# Machine Inertia

Machine inertia parameterized using machine inertia constant or anchor inertia

• Libraries:
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`.

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