperature, or Self-discharge resistance, Rleak otherwise.

Modeling Charge Dynamics

Batteries are not able to respond instantaneously to load changes. They require some time to achieve a steady-state. This time-varying property is a result of battery charge dynamics and is modeled using parallel RC sections in the equivalent circuit.

You can model battery charge dynamics using the Charge dynamics parameter:

No dynamics — The equivalent circuit contains no parallel RC sections. There is no delay between terminal voltage and internal charging voltage of the battery.
One time-constant dynamics — The equivalent circuit contains one parallel RC section. Specify the time constant using the First time constant, tau1(SOC,T) parameter if tabulating parameters over temperature or First time constant, tau1(SOC) otherwise.
Two time-constant dynamics — The equivalent circuit contains two parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T) and Second time constant, tau2(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC) and Second time constant, tau2(SOC) otherwise.
Three time-constant dynamics — The equivalent circuit contains three parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), and Third time constant, tau3(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), and Third time constant, tau3(SOC) otherwise.
Four time-constant dynamics — The equivalent circuit contains four parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), Third time constant, tau3(SOC,T), and Fourth time constant, tau4(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), Third time constant, tau3(SOC), and Fourth time constant, tau4(SOC) otherwise.
Five time-constant dynamics — The equivalent circuit contains five parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), Third time constant, tau3(SOC,T), Fourth time constant, tau4(SOC,T), and Fifth time constant, tau5(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), Third time constant, tau3(SOC), Fourth time constant, tau4(SOC), and Fifth time constant, tau5(SOC) otherwise.

This diagram shows the equivalent circuit for the block configured with two time-constant dynamics.

In the diagram:

R₁ and R₂ are the parallel RC resistances. Specify these values with the First polarization resistance, R1(SOC,T) and Second polarization resistance, R2(SOC,T) parameters, respectively, if tabulating parameters over temperature or First polarization resistance, R1(SOC) and Second polarization resistance, R2(SOC) otherwise.
C₁ and C₂ are the parallel RC capacitances. The time constant τ for each parallel section relates the R and C values using the relationship $C = τ / R$ . Specify τ for each section using the First time constant, tau1(SOC,T) and Second time constant, tau2(SOC,T) parameters, respectively, if tabulating parameters over temperature or First time constant, tau1(SOC) and Second time constant, tau2(SOC) otherwise.
R₀ is the series resistance. Specify this value with the Terminal resistance, R0(SOC,T) parameter if tabulating parameters over temperature or Terminal resistance, R0(SOC) otherwise.

Modeling Battery Fade

Battery fade is the deterioration of battery performance over repeated charge and discharge cycles. When the Fade characteristic parameter is set to Equations, the battery fade is modeled as follows.

The open-circuit voltage across the fundamental battery model fades proportionally with the number of discharge cycles n:

$v_{0, fade} = v_{0} (1 + \frac{δ_{v_{0}}}{100} \frac{n}{N})$

Where δ_v₀ is the percent change in open-circuit voltage after N discharge cycles. Specify δ_v₀ using the Change in open-circuit voltage after N discharge cycles (%) parameter.

Note

The Battery (Table-Based) block tracks the current and integrates it over time. The number of discharge cycles n increases by 1 every time an equivalent cell discharge capacity is extracted.

The nominal charge, from which state of charge is calculated, fades with the square root of number of discharge cycles:

$q_{n o m, fade} = q_{n o m} (1 + \frac{δ_{A H}}{100} \sqrt{\frac{n}{N}})$

All resistances in the battery model also fade with the square root of the number of discharge cycles:

$R_{i, fade} = R_{i} (1 + \frac{δ_{R_{i}}}{100} \sqrt{\frac{n}{N}})$

Where:

R_i is the i^th resistance
δ_{R_i} is the percent change in this resistance over N cycles

Depending on how you have configured the block, the resistances might include:

The series resistance — Specify the percent change over N cycles using the Change in terminal resistance after N discharge cycles (%) parameter.
The self-discharge resistance — Specify the percent change over N cycles using the Change in self-discharge resistance after N discharge cycles (%) parameter.
The first charge dynamics resistance — Specify the percent change over N cycles using the Change in first polarization resistance after N discharge cycles (%) parameter.
The second charge dynamics resistance — Specify the percent change over N cycles using the Change in second polarization resistance after N discharge cycles (%) parameter.
The third charge dynamics resistance — Specify the percent change over N cycles using the Change in third polarization resistance after N discharge cycles (%) parameter.
The fourth charge dynamics resistance — Specify the percent change over N cycles using the Change in fourth polarization resistance after N discharge cycles (%) parameter.
The fifth charge dynamics resistance — Specify the percent change over N cycles using the Change in fifth polarization resistance after N discharge cycles (%) parameter.

Note

You can also model the battery fade characteristic by using lookup tables (temperature independent) or lookup tables (temperature dependent). Choosing any of these two options changes the blocks parameters accordingly. For more information, see the Fade parameters tab.

Modeling Thermal Effects

The battery temperature is determined from a summation of all the ohmic losses included in the model:

$M_{t h} \dot{T} = \sum_{i} V_{T, i}^{2} / R_{T, i}$

Where:

M_th is the battery thermal mass.
i corresponds to the i^th ohmic loss contributor. Depending on how you have configured the block, the losses might include:
- The series resistance
- The self-discharge resistance
- The first charge dynamics segment
- The second charge dynamics segment
- The third charge dynamics segment
- The fourth charge dynamics segment
- The fifth charge dynamics segment
V_T,i is the voltage drop across resistor i.
R_T,i is resistor i.

Modeling Battery Aging

You can model the battery performance deterioration that occurs when the battery is not used. Calendar aging affects both the internal resistance and capacity. In particular, the resistance increase depends by various mechanisms such as the creation of Solid Electrolyte Interface (SEI) at both anode and cathode and the corrosion of the current collector. These processes mainly depends on the storage temperature, the storage state of charge, and time.

You can model the calendar aging in the Battery (Table-Based) block by setting the Modeling option parameter to:

Equation-based
Tabulated: temperature
Tabulated: time and temperature

Note

The Battery (Table-Based) block only applies the calendar aging during initialization. When you set the Internal resistance calendar aging or Capacity calendar aging parameters to Enabled, the block exposes the Vector of time intervals parameter that represents the time the battery has aged before the start of the simulation. Calendar aging during the simulation is not covered with this option.

Equation-based

This equation defines the terminal resistance increase of the battery due to calendar aging:

$\begin{matrix} α_{r} (T, V_{o c}) = (b V_{o c} - c) e^{- \frac{q d}{k T}}, \\ R = R_{0} (1 + \sum_{i = 1}^{i = n} α_{r} (T_{i}, V_{o c}) (t_{i}^{a} - t_{i - 1}^{a})), \end{matrix}$

where:

V_oc is the Normalized open-circuit voltage during storage, V/Vnom.
R₀ is the Internal resistance.
t_i is the time sample derived from the Vector of time intervals parameter.
T_i is derived from the Vector of temperatures, T parameter.
b is the Terminal resistance linear scaling for voltage, b.
c is the Terminal resistance constant offset for voltage, c.
d is the Terminal resistance temperature-dependent exponential increase, d.
a is the Terminal resistance time exponent, a.
q is the electron's elementary charge, in C.
k is the Boltzmann constant, in J/K.

