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

$J = \frac{2 H S_{r a t e d}}{{(2 π F_{r a t e d} / N)}^{2}},$

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

$ω_{b a s e} = \frac{2 π F_{r a t e d}}{N},$

$T_{b a s e} = \frac{S_{r a t e d}}{ω_{b a s e}},$

$D_{b a s e} = \frac{T_{b a s e}}{ω_{b a s e}},$

and

$D = D_{p u} D_{b a s e},$

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 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.

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

expand all

R — Machine rotor
mechanical

Mechanical rotational conserving port associated with the machine rotor.

Parameters

expand all

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.

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

Machine Inertia

Description

Display Option

Examples

Three-Phase Synchronous Machine Control

Ports

Conserving

R — Machine rotor mechanical

Parameters

Main

Rated apparent power — Rated apparent power 555e6 V*A (default)

Rated electrical frequency — Nominal electrical frequency 60 Hz (default)

Number of pole pairs — Number of pole pairs 1 (default)

Inertia

Specify inertia parameterization by — Inertia parameterization Inertia constant, H (default) | Actual Inertia, J

Inertia constant, H — Inertia constant 3.525 s*W/VA (default)

Dependencies

Actual inertia, J — Actual inertia 27548 kg*m^2 (default)

Dependencies

Specify damper parameterization by — Damping parameterization Per-unit damping coefficient, pu_D (default) | SI damping coefficient, D

Per-unit damping coefficient — Per-unit damping coefficient 0.01 (default)

Dependencies

SI damping coefficient — Damping coefficient 39.0509 Nm/(rad/s) (default)

Dependencies

Initial Conditions

Specify initialization by — Frequency initialization Initial electrical frequency (default) | Initial mechanical frequency

Initial electrical frequency — Initial electrical frequency 60 Hz (default)

Dependencies

Initial mechanical frequency — Initial mechanical frequency 60 Hz (default)

Dependencies

References

Extended Capabilities

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

Version History

See Also

R — Machine rotor
mechanical

Rated apparent power — Rated apparent power
`555e6` `V*A` (default)

Rated electrical frequency — Nominal electrical frequency
`60` `Hz` (default)

Number of pole pairs — Number of pole pairs
`1` (default)

Specify inertia parameterization by — Inertia parameterization
`Inertia constant, H` (default) | `Actual Inertia, J`

Inertia constant, H — Inertia constant
`3.525` `s*W/VA` (default)

Actual inertia, J — Actual inertia
`27548` `kg*m^2` (default)

Specify damper parameterization by — Damping parameterization
`Per-unit damping coefficient, pu_D` (default) | `SI damping coefficient, D`

Per-unit damping coefficient — Per-unit damping coefficient
`0.01` (default)

SI damping coefficient — Damping coefficient
`39.0509` `Nm/(rad/s)` (default)

Specify initialization by — Frequency initialization
`Initial electrical frequency` (default) | `Initial mechanical frequency`

Initial electrical frequency — Initial electrical frequency
`60` `Hz` (default)

Initial mechanical frequency — Initial mechanical frequency
`60` `Hz` (default)

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