Battery

The battery model.

blockType: AcausalElectricPowerSystems.Sources.Battery

Path in the library:

/Physical Modeling/Electrical/Sources/Battery

Description

Block Battery It is a simple battery model. You can also set the charge output port and the thermal port of the battery.

To measure the internal battery charge level, in the Main section, select the checkbox for the Expose charge measurement port parameter. This action displays the additional q port, which outputs the current battery charge value. Use this functionality to change the behavior of the load depending on the state of charge, without resorting to the complexities of building a charge level meter.

To simulate the thermal effects of a battery, check the box for the Thermal port option in the Thermal Port section. This action opens an additional thermal port H. When selecting this mode, additional parameters must be entered, in particular, the second temperature must be set. For more information, see the section Modeling thermal effects.

An equivalent battery circuit consists of a fundamental battery model, self-discharge resistance , models of charge dynamics and series resistance .

battery scheme 1

Battery Model

If the Battery charge capacity parameter is set to Infinite then the unit will model the battery as a series resistor and a constant voltage source. At the same time, the charge level does not change over time.

If the Battery charge capacity parameter is set to Finite The unit models the battery as a series resistor and a charge-dependent voltage source. In this case, the voltage is a function of charge and has the following relationship:

where:

SOC (State of charge) is the ratio of the current charge to the rated capacity of the battery.
— This is the voltage when the battery is fully charged when there is no load (rated voltage). It is set by the Nominal voltage parameter.
ß is a coefficient that is calculated so that the battery voltage is V1 when charged AH1. Set the voltage V1 and cell capacity AH1 using the block parameters. AH1 is a charge when the no—load (open circuit) voltage is V1 and V1 is less than the rated voltage.

The equation defines the approximate relationship between voltage and remaining charge. This approximation reproduces the increasing rate of voltage drop at low charge values and ensures that the battery voltage becomes zero when the charge level is zero. The advantage of this model is that it requires a small number of parameters, which are easily available in most technical data sheets.

Simulation of battery fading

For battery models with finite charge capacity, it is possible to simulate the deterioration of battery performance depending on the number of discharge cycles. This deterioration is called battery fading. To use it, check the box for the Battery fade option. This setting opens additional options in the Fade section.

The unit implements battery charge reduction by scaling certain values of the battery parameters that you specify in the Main section, depending on the number of completed discharge cycles. The block uses multipliers , and for the values of the parameters Cell capacity (Ah rating), Internal resistance and Voltage V1 when charge is AH1, respectively. These multipliers, in turn, depend on the number of discharge cycles.:

where:

— Multiplier for the rated battery capacity.
— Multiplier for sequential battery resistance.
— multiplier for voltage V1.
— the number of discharge cycles performed.
— the number of full discharge cycles completed before the start of the simulation.
— the rated capacity of the battery in ampere-hours.
— instantaneous battery output current.
— Heaviside function ("step") for instantaneous battery output current. This function returns 0 if the argument is negative, and 1 if the argument is positive.

The unit calculates the coefficients k₁, k₂ and k₃ by substituting the parameter values specified in the Fade section into these battery equations. For example, the default set of block parameters corresponds to the following coefficient values:

You can also determine the starting point for the simulation based on the previous charge-discharge history using the high-priority variable Discharge cycles.

Modeling of thermal effects

If the Thermal port option is checked, then additional parameters must be set at the second temperature to determine the behavior of the battery. The extended equations for the voltage when you expose the heat port are as follows:

where:

— battery temperature.
— nominal measurement temperature.
— the coefficient of dependence of the parameter on the temperature for .
.
— the coefficient of dependence of the parameter on the temperature for ß.
— calculated in the same way as described in the section Battery model, using a temperature-modified rated voltage .

Internal series resistance, self-discharge resistance, and any charging-dynamic resistances are also functions of temperature.:

where — the coefficient of dependence of the parameter on temperature.

All temperature dependence coefficients are determined from the corresponding values that you enter for the nominal and second measurement temperatures. If charge dynamics is included in the model, then the time constants change depending on temperature in a similar way.

The battery temperature is determined by summing up all ohmic losses included in the model:

where:

— the thermal mass of the battery.
— corresponds to the _i_th ohmic loss participant. Depending on the configuration of the unit, the losses may be as follows:
- Consistent resistance
- Self-discharge resistance
- The first segment of charge dynamics
- The second segment of charge dynamics
- The third segment of charge dynamics
- The fourth segment of charge dynamics
- The fifth segment of charge dynamics
— voltage drop at the _i_th resistance.
— this is the _i_th resistance.

