Single Phase Induction Machine
Description of the Single Phase Induction Machine component in Schematic Editor.
component | component dialog window | component parameters |
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The component nodes m_pos and m_neg (shown in Table 1) are the main stator winding terminals. Three types of single phase induction machines are modeled —split-phase, capacitor-start and capacitor-start-run.Figure 1, Figure 2 and Figure 3 show the internal connections of the main and auxiliary windings for each of the machine types. The stator is represented by the single phase variant of the voltage behind reactance interface.
Electrical sub-system model
The electrical part of the machine is represented by the following system of equations, modeled in the stationary αβ reference frame. All rotor variables and parameters are referred to the stator.
In the above equations, currents are obtained from the main winding and auxiliary winding stator currents using the following transformation:
symbol | description |
---|---|
ψαs | Alpha axis component of the stator flux [Wb] |
ψβs | Beta axis component of the stator flux [Wb] |
ψαr | Alpha axis component of the rotor flux, referred to the stator [Wb] |
ψβr | Beta axis component of the rotor flux, referred to the stator [Wb] |
iαs | Alpha axis component of the stator current [A] |
iβs | Beta axis component of the stator current [A] |
iαr | Alpha axis component of the rotor current, referred to the stator [A] |
iβr | Beta axis component of the rotor current, referred to the stator [A] |
vαs | Alpha axis component of the stator voltage [V] |
vβs | Beta axis component of the stator voltage [V] |
vαr | Alpha axis component of the rotor voltage, referred to the stator [V] |
vβr | Beta axis component of the rotor voltage, referred to the stator [V] |
Rsm | Stator main winding resistance [Ω] |
Rsa | Stator auxiliary winding resistance [Ω] |
Rrm | Rotor main winding resistance [Ω] |
Llsm | Stator main winding leakage inductance [H] |
Lmm | Main winding mutual inductance [H] |
Llsa | Stator auxiliary winding leakage inductance [H] |
Llrm | Rotor main winding leakage inductance [H] |
ωr | Rotor electrical speed [rad/s] ( ) |
p | Machine number of pole pairs |
Te | Machine developed electromagnetic torque [Nm] |
Auxiliary to main winding turns ratio (Na/Nm) |
Mechanical sub-system model
Motion equation:
symbol | description |
---|---|
ωm | Rotor mechanical speed [rad/s] |
Jm | Combined rotor and load moment of inertia [kgm2] |
Te | Machine developed electromagnetic torque [Nm] |
Tl | Shaft mechanical load torque [Nm] |
b | Machine viscous friction coefficient [Nms] |
θm | Rotor mechanical angle [rad] |
Electrical
symbol | description |
---|---|
Machine type | Type of machine: split-phase, capacitor-start or capacitor-start-run |
f | Nominal frequency of the machine [Hz] |
Rsm | Stator main winding resistance [Ω] |
Llsm | Stator main winding leakage inductance [H] |
Rsa | Stator auxiliary winding resistance [Ω] |
Llsa | Stator auxiliary winding leakage inductance [H] |
Lmm | Main winding mutual inductance [H] |
Rrm | Rotor main winding resistance [Ω] |
Llrm | Rotor main winding leakage inductance [H] |
Na/Nm | Auxiliary to main winding turns ratio |
Rst | Capacitor-start resistance [Ω] |
Cst | Capacitor-start capacitance [F] |
Rrun | Capacitor-run resistance [Ω] |
Crun | Capacitor-run capacitance [F] |
Mechanical
symbol | description |
---|---|
pms | Machine number of pole pairs |
Jm | Combined rotor and load moment of inertia [kgm2] |
Friction coefficient | Machine viscous friction coefficient [Nms] |
Disconnection speed coefficient | Rotor speed at which the auxiliary winding is disconnected (in % of synchronous speed) |
Unconstrained mechanical angle | Limiting mechanical angle between 0 and 2π |
Load
symbol | description |
---|---|
Load source | Load can be set from SCADA/external or from model (in model case, one signal processing input will appear) |
External/Model load type | External/Model load type: torque or speed |
Load ai pin | HIL analog input address for external torque command |
Load ai offset | Assigned offset value to the input signal representing external torque command |
Load ai gain | Assigned gain value to the input signal representing external torque command |
External load enables you to use an analog input signal from a HIL analog channel with the load_ai_pin address as an external torque/speed load, and to assign offset (V) and gain (Nm/V) to the input signal, according to the formula:
Feedback
symbol | description |
---|---|
Encoder ppr | Incremental encoder number of pulses per revolution |
Encoder Z pulse length | Z digital signal pulse length in periods. Can be Quarter length or Full period (default) |
Resolver pole pairs | Resolver number of pole pairs |
Resolver carrier source | Resolver carrier signal source selection (internal or external) |
External resolver carrier source type | External resolver carrier signal source type selection (single ended or differential); available only if the Resolver carrier source property is set to external |
Resolver carrier frequency | Resolver carrier signal frequency (internal carrier) [Hz] |
Resolver ai pin 1 | Resolver carrier input channel 1 address (external carrier) |
Resolver ai pin 2 | Resolver carrier input channel 2 address (external carrier); available only if the External resolver carrier source type property is set to differential |
Resolver ai offset | Resolver carrier input channel offset (external carrier) |
Resolver ai gain | Resolver carrier input channel gain (external carrier) |
Absolute encoder protocol | Standardized protocol providing the absolute machine encoder position |
If an external resolver carrier source is selected, the source signal type can be set as either single ended or differential. The single ended external resolver carrier source type enables use of an analog input signal from the HIL analog channel with the res_ai_pin_1 address as the external carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal, according to the formula:
The differential external resolver carrier source type enables use of two analog input signals from the HIL analog channels with the res_ai_pin_1 and the res_ai_pin_2 addresses. Analog signals from these HIL analog inputs are subtracted, and the resulting signal is used as the external differential carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal (similarly to the single ended case), according to the formula:
The following expression must hold in order to properly generate the encoder signals:
symbol | description |
---|---|
enc_ppr | Encoder number of pulses per revolution |
fm | Rotor mechanical frequency [Hz] |
Ts | Simulation time step [s] |
Output
This block tab enables a single, vectorized signal output from the machine. The output vector contains selected machine mechanical and/or electrical variables in the same order as listed in this tab.
symbol | description |
---|---|
Execution rate | Signal processing output execution rate [s] |
Electrical torque | Machine electrical torque [Nm] |
Mechanical speed | Machine mechanical angular speed [rad/s] |
Mechanical angle | Machine mechanical angle [rad] |
Stator alpha axis emf | Alpha axis component of the stator VBR equivalent back emf [V] |
Stator beta axis emf | Beta axis component of the stator VBR equivalent back emf [V] |
Rotor alpha axis current | Alpha axis component of the rotor current, referred to the stator [A] |
Rotor beta axis current | Beta axis component of the rotor current, referred to the stator [A] |
Stator alpha axis flux | Alpha axis component of the stator flux [Wb] |
Stator beta axis flux | Beta axis component of the stator flux [Wb] |
Rotor alpha axis flux | Alpha axis component of the rotor flux, referred to the stator [Wb] |
Rotor beta axis flux | Beta axis component of the rotor flux, referred to the stator [Wb] |