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
Battery fade
Charge dynamics

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 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.

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

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

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 Ampere-hour rating, AH(T) parameter along with the effects of the temperature dependent fade percentage change in ampere-hour rating, δ_AH(n, Tfade), specified in the Percentage change in ampere-hour rating, 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 Ampere-hour rating, AH(T) parameter.
SOC represents the normalized data with respect to q_nom.
For the lookup-table based fade characteristics option,

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

$q_{n o m} (T, n) = (1 + \frac{δ_{A H}}{100} \sqrt{\frac{n}{N}}) * A H (T) A h .$
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 ampere-hour rating of the battery. Specify this value using the Ampere-hour rating, AH(T) 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 ampere-hour rating 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 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:

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

Where δ_v₀ is the percent change in no-load voltage after N discharge cycles. Specify δ_v₀ 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:

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

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 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:

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

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.

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 manufacturer data sheets. To load a predefined parameterization, click on the Select a predefined parameterization hyperlink in the Battery (Table-Based) block mask and 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 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 up to 99% of the depth of discharge. Simple fading parameters are given for single temperature.

Note

Predefined parameterizations of Simscape components use available data sources for supplying parameter values. Engineering judgement and simplifying assumptions are used to fill in for missing data. As a result, deviations between simulated and actual physical behavior should be expected. To ensure requisite accuracy, you should validate simulated behavior against experimental data and refine component models as necessary.

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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`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

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

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

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

Parameters

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Main

`Vector of state-of-charge values, SOC` — SOC breakpoints
`[0, .25, .75, 1]` (default) | vector

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 Ampere-hour rating, AH(T) 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 Ampere-hour rating, AH(T) parameter, assuming a fresh battery with a number of cycles, N, equal to 1 and δ_AH(n = 1, T_fade) = 0.

$\begin{matrix} S O C = \frac{q_{b a t t e r y}}{q_{n o m} (T, n)} \\ f o r N = 1 a n d δ_{A H} (n, T_{f a d e}) = 0, q_{n o m} (T, n) = A H (T) . \end{matrix}$

`Temperature dependent tables` — Select whether to tabulate battery parameters over temperature
`Yes - tabulate parameters over temperature` (default) | `No - do not tabulate parameters over temperature`

Select whether to tabulate battery parameters over temperature.

`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.

`Vector of temperatures, T` — T breakpoints
`[273.15, 298.15, 323.15]` `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 Temperature dependent tables parameter is set to Yes - tabulate parameters over temperature.

`No-load voltage, V0(SOC,T)` — V0 lookup table with temperature breakpoint
`[3.2, 3.1, 3.14; 3.25, 3.27, 3.3; 3.28, 3.31, 3.34; 3.33, 3.5, 3.59]` `V` (default) | matrix of nonnegative numbers

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.

`No-load voltage, V0(SOC)` — V0 lookup table
`[3.1, 3.27, 3.31, 3.5]` `V` (default) | matrix of nonnegative numbers

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.

`Terminal resistance, R0(SOC,T)` — R0 lookup table with temperature breakpoint
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `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 Temperature dependent tables parameter is set to Yes - tabulate parameters over temperature 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
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `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

`Terminal resistance during charging, R0(SOC,T)` — R0 lookup table with temperature breakpoint during charging phase
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `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

`Terminal resistance, R0(SOC)` — R0 lookup table
`[.015, .017, .012, .013]` `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 Temperature dependent tables parameter is set to No - do not tabulate parameters over temperature and the Current directionality parameter is set to Disabled.