Simulation of charge dynamics

You can simulate the dynamics of battery charge using the Charge dynamics parameter.:

No dynamics — the equivalent circuit does not contain parallel RC sections. There is no delay between the voltage on the contacts and the internal battery voltage.
One time-constant dynamics — the equivalent circuit contains one parallel RC section. Specify the time constant using the First time constant parameter.
Two time-constant dynamics — the equivalent circuit contains two parallel RC sections. Set time constants using the First time constant and Second time constant parameters.
Three time-constant dynamics — the equivalent circuit contains three parallel RC sections. Set time constants using the First time constant, Second time constant, and Third time constant parameters.
Four time-constant dynamics — the equivalent circuit contains four parallel RC sections. Set time constants using the First time constant, Second time constant, Third time constant, and Fourth time constant parameters.
Five time-constant dynamics — the equivalent circuit contains five parallel RC sections. Specify time constants using the parameters First time constant, Second time constant, Third time constant, Fourth time constant and Fifth time constant.

This figure shows an equivalent circuit for a unit configured with two time-constant speakers.

battery scheme 2

On the diagram:

and — parallel RC resistances. Set these values using the First polarization resistance and Second polarization resistance parameters, respectively.
and — parallel RC capacitances. The time constant t for each parallel section relates the values R and C using the ratio . Set the tt for each section using the First time constant and Second time constant parameters, respectively.
— consistent resistance. Set this value using the Internal resistance parameter.

Simulating battery aging

For battery models with finite charge capacity, it is possible to simulate the deterioration of battery performance that occurs when not in use. To do this, check the box for the Calendar aging parameter. Calendar aging affects both internal resistance and capacity. In particular, the increase in resistance depends on various mechanisms, such as the formation of a solid electrolyte interface (SEI) at the anode and cathode and corrosion of the pantograph. These processes mainly depend on the storage temperature, state of charge, and time.

Block Battery applies calendar aging only during initialization. When you check the Calendar aging option, the Vector of time intervals option appears in the block settings, which stores the time intervals when the battery aged before the start of the simulation. Calendar aging during simulation is not covered by this parameter.

This equation determines the increase in battery contact resistance as a result of calendar aging.:

where:

— The open circuit voltage is normalized to the nominal value. The Normalized open-circuit voltage during storage, V/Vnom parameter.
— internal resistance. The Internal resistance parameter.
— a time sample obtained from the Vector of time intervals parameter.
— a sample of temperatures obtained from the Vector of temperatures parameter.
— the number of temperature sampling elements.
b is the linear voltage scale. The Linear scaling for voltage, b parameter.
c is a constant voltage offset. The Constant offset for voltage parameter, c.
d is an exponential increase depending on temperature. The Temperature-dependent exponential increase parameter, d.
a is a time indicator. The Time exponent parameter, a.
q is the charge of an electron, Cl.
k is the Boltzmann constant, J/K.

Variable R_age_multiplier The Data Inspector stores data on the calendar aging of the battery in contacts with increasing resistance:

For the thermal modeling options of the block, if you set the Storage condition parameter to Fixed open-circuit voltage then you must specify an additional parameter Open-circuit voltage measurement temperature to convert the open-circuit voltage of the storage circuit to a temperature-independent state of charge during storage:

The open circuit voltage, depending on the storage temperature, is determined by this equation:

Finally, this equation determines the increase in battery terminal resistance as a result of calendar aging, depending on the storage temperature.:

Assumptions and limitations

It is assumed that the self-discharge resistance does not depend on the number of discharge cycles.
For the battery thermal simulation option, you provide attenuation data only for operation at a reference temperature. The block applies the same multipliers , and to the values of the parameters corresponding to the second temperature.
When using the heat block simulation options, be careful when operating at temperatures outside the temperature range limited by the values of the Measurement temperature and Second measurement temperature parameters. The block uses linear interpolation for the coefficients of the derivatives of the equations, and the simulation results may become non-physical beyond the specified range.

Ports

Output

SOC — Pass battery charge level:Q[ ] scalar

The charge level. Use this output port to change the load behavior depending on the charge level, without resorting to the complexities of building a charge meter.

