Simplified Synchronous Machine

Simplified synchronous machine with electromotive force

Since R2020b

Libraries:
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:

$θ_{e} (t) = N θ_{r} (t),$

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. The Park transformation is defined by:

$P_{s} = \frac{2}{3} [\begin{matrix} - \cos θ_{e} & - \cos (θ_{e} - \frac{2 π}{3}) & - \cos (θ_{e} + \frac{2 π}{3}) \\ \sin θ_{e} & \sin (θ_{e} - \frac{2 π}{3}) & \sin (θ_{e} + \frac{2 π}{3}) \\ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \end{matrix}] .$

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

$e_{d} = \frac{1}{ω_{b a s e}} \frac{d ψ_{d}}{d t} - Ψ_{q} ω_{r} + R i_{d} + v_{d}$

$e_{q} = \frac{1}{ω_{b a s e}} \frac{d ψ_{q}}{d t} + Ψ_{d} ω_{r} + R i_{q} + v_{q}$

$e_{0} = \frac{1}{ω_{b a s e}} \frac{d Ψ_{0}}{d t} + R i_{0} + v_{0}$

where:

e_d, e_q, and e₀ are the d-axis, q-axis, and zero-sequence voltages, defined by:

$[\begin{matrix} e_{d} \\ e_{q} \\ e_{0} \end{matrix}] = P_{s} [\begin{matrix} e_{a} \\ e_{b} \\ e_{c} \end{matrix}] .$

e_a, e_b, and e_c are the per-unit internal voltage sources, defined by:

$\begin{array}{l} e_{a} = E_{p u} s i n θ_{e} \\ e_{b} = E_{p u} s i n (θ_{e} - 120 °) \\ e_{c} = E_{p u} s i n (θ_{e} + 120 °) \end{array}$

e_pu is the per-unit amplitude of the internal generated voltage.
v_d, v_q, and v₀ are defined by:

$[\begin{matrix} v_{d} \\ v_{q} \\ v_{0} \end{matrix}] = P_{s} [\begin{matrix} v_{a} \\ v_{b} \\ v_{c} \end{matrix}] .$

v_a, v_b, and v_c are the stator voltages measured from port ~ to neutral port n.
ω_base is the per-unit base electrical speed.
ψ_d, ψ_q, and ψ₀ are the d-axis, q-axis, and zero-sequence flux linkages.
ω_r is the per-unit rotor rotational speed.
R is the stator resistance.
i_d, i_q, and i₀ are the d-axis, q-axis, and zero-sequence stator currents, defined by:

$[\begin{matrix} i_{d} \\ i_{q} \\ i_{0} \end{matrix}] = P_{s} [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}] .$

i_a, i_b, and i_c are the stator currents flowing out of port ~.

The stator flux linkage equations are defined by

$\begin{array}{l} ψ_{d} = L \cdot i_{d} \\ ψ_{q} = L \cdot i_{q} \\ ψ_{0} = L \cdot i_{0} \end{array}$

where L is the stator leakage inductance.

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

$P = e_{d} i_{d} + e_{q} i_{q} .$

Plotting and Display Options

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

Right-click the block and, from the Electrical menu, select one of these options:

Display Base Values — Displays the machine per-unit base values in the MATLAB^® Command Window.
Display Associated Initial Conditions — Displays associated initial conditions in the MATLAB Command Window.

Model Thermal Effects

You can expose thermal ports to model the effects of generated heat and machine temperature. To expose the thermal ports, set the Modeling option parameter to either:

No thermal port — The block does not contain thermal ports.
Show thermal port — The block contains multiple thermal conserving ports.

For more information about using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

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

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E_si — Amplitude of internal generated voltage (phase-to-neutral)
vector of physical signals

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.

E_pu — Amplitude of internal generated voltage, in per-unit
vector of physical signals

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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o — Machine per-unit measurements
vector of physical signals

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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R — Machine rotor
mechanical rotational

Mechanical rotational conserving port associated with the machine rotor.

C — Machine case
mechanical rotational

Mechanical rotational conserving port associated with the machine case.

~ — Stator windings
electrical

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

Dependencies

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

n — Neutral phase
electrical

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

a — a-phase
electrical

Electrical conserving port associated with a-phase.

Dependencies

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

b — b-phase
electrical

Electrical conserving port associated with b-phase.

Dependencies

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

c — c-phase
electrical

Electrical conserving port associated with c-phase.

Dependencies

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

HA — a-phase terminal thermal port
thermal

Thermal conserving port associated with stator winding a.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HB — b-phase terminal thermal port
thermal

Thermal conserving port associated with stator winding b.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HC — c-phase terminal thermal port
thermal

Thermal conserving port associated with stator winding c.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HR — Rotor thermal port
thermal

Thermal conserving port associated with the rotor.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

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Modeling option — Option to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Option to enable the thermal ports of the block and model the effects of generated heat and machine temperature.

