# Machine Inertia

Machine inertia parameterized using machine inertia constant or anchor inertia

• Library:
• Simscape / Electrical / Electromechanical / Mechanical

## Description

The Machine Inertia block models inertia and damping that you connect to the mechanical rotational R port of a three-phase machine. The block has an internal connection to a mechanical rotational reference. The figure shows an equivalent configuration to the Machine Inertia block using Simscape™ mechanical rotational components.

Based on the value you select for the ```Specify inertia parameterization by``` parameter, you specify inertia J directly or using the machine inertia constant H.

If you specify the inertia constant, the block calculates inertia by

`$J=\frac{2H{S}_{rated}}{{\left(2\pi {F}_{rated}/N\right)}^{2}},$`

where:

• J is inertia in kg⋅m2.

• H is the inertia constant in sW/VA.

• Srated is the machine rated apparent power in VA.

• Frated is the machine rated electrical frequency in Hz.

• N is the number of machine pole pairs.

You specify damping that represents viscous friction between the machine rotor and mechanical rotational reference. Based on the value you select for the `Specify damper parameterization by` parameter, you specify a damping coefficient in SI units or in per-unit. If you specify the damping coefficient in per-unit, the block calculates the damping coefficient in SI units by

`${\omega }_{base}=\frac{2\pi {F}_{rated}}{N},$`

`${T}_{base}=\frac{{S}_{rated}}{{\omega }_{base}},$`

`${D}_{base}=\frac{{T}_{base}}{{\omega }_{base}},$`

and

`$D={D}_{pu}{D}_{base},$`

where:

• ωbase is the base mechanical angular speed in rad/s.

• Tbase is the base damping torque in Nm.

• Dbase is the base damping coefficient in Nm/(rad/s).

• Dpu is the damping coefficient in per-unit.

• D is the damping coefficient in SI units of Nm/(rad/s).

### Display Option

You can display machine parameters using the Electrical menu on the block context menu.

Right-click the block and, from the Electrical menu, select Display Parameters to display the machine per-unit base values and inertia parameters in the MATLAB® Command Window.

## Ports

### Conserving

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Mechanical rotational conserving port associated with the machine rotor.

## Parameters

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### Main

Machine rated apparent power.

Nominal electrical frequency corresponding to the machine rated apparent power.

Number of pole pairs of the connected machine.

### Inertia

Inertia specification.

Inertia constant.

#### Dependencies

To enable this parameter, set Specify inertia parameterization by to ```Inertia constant, H```.

Total rotational mechanical inertia of machine rotor. This parameter is visible only if you set Specify inertia parameterization by to ```Actual Inertia, J```.

#### Dependencies

To enable this parameter, set Specify inertia parameterization by to ```Actual Inertia, J```.

Damping specification.

Damping coefficient in per-unit.

#### Dependencies

To enable this parameter, set Specify damper parameterization by to ```Per-unit damping coefficient, pu_D```.

Damping coefficient in SI units.

#### Dependencies

To enable this parameter, set Specify damper parameterization by to ```SI damping coefficient, D```.

### Initial Conditions

Frequency initialization.

Initial electrical frequency, specified in SI frequency units, such as `Hz`, `kHz`, `MHz`, or `GHz`.

#### Dependencies

To enable this parameter, set Specify initialization by to ```Initial electrical frequency```.

Initial mechanical frequency, specified in SI frequency units, such as `Hz`, `kHz`, `MHz`, or `GHz`.

#### Dependencies

To enable this parameter, set Specify initialization by to ```Initial mechanical frequency```.

## References

[1] Kundur, P. Power System Stability and Control. New York, NY: McGraw Hill, 1993.

## Version History

Introduced in R2013b