Synchronous Machine (Six-Phase)

A six-phase synchronous machine.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.SixPhase

Path in the library:

/Physical Modeling/Electrical/Electromechanical/Synchronous/Synchronous Machine (Six-Phase)

Description

Block Synchronous Machine (Six-Phase) simulates a six-phase synchronous machine.

A six-phase synchronous machine has two groups of stator windings: group ABC and group XYZ. These two groups have a phase shift of 30 degrees.

The equivalent circuits of a six-phase synchronous machine for the longitudinal axis, the transverse axis, and the two zero sequences are as shown in the figures below.

synchronous machine six phase 1

synchronous machine six phase 2

synchronous machine six phase 3

The equations

The equations of a synchronous machine are written with respect to a rotating coordinate system, which is defined as follows:

where

— electric angle of the rotor;
— the number of pairs of poles;
— mechanical angle of the rotor;
— This is 0 if you determine the electric angle of the rotor with respect to -axes, or −pi/2 if you determine the electric angle of the rotor with respect to - axes.

Two Park transformations translate the equations of the synchronous machine into a rotating coordinate system relative to the electric angle. The Park transformation for the first group of stator windings, group ABC, is defined as follows:

The Park transformation for the second group of stator windings, the XYZ group, is defined as follows:

The transformation of the Park is written in relative units (OE).

The stator stress equations for group ABC are as follows:

where

, and — stator voltages for the ABC group along the axes , and the zero sequence, respectively, determined by the formula

,

where , and — stator voltages for group ABC, measured from port ~ABC to neutral port n1;
— base speed in relative units;
, and — flow couplings for the ABC group along the axes , and the zero sequence;
— the speed of rotation of the rotor in relative units;
— active resistance of the stator;
and — stator winding currents for group ABC along the axes , and the zero sequence, defined as

,

where , and — stator currents for group ABC from port ~ABC to neutral port n1.

The stator stress equations for the XYZ group are as follows:

where

, and — stator voltages for the XYZ group along the axes , and the zero sequence, respectively, determined by the formula

,

where , and — stator voltages for group XYZ, measured from port ~XYZ to neutral port n1;
, and — flow couplings for the XYZ group along the axes , and the zero sequence;
and — stator winding currents for the XYZ group along the axes , and the zero sequence, defined as

,

where , and — currents on the stator for the XYZ group from the port ~XYZ to the neutral port n1.

Rotor voltage equations:

where

— voltage of the excitation winding on the stator side;
and — voltage on the damper windings along the axes and from the stator side; they are all equal 0;
, and — magnetic fluxes connecting the excitation circuit, the damping winding along the axis and the damping winding along the axis ;
, , and — resistance of the excitation circuit of the rotor, the damper winding along the axis and the damping winding along the axis ;
, , and — currents flowing in the excitation circuit, in the damper winding along the axis and in the damping winding along the axis from the side of the stator.

The stator flow coupling equations are defined as follows:

where

— stator scattering inductance;
and — mutual inductors of the stator along the axes and .

The rotor flow coupling equations are defined as follows:

where

— inductance of the rotor excitation winding;
— the inductance of the rotor damper winding along the axis ;
— the inductance of the rotor damper winding along the axis ;

Rotor torque:

Modeling of thermal effects

A thermal port can be used to simulate losses during the conversion of energy into heat.

If the check box Enable thermal port If not installed, the unit does not contain any thermal ports.
If the check box Enable thermal port If installed, the unit contains thermal non-directional ports for each of the windings and for the rotor.

Variables

Use the Initial targets parameter group to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

For this block, the Initial targets parameters are visible only if for the parameter Initialization option the value is set Set targets for rotor angle and Park’s transform variables or if the checkbox is checked Enable thermal port.

Ports

Conserving

# HX — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_x

# C — machine body
rotational mechanics

Details

A mechanical port connected to the machine body.

Program usage name

case_flange

# HB — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_b

# n1 — neutral winding ABC
electricity

Details

The electrical port connected to the neutral of the ABC winding.

Dependencies

To use this port, set the parameter Zero sequence meaning Include.

Program usage name

n1

# ~ABC — stator windings ABC
electricity

Details

Expandable three-phase port connected to the ABC stator windings.

Program usage name

port1

# HC — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_c

# HY — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_y

# HR — thermal port of the rotor
warm

Details

The thermal port connected to the rotor.

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

rotor_thermal_port

# ~XYZ — XYZ stator windings
electricity

Details

Expandable three-phase port connected to XYZ stator windings.

Program usage name

port2

# fd− — negative terminal of the field winding
electricity

Details

An electrical port connected to the negative terminal of the field winding.

Program usage name

fd_n

# HZ — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_z

# HA — phase thermal port
warm

Details

Thermal port connected to the phase winding .