Charge level is a normalized value equal to the ratio of the current charge to the rated capacity of the battery . The unit evaluates the current battery charge by integrating the output current of the battery terminals. To convert the state of charge to an actual charge, you must use the correct rated battery capacity for each temperature.

Dependencies

To use this port, check the box for the Expose charge measurement port parameter, and set the value for the Measurement output type parameter. SOC.

q — current battery charge, Kl
scalar

Internal charge in coulombs. Use this output port to change the behavior of the load depending on the charge, without resorting to the complexities of building a charge meter.

Dependencies

To use this port, check the box for the Expose charge measurement port parameter, and set the value for the Measurement output type parameter. Charge in Coulombs.

Non-directional

+ — positive contact
electricity

The electrical port connected to the positive contact of the battery.

− — negative contact
electricity

The electrical port connected to the negative contact of the battery.

H — thermal port of the battery
warm

The thermal port connected to the thermal mass of the battery. When activating this port, specify additional parameters to determine the behavior of the battery. For more information, see the section Modeling thermal effects.

Dependencies

To use this port, select the checkbox for the Thermal port option in the Thermal Port section.

Parameters

Main

Nominal voltage, Vnom — nominal output voltage of a fully charged battery
12 V (default) | a positive number

The idling voltage of a fully charged battery.

Current directionality — influence of the current direction of
Disabled (by default) | Enabled

If this option is selected, the internal resistance will depend on the current direction.

Internal resistance — internal resistance of the pass battery:q[ ] 2 Ohms (default) | a positive number

The resistance of the battery’s internal connections.

Dependencies

To use this option, uncheck the Current directionality option.

Internal resistance during charging — internal resistance of the battery during charging
2 Ohms (default) | a positive number

The internal resistance of the battery during the charging phase.

Dependencies

To use this parameter, check the box for the Current directionality parameter.

Internal resistance during discharging — internal resistance of the battery during discharge
2 Ohms (default) | a positive number

The internal resistance of the battery during the discharge phase.

Dependencies

To use this parameter, check the box for the Current directionality parameter.

Battery charge capacity — selection of the pass battery model:q[ ] Infinite (by default) | Finite

Select one of the options for simulating battery capacity:

Infinite — Battery voltage is independent of the charge received from the battery, infinite capacity.
Finite — The battery voltage decreases as the charge decreases.

Cell capacity (Ah rating) — rated battery capacity at full charge
50 Ah (default) | a positive number

The maximum (nominal) battery charge in ampere-hours. To set a target value for the initial battery charge at the beginning of the simulation, use the high-priority variable Charge.

Dependencies

To use this parameter, set the Battery charge capacity parameter to Finite.

Voltage V1 when charge is AH1 — output voltage at charge level AH1
11.5 V (default) | a positive number

The main output voltage of the battery at the AH1 charge level, as specified in the parameter Charge AH1 when no-load voltage is V1. This parameter must be less than Nominal voltage, Vnom.

Dependencies

To use this parameter, set the Battery charge capacity parameter to Finite.

Charge AH1 when no-load voltage is V1 — charge level when no-load output voltage is V1
25 Ah (default) | a positive number

The battery charge level corresponding to the no-load output voltage set by the parameter Voltage V1 when charge is AH1.

Dependencies

To use this parameter, set the Battery charge capacity parameter to Finite.

Self-discharge — Select whether to simulate battery self-discharge.
Disabled (by default) | Enabled

If this option is selected, the unit simulates battery self-discharge. The unit simulates this effect like a resistor connected to the contacts of a fundamental battery model.

As the temperature increases, the self-discharge resistance decreases, which leads to an increase in self-discharge. If the resistance decreases too quickly, thermal discharge of the battery and numerical instability may occur. You can solve this problem by doing one of the following

Reduce thermal resistance.
Reduce the gradient of self-discharge resistance depending on the temperature.
Increase the self-discharge resistance.

Dependencies

To use this parameter, set the Battery charge capacity parameter to Finite.

Self-discharge resistance — resistance reflecting the self-discharge of the battery
2000 Ohms (default) | a positive number

The resistance in the fundamental model of the battery, reflecting the self-discharge of the battery.

Dependencies

To use this option, check the box for the Self-discharge option.

Measurement temperature — the temperature at which the parameters of the pass block are measured:q[ ] 298.15 K (default) | a positive number

The temperature T₁ at which the unit parameters are measured in the Main section. For more information, see the section Modeling thermal effects.

