Synchronous Machine GENTPJ

GENTPJ synchronous machine

Since R2024b

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Libraries:
Simscape / Electrical / Electromechanical / Synchronous

Description

The Synchronous Machine GENTPJ block models a GENTPJ synchronous generator model. GENTPJ synchronous generator models are widely used in power plant model verification and power system transient stability studies.

Synchronous Machine Initialization Using Load-Flow Target Values

If the block is in a network that is compatible with the frequency-time simulation mode, you can perform a load-flow analysis on the network. A load-flow analysis provides steady-state values that you can use to initialize the machine.

For more information, see Perform a Load-Flow Analysis Using Simscape Electrical and Frequency and Time Simulation Mode. For an example that shows how to initialize a synchronous machine using data from a load-flow analysis, see Synchronous Machine Initialization with Loadflow.

Equations

The synchronous machine equations are expressed with respect to a rotating reference frame,

$${\theta }_e(t)=N{\theta }_r(t),$$

where:

• θ_e is the electrical angle.

• N is the number of pole pairs.

• θ_r is the rotor angle.

The Park transformation maps the synchronous machine equations to the rotating reference frame with respect to the electrical angle. This equation defines the Park transformation:

$$P_s=\frac{2}{3}\left[\begin{array}{ccc}\cos {\theta }_e& \cos ({\theta }_e-\frac{2\pi }{3})& \cos ({\theta }_e+\frac{2\pi }{3})\\ -\sin {\theta }_e& -\sin ({\theta }_e-\frac{2\pi }{3})& -\sin ({\theta }_e+\frac{2\pi }{3})\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right].$$

The block uses the Park transformation to define the per-unit synchronous machine equations. These equations define the d-axis and q-axis stator voltages:

$$\begin{array}{l}{v}_d=e_d^{\text{'}\text{'}}{\omega }_r-R_a{i}_d+\left(\frac{X_q^{\text{'}\text{'}}-X_l}{1+S_q}+X_l\right)i_q\\ v_q=e_q^{\text{'}\text{'}}{\omega }_r-R_a{i}_q-\left(\frac{X_d^{\text{'}\text{'}}-X_l}{1+S_d}+X_l\right)i_d\end{array}$$

In these equations:

• e^''_d is the d-axis voltage behind the subtransient reactance.

• R_a is the stator resistance.

• i_d is the d-axis stator current.

• X^''_q is the q-axis subtransient reactance.

• X_l is the stator leakage reactance.

• S_q is the q-axis saturation factor.

• i_q is the q-axis stator current.

• e^''_q is the q-axis voltage behind the subtransient reactance.

• X^''_d is the d-axis subtransient reactance.

• S_d is the d-axis saturation factor.

These equations define the voltages behind the transient reactances:

$$\begin{array}{l}\frac{d{e^{″}}_d}{dt}=\frac{1}{{T^{″}}_{q0}}\left[\left(1+S_q\right)\left({e^{\prime }}_d-{e^{″}}_d\right)+i_q\left({X^{\prime }}_q-{X^{″}}_q\right)\right]\\ \frac{d{e^{″}}_q}{dt}=\frac{1}{{T^{″}}_{d0}}\left[\left(1+S_d\right)\left({e^{\prime }}_q-{e^{″}}_q\right)-i_d\left({X^{\prime }}_d-{X^{″}}_d\right)\right]\\ \frac{d{e^{\prime }}_d}{dt}=\frac{1+S_q}{{T^{\prime }}_{q0}}\left({e^{″}}_d\frac{X_q-{X^{\prime }}_q}{{X^{\prime }}_q-{X^{″}}_q}-{e^{\prime }}_d\frac{X_q-{X^{″}}_q}{{X^{\prime }}_q-{X^{″}}_q}\right)\\ \frac{d{e^{\prime }}_q}{dt}=\frac{E_{fd}}{{T^{\prime }}_{d0}}+\frac{1+S_d}{{T^{\prime }}_{d0}}\left({e^{″}}_q\frac{X_d-{X^{\prime }}_d}{{X^{\prime }}_d-{X^{″}}_d}-{e^{\prime }}_q\frac{X_d-{X^{″}}_d}{{X^{\prime }}_d-{X^{″}}_d}\right)\end{array}$$

In these equations:

• e^'_d is the d-axis voltage behind the transient reactance.

• e^'_q is the q-axis voltage behind the transient reactance.

• T^'_d0 is the d-axis transient open-circuit time constant.

• T^'_q0 is the q-axis transient open-circuit time constant.

• T^''_d0 is the d-axis subtransient open-circuit time constant.

