Machine Inertia

Machine inertia parameterized using machine inertia constant or anchor inertia

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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

$$J=\frac{2H{S}_{rated}}{{(2\pi F_{rated}/N)}^2},$$

where:

• J is inertia in kg⋅m².

• H is the inertia constant in sW/VA.

• S_rated is the machine rated apparent power in VA.

• F_rated 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:

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

• T_base is the base damping torque in Nm.

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

• D_pu is the damping coefficient in per-unit.

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

Display Option

You can display the machine per-unit base values and inertia parameters in the MATLAB^® Command Window. To display the machine parameters, in the Utilities section, click the Display button next to the Parameters parameter.

Examples

Three-Phase Synchronous Machine Control

Control and initialize a Synchronous Machine (SM). The test circuit shows the SM operating as a generator. The terminal voltage is controlled using an AVR and the speed is controlled using a governor.

• Open Model

Ports

Conserving

R — Machine rotor

mechanical

Mechanical rotational conserving port associated with the machine rotor.

Parameters

Main

Rated apparent power — Rated apparent power

555e6 V*A (default)

Machine rated apparent power.

Rated electrical frequency — Nominal electrical frequency

60 Hz (default)

Nominal electrical frequency corresponding to the machine rated apparent power.

Number of pole pairs — Number of pole pairs

1 (default)

Number of pole pairs of the connected machine.

Inertia

Specify inertia parameterization by — Inertia parameterization

Inertia constant, H (default) | Actual Inertia, J

Inertia specification.

Inertia constant, H — Inertia constant

3.525 s*W/VA (default)

Inertia constant.

Dependencies

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

Actual inertia, J — Actual inertia

27548 kg*m^2 (default)

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.

Specify damper parameterization by — Damping parameterization

Per-unit damping coefficient, pu_D (default) | SI damping coefficient, D

Damping specification.

Per-unit damping coefficient — Per-unit damping coefficient

0.01 (default)

Damping coefficient in per-unit.

Dependencies

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

SI damping coefficient — Damping coefficient

39.0509 Nm/(rad/s) (default)

Damping coefficient in SI units.

Dependencies

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

Initial Conditions

Specify initialization by — Frequency initialization

Initial electrical frequency (default) | Initial mechanical frequency

Frequency initialization.

Initial electrical frequency — Initial electrical frequency

60 Hz (default)

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

For more information about the unit of this parameter, see Units for Angular Velocity and Frequency.

Dependencies

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

Initial mechanical frequency — Initial mechanical frequency

60 Hz (default)

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

For more information about the unit of this parameter, see Units for Angular Velocity and Frequency.

Dependencies

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

Utilities

Parameters — Display machine per-unit base values and inertia parameters

button

Since R2026a

Display the machine per-unit base values and the inertia parameters in the MATLAB Command Window.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2013b

R2026a: Context menu usability improvements

The display option of the machine per-unit base values and inertia parameters has been moved from the context menu to the block dialog box or Property Inspector of the Machine Inertia block. To display the machine per-unit base values and inertia parameters, open the block dialog box or Property Inspector and, in the Utilities section, click the Display button next to the Parameters parameter.

Before R2026a, you plot the machine per-unit base values and inertia parameters by right-clicking the block and selecting Electrical > Display Parameters from the context menu.