Dependencies

To use this option, check the box for the Thermal Port option.

Expose charge measurement port — do I need to open the port to measure the charge
Disabled (by default) | Enabled

Check the box to open the charge measurement port and measure the internal charge level of the battery.

Measurement output type — signal selection in the measuring port
Charge in Coulombs (default) | SOC

The parameter has two values:

SOC — charge level values are sent to the output SOC.
Charge in Coulombs — charge values are sent to the output q in Pendants.

Dependencies

This parameter is used if the Expose measurement port parameter has the value enabled.

Dynamics

Choose a method for simulating battery charge dynamics. This parameter determines the number of parallel RC sections in the equivalent circuit.:

No dynamics — the equivalent circuit does not contain parallel RC sections. There is no delay between the voltage on the contacts and the internal battery voltage.
One time-constant dynamics — the equivalent circuit contains one parallel RC section. Specify the time constant using the First time constant parameter.
Two time-constant dynamics — the equivalent circuit contains two parallel RC sections. Set time constants using the First time constant and Second time constant parameters.
Three time-constant dynamics — the equivalent circuit contains three parallel RC sections. Set time constants using the First time constant, Second time constant and Third time constant parameters.
Four time-constant dynamics — the equivalent circuit contains four parallel RC sections. Set time constants using the First time constant, Second time constant, Third time constant, and Fourth time constant parameters.
Five time-constant dynamics — the equivalent circuit contains five parallel RC sections. Specify time constants using the parameters First time constant, Second time constant, Third time constant, Fourth time constant and Fifth time constant.

First polarization resistance — first RC resistance
0.005 ohms (default) | a positive number

Resistance of the first parallel RC section. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To use this parameter, set the Charge dynamics parameter to One time-constant dynamics, Two time-constant dynamics, Three time-constant dynamics, Four time-constant dynamics or Five time-constant dynamics.

First time constant — the first time constant of RC
30 seconds (default) | a positive number

The time constant of the first parallel RC section. This value is equal to R*C and affects the dynamics of the RC section.

Dependencies

Second polarization resistance — second RC pass resistance:q[ ] 0.005 ohms (default) | a positive number

Resistance of the second parallel RC section. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

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

Second time constant — second time constant RC
30 seconds (default) | a positive number

The time constant of the second parallel RC section. This value is equal to R*C and affects the dynamics of the RC section.

Dependencies

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

Third polarization resistance — third resistance RC
0.005 ohms (default) | a positive number

Resistance of the third parallel RC section. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

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

Third time constant — the third time constant of RC
30 seconds (default) | a positive number

The time constant of the third parallel RC section. This value is equal to R*C and affects the dynamics of the RC section.

Dependencies

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

Fourth polarization resistance — fourth RC pass resistance:q[ ] 0.005 ohms (default) | a positive number

Resistance of the fourth parallel RC section. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To use this parameter, set the Charge dynamics parameter to Four time-constant dynamics or Five time-constant dynamics.

Fourth time constant — the fourth time constant of RC
30 seconds (default) | a positive number

The time constant of the fourth parallel RC section. This value is equal to R*C and affects the dynamics of the RC section.

Dependencies

To use this parameter, set the Charge dynamics parameter to Four time-constant dynamics or Five time-constant dynamics.

Fifth polarization resistance — fifth resistance RC
0.005 ohms (default) | a positive number

Resistance of the fifth parallel RC section. This parameter primarily affects the ohmic losses of the RC section.

Dependencies

To use this parameter, set the Charge dynamics parameter to Five time-constant dynamics.

Fifth time constant — fifth time constant of RC
30 seconds (default) | a positive number

The time constant of the fifth parallel RC section. This value is equal to R*C and affects the dynamics of the RC section.

Dependencies

To use this parameter, set the Charge dynamics parameter to Five time-constant dynamics.

Fade

To use these parameters, set the Battery charge capacity parameter to Finite.

Battery fade — select whether to simulate the deterioration of battery performance during charge-discharge
Disabled (by default) | Enabled

If the box is checked, the unit simulates the battery fading.:

Turned off — Battery characteristics do not depend on the number of charge-discharge cycles.
Enabled — Battery characteristics vary depending on the number of completed charge-discharge cycles. Selecting this option opens additional options in this section that determine the characteristics of the battery after a certain number of discharge cycles. The block uses the values of these parameters to calculate the scale factors k₁, k₂ and k₃.