`Terminal resistance during discharging, R0(SOC)` — R0 lookup table during discharging phase
`[.015, .017, .012, .013]` `Ohm` (default) | matrix of nonnegative numbers

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

Dependencies

`Terminal resistance during charging, R0(SOC)` — R0 lookup table during charging phase
`[.015, .017, .012, .013]` `Ohm` (default) | matrix of nonnegative numbers

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

Dependencies

`Ampere-hour rating, AH(T)` — AH rating at temperature breakpoints
`[2.9, 4.1, 4.2]` `hr*A` (default) | vector of nonnegative numbers

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. In case of a fresh battery where number of cycles, n, is equal to 1 and δ_AH(n, T_fade) is equal to 0, SOC = 1 represents the capacity specified by this parameter for each temperature. To estimate the nominal capacity and calculate the SOC value, the block applies interpolation techniques over this parameter. The block then uses this SOC value to estimate the open circuit voltage and circuit resistances from the specified lookup table values.

Dependencies

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

`Ampere-hour rating, AH` — AH breakpoints
`4.1` `hr*A` (default) | nonnegative scalar

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.

`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

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

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

`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.

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.

`First polarization resistance, R1(SOC,T)` — First RC resistance at temperature breakpoints
`[.089, .076, .01; .042, .022, .099; .019, .007, .002; .051, .043, .029]` `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 Temperature dependent tables to Yes - tabulate parameters over temperature.

`First polarization resistance, R1(SOC)` — First RC resistance
`[.076, .022, .007, .043]` `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
`[44, 148, 235; 93, 110, 1000; 19, 27, 133; .5, 22, 3]` `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
`[148, 110, 27, 22]` `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
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `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 Temperature dependent tables to Yes - tabulate parameters over temperature.

`Second polarization resistance, R2(SOC)` — Second RC resistance
`[.382, .006, .007, .956]` `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
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `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
`[44, 24, 14, 13419]` `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
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `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 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.

`Third polarization resistance, R3(SOC)` — Third RC resistance
`[.382, .006, .007, .956]` `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 Temperature dependent tables to No - do not tabulate parameters over temperature.

`Third time constant, tau3(SOC,T)` — Third RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `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
`[44, 24, 14, 13419]` `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 Temperature dependent tables to Yes - tabulate parameters over temperature.

`Fourth polarization resistance, R4(SOC)` — Fourth RC resistance
`[.382, .006, .007, .956]` `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 Temperature dependent tables to No - do not tabulate parameters over temperature.

`Fourth time constant, tau4(SOC,T)` — Fourth RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `s` (default) | matrix of positive numbers

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

Dependencies

`Fourth time constant, tau4(SOC)` — Fourth RC time constant
`[44, 24, 14, 13419]` `s` (default) | matrix of positive numbers

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

Dependencies

`Fifth polarization resistance, R5(SOC,T)` — Fifth 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 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.

`Fifth polarization resistance, R5(SOC)` — Fifth RC resistance
`[.382, .006, .007, .956]` `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 Temperature dependent tables to No - do not tabulate parameters over temperature.

`Fifth time constant, tau5(SOC,T)` — Fifth RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `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 Temperature dependent tables to Yes - tabulate parameters over temperature.

`Fifth time constant, tau5(SOC)` — Fifth RC time constant
`[44, 24, 14, 13419]` `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 Temperature dependent tables to No - do not tabulate parameters over temperature.

Fade

`Fade characteristics defined by` — Select how to define fade characteristics
`Equations` (default) | `Lookup tables (temperature independent)` | `Lookup tables (temperature dependent)`

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.

`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 characteristics defined by to Equations.

`Change in no-load voltage after N discharge cycles (%)` — Percent change in no-load voltage after N cycles
`0` (default) | scalar

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.

`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 characteristics defined by to Equations.

`Change in ampere-hour rating after N discharge cycles (%)` — Percent change in ampere-hour rating after N cycles
`0` (default) | scalar

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.

`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 characteristics defined by 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 characteristics defined by 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 characteristics defined by 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 characteristics defined by to Equations.

`Vector of discharge cycle values, N` — Reference vector or numbers of cycles for percent change calculations
`[100, 200, 300]` (default) | number from `1` to `Inf`

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 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 characteristics defined by to Lookup tables (temperature dependent).

`Percentage change in no-load voltage, dV0(N)` — Vector of percent change in no-load voltage after N cycles
`[0, 0, 0]` (default) | vector of scalars

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).

