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Doubly-Fed Induction Machine
This block implements a doubly-fed induction machine (DFIM)
The DFIM block implements a three-phase induction machine (asynchronous machine) with an accessible wound rotor model with resolvers and encoders. The machine can operate in both motoring mode, when the mechanical torque is positive, and generating mode when the mechanical torque is negative.
Model Formulation
Q-d Transformation
The 3-phase to q-d transformation and the inverse used for the model are:
The induction machine model uses the rotor as a reference, thus the angle of theta_r.
Induction Machine Electrical Model
Induction machine models in state-space framework are based on magnetic fluxes. The state variables and winding currents (as the outputs) can be represented as follows:
where the coefficient matrices are as follows:
and
The Induction Machine is modeled in rotor reference frame so ω=ωr.
In the model, all the rotor parameters and variables are seen from the stator distinguished by a prime sign. The stator to rotor turn ratio (Nsr) is applied as follows to transfer input three-phase rotor voltage to the stator side, and transfer back the output three-phase rotor current measurements to the rotor side:
The electrical torque is calculated as follows:
Parameters and Measurements
The DFIM's parameters and measurements are separated in 4 different tabs, Electrical, Mechanical, Resolver and Encoder.
Electrical Parameters and Measurements
Symbol | Name | Description | Unit | Type |
---|---|---|---|---|
Rs | Stator resistance | Stator winding resistance of phase a, b, and c | Ω | Edit-input |
Lls | Stator leakage inductance | Stator winding leakage inductance of phase a, b, and c | H | Edit-input |
Rr' | Rotor resistance | Equivalent rotor winding resistance referred to the stator of phase a, b, and c | Ω | Edit-input |
Llr' | Rotor leakage inductance | Equivalent rotor winding leakage inductance referred to the stator of phase a, b, and c | H | Edit-input |
Lm | Mutual inductance | Stator-rotor mutual (magnetizing) inductance of phase a, b, and c | H | Edit-input |
pp | Number of pole pairs | Number of pole pairs | N/A | Edit-input |
is | Stator phase currents | Stator currents measured at phases a, b and c | A | Measurement |
isdq | Stator dq currents | Stator currents in dq frame | A | Measurement |
Φsdq | Stator dq fluxes | Stator fluxes in dq frame | Wb | Measurement |
Vsdq | Stator dq voltages | Stator voltages in dq frame | V | Measurement |
ir' | Rotor phase currents | Rotor equivalent phase a, b, and c currents, referred to the stator | A | Measurement |
irdq | Rotor dq currents | Rotor currents in dq frame, referred to the stator | A | Measurement |
Φrdq' | Rotor dq fluxes | Rotor fluxes in dq frame, referred to the stator | Wb | Measurement |
Vrdq | Rotor dq voltages | Rotor voltages in dq frame, referred to the stator | V | Measurement |
Rsn | Snubber resistance | Resistances of the snubber on phase A, B and C | Ω | Input |
Csn | Snubber capacitance | Capacitance of the snubber on phase A, B and C | F | Input |
Mechanical Parameters and Measurements
Symbol | Name | Description | Unit | Type |
---|---|---|---|---|
J | Rotor inertia | Moment of inertia of the rotor | kg*m2 | Input |
Fv | Viscous friction coefficient | Viscous friction | N*m*s/rad | Input |
Fs | Static friction torque | Static friction | N*m | Input |
ctrl | Mechanical control mode | Control mode of the mechanical model. Has two possible values: speed or torque. In speed mode, the mechanical model is bypassed and the speed command is sent directly. In torque mode, the torque command is used to measure the speed using the mechanical parameters of the machine. | Input | |
T | Torque command | Torque command sent to the mechanical model | N*m | Input |
ωrc | Rotor speed command | Speed command sent to the mechanical model | rpm | Input |
ωr | Rotor speed | Speed of the rotor | rpm | Measurement |
Te | Electromagnetic torque | Torque measured at the rotor | N*m | Measurement |
θ0 | Initial rotor angle | Rotor position at time t = 0 | ° | Input |
θ | Rotor angle | Rotor position from 0 to 360 degrees | ° | Measurement |
Resolver Parameters and Measurements
Symbol | Name | Description | Unit | Type |
---|---|---|---|---|
Ren | Enable resolver | Whether or not to enable the resolver | N/A | Input |
Rsc | Resolver feedback signals | The two two-phase windings producing a sine and cosine feedback current proportional to the sine and cosine of the angle of the motor | N/A | Measurement |
Rpp | Number of resolver pole pairs | Number of pole pairs of the resolver | N/A | Input |
Rdir | Direction of the sensor rotation | Direction in which the sensor is turning, either clockwise or counterclockwise | N/A | Input |
Rθ | Angle offset Δθ ( Sensor- Rotor ) | Angle offset between the resolver and the rotor position from 0 to 360 degrees | ° | Input |
Rk | Resolver sine cosine gains | The sine/cosine modulation output sine/cosine component amplitude. Default value are 1, 0, 0 and 1 | N/A | Input |
Etype | Excitation source type | The source from which the excitation of the resolver is generated. Can either be AC, which is generated inside the FPGA with the specified frequency, DC, which is generated with a 90° from the rotor and External, which is generated from outside the model | N/A | Input |
Ef | Excitation frequency | Frequency of the excitation when in AC mode | Hz | Input |
Esrc | Excitation source | Source of the external excitation source when in External mode | N/A | Input |
Ets | Excitation time shift | This parameter is used to compensate the time offset between the carrier generation's input in the system and modulated signals' output | s | Input |
Encoder Parameters and Measurements
Symbol | Name | Description | Unit | Type |
---|---|---|---|---|
Encen | Enable encoder | Whether or not to enable the encoder | N/A | Input |
QABZ | A B Z encoder signals | A B and Z signals of the encoder | N/A | Measurement |
Qppr | Number of pulses per revolution | Number of pulses in one full revolution of the encoder | N/A | Input |
Qdir | Direction of the sensor rotation | Direction in which the sensor is turning, either clockwise or counterclockwise | N/A | Input |
θoffset | Angle offset Δθ ( Sensor - Rotor ) | Angle offset between the encoder and the rotor position from 0 to 360 degrees | ° | Input |
Visualization of Resolver Encoder Parameters effects
Number of resolver pole pairs affects the number of electrical turns per mechanical turns. On the left figure, the number of resolver pole pairs is 2, on the right figure, the number of resolver pole pairs is 4.
Resolver sine cosine gains affect the sine ( first axe ) and cosine ( second axe ) modulation output. Default values set to 1, 0, 0, 1 make it so the sine modulation has a sine form and the cosine modulation has a cosine form. If set to 0, 1, 1, 0, the sine modulation would have a cosine and the cosine modulation would have a sine form.
Excitation frequency, in AC excitation source type, affects the frequency of the carrier signal. We can see the time step highlighted in red. ( Figure 3 is a zoomed in view of Figure 2 )
Number of pulses per revolution (Qppr) defines how many times signals A and B pulse between two Z pulses ( one full rotation ).
Direction of the sensor rotation describes if A leads B ( Clockwise ) or if B leads A ( Counterclockwise )
Electrical ports
This block has six electrical ports, the three terminals of the stator on the left side and three terminals of the rotor on the right side.