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Permanent Magnet Synchronous Machine (PMSM)
The Permanent Magnet Synchronous Machine (PMSM) component is a Norton equivalent (non-iterative) model. The machine electrical parameters must be specified with fundamental parameters (in per unit). Furthermore, the control of the PMSM can only be done externally through the power or the mechanical torque pin.
The model has the following features:
- Dampers: up to 2 damper windings on each of the d and q axes.
- Magnetic saturation: total, independent or only on the d axis.
- Stator connection: Wye with neutral, Wye grounded, or delta.
- Shaft: maximum 5 masses.
The PMSM participates in the load flow as a PV node and is represented as a source behind an impedance. The result of the load flow is valid only for a PMSM whose reactances of axis d and q are equal (surface-mounted PMSM).
Mask and Parameters
Electrical Parameters
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Base power | Nominal power | MVA | |
Base voltage | Nominal voltage (line to line) | kV | |
Frequency | Nominal frequency | Hz | |
Number of poles | Number of poles | - | |
d-axis damper | Number of damper on d-axis (max 2 allowed) | - | |
q-axis damper | Number of dampers on q-axis (max 2 allowed) | - | |
Stator connection | Stator windings connection (wye or delta) | - | |
Rs | Stator resistance | pu | |
Xl | Stator leakage reactance | pu | |
X0 | Zero sequence reactance | pu | |
Xd | d-axis synchronous reactance | pu | |
Xq | q-axis synchronous reactance | pu | |
XlD1 | D1 damper winding leakage reactance (must be defined when including 1 or 2 d-axes dampers - ignored otherwise) | pu | |
RD1 | D1 damper winding resistance (must be defined when including 1 or 2 d-axes dampers - ignored otherwise) | pu | |
XlD2 | D2 damper winding leakage reactance (must be defined when including 2 d-axes dampers - ignored otherwise) | pu | |
RD2 | D2 damper winding resistance (must be defined when including 2 d-axes dampers - ignored otherwise) | pu | |
XlQ1 | Q1 damper winding leakage reactance (must be defined when including 1 or 2 q-axes dampers - ignored otherwise) | pu | |
RQ1 | Q1 damper winding resistance (must be defined when including 1 or 2 q-axes dampers - ignored otherwise) | pu | |
XlQ2 | Q2 damper winding leakage reactance (must be defined when including 2 q-axes dampers - ignored otherwise) | pu | |
RQ2 | Q2 damper winding resistance (must be defined when including 2 q-axes dampers - ignored otherwise) | pu | |
Flux magnet | Permanent magnet flux | Wb |
Mechanical Data Parameters
Number of mass allows addition of up to 5 masses on the machine shaft.
- Selection of 1 mass is default, meaning only 1 mass shaft is simulated corresponding to the machine itself.
- Selection of 2 masses means the machine and the Low Pressure Turbine A (corresponding to mass 2 in the following figure) are simulated.
- Similarly selection of additional masses adds the next mass shown in the figure below.
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
H | Depending on the number of masses, the table of inertia constants is as follows:
| s | |
Kd | Depending on the number of masses, the table of absolute damping coefficients is as follows:
| Nm/rad/s | |
Kij | Depending on the number of masses, the table of stiffness coefficients is as follows:
| Nm/rad | |
D | Depending on the number of masses, the table of self damping coefficients is as follows:
| Nm/rad/s | |
Dij | Depending on the number of masses, the table of mutual speed deviation damping coefficients is as follows:
| Nm/rad/s | |
F | Depending on the number of masses, the table of fraction of external torque is defined as the fraction of the total external torque applied to each mass as follows:
Note that the sum of F must always be equal to 1. | - |
Control Parameters
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Mechanical control | The mechanical control can be done as follows:
| pu |
Both mechanical control use torque and and therefore mechanical data from the PMSM. In the mechanical power control, the torque reference is computed internally from the reference power and the actual PMSM speed. As for the mechanical torque control, torque reference is directly provided to the PMSM.
Saturation Parameters
In the Saturation tab, the user must specify proper saturation curve points if the saturation is set to Enabled. In the case of independent saturation of axes d and q, the two tables represent the positive part of the curve, whereas the negative part is deduced by symmetry. Furthermore, the number of points that can be specified for the d-axis and q-axis curves can be different. On the other hand, in the case of full saturation or d axis only, only the d-axis table is used.
Important: The first point of each saturation curve must not be set to zero. Additionally, the first point corresponds to the linear inductance of the machine in the case of independent saturation or d axis only.