`Percentage change in terminal resistance, dR0(N)` — Vector of percent change in series resistance after N cycles
`[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 characteristics defined by to Lookup tables (temperature independent).

`Percentage change in ampere-hour rating, dAH(N)` — Vector of percent change in ampere-hour rating after N cycles
`[0, 0, 0]` (default) | vector of scalars

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).

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

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).

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

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).

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

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

Dependencies

`Percent change in fourth polarization resistance, dR4(N)` — Vector of percent change in fourth RC resistance after N cycles
`[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 characteristics defined by 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]` (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 characteristics defined by to Lookup tables (temperature independent).

`Percentage change in no-load voltage, dV0(N, Tfade)` — Matrix of percent change in no-load voltage after N cycles
`[0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

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).

`Percentage change in terminal resistance, dR0(N, Tfade)` — Matrix of percent change in series resistance after N cycles
`[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 characteristics defined by to Lookup tables (temperature dependent).

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

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).

`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]` (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 characteristics defined by 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]` (default) | matrix of scalars

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).

`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]` (default) | matrix of scalars

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).

`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]` (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]` (default) | matrix of scalars

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

Dependencies

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

Thermal

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

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` — Thermal mass associated with the thermal port
`30000` `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

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

Documentation

Battery (Table-Based)

Description

Battery Model

Modeling Self-Discharge

Modeling Charge Dynamics

Modeling Battery Fade

Modeling Thermal Effects

Predefined Parameterization

Plotting Voltage-Charge Characteristics

Ports

Output

SOC — Battery charge level, C physical signal

Dependencies

Conserving

+ — Positive terminal electrical

- — Negative terminal electrical

H — Battery thermal mass thermal

Dependencies

Parameters

Main

Vector of state-of-charge values, SOC — SOC breakpoints [0, .25, .75, 1] (default) | vector

Temperature dependent tables — Select whether to tabulate battery parameters over temperature Yes - tabulate parameters over temperature (default) | No - do not tabulate parameters over temperature

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

Vector of temperatures, T — T breakpoints [273.15, 298.15, 323.15] K (default) | vector of positive numbers

Dependencies

No-load voltage, V0(SOC,T) — V0 lookup table with temperature breakpoint [3.2, 3.1, 3.14; 3.25, 3.27, 3.3; 3.28, 3.31, 3.34; 3.33, 3.5, 3.59] V (default) | matrix of nonnegative numbers

Dependencies

No-load voltage, V0(SOC) — V0 lookup table [3.1, 3.27, 3.31, 3.5] V (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance, R0(SOC,T) — R0 lookup table with temperature breakpoint [.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during discharging, R0(SOC,T) — R0 lookup table with temperature breakpoint during discharging phase [.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during charging, R0(SOC,T) — R0 lookup table with temperature breakpoint during charging phase [.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance, R0(SOC) — R0 lookup table [.015, .017, .012, .013] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during discharging, R0(SOC) — R0 lookup table during discharging phase [.015, .017, .012, .013] Ohm (default) | matrix of nonnegative numbers

Dependencies

Terminal resistance during charging, R0(SOC) — R0 lookup table during charging phase [.015, .017, .012, .013] Ohm (default) | matrix of nonnegative numbers

Dependencies

Ampere-hour rating, AH(T) — AH rating at temperature breakpoints [2.9, 4.1, 4.2] hr*A (default) | vector of nonnegative numbers

Dependencies

Ampere-hour rating, AH — AH breakpoints 4.1 hr*A (default) | nonnegative scalar

Dependencies

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

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

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

First polarization resistance, R1(SOC,T) — First RC resistance at temperature breakpoints [.089, .076, .01; .042, .022, .099; .019, .007, .002; .051, .043, .029] Ohm (default) | matrix of positive numbers

Dependencies

First polarization resistance, R1(SOC) — First RC resistance [.076, .022, .007, .043] Ohm (default) | matrix of positive numbers