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` `V*A` (default) | scalar

Rated apparent power.

Rated voltage — RMS rated line-to-line voltage
`24e3` `V` (default) | scalar

RMS rated line-to-line voltage.

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

Nominal electrical frequency at which rated apparent power is quoted.

Number of pole pairs — Number of pole pairs
`2` (default) | scalar

Number of machine pole pairs.

Parameterization unit — Block parameterization
`SI` (default) | `Per unit`

Block parameterization method. Options are:

SI
Per unit

Internal resistance (pu) — Internal per-unit resistance
`0.05` (default) | scalar

Internal per-unit resistance.

Dependencies

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

Internal inductance (pu) — Internal per-unit inductance
`0.3` (default) | scalar

Internal per-unit inductance in per-unit.

Dependencies

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

Internal resistance — Internal resistance
`0.0519` `Ohm` (default) | scalar

Internal resistance.

Dependencies

To enable this parameter, set Parameterization unit to SI.

Internal inductance — Internal inductance
`8.2589e-04` `H` (default) | scalar

Internal inductance.

Dependencies

To enable this parameter, set Parameterization unit to SI.

Initial Conditions

Initialization option — Initialization option
`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`

Model for specifying values for certain parameters and variables at the start of simulation. To:

Set an operating point regardless of the connected network, select Set real power, reactive power, terminal voltage and terminal phase.
Specify the priority and initial target values for block variables before simulation using the Variables settings, select Set targets for rotor angle and Park's transform variables. For more information, see Set Priority and Initial Target for Block Variables.
Select a bus type and specify the related parameters for a load-flow analysis in the Initial Conditions settings, select Set targets for load flow variables.

Dependencies

If you set this parameter to:

Set targets for rotor angle and Park's transform variables — The Variables settings become visible.
Set real power, reactive power, terminal voltage, and terminal phase — Related parameters become visible.
Set targets for load flow variables — Related parameters become visible.

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 and Source type to Swing bus or PV bus.

Terminal voltage magnitude — Terminal voltage magnitude
`24e3` `V` (default)

Terminal voltage magnitude.

Dependencies

To enable this parameter, set Initialization option to Set real power, reactive power, terminal voltage, and terminal phase or 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)

Terminal voltage angle.

Dependencies

Active power generated — Active power generated
`500e6` `V*A` (default)

Active power generated.

Dependencies

Reactive power generated — Reactive power generated
`0` `V*A` (default)

Reactive power generated.

Dependencies

Minimum terminal voltage magnitude (pu) — Minimum terminal voltage magnitude
`0.95` (default)

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 that defines the phase angle search range.

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)

Parasitic conductance to the electrical reference.

Dependencies

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

Thermal

To enable these parameters, set Modeling option to Show thermal port.

Measurement temperature — Rated temperature
`298.15` `k` (default) | real scalar

Temperature for which motor parameters are quoted.

Resistance temperature coefficient — Temperature coefficient
`3.93e-3` `1/K` (default) | positive scalar

Coefficient α in the equation relating resistance to temperature for all three windings, as described in Thermal Model for Actuator Blocks. The default value, 3.93e-3 1/K, is for copper.

Thermal mass for each stator winding — Winding thermal mass
`100` `J/K` (default) | positive scalar

Thermal mass value for each stator winding. The thermal mass is the energy required to raise the temperature by one degree.

Rotor thermal mass — Rotor thermal mass
`200` `J/K` (default) | positive scalar

Thermal mass of the rotor. The thermal mass is the energy required to raise the temperature of the rotor by one degree.

Extended Capabilities

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

Version History

Introduced in R2020b

expand all

R2021b: Electrical connection ports update

From R2021b forward, to switch between composite and expanded ports, set the Electrical connection parameter to either Composite three-phase ports or Expanded three-phase ports. Also, the simlog format is identical for Composite three-phase ports and Expanded three-phase ports.

As a result of these changes, inside a model saved in an earlier release, review the Electrical connection parameter of this block.