For more information, see the section Battery fade simulation.

Number of discharge cycles, N — number of completed charge-discharge cycles
100 (default) | a positive number

The number of charge-discharge cycles after which the remaining parameters are measured in this section. It defines the scale factors k₁, k₂, and k₃ used in simulating battery decay.

Dependencies

To use this option, check the box for the Battery fade option.

Cell capacity after N discharge cycles — maximum battery capacity after N discharge cycles
45 Ah (default) | a positive number

The maximum battery charge, in ampere-hours, after the number of discharge cycles set by the parameter Number of discharge cycles, N.

Dependencies

To use this option, check the box for the Battery fade option.

Internal resistance after N discharge cycles — internal resistance of the battery after N discharge cycles
2.02 ohms (default) | a positive number

The internal resistance of the battery after the number of discharge cycles set by the parameter Number of discharge cycles, N.

Dependencies

To use this option, check the box for the Battery fade parameter, and uncheck the box for the Current Directionality parameter in the Main section.

Average internal resistance after N discharge cycles — average internal resistance of the battery after N discharge cycles
2.02 ohms (default) | a positive number

The average value of the battery’s internal resistance during charge and discharge after the number of discharge cycles set by the parameter Number of discharge cycles, N.

Dependencies

To use this option, check the boxes for the Battery fade parameter and for the Current Directionality parameter in the Main section.

Voltage V1 at charge AH1 after N discharge cycles — output voltage at charge level AH1 after N discharge cycles
10.35 V (default) | a positive number

The output voltage of the fundamental battery model at the AH1 charge level after the number of discharge cycles set by the parameter Number of discharge cycles, N.

Dependencies

To use this option, check the box for the Battery fade option.

Calendar Aging

To use these parameters, set the Battery charge capacity parameter to Finite.

Calendar aging — the possibility of calendar aging
Disabled (by default) | Enabled

If this option is selected, the unit uses calendar battery aging.

Storage condition — pass storage conditions:q[ ] Fixed open-circuit voltage (default) | Fixed state of charge

You need to select a parameter that determines the state of charge during storage- the open circuit voltage or the state of charge during storage.

Dependencies

To use this option, check the box for the Calendar aging option.

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

Rated open circuit voltage during storage.

Dependencies

To use this parameter, select the Calendar aging checkbox and set the value for the Storage condition parameter Fixed open-circuit voltage.

Open-circuit measurement temperature — temperature of the open circuit
298.15 K (default) | a positive number

The temperature at which the open circuit voltage was measured.

Dependencies

To use this parameter, open the thermal port of the unit, check the box for the Calendar aging parameter, and set the value for the Storage condition parameter Fixed open-circuit voltage.

State of charge during storage (%) — percentage state of charge during storage
50 (default) | a positive number

State of charge during storage, as a percentage.

Dependencies

To use this parameter, check the box for the Calendar aging parameter and for the Storage condition parameter. Fixed state of charge.

Vector of time intervals — vector of time intervals
[0] (default) | vector

Storage time intervals. This parameter must be equal in size to the Vector of temperatures.

Dependencies

To use this option, check the box for the Calendar aging option.

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

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

Dependencies

To use this option, check the box for the Calendar aging option.

Linear scaling for voltage, b — linear voltage scaling
2.2134e6 (default) | scalar

The linear scaling factor for the open circuit voltage.

Dependencies

To use this option, check the box for the Calendar aging option.

Constant offset for voltage, c — constant voltage offset
1.632e6 (default) | scalar

Constant offset for the open circuit voltage.

Dependencies

To use this option, check the box for the Calendar aging option.

Temperature-dependent exponential increase, d is an exponential multiplier of temperature dependence
0.515833569 (default) | scalar

Exponential growth depending on temperature.

Dependencies

To use this option, check the box for the Calendar aging option.

Time exponent, a is the exponent of time
0.75 (default) | scalar

The exponent multiplier that determines the dependence on time.

Dependencies

To use this option, check the box for the Calendar aging option.

Temperature Dependence

To use these parameters, set the Thermal port parameter to Enabled.

Nominal voltage at second measurement temperature — output voltage with fully charged battery
12 V (default) | a positive number

The battery idling voltage is at the second measurement temperature when it is fully charged.

Internal resistance at second measurement temperature — internal resistance of the battery
2.2 Ohms (default) | a positive number

The resistance of the internal connection of the battery at the second measurement temperature.

