# Battery (Table-Based)

Tabulated battery model

• Library:
• Simscape / Electrical / Sources

## Description

The Battery (Table-Based) block represents a high-fidelity battery model. The block calculates no-load voltage as a function of charge level and optional temperature using lookup tables and includes several modeling options:

• Self-discharge

• Charge dynamics

• Calendar aging

Note

The block can use linear or nearest interpolation and extrapolation for all the table based parameters. 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 no-load 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 RSD, the charge dynamics model, and the series resistance R0.

### Battery Model

The block calculates the no-load voltage, or the voltage across the fundamental battery model by interpolation:

`${v}_{0}={v}_{0}\left(\text{SOC},T\right)$`

Where:

• v0 is the no-load voltage of the battery. Specify the grid of lookup values using the No-load voltage, V0(SOC,T) parameter if tabulating parameters over temperature, or No-load 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, δAH(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 characteristics and the Cell capacity, AH parameter.

`SOC` represents the normalized data with respect to qnom.

For the lookup-table based fade characteristics option,

`${q}_{nom}\left(T,n\right)=\left(1+\frac{{\delta }_{AH}\left(n,{T}_{fade}\right)}{100}\right)*AH\text{\hspace{0.17em}}Ah.$`

For the equation-based fade characteristics option,

`${q}_{nom}\left(T,n\right)=\left(1+\frac{{\delta }_{AH}}{100}\sqrt{\frac{n}{N}}\right)*AH\text{\hspace{0.17em}}Ah.$`

Finally, `SOC` is obtained from the following equation.

`$SOC\left(t\right)=\frac{1}{{q}_{nom}\left(T,n\right)}\int \left(i\left(t\right)-\frac{{V}_{open}\left(T,n,t\right)}{{R}_{SD}\left(T,n\right)}\right)dt$`

Where:

• qnom 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.

• δAH 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 RSD(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 $C=\tau /R$. 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.

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

The no-load voltage across the fundamental battery model fades proportionally with the number of discharge cycles n:

`${v}_{0,\text{fade}}={v}_{0}\left(1+\frac{{\delta }_{{v}_{0}}}{100}\frac{n}{N}\right)$`

Where δv0 is the percent change in no-load voltage after N discharge cycles. Specify δv0 using the Change in no-load voltage after N discharge cycles (%) parameter.

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

`${q}_{nom,\text{fade}}={q}_{nom}\left(1+\frac{{\delta }_{AH}}{100}\sqrt{\frac{n}{N}}\right)$`

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

`${R}_{i,\text{fade}}={R}_{i}\left(1+\frac{{\delta }_{{R}_{i}}}{100}\sqrt{\frac{n}{N}}\right)$`

Where:

• Ri is the ith resistance

• δRi 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 characteristics 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:

`${M}_{th}\stackrel{˙}{T}=\sum _{i}{V}_{T,i}{}^{2}/{R}_{T,i}$`

Where:

• Mth is the battery thermal mass.

• i corresponds to the ith 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

• VT,i is the voltage drop across resistor i.

• RT,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`

Equation-based

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

`$\begin{array}{c}{\alpha }_{r}\left(T,{V}_{oc}\right)=\left(b{V}_{oc}-c\right){e}^{-\frac{qd}{kT}},\\ R={R}_{0}\left(1+\sum _{i=1}^{i=n}{\alpha }_{r}\left({T}_{i},{V}_{oc}\right)\left({t}_{i}^{a}-{t}_{i-1}^{a}\right)\right),\end{array}$`

where:

• Voc is the Normalized open-circuit voltage during storage, V/Vnom.

• R0 is the Internal resistance.

• ti is the time sample derived from the Vector of time intervals parameter.