Dependencies

First time constant, tau1(SOC,T) — First RC time constant at temperature breakpoints [44, 148, 235; 93, 110, 1000; 19, 27, 133; .5, 22, 3] s (default) | matrix of positive numbers

Dependencies

First time constant, tau1(SOC) — First RC time constant [148, 110, 27, 22] s (default) | matrix of positive numbers

Dependencies

Second polarization resistance, R2(SOC,T) — Second RC resistance at temperature breakpoints [.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912] Ohm (default) | matrix of positive numbers

Dependencies

Second polarization resistance, R2(SOC) — Second RC resistance [.382, .006, .007, .956] Ohm (default) | matrix of positive numbers

Dependencies

Second time constant, tau2(SOC,T) — Second RC time constant at temperature breakpoints [1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216] s (default) | matrix of positive numbers

Dependencies

Second time constant, tau2(SOC) — Second RC time constant [44, 24, 14, 13419] s (default) | matrix of positive numbers

Dependencies

Third polarization resistance, R3(SOC,T) — Third RC resistance at temperature breakpoints [.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912] Ohm (default) | matrix of positive numbers

Dependencies

Third polarization resistance, R3(SOC) — Third RC resistance [.382, .006, .007, .956] Ohm (default) | matrix of positive numbers

Dependencies

Third time constant, tau3(SOC,T) — Third RC time constant at temperature breakpoints [1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216] s (default) | matrix of positive numbers

Dependencies

Third time constant, tau3(SOC) — Third RC time constant [44, 24, 14, 13419] s (default) | matrix of positive numbers

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

Dependencies

`SOC` — Battery charge level, C
physical signal

`+` — Positive terminal
electrical

`-` — Negative terminal
electrical

`H` — Battery thermal mass
thermal

`Vector of state-of-charge values, SOC` — SOC breakpoints
`[0, .25, .75, 1]` (default) | vector

`Temperature dependent tables` — Select whether to tabulate battery parameters over temperature
`Yes - tabulate parameters over temperature` (default) | `No - do not tabulate parameters over temperature`

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

`Vector of temperatures, T` — T breakpoints
`[273.15, 298.15, 323.15]` `K` (default) | vector of positive numbers

`No-load voltage, V0(SOC,T)` — V0 lookup table with temperature breakpoint
`[3.2, 3.1, 3.14; 3.25, 3.27, 3.3; 3.28, 3.31, 3.34; 3.33, 3.5, 3.59]` `V` (default) | matrix of nonnegative numbers

`No-load voltage, V0(SOC)` — V0 lookup table
`[3.1, 3.27, 3.31, 3.5]` `V` (default) | matrix of nonnegative numbers

`Terminal resistance, R0(SOC,T)` — R0 lookup table with temperature breakpoint
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `Ohm` (default) | matrix of nonnegative numbers

`Terminal resistance during discharging, R0(SOC,T)` — R0 lookup table with temperature breakpoint during discharging phase
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `Ohm` (default) | matrix of nonnegative numbers

`Terminal resistance during charging, R0(SOC,T)` — R0 lookup table with temperature breakpoint during charging phase
`[.03, .015, .002; .04, .017, .008; .039, .012, .006; .027, .013, .021]` `Ohm` (default) | matrix of nonnegative numbers

`Terminal resistance, R0(SOC)` — R0 lookup table
`[.015, .017, .012, .013]` `Ohm` (default) | matrix of nonnegative numbers

`Terminal resistance during discharging, R0(SOC)` — R0 lookup table during discharging phase
`[.015, .017, .012, .013]` `Ohm` (default) | matrix of nonnegative numbers

`Terminal resistance during charging, R0(SOC)` — R0 lookup table during charging phase
`[.015, .017, .012, .013]` `Ohm` (default) | matrix of nonnegative numbers

`Ampere-hour rating, AH(T)` — AH rating at temperature breakpoints
`[2.9, 4.1, 4.2]` `hr*A` (default) | vector of nonnegative numbers

