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Simplified Synchronous Machine

Simplified synchronous machine with electromotive force

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  • Simscape / Electrical / Electromechanical / Synchronous

Description

The Simplified Synchronous Machine block models a simplified synchronous machine with a voltage source that represents electromotive force (EMF). You can specify the internal resistance and inductance with per-unit or SI parameters.

The equivalent circuits of the simplified synchronous machine for the direct axis, the quadrature axis, and the zero sequence are:

Equations

The simplified synchronous machine equations are expressed with respect to a rotating reference frame, which is defined by:

θe(t)=Nθr(t),

where:

  • θe is the electrical angle.

  • N is the number of pole pairs.

  • θr is the rotor angle.

The Park transformation maps the synchronous machine equations to the rotating reference frame with respect to the electrical angle. The Park transformation is defined by:

Ps=23[cosθecos(θe2π3)cos(θe+2π3)sinθesin(θe2π3)sin(θe+2π3)121212].

The Park transformation is used to define the per-unit simplified synchronous machine equations. The voltage equations are defined by:

ed=1ωbasedψddtΨqωr+Rid+vd

eq=1ωbasedψqdt+Ψdωr+Riq+vq

e0=1ωbasedΨ0dt+Ri0+v0

where:

  • ed, eq, and e0 are the d-axis, q-axis, and zero-sequence voltages, defined by:

    [edeqe0]=Ps[eaebec].

    ea, eb, and ec are the per-unit internal voltage sources, defined by:

    ea=Epusinθeeb=Epusin(θe120°)ec=Epusin(θe+120°)

    epu is the per-unit amplitude of the internal generated voltage.

  • vd, vq, and v0 are defined by:

    [vdvqv0]=Ps[vavbvc].

    va, vb, and vc are the stator voltages measured from port ~ to neutral port n.

  • ωbase is the per-unit base electrical speed.

  • ψd, ψq, and ψ0 are the d-axis, q-axis, and zero-sequence flux linkages.

  • ωr is the per-unit rotor rotational speed.

  • R is the stator resistance.

  • id, iq, and i0 are the d-axis, q-axis, and zero-sequence stator currents, defined by:

    [idiqi0]=Ps[iaibic].

    ia, ib, and ic are the stator currents flowing out of port ~.

The stator flux linkage equations are defined by

ψd=Lidψq=Liqψ0=Li0

where L is the stator leakage inductance.

The power equation of the simplified synchronous machine in per-unit is defined by:

P=edid+eqiq.

Ports

Input

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Physical signal port associated with the amplitude of the internal generated voltage (phase-to-neutral), specified as a vector of physical signals.

Dependencies

To enable this port, set Parameterization unit to SI.

Physical signal port associated with the per-unit amplitude of the internal generated voltage, specified as a vector of physical signals.

Dependencies

To enable this port, set Parameterization unit to Per unit.

Output

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Physical signal port associated with the machine per-unit measurements, returned as a vector of physical signals. The vector elements are:

  • Electromotive force associated with phase a, pu_EMF(1)

  • Electromotive force associated with phase b, pu_EMF(2)

  • Electromotive force associated with phase c, pu_EMF(3)

  • Electrical torque, pu_torque

  • Rotor velocity, pu_velocity

  • Stator d-axis voltage, pu_vd

  • Stator q-axis voltage, pu_vq

  • Stator zero-sequence voltage, pu_e0

  • Stator d-axis current, pu_id

  • Stator q-axis current, pu_iq

  • Stator zero-sequence current, pu_i0

  • Rotor electrical angle, electrical_angle_out

To connect to this port, use the Synchronous Machine Measurement block.

Conserving

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Mechanical rotational conserving port associated with the machine rotor.

Mechanical rotational conserving port associated with the machine case.

Expandable three-phase electrical port associated with the stator windings.

Electrical conserving port associated with the neutral point of the wye winding configuration.

Parameters

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Main

Rated apparent power.

RMS rated line-to-line voltage.

Nominal electrical frequency at which rated apparent power is quoted.

Number of machine pole pairs.

Block parameterization method. Options are:

  • SI

  • Per unit

Internal per-unit resistance.

Dependencies

To enable this parameter, set Parameterization unit to Per unit.

Internal per-unit inductance in per-unit.

Dependencies

To enable this parameter, set Parameterization unit to Per unit.

Internal resistance.

Dependencies

To enable this parameter, set Parameterization unit to SI.

Internal inductance.

Dependencies

To enable this parameter, set Parameterization unit to SI.

Extended Capabilities

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

Introduced in R2020b