• Ti 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:

`$\begin{array}{l}{\alpha }_{c}\left(T,{V}_{oc}\right)=\left(b{V}_{oc}-c\right){e}^{-\frac{qd}{kT}},\\ C={C}_{0}\left(1-\sum _{i=1}^{i=n}{\alpha }_{c}\left({T}_{i},{V}_{oc}\right)\left({t}_{i}^{a}-{t}_{i-1}^{a}\right)\right),\end{array}$`

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:

`${R}_{0}\left(SOC,T;{t}_{st},{T}_{st}\right)={R}_{0}\left(SOC,T\right)\left(1+\sum _{i=1}^{n}\frac{d{R}_{0}\left({T}_{st,i}\right)}{100}\left(\frac{{t}^{a}{}_{st,i}-{t}^{a}{}_{st,i-1}}{{t}^{a}{}_{st,m}}\right)\right),$`

where:

• T is the battery temperature. Specify the T breakpoints using the Vector of temperatures, T parameter if tabulating the parameters over temperature.

• Tst is the Vector of storage temperatures.

• tst,i and tst,i-1 are the time samples derived from the Vector of time intervals.

• t0 is assumed to be null.

• tst,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:

`${R}_{0}\left(SOC,T;\Delta {t}_{st},{T}_{st}\right)={R}_{0}\left(SOC,T\right)\left(1+\sum _{i=1}^{n}\frac{d{R}_{0}\left(\Delta {t}_{st,i},{T}_{st,i}\right)}{100}\right).$`

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 No-load voltage, V0(SOC), Terminal resistance, R0(SOC, T), Cell capacity, AH, Percentage change in cell capacity, dAH, and Percentage change in no-load 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 No-load 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.

### Plotting Voltage-Charge Characteristics

A quick plot feature lets you visualize the voltage-charge characteristic for the battery model parameter values. To plot the characteristics, right-click a Battery (Table-Based) block in your model and, from the context menu, select Electrical > Basic characteristics. The software automatically computes a set of bias conditions, based on the block parameter values, and opens a figure window containing a plot of no-load voltage versus the state-of-charge (SOC) for the block. For more information, see Plot Basic Characteristics for Battery Blocks.

## Ports

### Output

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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, qnom(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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Electrical conserving port associated with the battery positive terminal.

Electrical conserving port associated with the battery negative terminal.

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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Whether 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 on the Block Parameterization Manager, see Load Predefined Parameterizations.

### Main

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, qbattery and the nominal battery capacity, qnom(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 δAH(n = 1, Tfade) = 0.

`$\begin{array}{c}SOC=\frac{{q}_{battery}}{{q}_{nom}\left(T,n\right)}\\ for\text{\hspace{0.17em}}N=1\text{\hspace{0.17em}}and\text{\hspace{0.17em}}{\delta }_{AH}\left(n,{T}_{fade}\right)=0,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{q}_{nom}\left(T,n\right)=AH.\end{array}$`

Select whether to tabulate battery parameters over temperature.

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

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 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 Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature```.

Lookup data for no-load voltages across the fundamental battery model at the specified SOC and temperature breakpoints.

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature```.

Lookup data for no-load voltages across the fundamental battery model at the specified SOC.

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```No - do not tabulate parameters over temperature```.

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

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature``` and the Current directionality parameter is set to `Disabled`.

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 Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature``` and the Current directionality parameter is set to `Enabled`.

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 Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature``` and the Current directionality parameter is set to `Enabled`.

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

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```No - do not tabulate parameters over temperature``` and the Current directionality parameter is set to `Disabled`.

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

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```No - do not tabulate parameters over temperature``` and the Current directionality parameter is set to `Enabled`.

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

#### Dependencies

This parameter is visible only when the Temperature dependent tables parameter is set to ```No - do not tabulate parameters over temperature``` and the Current directionality parameter is set to `Enabled`.

Lookup data for the 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.

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

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 Temperature dependent tables is set to ```Yes - tabulate parameters over temperature```.

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 Temperature dependent tables parameter is set to ```No - do not tabulate parameters over temperature```.

.

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.