This equation defines the capacity decrease of the battery due to calendar aging:

$\begin{array}{l} α_{c} (T, V_{o c}) = (b V_{o c} - c) e^{- \frac{q d}{k T}}, \\ C = C_{0} (1 - \sum_{i = 1}^{i = n} α_{c} (T_{i}, V_{o c}) (t_{i}^{a} - t_{i - 1}^{a})), \end{array}$

where:

C₀ is the initial capacity.
b is the Capacity linear scaling for voltage, b.
c is the Capacity constant offset for voltage, c.
d is the Capacity temperature-dependent exponential increase, d.
a is the Capacity time constant, a.

If you set the Storage condition parameter to Specify state-of-charge during storage, the block converts the state of charge during storage into normalized open-circuit voltage using the tabulated voltage V₀ against the state of charge and the temperature during storage.

Tabulated: temperature

The aged terminal resistance is the product between the terminal resistance, R₀(SOC,T), the percentage resistance increase, dR₀, and the power law that describes the time dependence of the calendar aging:

$R_{0} (S O C, T; t_{st}, T_{st}) = R_{0} (S O C, T) (1 + \sum_{i = 1}^{n} \frac{d R_{0} (T_{st, i})}{100} (\frac{t^{a}_{st, i} - t^{a}_{st, i - 1}}{t^{a}_{st,m}})),$

where:

T is the battery temperature. Specify the T breakpoints using the Vector of temperatures, T parameter if tabulating the parameters over temperature.
T_st is the Vector of storage temperatures.
t_st,i and t_st,i-1 are the time samples derived from the Vector of time intervals.
t₀ is assumed to be null.
t_st,m is the moment in time at which the resistance increase, dR₀, is measured.

The same equation applies to the calculation of the aged battery capacity.

Tabulated: time and temperature

The aged terminal resistance is the product between the terminal resistance, R₀(SOC,T) and dR₀:

$R_{0} (S O C, T; Δ t_{st}, T_{st}) = R_{0} (S O C, T) (1 + \sum_{i = 1}^{n} \frac{d R_{0} (Δ t_{st, i}, T_{st, i})}{100}) .$

The same equation applies to the calculation of the aged battery capacity.

Predefined Parameterization

There are multiple available built-in parameterizations for the Battery (Table-Based) block.

This pre-parameterization data allows you to set up the block to represent components by specific suppliers. The parameterizations of these batteries match the discharge curves in the manufacturer data sheets. To load a predefined parameterization, double-click the Battery (Table-Based) block, click the <click to select> hyperlink of the Selected part parameter and, in the Block Parameterization Manager window, select the part you want to use from the list of available components.

The available pre-parameterized data model steady state electrical parameters of a lithium-ion battery. The Open-circuit voltage, V0(SOC), Terminal resistance, R0(SOC, T), Cell capacity, AH, Percentage change in cell capacity, dAH, and Percentage change in Open-circuit voltage, dV0(N) parameters are parameterized from characteristics curves in the manufacture datasheets. The change in series resistance with the battery cycle life, the thermal mass, and the dynamic RC network parameters are not parameterized. Instead, the net resistance of the RC network resistors is summed to the series resistance of the specific pre-parameterized data. If you need to fill the RC parameter data, subtract the net RC network resistance from the series resistance data.

The available data is parameterized for 1C discharge current for different temperatures up to the minimum terminal voltage in the datasheet. The data below the minimum terminal voltage is extrapolated. The Open-circuit voltage, V0(SOC) parameter is approximated to be temperature independent. At lower temperature, in the low SOC region, the terminal resistances are constant and equal to the value of the resistance at the minimum terminal voltage. This might lead to higher thermal losses.

Note

The predefined parameterizations of Simscape™ components use available data sources for the parameter values. Engineering judgement and simplifying assumptions are used to fill in for missing data. As a result, expect deviations between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine component models as necessary.

For more information about pre-parameterization and for a list of the available components, see List of Pre-Parameterized Components.

Plot Basic Voltage-Charge Characteristics

You can plot the basic voltage-charge characteristics of the Battery (Table-Based) block without building a complete model. Use the plots to explore the impact of your parameter choices on device characteristics. If you parameterize the block from a datasheet, you can compare your plots to the datasheet to check that you parameterized the block correctly. If you have a complete working model but do not know which manufactured part to use, you can compare your plots to datasheets to help you decide.

To plot the basic characteristics, right-click the block and select Battery > Basic characteristics from the context menu. For more information about the Basic characteristics option, see Plot Basic Voltage-Charge Characteristics of Battery Blocks.

Examples

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Use Simscape™ Electrical™ to model a helicopter with coaxial rotors suitable to fly on Mars. This helicopter takes inspiration from Ingenuity, the robotic helicopter developed by NASA, which accomplished the first powered flight on another planet.

Open Model

DC Fast Charger for Electric Vehicle

Models a DC fast charging station connected with the battery pack of an Electric Vehicle (EV).

Open Model

Battery Pack Fault Protection

Model fault and fault protection using a fuse in an automotive battery pack. The battery pack consists of several battery modules, which are combinations of cells in series and parallel. Each battery cell is modeled using the Battery (Table-Based) Simscape Electrical block. In this example, the initial temperature and the state of charge are the same for all cells. Four battery modules, three similar and one differing from the other three, are connected in series to simulate a battery pack. The results in this example assume an initial ambient temperature equal to 25 degree Celsius. The Control subsystem defines the logic used to determine the battery pack coolant flow rate. A fuse is placed inline to battery pack as a measure of fault protection.

Open Model

Ports

Output

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SOC — Battery charge level, C
physical signal

Physical signal port that outputs the internal state of charge. Use this output port to change load behavior as a function of state of charge, without the complexity of building a charge state estimator. The state of charge is the normalized value estimated from the ratio of current charge with the nominal battery capacity, q_nom(T,n). The block estimates the current battery charge by integrating the battery terminal output current. To convert the state of charge into actual charge, you must use the correct nominal battery capacity for each temperature.

Dependencies

To enable this port, in the Main setting, set the Expose SOC measurement port parameter to Yes.

Conserving

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+ — Positive terminal
electrical

Electrical conserving port associated with the battery positive terminal.

- — Negative terminal
electrical

Electrical conserving port associated with the battery negative terminal.

H — Battery thermal mass
thermal

Thermal conserving port that represents the battery thermal mass.

Dependencies

To enable this port, in the Thermal setting, set the Thermal port parameter to Yes.