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Saturation | User can disable or enable Independent, Total or dAxisOnly saturation | - | |
d-axis saturation curve points | Number of d-axis saturation curve points (max 10 points can be added). | - | |
Imd | d-axis magnetizing current points of saturation curve. | pu | |
Fluxmd | d-axis magnetizing flux points of saturation curve. | pu | |
q-axis saturation curve points | Number of q-axis saturation curve points (max 10 points can be added). | - | |
Imq | q-axis magnetizing current points of saturation curve. | pu | |
Fluxmq | q-axis magnetizing flux points of saturation curve. | pu |
Load Flow Parameters
Variable | Description | Unit | Variable = {Possible Values} |
---|---|---|---|
Voltage | Desired voltage at the terminal of the machine | pu | |
Active power | Desired active power output at the terminal of the machine | MW |
Ports, Inputs, Outputs and Signals Available for Monitoring
Ports
Name | Description |
---|---|
S | AC side stator connector (supports only 3-phase connections) |
N | AC side neutral connector (supports only 1-phase connections) |
Inputs
Name | Description | Unit |
---|---|---|
Tm_i | Mechanical torque | |
Pm_i | Mechanical power |
Outputs
None
Sensors
Name | Description | Unit |
---|---|---|
Flux0s | Stator zero sequence flux | pu |
Fluxds | Stator d-axis flux | pu |
Fluxqs | q axis stator flux | pu |
Fluxm | Mutual magnetization flux | pu |
Fluxmd | d axis mutual magnetization flux | pu |
Fluxmq | q axis mutual magnetization flux | pu |
I0s | Zero sequence stator current | pu |
ID1 | d axis damper D1 winding current | pu |
ID2 | d axis damper D2 winding current | pu |
IQ1 | q axis damper Q1 winding current | pu |
IQ2 | q axis damper Q2 winding current | pu |
Ias | Phase A stator current | A |
Ibs | Phase B stator current | A |
Ics | Phase C stator current | A |
Ids | d axis stator current | pu |
Iqs | q axis stator current | pu |
Im | Magnetization current | pu |
Imd | d axis magnetization current | pu |
Imq | q axis magnetization current | pu |
Pm_i | Mechanical power input | pu |
Pmec | Mechanical power SI | Nm |
Pmec_pu | Mechanical power pu | pu |
Pmec_ss | Calculated mechanical power by load-flow. It is used to initialize the turbine/prime mover block | pu |
PowerAngle | Machine load angle | rad |
Ps | Active power SI | W |
Ps_pu | Active power pu | pu |
Qs | Reactive power SI | VAr |
RotorAngle | Synchronous machine rotor angle (relative to a synchronous reference frame) | rad |
RotorAngle_HP | Mass 5 (HP turbine) rotor angle (relative to a synchronous reference frame) | rad |
RotorAngle_IP | Mass 4 (IP turbine) rotor angle (relative to a synchronous reference frame) | rad |
RotorAngle_LPA | Mass 3 (LPA turbine) rotor angle (relative to a synchronous reference frame) | rad |
RotorAngle_LPB | Mass 2 (LPB turbine) rotor angle (relative to a synchronous reference frame) | rad |
Tem | Machine electromagnetic torque SI | Nm |
Tem_pu | Machine electromagnetic torque pu | pu |
ThetaS | Rotor electrical angle (angle between the axis of phase a and d) | rad |
Tm_i | Mechanical torque on the shaft | pu |
Tmec | Mechanical torque on the shaft SI | Nm |
Tmec_pu | Mechanical torque on the shaft pu | pu |
Tmec_HP | Mechanical torque applied to mass (HP turbine) | pu |
Tmec_HP_IP | Mechanical torque between the HP and IP turbine masses | pu |
Tmec_IP | Mechanical torque applied to mass (IP turbine) | pu |
Tmec_IP_LPA | Mechanical torque between the IP and LPA turbine masses | pu |
Tmec_LPA | Mechanical torque applied to mass (LPA turbine) | pu |
Tmec_LPA_LPB | Mechanical torque between the LPA and LPB turbine masses | pu |
Tmec_LPB | Mechanical torque applied to mass (LPB turbine) | pu |
Tmec_LPB_GEN | Mechanical torque between the LPB turbine masses and the machine | pu |
V0s | Zero sequence stator voltage | pu |
Vds | d axis stator voltage | pu |
Vqs | q axis stator voltage | pu |
Vt | Machine terminal voltage | pu |
Wm | Mechanical or electrical speed of the machine | pu |
Wm_HP | Mechanical or electrical speed of the HP turbine | pu |
Wm_IP | Mechanical or electrical speed of the IP turbine | pu |
Wm_LPA | Mechanical or electrical speed of the LPA turbine | pu |
Wm_LPB | Mechanical or electrical speed of the LPB turbine | pu |
Wrpm | Mechanical speed of the machine | r/min |
Additional Information & Model Equations
Additional Information
- The machine can have in the q axis 2 damper windings, Q1 and Q2. Similarly, it can have in the d axis 2 damper windings, D1 and D2.
- The rotor reference frame is such that the q axis is rad ahead of the d axis.
Base Values for PU Conversion
Base Value | Description |
---|---|
Base power | |
Base stator voltage (peak) for wye connection | |
Base stator voltage (peak) for delta connection | |
Base stator current (peak) | |
Base mechanical torque | |
Base flux (peak) |
Model Equations
The Park transform is defined as follows:
Where is the angle between phase a and the d-axis
The equations of the electrical system (p.u. and generating convention) are given by:
Where
: Electric speed (rad / s)
: The flux produced by the permanent magnets (pu)
NB: The flux equations are in per unit. Therefore in this case, any reactance can also be specified as an inductance.
The electromagnetic torque (p.u.) developed by the PMSM is given by:
The mechanical (general) equation of mass i is described as follows:
Where
: The mechanical torque developed on the ith mass (Nm)
: The electromagnetic torque developed by the PMSM (Nm)
: The mechanical speed of mass i (rad / s)