• T^''_q0 is the q-axis subtransient open-circuit time constant.

• X^'_d is the d-axis transient reactance.

• X^'_q is the q-axis transient reactance.

• E_fd is the per-unit field voltage.

These equations define the machine saturations,

$$\begin{array}{l}{\psi }_{ad}=v_q+R_a{i}_q+X_l{i}_d\\ {\psi }_{aq}=v_d+R_a{i}_d-X_l{i}_q\\ {\psi }_{at}=\sqrt{{\psi }_{ad}{}^2+{\psi }_{aq}{}^2}\\ S_d=f\left({\psi }_{at}+K_{is}\sqrt{i_d{}^2+i_q{}^2}\right)\\ S_q=\frac{X_q}{X_d}f\left({\psi }_{at}+K_{is}\sqrt{i_d{}^2+i_q{}^2}\right)\end{array}$$

where:

• ψ_ad is the d-axis air-gap flux linkage.

• ψ_aq is the q-axis air-gap flux linkage.

• ψ_at is the air-gap flux linkage.

• K_is represents the effect of the stator current on the saturation.

• S_d and S_q are the d-axis and q-axis saturation factors, respectively. If you set the Magnetic saturation representation parameter to None, S_d and S_q are equal to zero. If you set the Magnetic saturation representation parameter to Quadratic, Scaled quadratic, or Exponential, the block calculates the saturation factor function, f, from the value of the Saturation factor, S10 and Saturation factor, S12 parameters. If you set the Magnetic saturation representation parameter to Open-circuit lookup table, the block calculates the saturation factor function, f, from the per-unit field current and air-gap voltage saturation data.

This equation defines the per-unit field current in a non-reciprocal per-unit system:

$$I_{fd}=\left(1+S_d\right)\left({e^{\prime }}_q\frac{X_d-{X^{″}}_d}{{X^{\prime }}_d-{X^{″}}_d}-{e^{″}}_q\frac{X_d-{X^{\prime }}_d}{{X^{\prime }}_d-{X^{″}}_d}\right).$$

This equation defines the rotor torque:

$$T{}_e={e^{″}}_d{i}_d+{e^{″}}_q{i}_q-\left(\frac{{X^{″}}_d-X_l}{1+S_d}-\frac{{X^{″}}_q-X_l}{1+S_q}\right)i_d{i}_q.$$

Plotting and Display Options

You can perform plotting and display actions using the Electrical menu on the block context menu.

Right-click the block. From the Electrical menu, select an option:

• Display Base Values — Display the machine per-unit base values in the MATLAB^® Command Window.

• Display Associated Initial Conditions — Display associated initial conditions in the MATLAB Command Window.

• Plot Open-Circuit Saturation (pu) — Plot air-gap voltage, V_ag, versus field current, i_fd, both measured in per-unit, in a MATLAB figure window. The plot contains two traces:

  • Unsaturated — Stator d-axis mutual inductance (unsaturated), Ladu that you specify

  • Saturated — Per-unit open-circuit lookup table (Vag versus ifd) that you specify

• Plot Saturation Factor (pu) — Plot the saturation factor, f, versus magnetic flux linkage, ψ_at, both measured in per-unit, in a MATLAB figure window using the machine parameters. If you set the Magnetic saturation representation parameter to Quadratic, Scaled quadratic, or Exponential, the block derives the saturation factor function from the value of the Saturation factor, S10 and Saturation factor, S12 parameters.

  If you set the Magnetic saturation representation to Open-circuit lookup table, the block derives the saturation factor function from the value of the Non-reciprocal per-unit field current saturation data, ifd and Per-unit air-gap voltage saturation data, Vag parameters.

• Plot Power Capability Curves — Plot active power P versus reactive power Q, both measured in per-unit, in a MATLAB figure window. The plot can contain multiple traces. Each trace corresponds to a maximum field circuit voltage measured per unit (non-reciprocal per-unit system). The plot shows the maximum reactive power that the generator produces when operating with a lagging power factor and the minimum reactive power that the generator absorbs when operating with a leading power factor.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

For this block, the Initial Targets settings are visible only if, in the Initial Conditions section, you set the Initialization option parameter to Set targets for rotor angle and Park's transform variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Ports

Input

Efd — Per-unit field voltage

physical

Physical signal port associated with the per-unit field voltage.

Output

pu — Machine per-unit measurements

physical

Physical signal vector port associated with the machine per-unit measurements. The vector elements are:

• Field voltage (field circuit base, Efd), pu_fd_Efd

• Field current (field circuit base, Ifd), pu_fd_Ifd

• Electrical torque, pu_torque

• Rotor velocity, pu_velocity

• Stator d-axis voltage, pu_ed

• Stator q-axis voltage, pu_eq

• 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

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.