Parameters

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Selected part — Predefined parameterization option
`<click to select>` (default)

Option to parameterize the block to represent components by specific suppliers. Click the <click to select> hyperlink to open the Block Parameterization Manager window. For more information about the Block Parameterization Manager, see Load Predefined Parameterizations.

Main

Vector of state-of-charge values, SOC — SOC breakpoints
`[0, .1, .25, .5, .75, .9, 1]` (default) | vector of scalars in the range [0,1]

Vector of state-of-charge breakpoints defining the points at which you specify lookup data. This vector must be strictly ascending. The state-of-charge value is calculated with respect to the nominal battery capacity specified in the Cell capacity, AH parameter. SOC is the ratio of the available battery charge, q_battery and the nominal battery capacity, q_nom(T,n). You must make sure that, for each temperature, SOC = 1 represents the respective battery charge capacity specified in the Cell capacity, AH parameter, assuming a fresh battery with a number of cycles, N, equal to 1 and δ_AH(n = 1, T_fade) = 0.

$S O C = \frac{q_{battery}}{q_{nom} (T, n)} for N = 1 and δ_{AH} (n, T_{fade}) = 0, q_{nom} (T, n) = A H$

Tabulate parameters over temperature — Select whether to tabulate battery parameters over temperature
`Yes` (default) | `No`

Select whether to tabulate battery parameters over temperature.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`T_dependence`
Values:	`"yes"` (default) \| `"no"`

Current directionality — Enable direction of current
`Disabled` (default) | `Enabled`

Whether to enable current directionality. If you set this parameter to Enabled, the terminal resistance depends on the direction of the current.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_dir`
Values:	`"currentDirectionality"` (default) \| `"noCurrentDirectionality"`

Terminal voltage operating range [Min Max] — Terminal voltage operating range
`[0, inf]` `V` (default) | vector of positive numbers

Operating range of the terminal voltage. This parameter must be a vector of size 1-by-2 that defines the minimum and maximum values of the terminal voltage.

Vector of temperatures, T — T breakpoints
`[278, 293, 313]` `K` (default) | vector of positive numbers

Vector of temperature breakpoints defining the points at which you specify lookup data. This vector must be strictly ascending and greater than 0 K.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to Yes.

Open-circuit voltage, V0(SOC,T) — V0 lookup table with temperature breakpoint
`[3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19]` `V` (default) | matrix of nonnegative numbers

Lookup data for open-circuit voltages across the fundamental battery model at the specified SOC and temperature breakpoints.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to Yes.

Open-circuit voltage, V0(SOC) — V0 lookup table
`[3.5057, 3.566, 3.6337, 3.7127, 3.9259, 4.0777, 4.1928]` `V` (default) | matrix of nonnegative numbers

Lookup data for open-circuit voltages across the fundamental battery model at the specified SOC.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to No.

Terminal resistance, R0(SOC,T) — R0 lookup table with temperature breakpoint
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC and temperature breakpoints.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to Yes and the Current directionality parameter is set to Disabled.

Terminal resistance during discharging, R0(SOC,T) — R0 lookup table with temperature breakpoint during discharging phase
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC and temperature breakpoints during the discharging phase.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to Yes and the Current directionality parameter is set to Enabled.

Terminal resistance during charging, R0(SOC,T) — R0 lookup table with temperature breakpoint during charging phase
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC and temperature breakpoints during the charging phase.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to Yes and the Current directionality parameter is set to Enabled.

Terminal resistance, R0(SOC) — R0 lookup table
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to No and the Current directionality parameter is set to Disabled.

Terminal resistance during discharging, R0(SOC) — R0 lookup table during discharging phase
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC during the discharging phase.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to No and the Current directionality parameter is set to Enabled.

Terminal resistance during charging, R0(SOC) — R0 lookup table during charging phase
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Lookup data for series resistance of the battery at the specified SOC during the charging phase.

Dependencies

This parameter is visible only when the Tabulate parameters over temperature parameter is set to No and the Current directionality parameter is set to Enabled.

Cell capacity, AH — Battery capacity when fully charged
`27` `hr*A` (default) | nonnegative scalar

Cell capacity of the battery. The block calculates the state of charge by dividing the accumulated charge by this value. The block calculates accumulated charge by integrating the battery current.

Self-discharge — Select whether to model the self-discharge resistance of the battery
`Disabled` (default) | `Enabled`

Select whether to model the self-discharge resistance of the battery. The block models this effect as a resistor across the terminals of the fundamental battery model.

As temperature increases, self-discharge resistance decreases, causing self-discharge to increase. If the decrease in resistance is too fast, thermal runaway of the battery and numerical instability can occur. You can resolve this instability by making any of these changes:

Decrease the thermal resistance
Decrease the gradient of the self-discharge resistance with respect to temperature
Increase the self-discharge resistance

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_leak`
Values:	`"disabled"` (default) \| `"enabled"`

Self-discharge resistance, Rleak(T) — Resistance that represents battery self-discharge at temperature breakpoints
`[8000, 7000, 6000]` `Ohm` (default) | vector of positive numbers

Lookup data for self-discharge resistance of the battery at the specified temperature breakpoints. This resistance acts across the terminals of the fundamental battery model.

Dependencies

Enabled when the Self-discharge parameter is set to Enabled and Tabulate parameters over temperature is set to Yes.

Self-discharge resistance, Rleak — Resistance that represents battery self-discharge
`7e3` `Ohm` (default) | positive scalar

Lookup data for self-discharge resistance of the battery. This resistance acts across the terminals of the fundamental battery model.

Dependencies

This parameter is visible only when the Self-discharge parameter is set to Enabled and the Tabulate parameters over temperature parameter is set to No.

Extrapolation method for all tables — Method of extrapolation for tables
`Nearest` (default) | `Linear` | `Error`

Extrapolation method for all the table based parameters:

Linear — Estimates values beyond the dataset by creating a tangent line at the end of the known data and extending it beyond that limit.
Nearest — Extrapolates a value at query point that is the value at the nearest sample grid point.
Error — Returns an error if the value goes beyond the known dataset. If you select this option, the block does not use extrapolation.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`extrapolation_option`
Values:	`"nearest"` (default) \| `"linear"` \| `"error"`

Expose SOC measurement port — Method of extrapolation for tables
`No` (default) | `Yes`

Whether to expose the state-of-charge measurement port.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`SOC_port`
Values:	`"no"` (default) \| `"yes"` \| `"error"`

Dynamics

Charge dynamics — Battery charge dynamics model
`No dynamics` (default) | `One time-constant dynamics` | `Two time-constant dynamics` | `Three time-constant dynamics` | `Four time-constant dynamics` | `Five time-constant dynamics`

Select how to model battery charge dynamics. This parameter determines the number of parallel RC sections in the equivalent circuit:

