Machine Mechanical Power

Machine mechanical power defined in the SI or per-unit system

Libraries:
Simscape / Electrical / Electromechanical / Mechanical

Description

The Machine Mechanical Power block supplies specified power to, or draws specified power from, the machine that it connects to. It includes a representation of machine inertia and a mechanical rotational reference. In generator mode, the physical signal input defines the mechanical power that is input to the machine. In motor mode, it defines the mechanical power output from the machine.

The figure shows an equivalent configuration to the per-unit variant model of the Machine Mechanical Power block using Simscape™ mechanical rotational components.

Electrical Defining Equations

The SI model converts the SI values that you enter in the dialog box to per-unit values for simulation. For information on the relationship between SI and per-unit machine parameters, see Per-Unit Conversion for Machine Parameters. For information on per-unit parameterization, see Per-Unit System of Units.

To calculate the torque that it applies to the inertia, the block divides the power demand by the present speed. To set the peak torque limit, specify a value for the Peak torque to rated torque ratio parameter. Use the Specify inertia parameterization by parameter to specify inertia, J, directly or indirectly, with the inertia constant for the machine, H.

If you specify the inertia constant for the machine, the block calculates inertia as

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

where:

J is inertia in kg⋅m².
H is the inertia constant in sW/VA.
S_rated is the rated apparent power of the connected machine in VA.
F_rated is the rated electrical frequency of the connected machine in Hz.
N is the number of machine pole pairs.

Damping 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 per-unit or in SI units. If you specify the damping coefficient in per-unit, the block calculates the damping coefficient in SI units using these equations:

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

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

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

and

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

where:

ω_base is the base mechanical 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).

Examples

Three-Phase Asynchronous Wind Turbine Generator

Model an induction machine used as a wind turbine generator.

Open Model

Ports

Input

expand all

Pm — Mechanical power
physical | positive

Physical signal input port associated with mechanical power, in W.

Dependencies

This port is visible only if you set the PS input unit parameter in the Main setting to SI.

pu — Per-unit mechanical power
physical | positive

Physical signal input port associated with mechanical power, in per-unit.

Dependencies

This port is visible only if you set the PS input unit parameter in the Main setting to Per unit.

Conserving

expand all

R — Machine rotor
mechanical

Mechanical rotational conserving port associated with the machine rotor.

C — Machine case
mechanical

Mechanical rotational conserving port associated with the machine case.

Parameters

expand all

Main

Input power sign convention — Type specification
`Generator` (default) | `Motor`

Machine type specification.

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

Rated apparent power of the connected machine.

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

Nominal electrical frequency corresponding to the rated apparent power of the connected machine.

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

Number of pole pairs of the connected machine.

PS input unit — Physical signal unit system
`SI` (default) | `Per unit`

Unit system for physical signal input.

Select SI to expose the Pm port or Per unit to expose the pu port.

Peak torque to rated torque ratio — Peak torque to rated torque ratio
`2` (default)

Ratio that the block multiplies by the base torque to provide the upper limit for the torque that accelerates the inertia.

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

This parameter is visible only if you set the Specify inertia parameterization by parameter 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

This parameter is visible only if you set the Specify inertia parameterization by parameter 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

This parameter is visible only if you set the Specify damper parameterization by parameter to Per-unit damping coefficient, pu_D.

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

Damping coefficient in SI units.

Dependencies

This parameter is visible only if you set the Specify damper parameterization by parameter 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.

Dependencies

This parameter is visible only if you set the Specify initialization by parameter to Initial electrical frequency.

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

Initial mechanical frequency.

Dependencies

This parameter is visible only if you set the Specify initialization by parameter to Initial mechanical frequency.

Extended Capabilities

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

Version History

Introduced in R2014b

Machine Mechanical Power

Description

Electrical Defining Equations

Examples

Three-Phase Asynchronous Wind Turbine Generator

Ports

Input

Pm — Mechanical power physical | positive

Dependencies

pu — Per-unit mechanical power physical | positive

Dependencies

Conserving

R — Machine rotor mechanical

C — Machine case mechanical

Parameters

Main

Input power sign convention — Type specification Generator (default) | Motor

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)

PS input unit — Physical signal unit system SI (default) | Per unit

Peak torque to rated torque ratio — Peak torque to rated torque ratio 2 (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

Extended Capabilities

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

Version History

See Also

Pm — Mechanical power
physical | positive

pu — Per-unit mechanical power
physical | positive

R — Machine rotor
mechanical

C — Machine case
mechanical

Input power sign convention — Type specification
`Generator` (default) | `Motor`

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)

PS input unit — Physical signal unit system
`SI` (default) | `Per unit`

Peak torque to rated torque ratio — Peak torque to rated torque ratio
`2` (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™.