Documentation

# 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

### Note

The block uses linear 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 four modeling variants, accessible by right-clicking the block in your block diagram and then selecting the appropriate option from the context menu, under Simscape > Block choices:

• Uninstrumented | No thermal port — Basic model that does not output battery charge level and simulates at a fixed temperature. This modeling variant is the default.

• Uninstrumented | Show thermal port — Model with exposed thermal port. This model does not output internal charge level of the battery.

• Instrumented | No thermal port — Model with exposed charge output port. This model uses a fixed temperature throughout the simulation.

• Instrumented | Show thermal port — Model that lets you output internal charge level of the battery. Both the thermal port and the charge output port are exposed.

The instrumented variants have an extra physical signal port that outputs the internal state of charge. Use this functionality to change load behavior as a function of state of charge, without the complexity of building a charge state estimator.

The thermal port variants expose a thermal port, which represents the battery thermal mass.

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 rated battery capacity. Specify the SOC breakpoints using the Vector of state-of-charge values, SOC parameter.

• 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:

• N is the reference number of discharge cycles over which you specify percent change of various battery parameters. Set this value using the Number of discharge cycles, N parameter.

• 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:

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

Where:

• qnom is the ampere-hour rating of the battery. Specify this value using the Ampere-hour rating, AH(T) parameter.

• δAH is the percent change in ampere-hour rating of the battery after N discharge cycles.

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

For thermal variants of the block, 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.

### 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

expand all

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.

#### Dependencies

Enabled for the instrumented variants of the block: Instrumented | No thermal port and Instrumented | Show thermal port.

### Conserving

expand all

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

Enabled for the thermal variants of the block: Uninstrumented | Show thermal port and Instrumented | Show thermal port.

## Parameters

expand all

### Main

Vector of state-of-charge breakpoints defining the points at which you specify lookup data. This vector must be strictly ascending.

Select whether to tabulate battery parameters over temperature.

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```.

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```.

Lookup data for the ampere-hour rating of the battery at the specified temperature breakpoints. 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.

#### Dependencies

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

Lookup data for the ampere-hour rating 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.

#### Dependencies

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

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```.

.

### 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 ampere-hour rating 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 ampere-hour rating 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 ampere-hour rating 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 ampere-hour rating 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)```.

### Thermal

Battery temperature used in lookup tables throughout simulation.

#### Dependencies

This section appears only for blocks without an exposed thermal port and when the Temperature dependent tables parameter is set to ```Yes - tabulate parameters over temperature``` or Fade characteristics defined by is set 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

Enabled for blocks with an exposed thermal port. For more information, see Modeling Thermal Effects.