No dynamics — The equivalent circuit contains no parallel RC sections. There is no delay between terminal voltage and internal charging voltage of the battery.
One time-constant dynamics — The equivalent circuit contains one parallel RC section. Specify the time constant using the First time constant, tau1(SOC,T) parameter if tabulating parameters over temperature or First time constant, tau1(SOC) otherwise.
Two time-constant dynamics — The equivalent circuit contains two parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T) and Second time constant, tau2(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC) and Second time constant, tau2(SOC) otherwise.
Three time-constant dynamics — The equivalent circuit contains three parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), and Third time constant, tau3(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), and Third time constant, tau3(SOC) otherwise.
Four time-constant dynamics — The equivalent circuit contains four parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), Third time constant, tau3(SOC,T), and Fourth time constant, tau4(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), Third time constant, tau3(SOC), and Fourth time constant, tau4(SOC) otherwise.
Five time-constant dynamics — The equivalent circuit contains five parallel RC sections. Specify the time constants using the First time constant, tau1(SOC,T), Second time constant, tau2(SOC,T), Third time constant, tau3(SOC,T), Fourth time constant, tau4(SOC,T), and Fifth time constant, tau5(SOC,T) parameters if tabulating parameters over temperature or First time constant, tau1(SOC), Second time constant, tau2(SOC), Third time constant, tau3(SOC), Fourth time constant, tau4(SOC), and Fifth time constant, tau5(SOC) otherwise.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_dyn`
Values:	`"off"` (default) \| `"rc1"` \| `"rc2"` \| `"rc3"` \| `"rc4"` \| `"rc5"`

First polarization resistance, R1(SOC,T) — First RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Lookup data for the first parallel RC resistance at the specified SOC and temperature breakpoints. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to One time-constant dynamics, Two time-constant dynamics, Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics and Tabulate parameters over temperature to Yes.

First polarization resistance, R1(SOC) — First RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Lookup data for the first parallel RC resistance at the specified SOC. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

First time constant, tau1(SOC,T) — First RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Lookup data for the first parallel RC time constant at the specified SOC and temperature breakpoints.

Dependencies

First time constant, tau1(SOC) — First RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Lookup data for the first parallel RC time constant at the specified SOC.

Dependencies

Second polarization resistance, R2(SOC,T) — Second RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Lookup data for the second parallel RC resistance at the specified SOC and temperature breakpoints. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Two time-constant dynamics, Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics and Tabulate parameters over temperature to Yes.

Second polarization resistance, R2(SOC) — Second RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Lookup data for the second parallel RC resistance at the specified SOC. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

Second time constant, tau2(SOC,T) — Second RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Lookup data for the second parallel RC time constant at the specified SOC and temperature breakpoints.

Dependencies

Second time constant, tau2(SOC) — Second RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Lookup data for the second parallel RC time constant at the specified SOC.

Dependencies

Third polarization resistance, R3(SOC,T) — Third RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Lookup data for the third parallel RC resistance at the specified SOC and temperature breakpoints. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics.

Third polarization resistance, R3(SOC) — Third RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Lookup data for the third parallel RC resistance at the specified SOC. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics and Tabulate parameters over temperature to No.

Third time constant, tau3(SOC,T) — Third RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Lookup data for the third parallel RC time constant at the specified SOC and temperature breakpoints.

Dependencies

Third time constant, tau3(SOC) — Third RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Lookup data for the third parallel RC time constant at the specified SOC.

Dependencies

Fourth polarization resistance, R4(SOC,T) — Fourth RC resistance at temperature breakpoints
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `Ohm` (default) | matrix of positive numbers

Lookup data for the fourth parallel RC resistance at the specified SOC and temperature breakpoints. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics or Five time-constant dynamics and Tabulate parameters over temperature to Yes.

Fourth polarization resistance, R4(SOC) — Fourth RC resistance
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Lookup data for the fourth parallel RC resistance at the specified SOC. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics or Five time-constant dynamics and Tabulate parameters over temperature to No.

Fourth time constant, tau4(SOC,T) — Fourth RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Lookup data for the fourth parallel RC time constant at the specified SOC and temperature breakpoints.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics or Five time-constant dynamics and Tabulate parameters over temperature to Yes.

Fourth time constant, tau4(SOC) — Fourth RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Lookup data for the fourth parallel RC time constant at the specified SOC.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics or Five time-constant dynamics and Tabulate parameters over temperature to No.

Fifth polarization resistance, R5(SOC,T) — Fifth RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Lookup data for the fifth parallel RC resistance at the specified SOC and temperature breakpoints. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Tabulate parameters over temperature to Yes.

Fifth polarization resistance, R5(SOC) — Fifth RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Lookup data for the fifth parallel RC resistance at the specified SOC. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Tabulate parameters over temperature to No.

Fifth time constant, tau5(SOC,T) — Fifth RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Lookup data for the fifth parallel RC time constant at the specified SOC and temperature breakpoints.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Tabulate parameters over temperature to Yes.

Fifth time constant, tau5(SOC) — Fifth RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Lookup data for the fifth parallel RC time constant at the specified SOC.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Tabulate parameters over temperature to No.

Fade

Fade characteristic — Select how to define fade characteristic
`Disabled` (default) | `Equations` | `Lookup tables (temperature independent)` | `Lookup tables (temperature dependent)`

Select how to define fade characteristic:

Disabled — The block does not model fade characteristic.
Equations — The cell capacity and terminal resistance will be proportional to $\sqrt{N}$ whilst the open-circuit voltage will be proportional to N. If the self-discharge resistance or any number of the time constants are enabled, their values will be proportional to $\sqrt{N}$ .
Lookup tables (temperature independent) — Set tabulated data for the percentage change in parameters as a function of N.
Lookup tables (temperature dependent) — Set tabulated data for the percentage change in parameters as a function of N and temperature.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_fade`
Values:	`"disabled"` (default) \| `"equations"` \| `"tableN"` \| `"tableNandT"`

Number of discharge cycles, N — Reference number of cycles for percent change calculations
`100` (default) | number from `1` to `Inf`

The number of charge-discharge cycles over which the specified percent changes occur.

Dependencies

To enable this parameter, set Fade characteristic to Equations.

Change in open-circuit voltage after N discharge cycles (%) — Percent change in open-circuit voltage after N cycles
`0` (default) | scalar

Percent change in the open-circuit voltage after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Equations.

Change in terminal resistance after N discharge cycles (%) — Percent change in series resistance after N cycles
`0` (default) | scalar

Percent change in the series resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Equations.

Change in cell capacity after N discharge cycles (%) — Percent change in cell capacity after N cycles
`0` (default) | scalar

Percent change in the cell capacity after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Equations.

Change in self-discharge resistance after N discharge cycles (%) — Percent change in self-discharge resistance after N cycles
`0` (default) | scalar

Percent change in the self-discharge resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Self-discharge to Enabled and Fade characteristic to Equations.

Change in first polarization resistance after N discharge cycles (%) — Percent change in first RC resistance after N cycles
`0` (default) | scalar

Percent change in the first RC resistance after the battery undergoes N discharge cycles.