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

### 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.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

Lookup data for the first 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 `One time-constant dynamics`, `Two time-constant dynamics`, `Three time-constant dynamics`, `Four time-constant dynamics`, or `Five time-constant dynamics` and Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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

#### 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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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

#### 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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

Lookup data for the second 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 `Two time-constant dynamics`, `Three time-constant dynamics`, `Four time-constant dynamics`, or `Five time-constant dynamics` and Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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

#### 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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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

#### 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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 and Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

#### Dependencies

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

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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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

#### Dependencies

To enable this parameter, set Charge dynamics to `Three time-constant dynamics`, `Four time-constant dynamics`, or `Five time-constant dynamics` and Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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

#### Dependencies

To enable this parameter, set Charge dynamics to `Three time-constant dynamics`, `Four time-constant dynamics`, or `Five time-constant dynamics` and Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

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 Temperature dependent tables to ```Yes - tabulate parameters over temperature```.

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 Temperature dependent tables to ```No - do not tabulate parameters over temperature```.

Select how to define fade characteristics:

• `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.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to `Equations`.

Percent change in the no-load voltage after the battery undergoes N discharge cycles.

#### Dependencies

To enable this parameter, set Fade characteristics defined by to `Equations`.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to `Equations`.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to `Equations`.

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 characteristics defined by to `Equations`.

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

#### 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 Fade characteristics defined by to `Equations`.

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

#### 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 Fade characteristics defined by to `Equations`.

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 characteristics defined by to `Equations`.

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 characteristics defined by to `Equations`.

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 characteristics defined by to `Equations`.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature independent)``` or ```Lookuptables (temperature dependent)```.

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 characteristics defined by to ```Lookup tables (temperature dependent)```.

Vector of percent changes in the no-load voltage after the battery undergoes N discharge cycles.

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature independent)```.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature independent)```.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature independent)```.

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 characteristics defined by to ```Lookup tables (temperature independent)```.

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

#### 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 Fade characteristics defined by to ```Lookup tables (temperature independent)```.

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

#### 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 Fade characteristics defined by to ```Lookup tables (temperature independent)```.

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 characteristics defined by to ```Lookup tables (temperature independent)```.

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 characteristics defined by to ```Lookup tables (temperature independent)```.

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 characteristics defined by to ```Lookup tables (temperature independent)```.

Matrix of percent changes in the no-load voltage after the battery undergoes N discharge cycles.

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature dependent)```.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature dependent)```.

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

#### Dependencies

To enable this parameter, set Fade characteristics defined by to ```Lookup tables (temperature dependent)```.

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 characteristics defined by to ```Lookup tables (temperature dependent)```.

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

#### 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 Fade characteristics defined by to ```Lookup tables (temperature dependent)```.

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

#### 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 Fade characteristics defined by to ```Lookup tables (temperature dependent)```.

Matrix 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 characteristics defined by to ```Lookup tables (temperature dependent)```.

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 characteristics defined by to ```Lookup tables (temperature dependent)```.

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 characteristics defined by to ```Lookup tables (temperature dependent)```.

### Calendar Aging

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

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

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`.

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```.

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```.

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`.

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, in percentage.

#### Dependencies

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

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`.

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`.

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`.

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`.

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`.

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`.

Temperature-dependent exponential increase in capacity.

#### Dependencies

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

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.

#### 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.

#### Dependencies

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

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: time```.

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.

#### Dependencies

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

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: time```.

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

#### 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.

#### 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.

#### 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.

#### Dependencies

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

### Thermal

Whether to expose the thermal port.

Battery temperature used in lookup tables throughout simulation.

#### Dependencies

To enable this parameter, set Thermal port to `Omit` and Temperature dependent tables to ```Yes - tabulate parameters over temperature``` or Fade characteristics defined by to ```Lookup tables (temperature dependent)```. For more information, see Modeling Thermal Effects.

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.

## Version History

Introduced in R2018a