~ — Stator windings

electrical

Expandable three-phase electrical conserving port associated with the stator windings. For more information, see Three-phase ports.

Dependencies

To enable this port, set Electrical connection to Composite three-phase ports.

a — a-phase

electrical

Electrical conserving port associated with the a-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

b — b-phase

electrical

Electrical conserving port associated with the b-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

c — c-phase

electrical

Electrical conserving port associated with the c-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main

Electrical connection — Electrical connection

Composite three-phase ports (default) | Expanded three-phase ports

Whether to have composite or expanded three-phase ports.

Rated apparent power — Rated apparent power

555e6 A*V (default)

Rated apparent power.

Rated voltage — RMS rated line-line voltage

24e3 V (default)

Root mean square (RMS) of the rated line-line voltage.

Rated electrical frequency — Nominal electrical frequency

60 Hz (default)

Nominal electrical frequency at which the block quotes the rated apparent power.

Number of pole pairs — Number of machine pole pairs

1 (default)

Number of pole pairs of the machine.

Rotor angle definition — Reference point for the rotor angle measurement

Angle between the a-phase magnetic axis and the d-axis (default) | Angle between the a-phase magnetic axis and the q-axis

Reference point for the rotor angle measurement.

When you select the default value, the rotor d-axis and stator a-phase magnetic axis are aligned when the rotor angle is zero.

The other value you can choose for this parameter is Angle between the a-phase magnetic axis and the q-axis. When you select this value, the rotor q-axis and stator a-phase magnetic axis are aligned when the rotor angle is zero.

Impedances

Stator resistance, Ra — Resistance of stator

0.003 (default) | positive scalar

Resistance of the stator.

Stator leakage reactance, Xl — Leakage reactance of stator

0.15 (default) | positive scalar

Leakage reactance of the stator.

d-axis synchronous reactance, Xd — d-axis synchronous reactance

1.81 (default) | positive scalar

d-axis synchronous reactance.

q-axis synchronous reactance, Xq — q-axis synchronous reactance

1.76 (default) | positive scalar

q-axis synchronous reactance.

d-axis transient reactance, Xd' — d-axis transient reactance

0.3 (default) | positive scalar

d-axis transient reactance.

q-axis transient reactance, Xq' — q-axis transient reactance

0.65 (default) | positive scalar

q-axis transient reactance.

d-axis subtransient reactance, Xd'' — d-axis subtransient reactance

0.23 (default) | positive scalar

d-axis subtransient reactance.

q-axis subtransient reactance, Xq'' — q-axis subtransient reactance

0.25 (default) | positive scalar

q-axis subtransient reactance.

Time Constants

d-axis transient open-circuit, Td0' — d-axis transient open-circuit

8 s (default) | positive scalar

d-axis transient open-circuit time constant. This parameter value must be:

• Greater than 0

• Greater than d-axis subtransient open-circuit, Td0''

d-axis subtransient open-circuit, Td0'' — d-axis subtransient open-circuit

0.03 s (default) | positive scalar

d-axis subtransient open-circuit time constant.

q-axis transient open-circuit, Tq0' — q-axis transient open-circuit

1 s (default) | positive scalar

q-axis transient open-circuit time constant. This parameter value must be:

• Greater than 0

• Greater than q-axis subtransient open-circuit, Tq0''

q-axis subtransient open-circuit, Tq0'' — q-axis subtransient open-circuit

0.07 s (default) | positive scalar

q-axis subtransient open-circuit time constant.

Saturation

Magnetic saturation representation — Magnetic saturation representation

None (default) | Quadratic | Scaled quadratic | Exponential | Open-circuit lookup table

Option to represent the magnetic saturation of the block:

• None — The block does not model the magnetic saturation.

• Quadratic — The block models the magnetic saturation by using a quadratic function.

• Scaled quadratic — The block models the magnetic saturation by using a scaled function.

• Exponential — The block models the magnetic saturation by using an exponential function.

• Open-circuit lookup table — The block models the magnetic saturation by using per-unit non-reciprocal field current and per-unit air-gap voltage saturation data.

Saturation factor, S10 — Saturation factor, S10

0.005 (default) | positive scalar

Saturation factor that corresponds to 1.0 per-unit terminal voltage.

Dependencies

To enable this parameter, set Magnetic saturation representation to Quadratic, Scaled quadratic, or Exponential.

Saturation factor, S12 — Saturation factor, S12

0.08 (default) | positive scalar

Saturation factor that corresponds to 1.2 per-unit terminal voltage. The value of this parameter must be greater than the value of the Saturation factor, S10 parameter.