Dependencies

Change in second polarization resistance after N discharge cycles (%) — Percent change in second RC resistance after N cycles
`0` (default) | scalar

Percent change in the second RC resistance after the battery undergoes N discharge cycles.

Dependencies

Change in third polarization resistance after N discharge cycles (%) — Percent change in third RC resistance after N cycles
`0` (default) | scalar

Percent change in the third RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics and Fade characteristic to Equations.

Change in fourth polarization resistance after N discharge cycles (%) — Percent change in fourth RC resistance after N cycles
`0` (default) | scalar

Percent change in the fourth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics, or Five time-constant dynamics and Fade characteristic to Equations.

Change in fifth polarization resistance after N discharge cycles (%) — Percent change in fifth RC resistance after N cycles
`0` (default) | scalar

Percent change in the fifth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Fade characteristic to Equations.

Vector of discharge cycle values, N — Reference vector or numbers of cycles for percent change calculations
`[0, 100, 200, 300]` (default) | number from `0` to `Inf`

Vector of numbers of charge-discharge cycles over which the specified percent changes occur.

The block supports the definition of breakpoint values for the fading and calendar aging options when the number of discharge cycles is zero. If you do not define the zero breakpoint values, unexpected behavior might occur depending on the extrapolation option.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature independent) or Lookup tables (temperature dependent).

Vector of temperatures for fade data, Tfade — Vector temperatures at which fade lookup tables has been extracted
`[298.15, 323.15]` `K` (default) | number from `1` to `Inf`

Vector of temperatures at which fade lookup tables has been extracted. These temperatures are completely independent of Vectors of temperatures, T parameter from the Main tab.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature dependent).

Percentage change in open-circuit voltage, dV0(N) — Vector of percent change in open-circuit voltage after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent changes in the open-circuit voltage after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature independent).

Percentage change in terminal resistance, dR0(N) — Vector of percent change in series resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the series resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature independent).

Percentage change in cell capacity, dAH(N) — Vector of percent change in cell capacity after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the cell capacity after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature independent).

Percentage change in self-discharge resistance, dRleak(N) — Vector of percent change in self-discharge resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the self-discharge resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Self-discharge to Enabled and Fade characteristic to Lookup tables (temperature independent).

Percentage change in first polarization resistance, dR1(N) — Vector of percent change in first RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the first RC resistance after the battery undergoes N discharge cycles.

Dependencies

Percent change in second polarization resistance, dR2(N) — Vector of percent change in second RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the second RC resistance after the battery undergoes N discharge cycles.

Dependencies

Percent change in third polarization resistance, dR3(N) — Vector of percent change in third RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the third RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Three time-constant dynamics, Four time-constant dynamics, or Five time-constant dynamics and Fade characteristic to Lookup tables (temperature independent).

Percent change in fourth polarization resistance, dR4(N) — Vector of percent change in fourth RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the fourth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics, or Five time-constant dynamics and Fade characteristic to Lookup tables (temperature independent).

Percent change in fifth polarization resistance, dR5(N) — Vector of percent change in fifth RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Vector of percent change in the fifth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Fade characteristic to Lookup tables (temperature independent).

Percentage change in open-circuit voltage, dV0(N, Tfade) — Matrix of percent change in open-circuit voltage after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent changes in the open-circuit voltage after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature dependent).

Percentage change in terminal resistance, dR0(N, Tfade) — Matrix of percent change in series resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the series resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature dependent).

Percentage change in cell capacity, dAH(N, Tfade) — Matrix of percent change in cell capacity after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the cell capacity after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Fade characteristic to Lookup tables (temperature dependent).

Percentage change in self-discharge resistance, dRleak(N, Tfade) — Matrix of percent change in self-discharge resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the self-discharge resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Self-discharge to Enabled and Fade characteristic to Lookup tables (temperature dependent).

Percentage change in first polarization resistance, dR1(N, Tfade) — Matrix of percent change in first RC resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the first RC resistance after the battery undergoes N discharge cycles.

Dependencies

Percent change in second polarization resistance, dR2(N, Tfade) — Matrix of percent change in second RC resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the second RC resistance after the battery undergoes N discharge cycles.

Dependencies

Percent change in third polarization resistance, dR3(N, Tfade) — Matrix of percent change in third RC resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the third RC resistance after the battery undergoes N discharge cycles.

Dependencies

Percent change in fourth polarization resistance, dR4(N, Tfade) — Matrix of percent change in fourth RC resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the fourth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Four time-constant dynamics, or Five time-constant dynamics and Fade characteristic to Lookup tables (temperature dependent).

Percent change in fifth polarization resistance, dR5(N, Tfade) — Matrix of percent change in fifth RC resistance after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

Matrix of percent change in the fifth RC resistance after the battery undergoes N discharge cycles.

Dependencies

To enable this parameter, set Charge dynamics to Five time-constant dynamics and Fade characteristic to Lookup tables (temperature dependent).

Calendar Aging

Internal resistance calendar aging — Calendar aging for internal resistance
`Disabled` (default) | `Enabled`

Whether to enable calendar aging of the internal resistance of the battery.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_age_resistance`
Values:	`"disabled"` (default) \| `"enabled"`

Capacity calendar aging — Calendar aging for capacity
`Disabled` (default) | `Enabled`

Whether to enable calendar aging of the capacity of the battery.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_age_capacity`
Values:	`"disabled"` (default) \| `"enabled"`

Modeling option — Calendar aging option
`Equation-based` (default) | `Tabulated: temperature` | `Tabulated: time and temperature`

Modeling option for internal resistance and capacity calendar aging.

Dependencies

To enable this parameter, set either Internal resistance calendar aging or Capacity calendar aging to Enabled.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_age_modeling`
Values:	`"equation"` (default) \| `"tableT"` \| `"tableTandTime"`

Vector of time intervals — Time intervals
`[0]` `d` (default) | vector of scalars

Time intervals. This parameter must be equal in size to Vector of storage temperatures.

Dependencies

To enable this parameter, set Modeling option to either Equation-based, Tabulated: temperature, or Tabulated: time and temperature.

Vector of storage temperatures — Storage temperatures
`[273]` `K` (default) | vector of scalars

Set of storage temperatures. This parameter must be equal in size to Vector of time intervals.

Dependencies

To enable this parameter, set Modeling option to either Equation-based, Tabulated: temperature, or Tabulated: time and temperature.

Storage condition — Storage condition
`Specify open-circuit voltage during storage` (default) | `Specify state-of-charge during storage`

Whether to specify the open-circuit voltage or the state of charge during storage.

Dependencies

To enable this parameter, set Modeling option to Equation-based.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`prm_age_OCV`
Values:	`"OCV"` (default) \| `"SOC"`

Normalized open-circuit voltage during storage, V/Vnom — Normalized open-circuit voltage during storage
`0.9` (default) | scalar

Normalized open-circuit voltage during storage.