Dependencies

To use this port, check the box Enable thermal port.

Program usage name

stator_thermal_port_a

# R — the rotor of the machine
rotational mechanics

Details

A mechanical port connected to the rotor of the machine.

Program usage name

rod_flange

# fd+ — positive terminal of the field winding
electricity

Details

An electrical port connected to the positive terminal of the excitation winding.

Program usage name

fd_p

# n2 — winding neutral XYZ
electricity

Details

The electrical port connected to the neutral winding XYZ.

Dependencies

To use this port, set the parameter Zero sequence meaning Include.

Program usage name

n2

Parameters

Main

# Nominal voltage (line-to-line,rms) — Rated RMS voltage
V | uV | mV | kV | MV

Details

The nominal RMS line voltage.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`240.0 V`
Program usage name	`V_rated`
Evaluatable	Yes

# Nominal power — Rated power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Rated power.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`100e3 V*A`
Program usage name	`S_rated`
Evaluatable	Yes

# Rotor angle definition — a reference point for measuring the rotation angle of the rotor
Angle between the a-phase magnetic axis and the q-axis | Angle between the a-phase magnetic axis and the d-axis

Details

A reference point for measuring the rotation angle of the rotor.

When selecting a value Angle between the a-phase magnetic axis and the d-axis the axis the rotor and -the phase magnetic axis of the stator is aligned when the rotation angle of the rotor is zero.

When selecting a value Angle between the a-phase magnetic axis and the q-axis the axis the rotor and -the phase magnetic axis of the stator is aligned when the rotation angle of the rotor is zero.

Values	`Angle between the a-phase magnetic axis and the q-axis` \| `Angle between the a-phase magnetic axis and the d-axis`
Default value	`Angle between the a-phase magnetic axis and the d-axis`
Program usage name	`axes_parameterization`
Evaluatable	No

# Zero sequence — the zero sequence model
Exclude | Include

Details

The zero-sequence model:

Include — priority is given to the accuracy of the model. When zero sequence conditions are enabled for simulations using Partitioning solving, errors occur.

Exclude — Priority is given to simulation speed for desktop simulation or real-time deployment.

Values	`Exclude` \| `Include`
Default value	`Include`
Program usage name	`zero_sequence`
Evaluatable	No

# Nominal electrical frequency — Rated electrical frequency
Hz | kHz | MHz | GHz

Details

The rated electrical frequency at which the rated power is indicated.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`50.0 Hz`
Program usage name	`f_rated`
Evaluatable	Yes

# Number of pole pairs — number of pairs of poles

Details

The number of pairs of poles of the machine.

Default value	`2`
Program usage name	`N_pole_pairs`
Evaluatable	Yes

Thermal

Details

Ratio in the equation relating resistance to temperature.

Default value 3.93e−3 1/K corresponds to copper.

Dependencies

To use this option, check the box Enable thermal port.

Units	`1/K` \| `1/degR` \| `1/deltaK` \| `1/deltadegC` \| `1/deltadegF` \| `1/deltadegR`
Default value	`0.00393 1/K`
Program usage name	`alpha`
Evaluatable	Yes

# Rotor thermal mass — heat capacity of the rotor
J/K | kJ/K

Details

The value of the heat capacity for the rotor. Heat capacity is the energy required to raise the temperature by one degree.

Dependencies

To use this option, check the box Enable thermal port.

Units	`J/K` \| `kJ/K`
Default value	`200.0 J/K`
Program usage name	`rotor_thermal_mass`
Evaluatable	Yes

# Enable thermal port — switching on thermal ports

Details

Select this option to use the thermal port of the unit and simulate losses when converting energy to heat.

Default value	`false (switched off)`
Program usage name	`has_thermal_port`
Evaluatable	No

Details

The temperature for which the engine parameters are specified.

Dependencies

To use this option, check the box Enable thermal port.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`298.15 K`
Program usage name	`T_measurement`
Evaluatable	Yes

# Thermal mass for each stator winding — the heat capacity of the winding
J/K | kJ/K

Details

The value of the heat capacity for each stator winding. Heat capacity is the energy required to raise the temperature by one degree.

Dependencies

To use this option, check the box Enable thermal port.

Units	`J/K` \| `kJ/K`
Default value	`100.0 J/K`
Program usage name	`stator_thermal_mass`
Evaluatable	Yes

Initial Conditions

# Initialization option — initialization option
Set targets for rotor angle and Park’s transform variables | Set real power, reactive power, terminal voltage, and terminal phase

Details

A model for setting values of certain parameters and variables at the beginning of the simulation:

To set an operating point independent of the connected network, select Set real power, reactive power, terminal voltage, and terminal phase.
To specify the priority and initial target values of the block variables before modeling, select Set targets for rotor angle and Park’s transform variables. For more information, see Configuring physical blocks using target values.

