Machine Inertia

Machine inertia

Library

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

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

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 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 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

• Inertia Tab

• Initial Conditions Tab

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.

Introduced in R2013b

Was this topic helpful?