Dependencies

To enable this parameter, set Modeling option to Equation-based and Storage condition to Specify open-circuit voltage during storage.

State of charge during storage — Percentage state of charge during storage
`60` (default) | positive number

State of charge during storage, in percentage.

Dependencies

To enable this parameter, set Modeling option to Equation-based and Storage condition to Specify state-of-charge during storage.

Terminal resistance linear scaling for voltage, b — Voltage linear scaling in terminal resistance
`2.2134e6` (default) | scalar

Linear scaling coefficient in terminal resistance for open-circuit voltage.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Equation-based.

Terminal resistance constant offset for voltage, c — Voltage constant offset in terminal resistance
`1.632e6` (default) | scalar

Constant offset in terminal resistance for open-circuit voltage.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Equation-based.

Terminal resistance temperature-dependent exponential increase, d — Temperature-dependent exponential increase in terminal resistance
`0.515833569` `V` (default) | scalar

Temperature-dependent exponential increase in terminal resistance.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Equation-based.

Terminal resistance time exponent, a — Time exponent in terminal resistance
`0.75` (default) | scalar

Time exponent in terminal resistance.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to either Equation-based or Tabulated: temperature.

Capacity linear scaling for voltage, b — Voltage linear scaling in capacity
`1.5097e07` (default) | scalar

Linear scaling coefficient in capacity for open-circuit voltage.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Equation-based.

Capacity constant offset for voltage, c — Voltage constant offset in capacity
`8.3625e06` (default) | scalar

Constant offset in capacity for open-circuit voltage.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Equation-based.

Capacity temperature-dependent exponential increase, d — Temperature-dependent exponential increase in capacity
`0.6011` `V` (default) | scalar

Temperature-dependent exponential increase in capacity.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Equation-based.

Capacity time exponent, a — Time exponent in capacity
`0.75` (default) | scalar

Time exponent in capacity.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to either Equation-based or Tabulated: temperature.

Vector of sampled temperatures for terminal resistance calendar aging, T_ar — Sampled temperatures for terminal resistance calendar aging
`[273.15, 298.15, 323.15]` `K` (default) | vector of scalars

Vector of sampled temperatures for terminal resistance calendar aging.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to either Tabulated: temperature or Tabulated: time and temperature.

Percentage change in terminal resistance due to calendar aging, dR0(T_ar) — Percentage change in terminal resistance due to calendar aging
`[0,0,0]` (default) | vector of scalars

Percentage change in terminal resistance due to calendar aging.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Tabulated: temperature.

Time between terminal resistance beginning of life and dR(T_ar) measurement — Time between terminal resistance beginning of life and dR(T_ar) measurement
`100` `d` (default) | scalar

Time between the beginning of life of the terminal resistance and the dR(T_ar) measurement.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Tabulated: temperature.

Vector of sampled temperatures for capacity calendar aging, T_ac — Sampled temperatures for capacity calendar aging
`[273.15, 298.15, 323.15]` `K` (default) | vector of scalars

Vector of sampled temperatures for capacity calendar aging.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to either Tabulated: temperature or Tabulated: time and temperature.

Percentage change in capacity due to calendar aging, dAH(T_ac) — Percentage change in capacity due to calendar aging
`[0,0,0]` (default) | vector of scalars

Percentage change in capacity due to calendar aging.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Tabulated: temperature.

Time between capacity beginning of life and dAH(T_ac) measurement — Time between capacity beginning of life and dAH(T_ac) measurement
`100` `d` (default) | scalar

Time between the beginning of life of the capacity and the dR(T_ac) measurement.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Tabulated: temperature.

Vector of sampled storage time intervals for terminal resistance calendar aging, t_ar — Sampled storage time intervals for terminal resistance calendar aging
`[0, 90, 180, 270, 360]` `d` (default) | vector of scalars

Vector of sampled storage time intervals for terminal resistance calendar aging.

The block supports the definition of breakpoint values for the fading and calendar aging options when the number of time intervals is zero. If you do not define the zero breakpoint values, unexpected behavior might occur depending on the extrapolation option.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Tabulated: time and temperature.

Percentage change in terminal resistance due to calendar aging, dR0(t_ar,T_ar) — Percentage change in terminal resistance due to calendar aging
`[0, 0, 0; 0, 0, 0; 0, 0, 0; 0, 0, 0]` (default) | matrix of scalars

Percentage change in terminal resistance due to calendar aging.

Dependencies

To enable this parameter, set Internal resistance calendar aging to Enabled and Modeling option to Tabulated: time and temperature.

Vector of sampled storage time intervals for capacity calendar aging, t_ac — Sampled storage time intervals for capacity calendar aging
`[0, 90, 180, 270, 360]` `d` (default) | vector of scalars

Vector of sampled storage time intervals for capacity calendar aging.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Tabulated: time and temperature.

Percentage change in capacity due to calendar aging, dAH(t_ac,T_ac) — Percentage change in capacity due to calendar aging
`[0, 0, 0; 0, 0, 0; 0, 0, 0; 0, 0, 0]` (default) | matrix of scalars

Percentage change in capacity due to calendar aging.

Dependencies

To enable this parameter, set Capacity calendar aging to Enabled and Modeling option to Tabulated: time and temperature.

Thermal

Thermal port — Thermal port visibility
`Omit` (default) | `Model`

Whether to expose the thermal port.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	`thermal_port`
Values:	`"omit"` (default) \| `"model"`

Simulation temperature — Battery temperature
`298.15` `K` (default) | positive number

Battery temperature used in lookup tables throughout simulation.

Dependencies

To enable this parameter, set Thermal port to Omit and Tabulate parameters over temperature to Yes or Fade characteristic to Lookup tables (temperature dependent). For more information, see Modeling Thermal Effects.

Thermal mass — Thermal mass associated with thermal port
`100` `J/K` (default)

Thermal mass associated with the thermal port H. It represents the energy required to raise the temperature of the thermal port by one degree.

Dependencies

To enable this parameter, set Thermal port to Model. For more information, see Modeling Thermal Effects.

References

[1] Tarun, H., M. Ceraolo, J. Gazzarri, and R. Jackey. “High Fidelity Electrical Model with Thermal Dependence for Characterization and Simulation of High Power Lithium Battery Cells.” In 2012 IEEE International Electric Vehicle Conference, 1–8, 2012. https://doi.org/10.1109/IEVC.2012.6183271.

[2] Schmalstieg, J., S. Käbitz, M. Ecker, and D. U. Sauer. “A Holistic Aging Model for Li(NiMnCo)O₂ Based 18650 Lithium-Ion Batteries.” Journal of Power Sources 257 (July 2014): 325–334. https://doi.org/10.1016/j.jpowsour.2014.02.012.