Voltage V1 at second measurement temperature — output voltage at charge level AH1
11.4 V (default) | a positive number

The output voltage of the main battery model at the temperature of the second measurement and the charge level AH1, set by the parameter AH1 charge at idle voltage V1.

Dependencies

To use this parameter, set the Battery charge capacity parameter to Finite.

Self-discharge resistance at second measurement temperature — resistance reflecting battery self-discharge
2200 ohms (default) | a positive number

The resistance in the fundamental model of the battery at the second measurement temperature, reflecting the self-discharge of the battery.

Dependencies

To use this option, check the box for the Self-discharge option.

First polarization resistance at second measurement temperature — first RC resistance at the second measurement temperature
0.005 ohms (default) | a positive number

Resistance of the first parallel RC section at the second measurement temperature.

Dependencies

First time constant at second measurement temperature — the first time constant RC at the second measurement temperature
30 seconds (default) | a positive number

The time constant of the first parallel RC section at the second measurement temperature.

Dependencies

Second polarization resistance at second measurement temperature — second RC resistance at the second measurement temperature
0.005 ohms (default) | a positive number

Resistance of the second parallel RC section at the second measurement temperature.

Dependencies

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

Second time constant at second measurement temperature — the second time constant RC at the second measurement temperature
30 seconds (default) | a positive number

The time constant of the second parallel RC section at the second measurement temperature.

Dependencies

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

Third polarization resistance at second measurement temperature — third RC resistance at the second measurement temperature
0.005 ohms (default) | a positive number

Resistance of the third parallel RC section at the second measurement temperature.

Dependencies

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

Third time constant at second measurement temperature — the third time constant RC at the second measurement temperature
30 seconds (default) | a positive number

The time constant of the third parallel RC section at the second measurement temperature.

Dependencies

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

Fourth polarization resistance at second measurement temperature — fourth RC resistance at the second measurement temperature
0.005 ohms (default) | a positive number

Resistance of the fourth parallel RC section at the second measurement temperature.

Dependencies

To use this parameter, set the Charge dynamics parameter to Four time-constant dynamics or Five time-constant dynamics.

Fourth time constant at second measurement temperature — the fourth time constant RC at the second measurement temperature
30 seconds (default) | a positive number

The time constant of the fourth parallel RC section at the second measurement temperature.

Dependencies

To use this parameter, set the Charge dynamics parameter to Four time-constant dynamics or Five time-constant dynamics.

Fifth polarization resistance at second measurement temperature — fifth RC resistance at the second measurement temperature
0.005 ohms (default) | a positive number

Resistance of the fifth parallel RC section at the second measurement temperature.

Dependencies

To use this parameter, set the Charge dynamics parameter to Five time-constant dynamics.

Fifth time constant at second measurement temperature — fifth time constant RC at the second measurement temperature
30 seconds (default) | a positive number

The time constant of the fifth parallel RC section at the second measurement temperature.

Dependencies

To use this parameter, set the Charge dynamics parameter to Five time-constant dynamics.

Second measurement temperature — the temperature at which the parameters of the pass block are measured:q[ ] 273.15 K (default) | a positive number

The temperature T₂, at which the unit parameters are measured in the Temperature Dependence section.

Thermal Port

Thermal port — enabling the thermal port
disabled (by default) | enabled

Select this option to enable the thermal port of the unit and simulate the thermal effects of the battery.

Thermal mass — the thermal mass associated with the thermal port
30,000 J/K (default) | a positive number

The thermal mass associated with the thermal port H. It represents the energy needed to increase the temperature of the heating port by one degree.

Dependencies

To use this option, check the box for the Thermal port option.

Literature

Ramadass, P., B. Haran, R. E. White, and B. N. Popov. “Mathematical modeling of the capacity fade of Li-ion cells.” Journal of Power Sources. 123 (2003), pp. 230–240.
Ning, G., B. Haran, and B. N. Popov. “Capacity fade study of lithium-ion batteries cycled at high discharge rates.” Journal of Power Sources. 117 (2003), pp. 160–169.

Battery

Description

Battery Model

Simulation of battery fading

Modeling of thermal effects

Simulation of charge dynamics

Simulating battery aging

Assumptions and limitations

Ports

Output

Non-directional

Parameters

Main

Dynamics

Fade

Calendar Aging

Temperature Dependence

Thermal Port

Literature

Examples