`Ampere-hour rating, AH` — AH breakpoints
`4.1` `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`

`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
`[.089, .076, .01; .042, .022, .099; .019, .007, .002; .051, .043, .029]` `Ohm` (default) | matrix of positive numbers

`First polarization resistance, R1(SOC)` — First RC resistance
`[.076, .022, .007, .043]` `Ohm` (default) | matrix of positive numbers

`First time constant, tau1(SOC,T)` — First RC time constant at temperature breakpoints
`[44, 148, 235; 93, 110, 1000; 19, 27, 133; .5, 22, 3]` `s` (default) | matrix of positive numbers

`First time constant, tau1(SOC)` — First RC time constant
`[148, 110, 27, 22]` `s` (default) | matrix of positive numbers

`Second polarization resistance, R2(SOC,T)` — Second RC resistance at temperature breakpoints
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `Ohm` (default) | matrix of positive numbers

`Second polarization resistance, R2(SOC)` — Second RC resistance
`[.382, .006, .007, .956]` `Ohm` (default) | matrix of positive numbers

`Second time constant, tau2(SOC,T)` — Second RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `s` (default) | matrix of positive numbers

`Second time constant, tau2(SOC)` — Second RC time constant
`[44, 24, 14, 13419]` `s` (default) | matrix of positive numbers

`Third polarization resistance, R3(SOC,T)` — Third RC resistance at temperature breakpoints
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `Ohm` (default) | matrix of positive numbers

`Third polarization resistance, R3(SOC)` — Third RC resistance
`[.382, .006, .007, .956]` `Ohm` (default) | matrix of positive numbers

`Third time constant, tau3(SOC,T)` — Third RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `s` (default) | matrix of positive numbers

`Third time constant, tau3(SOC)` — Third RC time constant
`[44, 24, 14, 13419]` `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
`[.382, .006, .007, .956]` `Ohm` (default) | matrix of positive numbers

`Fourth time constant, tau4(SOC,T)` — Fourth RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `s` (default) | matrix of positive numbers

`Fourth time constant, tau4(SOC)` — Fourth RC time constant
`[44, 24, 14, 13419]` `s` (default) | matrix of positive numbers

`Fifth polarization resistance, R5(SOC,T)` — Fifth RC resistance at temperature breakpoints
`[.014, .382, .407; .028, .006, .007; .014, .007, .006; .333, .956, .912]` `Ohm` (default) | matrix of positive numbers

`Fifth polarization resistance, R5(SOC)` — Fifth RC resistance
`[.382, .006, .007, .956]` `Ohm` (default) | matrix of positive numbers

`Fifth time constant, tau5(SOC,T)` — Fifth RC time constant at temperature breakpoints
`[1, 44, 5644; 11, 24, 506; 2, 14, 330; 3310, 13419, 30216]` `s` (default) | matrix of positive numbers

`Fifth time constant, tau5(SOC)` — Fifth RC time constant
`[44, 24, 14, 13419]` `s` (default) | matrix of positive numbers

`Fade characteristics defined by` — Select how to define fade characteristics
`Equations` (default) | `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 no-load voltage after N discharge cycles (%)` — Percent change in no-load 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 ampere-hour rating after N discharge cycles (%)` — Percent change in ampere-hour rating 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
`[100, 200, 300]` (default) | number from `1` 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 no-load voltage, dV0(N)` — Vector of percent change in no-load voltage after N cycles
`[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]` (default) | vector of scalars

`Percentage change in ampere-hour rating, dAH(N)` — Vector of percent change in ampere-hour rating after N cycles
`[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]` (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]` (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]` (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]` (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]` (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]` (default) | vector of scalars

`Percentage change in no-load voltage, dV0(N, Tfade)` — Matrix of percent change in no-load voltage after N cycles
`[0, 0; 0, 0; 0, 0]` (default) | matrix of scalars

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

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

`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]` (default) | matrix of scalars

`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]` (default) | matrix of scalars

`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]` (default) | matrix of scalars