[3] Zhang, R., and Z. Pan. “Model Identification of Lithium-Ion Batteries Considering Current-Rate Effects on Battery Impedance.” In 2019 4th International Conference on Power and Renewable Energy (ICPRE), 305–309, 2019. https://doi.org/10.1109/ICPRE48497.2019.9034704.

[4] Baronti, F., N. Femia, R. Saletti, C. Visone, and W. Zamboni. “Hysteresis Modeling in Li-Ion Batteries.” IEEE Transactions on Magnetics 50, no. 11 (November 2014): 1–4. https://doi.org/10.1109/TMAG.2014.2323426.

[5] Baronti, F., W. Zamboni, N. Femia, R. Roncella, and R. Saletti. “Experimental Analysis of Open-Circuit Voltage Hysteresis in Lithium-Iron-Phosphate Batteries.” In IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, 6728–6733, 2013. https://doi.org/10.1109/IECON.2013.6700246.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a

expand all

R2023b: Define breakpoint values for the fading and calendar aging options when the number of discharge cycles or time intervals is zero

You can define the breakpoint values for the fading and calendar aging options when the number of discharge cycles or time intervals is zero.

If you do not define the zero breakpoint values:

If you set the Extrapolation method for all tables parameter to Linear, the block might extrapolate an incorrect value depending on the table data. For example, the extrapolated capacity can rise above one, meaning that the capacity of the cell at that point is greater than the nominal capacity of the cell.
If you set the Extrapolation method for all tables parameter to Nearest, the block extrapolates the nearest value. For a brand new battery, this means that the fading and calendar aging would have already occurred.
If you set the Extrapolation method for all tables parameter to Error, the software throws an error if the number of discharge cycles or storage duration is lower than the lowest breakpoint for this table data.

Battery (Table-Based)

Description

Battery Model

Modeling Self-Discharge

Modeling Charge Dynamics

Modeling Battery Fade

Modeling Thermal Effects

Modeling Battery Aging

Predefined Parameterization

Plot Basic Voltage-Charge Characteristics

Examples

Mars Helicopter System-Level Design

DC Fast Charger for Electric Vehicle

Battery Pack Fault Protection

Ports

Output

SOC — Battery charge level, C physical signal

Dependencies

Conserving

+ — Positive terminal electrical

- — Negative terminal electrical

H — Battery thermal mass thermal

Dependencies

Parameters

Selected part — Predefined parameterization option <click to select> (default)

Main

Vector of state-of-charge values, SOC — SOC breakpoints [0, .1, .25, .5, .75, .9, 1] (default) | vector of scalars in the range [0,1]

Tabulate parameters over temperature — Select whether to tabulate battery parameters over temperature Yes (default) | No

Programmatic Use

Current directionality — Enable direction of current Disabled (default) | Enabled

Programmatic Use

Terminal voltage operating range [Min Max] — Terminal voltage operating range [0, inf] V (default) | vector of positive numbers

Vector of temperatures, T — T breakpoints [278, 293, 313] K (default) | vector of positive numbers

Dependencies

Open-circuit voltage, V0(SOC,T) — V0 lookup table with temperature breakpoint [3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19] V (default) | matrix of nonnegative numbers

Dependencies

Open-circuit voltage, V0(SOC) — V0 lookup table [3.5057, 3.566, 3.6337, 3.7127, 3.9259, 4.0777, 4.1928] V (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance, R0(SOC,T) — R0 lookup table with temperature breakpoint [.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089] Ohm (default) | matrix of nonnegative numbers

Dependencies

Dependencies

Dependencies

Terminal resistance, R0(SOC) — R0 lookup table [.0085, .0085, .0087, .0082, .0083, .0085, .0085] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during discharging, R0(SOC) — R0 lookup table during discharging phase [.0085, .0085, .0087, .0082, .0083, .0085, .0085] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during charging, R0(SOC) — R0 lookup table during charging phase [.0085, .0085, .0087, .0082, .0083, .0085, .0085] Ohm (default) | matrix of nonnegative numbers

Dependencies

Cell capacity, AH — Battery capacity when fully charged 27 hr*A (default) | nonnegative scalar

Self-discharge — Select whether to model the self-discharge resistance of the battery Disabled (default) | Enabled

Programmatic Use

Self-discharge resistance, Rleak(T) — Resistance that represents battery self-discharge at temperature breakpoints [8000, 7000, 6000] Ohm (default) | vector of positive numbers

Dependencies

Self-discharge resistance, Rleak — Resistance that represents battery self-discharge 7e3 Ohm (default) | positive scalar

Dependencies

Extrapolation method for all tables — Method of extrapolation for tables Nearest (default) | Linear | Error

Programmatic Use

Expose SOC measurement port — Method of extrapolation for tables No (default) | Yes

Programmatic Use

Dynamics

Charge dynamics — Battery charge dynamics model No dynamics (default) | One time-constant dynamics | Two time-constant dynamics | Three time-constant dynamics | Four time-constant dynamics | Five time-constant dynamics

Programmatic Use

First polarization resistance, R1(SOC,T) — First RC resistance at temperature breakpoints [.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011] Ohm (default) | matrix of positive numbers

Dependencies

First polarization resistance, R1(SOC) — First RC resistance [.0029, .0024, .0026, .0016, .0023, .0018, .0017] Ohm (default) | matrix of positive numbers

Dependencies

First time constant, tau1(SOC,T) — First RC time constant at temperature breakpoints [20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33] s (default) | matrix of positive numbers

Dependencies

First time constant, tau1(SOC) — First RC time constant [36, 45, 105, 29, 77, 33, 39] s (default) | matrix of positive numbers

Dependencies

Second polarization resistance, R2(SOC,T) — Second RC resistance at temperature breakpoints [.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011] Ohm (default) | matrix of positive numbers

Dependencies

Second polarization resistance, R2(SOC) — Second RC resistance [.0029, .0024, .0026, .0016, .0023, .0018, .0017] Ohm (default) | matrix of positive numbers

Dependencies

Second time constant, tau2(SOC,T) — Second RC time constant at temperature breakpoints [20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33] s (default) | matrix of positive numbers

Dependencies

Second time constant, tau2(SOC) — Second RC time constant [36, 45, 105, 29, 77, 33, 39] s (default) | matrix of positive numbers

Dependencies

Third polarization resistance, R3(SOC,T) — Third RC resistance at temperature breakpoints [.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011] Ohm (default) | matrix of positive numbers

Dependencies

SOC — Battery charge level, C
physical signal

+ — Positive terminal
electrical

- — Negative terminal
electrical

H — Battery thermal mass
thermal

Selected part — Predefined parameterization option
`<click to select>` (default)

Vector of state-of-charge values, SOC — SOC breakpoints
`[0, .1, .25, .5, .75, .9, 1]` (default) | vector of scalars in the range [0,1]

Tabulate parameters over temperature — Select whether to tabulate battery parameters over temperature
`Yes` (default) | `No`

Current directionality — Enable direction of current
`Disabled` (default) | `Enabled`