Dependencies

To enable this parameter, set Magnetic saturation representation to Quadratic, Scaled quadratic, or Exponential.

Non-reciprocal per-unit field current saturation data, ifd — Per-unit field current saturation data

[0, .8, 1.26, 2.29, 2.97] (default) | vector of nonnegative values

Nonreciprocal field current, i_fd, data that populates the air-gap voltage, V_ag, versus field current, i_fd, lookup table. This parameter value must contain a vector with at least five elements.

Dependencies

To enable this parameter, set Magnetic saturation representation to Open-circuit lookup table.

Per-unit air-gap voltage saturation data, Vag — Per-unit air-gap voltage saturation data

[0, .8, 1.08, 1.31, 1.4] (default) | vector of nonnegative values

Air-gap voltage, V_ag, data that populates the air-gap voltage, V_ag, versus field current, i_fd, lookup table. This parameter value must contain a vector with at least five elements.

Dependencies

To enable this parameter, set Magnetic saturation representation to Open-circuit lookup table.

Kis — Effect of stator current on saturation

0.05 (default) | nonnegative scalar

Effect of the stator current on the saturation. The block uses the value of this parameter to calculate the d-axis and q-axis saturation factors.

Initial Conditions

Initialization option — Option for specifying values at start of simulation

Set real power, reactive power, terminal voltage, and terminal phase (default) | Set targets for rotor angle and Park's transform variables | Set targets for load flow variables

Option for specifying values for certain parameters and variables at the start of simulation:

• Set real power, reactive power, terminal voltage, and terminal phase — Set an operating point regardless of the connected network.

• Set targets for rotor angle and Park's transform variables — Specify the priority and initial target values for block variables before simulation using the Variables settings. For more information, see Set Priority and Initial Target for Block Variables.

• Set targets for load flow variables — Select a bus type and specify the related parameters for a load-flow analysis in the Initial Conditions settings.

Source type — Voltage source model

Swing bus (default) | PV bus | PQ bus

Type of voltage source that the block models.

Dependencies

To enable this parameter, set Initialization option to Set targets for load flow variables.

Terminal voltage magnitude — Terminal voltage magnitude

24e3 V (default) | positive scalar

Terminal voltage magnitude.

Dependencies

To enable this parameter, set Initialization option to Set real power, reactive power, terminal voltage, and terminal phase. Alternatively, set Initialization option to Set targets for load flow variables and Source type to Swing bus or PV bus.

Terminal voltage angle — Terminal voltage angle

0 deg (default) | scalar

Terminal voltage angle.

Dependencies

To enable this parameter, set Initialization option to Set real power, reactive power, terminal voltage, and terminal phase. Alternatively, set Initialization option to Set targets for load flow variables and Source type to Swing bus.

Active power generated — Generated active power

500e6 V*A (default) | scalar

Active power that the machine generates.

Dependencies

To enable this parameter, set Initialization option to Set real power, reactive power, terminal voltage, and terminal phase. Alternatively, set Initialization option to Set targets for load flow variables and Source type to PV bus or PQ bus.

Reactive power generated — Generated reactive power

0 V*A (default) | scalar

Reactive power that the machine generates.

Dependencies

To enable this parameter, set Initialization option to Set real power, reactive power, terminal voltage, and terminal phase. Alternatively, set Initialization option to Set targets for load flow variables and Source type to PQ bus.

Minimum terminal voltage magnitude (pu) — Minimum terminal voltage magnitude

0.95 (default) | positive scalar

Per-unit minimum steady-state voltage magnitude.

Dependencies

To enable this parameter, set Initialization option to Set targets for load flow variables and Source type to PQ bus.

Phase search range at terminals — Phase search range at terminals

[-inf, inf] deg (default) | vector of two elements

Vector that defines the search range of the phase angle at the terminals.

Dependencies

To enable this parameter, set Initialization option to Set targets for load flow variables and Source type to PV bus or PQ bus.

Parasitic conductance to electrical reference — Parasitic conductance to electrical reference

1e-6 S (default) | positive scalar

Parasitic conductance to the electrical reference.

Dependencies

To enable this parameter, set Initialization option to Set targets for load flow variables.

References

[1] Undrill, John. The GENTPJ Model. Western Electricity Coordinating Council, June 2012.

[2] "IEEE Recommended Practice for Excitation System Models for Power System Stability Studies". IEEE Standard 421.5-2016 (revision of IEEE 421.5-2005).

Extended Capabilities

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

Version History

Introduced in R2024b