Simple battery model

Sources

The Generic Battery block represents a simple
battery model. If you select `Infinite`

for
the **Battery charge capacity** parameter, the block
models the battery as a series resistor and a constant voltage source.
If you select `Finite`

for the **Battery
charge capacity** parameter, the block models the battery
as a series resistor and a charge-dependent voltage source whose voltage
as a function of charge has the following reciprocal relationship:

$$V={V}_{0}\left[1-\left(\frac{\alpha (1-x)}{1-\beta (1-x)}\right)\right]$$

where:

*x*is the ratio of the ampere-hours left to the number of ampere-hours,*AH*, for which the battery is rated.*V*is the voltage when the battery is fully charged, as defined by the_{0}**Nominal voltage, V_nominal**parameter.The block calculates the constants

*α*and*β*to satisfy the following battery conditions:The battery voltage is zero when the charge is zero, that is, when

*x*= 0.The battery voltage is

*V1*(the**Voltage V1 < V_nominal when charge is AH1**parameter value) when the charge is the**Charge AH1 when no-load volts are V1**parameter value, that is, when*x*=*AH1*/*AH*.

The equation defines a reciprocal relationship between voltage and remaining charge. It is an approximation to what happens in a real battery, but it does replicate the increasing rate of voltage drop at low charge values. It also ensures that the battery voltage becomes zero when the charge level is zero. This simple model has the advantage of requiring very few parameters, and these are parameters that are readily available on most datasheets.

**Nominal voltage, V_nominal**The voltage at the output port when the battery is fully charged. The default value is

`12`

V.**Internal resistance, R1**Internal connection resistance. The default value is

`2`

Ω.**Battery charge capacity**Select one of the following options for modeling the charge capacity of the battery:

`Infinite`

— The battery voltage is independent of charge drawn from the battery. This is the default option.`Finite`

— The battery voltage decreases as charge decreases.

**Ampere-Hour rating, AH**The maximum battery charge in ampere-hours. This parameter is only visible when you select

`Finite`

for the**Battery charge capacity**parameter. The default value is`50`

hr*A.**Initial charge**The battery charge at the start of the simulation. This parameter is only visible when you select

`Finite`

for the**Battery charge capacity**parameter. The default value is`50`

hr*A.**Voltage V1 < V_nominal when charge is AH1**The battery output voltage when the charge level is AH1 hr*A. This parameter is only visible when you select

`Finite`

for the**Battery charge capacity**parameter. The default value is`11.5`

V.**Charge AH1 when no-load volts are V1**The battery charge level in hr*A when the no-load output voltage is V1. This parameter is only visible when you select

`Finite`

for the**Battery charge capacity**parameter. The default value is`25`

hr*A.**Self-discharge resistance, R2**Select one of the following options for modeling the self-discharge resistance of the battery:

`Omit`

— Do not include resistance across the battery output terminals in the model.`Include`

— Include resistance R2 across the battery output terminals in the model.

**R2**The resistance across the battery output terminals that represents battery self-discharge. This parameter is only visible when you select

`Include`

for the**Self-discharge resistance, R2**parameter. The default value is`2e+03`

Ω.

The block has the following ports:

`+`

Positive electrical voltage

`-`

Negative electrical voltage

For an example of how you can create a detailed battery model, see the Simscape™ Lead-Acid Battery example.

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