Values	`Set targets for rotor angle and Park’s transform variables` \| `Set real power, reactive power, terminal voltage, and terminal phase`
Default value	`Set real power, reactive power, terminal voltage, and terminal phase`
Program usage name	`initialization_option`
Evaluatable	No

# Terminal reactive power (ABC group) — reactive power at terminals corresponding to group ABC
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The reactive power at the terminals generated by the stator windings of the ABC group.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0.0 V*A`
Program usage name	`Q1_t_start`
Evaluatable	Yes

# Terminal reactive power (XYZ group) — reactive power at terminals corresponding to XYZ group
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The reactive power at the terminals generated by the XYZ group stator windings.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0.0 V*A`
Program usage name	`Q2_t_start`
Evaluatable	Yes

# Terminal voltage magnitude — terminal voltage
V | uV | mV | kV | MV

Details

The voltage value at the terminals.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`240.0 V`
Program usage name	`V_mag_start`
Evaluatable	Yes

# Terminal active power (XYZ group) — active power at terminals corresponding to XYZ group
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The active terminal power generated by the XYZ group stator windings.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`20e3 V*A`
Program usage name	`P2_t_start`
Evaluatable	Yes

# Terminal active power (ABC group) — active power at terminals corresponding to group ABC
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The active terminal power generated by the stator windings of the ABC group.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`50e3 V*A`
Program usage name	`P1_t_start`
Evaluatable	Yes

# Terminal voltage angle corresponding to ABC group — voltage angle at terminals corresponding to group ABC
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The voltage angle at the terminals corresponding to the stator of the ABC group.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`0.0 deg`
Program usage name	`V_ang_start`
Evaluatable	Yes

Impedances

# Rotor field winding inductance, Llfd' — inductance of the rotor excitation winding

Details

The inductance of the rotor excitation winding. This parameter should be higher. 0.

Default value	`0.0813`
Program usage name	`L_l_fd`
Evaluatable	Yes

# Stator q-axis mutual inductance, Lmq — mutual axis inductance the stator

Details

Mutual inductance along the axis the stator. This parameter should be higher. 0.

Default value	`0.9045`
Program usage name	`L_mq`
Evaluatable	Yes

# Rotor field winding resistance, Rfd' — resistance of the rotor excitation winding

Details

Resistance of the rotor excitation winding. This parameter should be higher. 0.

Default value	`0.0028`
Program usage name	`R_fd`
Evaluatable	Yes

# Rotor d-axis damper winding inductance, Llkd' — inductance of the rotor damper winding along the axis

Details

Inductance of the rotor damper winding along the axis . This parameter should be higher. 0.

Default value	`0.0918`
Program usage name	`L_l_kd`
Evaluatable	Yes

# Stator leakage inductance, Ll — stator scattering inductance

Details

The stator scattering inductance. This parameter should be higher. 0.

Default value	`0.0969`
Program usage name	`L_l`
Evaluatable	Yes

# Rotor q-axis damper winding resistance, Rkq' — resistance of the rotor damper winding along the axis

Details

Resistance of the rotor damper winding along the axis . This parameter should be higher. 0.

Default value	`0.0043`
Program usage name	`R_kq`
Evaluatable	Yes

# Stator d-axis mutual inductance, Lmd — mutual axis inductance the stator

Details

Mutual inductance along the axis the stator. This parameter should be higher. 0.

Default value	`1.9583`
Program usage name	`L_md`
Evaluatable	Yes

# Stator resistance, Rs — stator resistance

Details

Stator resistance. This parameter should be higher. 0.

Default value	`0.0288`
Program usage name	`R_s`
Evaluatable	Yes

# Rotor d-axis damper winding resistance, Rkd' — resistance of the rotor damper winding along the axis

Details

Resistance of the rotor damper winding along the axis . This parameter should be higher. 0.

Default value	`0.0041`
Program usage name	`R_kd`
Evaluatable	Yes

# Rotor q-axis damper winding inductance, Llkq' — inductance of the rotor damper winding along the axis

Details

Inductance of the rotor damper winding along the axis . This parameter should be higher. 0.

Default value	`0.1174`
Program usage name	`L_l_kq`
Evaluatable	Yes

Literature

Kieferndorf, F., Burzanowska , H., Kanerva S., Sario P. Modeling of rotor based harmonics in dual-star, wound field, synchronous machines. 2008 18th International Conference on Electrical Machines: Vilamoura, 1–6.
Burzanowska , H., Sario P, Stulz C., Joerg P. Redundant Drive with Direct Torque Control (DTC) and dual-star synchronous machine, simulations and verifications. 2007 European Conference on Power Electronics and Applications: Aalborg, 1–10.