Simplified Synchronous Machine

Description

Equations

Plotting and Display Options

Model Thermal Effects

Variables

Ports

Input

E_si — Amplitude of internal generated voltage (phase-to-neutral) vector of physical signals

Dependencies

E_pu — Amplitude of internal generated voltage, in per-unit vector of physical signals

Dependencies

Output

o — Machine per-unit measurements vector of physical signals

Conserving

R — Machine rotor mechanical rotational

C — Machine case mechanical rotational

~ — Stator windings electrical

Dependencies

n — Neutral phase electrical

a — a-phase electrical

Dependencies

b — b-phase electrical

Dependencies

c — c-phase electrical

Dependencies

HA — a-phase terminal thermal port thermal

Dependencies

HB — b-phase terminal thermal port thermal

Dependencies

HC — c-phase terminal thermal port thermal

Dependencies

HR — Rotor thermal port thermal

Dependencies

Parameters

Modeling option — Option to enable thermal ports No thermal port (default) | Show thermal port

Main

Electrical connection — Electrical connection Composite three-phase ports (default) | Expanded three-phase ports

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

Rated voltage — RMS rated line-to-line voltage 24e3 V (default) | scalar

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

Number of pole pairs — Number of pole pairs 2 (default) | scalar

Parameterization unit — Block parameterization SI (default) | Per unit

Internal resistance (pu) — Internal per-unit resistance 0.05 (default) | scalar

Dependencies

Internal inductance (pu) — Internal per-unit inductance 0.3 (default) | scalar

Dependencies

Internal resistance — Internal resistance 0.0519 Ohm (default) | scalar

Dependencies

Internal inductance — Internal inductance 8.2589e-04 H (default) | scalar

Dependencies

Initial Conditions

Initialization option — Initialization option 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

Dependencies

Source type — Voltage source model Swing bus (default) | PV bus | PQ bus

Dependencies

Terminal voltage magnitude — Terminal voltage magnitude 24e3 V (default)

Dependencies

Terminal voltage angle — Terminal voltage angle 0 deg (default)

Dependencies

Active power generated — Active power generated 500e6 V*A (default)

Dependencies

Reactive power generated — Reactive power generated 0 V*A (default)

Dependencies

Dependencies

Minimum terminal voltage magnitude (pu) — Minimum terminal voltage magnitude 0.95 (default)

Dependencies

Phase search range at terminals — Phase search range at terminals [-inf, inf] deg (default)

Dependencies

Parasitic conductance to electrical reference — Parasitic conductance to electrical reference 1e-6 S (default)

Dependencies

Thermal

Measurement temperature — Rated temperature 298.15 k (default) | real scalar

Resistance temperature coefficient — Temperature coefficient 3.93e-3 1/K (default) | positive scalar

Thermal mass for each stator winding — Winding thermal mass 100 J/K (default) | positive scalar

Rotor thermal mass — Rotor thermal mass 200 J/K (default) | positive scalar

Extended Capabilities

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

Version History

R2021b: Electrical connection ports update

E_si — Amplitude of internal generated voltage (phase-to-neutral)
vector of physical signals

E_pu — Amplitude of internal generated voltage, in per-unit
vector of physical signals

o — Machine per-unit measurements
vector of physical signals

R — Machine rotor
mechanical rotational

C — Machine case
mechanical rotational

~ — Stator windings
electrical

n — Neutral phase
electrical

a — a-phase
electrical

b — b-phase
electrical

c — c-phase
electrical

HA — a-phase terminal thermal port
thermal

HB — b-phase terminal thermal port
thermal

HC — c-phase terminal thermal port
thermal

HR — Rotor thermal port
thermal

Modeling option — Option to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

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

Rated voltage — RMS rated line-to-line voltage
`24e3` `V` (default) | scalar

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

Number of pole pairs — Number of pole pairs
`2` (default) | scalar

Parameterization unit — Block parameterization
`SI` (default) | `Per unit`

Internal resistance (pu) — Internal per-unit resistance
`0.05` (default) | scalar

Internal inductance (pu) — Internal per-unit inductance
`0.3` (default) | scalar

Internal resistance — Internal resistance
`0.0519` `Ohm` (default) | scalar

Internal inductance — Internal inductance
`8.2589e-04` `H` (default) | scalar

Initialization option — Initialization option
`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`

Source type — Voltage source model
`Swing bus` (default) | `PV bus` | `PQ bus`

Terminal voltage magnitude — Terminal voltage magnitude
`24e3` `V` (default)

Terminal voltage angle — Terminal voltage angle
`0` `deg` (default)

Active power generated — Active power generated
`500e6` `V*A` (default)

Reactive power generated — Reactive power generated
`0` `V*A` (default)

Minimum terminal voltage magnitude (pu) — Minimum terminal voltage magnitude
`0.95` (default)

Phase search range at terminals — Phase search range at terminals
`[-inf, inf]` `deg` (default)

Parasitic conductance to electrical reference — Parasitic conductance to electrical reference
`1e-6` `S` (default)

Measurement temperature — Rated temperature
`298.15` `k` (default) | real scalar

Resistance temperature coefficient — Temperature coefficient
`3.93e-3` `1/K` (default) | positive scalar

Thermal mass for each stator winding — Winding thermal mass
`100` `J/K` (default) | positive scalar

Rotor thermal mass — Rotor thermal mass
`200` `J/K` (default) | positive scalar

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