# Machine Inertia

Machine inertia

Machines

## 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 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 Power Systems menu on the block context menu.

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

## Parameters

### Main Tab

Rated apparent power

Machine rated apparent power. The default value is `555e6` `V*A`.

Rated electrical frequency

Nominal electrical frequency corresponding to the machine rated apparent power. The default value is `60` `Hz`.

Number of pole pairs

Number of machine pole pairs. The default value is `1`.

### Inertia Tab

Specify inertia parameterization by

Inertia specification. The default value is ```Inertia constant, H```.

Inertia constant, H

Inertia constant. This parameter is visible only if you set Specify inertia parameterization by to ```Inertia constant, H```. The default value is `3.525` `sW/VA`.

Actual inertia, J

Inertia. This parameter is visible only if you set Specify inertia parameterization by to ```Actual inertia, J```. The default value is `27548` kg⋅m2.

Specify damper parameterization by

Damping specification. The default value is ```Per-unit damping coefficient, pu_D```.

Per-unit damping coefficient

Damping coefficient in per-unit. This parameter is visible only if you set Specify damper parameterization by to ```Per-unit damping coefficient, pu_D```. The default value is `0.01`.

SI damping coefficient

Damping coefficient in SI units. This parameter is visible only if you set Specify damper parameterization by to ```SI damping coefficient, D```. The default value is `39.0509` Nm/(rad/s).

### Initial Conditions Tab

Specify initialization by

Frequency initialization. The default value is ```Initial electrical frequency```.

Initial electrical frequency

Initial electrical frequency. This parameter is visible only if you set Specify initialization by to ```Initial electrical frequency```. The default value is `60` `Hz`.

Initial mechanical frequency

Initial mechanical frequency. This parameter is visible only if you set Specify initialization by to ```Initial mechanical frequency```. The default value is `60` `Hz`.

## Ports

The block has the following ports:

`R`

Mechanical rotational conserving port associated with the machine rotor

## References

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