Terminal voltage operating range [Min Max] — Terminal voltage operating range
`[0, inf]` `V` (default) | vector of positive numbers

Vector of temperatures, T — T breakpoints
`[278, 293, 313]` `K` (default) | vector of positive numbers

Open-circuit voltage, V0(SOC,T) — V0 lookup table with temperature breakpoint
`[3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19]` `V` (default) | matrix of nonnegative numbers

Open-circuit voltage, V0(SOC) — V0 lookup table
`[3.5057, 3.566, 3.6337, 3.7127, 3.9259, 4.0777, 4.1928]` `V` (default) | matrix of nonnegative numbers

Terminal resistance, R0(SOC,T) — R0 lookup table with temperature breakpoint
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` `Ohm` (default) | matrix of nonnegative numbers

Terminal resistance, R0(SOC) — R0 lookup table
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Terminal resistance during discharging, R0(SOC) — R0 lookup table during discharging phase
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Terminal resistance during charging, R0(SOC) — R0 lookup table during charging phase
`[.0085, .0085, .0087, .0082, .0083, .0085, .0085]` `Ohm` (default) | matrix of nonnegative numbers

Cell capacity, AH — Battery capacity when fully charged
`27` `hr*A` (default) | nonnegative scalar

Self-discharge — Select whether to model the self-discharge resistance of the battery
`Disabled` (default) | `Enabled`

Self-discharge resistance, Rleak(T) — Resistance that represents battery self-discharge at temperature breakpoints
`[8000, 7000, 6000]` `Ohm` (default) | vector of positive numbers

Self-discharge resistance, Rleak — Resistance that represents battery self-discharge
`7e3` `Ohm` (default) | positive scalar

Extrapolation method for all tables — Method of extrapolation for tables
`Nearest` (default) | `Linear` | `Error`

Expose SOC measurement port — Method of extrapolation for tables
`No` (default) | `Yes`

Charge dynamics — Battery charge dynamics model
`No dynamics` (default) | `One time-constant dynamics` | `Two time-constant dynamics` | `Three time-constant dynamics` | `Four time-constant dynamics` | `Five time-constant dynamics`

First polarization resistance, R1(SOC,T) — First RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

First polarization resistance, R1(SOC) — First RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

First time constant, tau1(SOC,T) — First RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

First time constant, tau1(SOC) — First RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Second polarization resistance, R2(SOC,T) — Second RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Second polarization resistance, R2(SOC) — Second RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Second time constant, tau2(SOC,T) — Second RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Second time constant, tau2(SOC) — Second RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Third polarization resistance, R3(SOC,T) — Third RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Third polarization resistance, R3(SOC) — Third RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Third time constant, tau3(SOC,T) — Third RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Third time constant, tau3(SOC) — Third RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Fourth polarization resistance, R4(SOC,T) — Fourth RC resistance at temperature breakpoints
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `Ohm` (default) | matrix of positive numbers

Fourth polarization resistance, R4(SOC) — Fourth RC resistance
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Fourth time constant, tau4(SOC,T) — Fourth RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Fourth time constant, tau4(SOC) — Fourth RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Fifth polarization resistance, R5(SOC,T) — Fifth RC resistance at temperature breakpoints
`[.0109, .0029, .0013; .0069, .0024, .0012; .0047, .0026, .0013; .0034, .0016, .001; .0033, .0023, .0014; .0033, .0018, .0011; .0028, .0017, .0011]` `Ohm` (default) | matrix of positive numbers

Fifth polarization resistance, R5(SOC) — Fifth RC resistance
`[.0029, .0024, .0026, .0016, .0023, .0018, .0017]` `Ohm` (default) | matrix of positive numbers

Fifth time constant, tau5(SOC,T) — Fifth RC time constant at temperature breakpoints
`[20, 36, 39; 31, 45, 39; 109, 105, 61; 36, 29, 26; 59, 77, 67; 40, 33, 29; 25, 39, 33]` `s` (default) | matrix of positive numbers

Fifth time constant, tau5(SOC) — Fifth RC time constant
`[36, 45, 105, 29, 77, 33, 39]` `s` (default) | matrix of positive numbers

Fade characteristic — Select how to define fade characteristic
`Disabled` (default) | `Equations` | `Lookup tables (temperature independent)` | `Lookup tables (temperature dependent)`

Number of discharge cycles, N — Reference number of cycles for percent change calculations
`100` (default) | number from `1` to `Inf`

Change in open-circuit voltage after N discharge cycles (%) — Percent change in open-circuit voltage after N cycles
`0` (default) | scalar

Change in terminal resistance after N discharge cycles (%) — Percent change in series resistance after N cycles
`0` (default) | scalar

Change in cell capacity after N discharge cycles (%) — Percent change in cell capacity after N cycles
`0` (default) | scalar

Change in self-discharge resistance after N discharge cycles (%) — Percent change in self-discharge resistance after N cycles
`0` (default) | scalar

Change in first polarization resistance after N discharge cycles (%) — Percent change in first RC resistance after N cycles
`0` (default) | scalar

Change in second polarization resistance after N discharge cycles (%) — Percent change in second RC resistance after N cycles
`0` (default) | scalar

Change in third polarization resistance after N discharge cycles (%) — Percent change in third RC resistance after N cycles
`0` (default) | scalar

Change in fourth polarization resistance after N discharge cycles (%) — Percent change in fourth RC resistance after N cycles
`0` (default) | scalar

Change in fifth polarization resistance after N discharge cycles (%) — Percent change in fifth RC resistance after N cycles
`0` (default) | scalar

Vector of discharge cycle values, N — Reference vector or numbers of cycles for percent change calculations
`[0, 100, 200, 300]` (default) | number from `0` to `Inf`

Vector of temperatures for fade data, Tfade — Vector temperatures at which fade lookup tables has been extracted
`[298.15, 323.15]` `K` (default) | number from `1` to `Inf`

Percentage change in open-circuit voltage, dV0(N) — Vector of percent change in open-circuit voltage after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percentage change in terminal resistance, dR0(N) — Vector of percent change in series resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percentage change in cell capacity, dAH(N) — Vector of percent change in cell capacity after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percentage change in self-discharge resistance, dRleak(N) — Vector of percent change in self-discharge resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percentage change in first polarization resistance, dR1(N) — Vector of percent change in first RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percent change in second polarization resistance, dR2(N) — Vector of percent change in second RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percent change in third polarization resistance, dR3(N) — Vector of percent change in third RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percent change in fourth polarization resistance, dR4(N) — Vector of percent change in fourth RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percent change in fifth polarization resistance, dR5(N) — Vector of percent change in fifth RC resistance after N cycles
`[0, 0, 0, 0]` (default) | vector of scalars

Percentage change in open-circuit voltage, dV0(N, Tfade) — Matrix of percent change in open-circuit voltage after N cycles
`[0, 0; 0, 0; 0, 0; 0, 0]` (default) | matrix of scalars