Three Phase Switched Reluctance Machine
Description of the Three Phase Switched Reluctance Machine component in Schematic Editor.
component | component dialog window | component parameters |
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Electrical sub-system model
The electrical part of the machine is represented by the following system of equations.
where:
where:
symbol | description |
---|---|
ψas | Stator phase A flux [Wb] |
ψbs | Stator phase B flux [Wb] |
ψcs | Stator phase C flux [Wb] |
ias | Stator phase A current [A] |
ibs | Stator phase B current [A] |
ics | Stator phase C current [A] |
vas | Stator phase A voltage[V] |
vbs | Stator phase B voltage[V] |
vcs | Stator phase C voltage[V] |
Rs | Stator phase resistance [Ω] |
θr | Rotor mechanical angle [rad] |
Te | Machine developed electromagnetic torque [Nm] |
Tea | Machine developed electromagnetic torque in phase a [Nm] |
Teb | Machine developed electromagnetic torque in phase b [Nm] |
Tec | Machine developed electromagnetic torque in phase c [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 |
---|---|
Rs | Stator phase resistance [Ω] |
Ns | Number of stator poles |
Nr | Number of rotor poles |
theta vector | Mechanical angle input vector [deg] |
current vector | Stator phase current input vector [A] |
flux linkage vector | Flux linkage input vector [Wb] |
flux linkage table | Flux linkage lookup table [Wb] |
current table | Stator phase current lookup table [A] |
Te table | Electrical torque lookup table [Nm] |
- Flux linkage and torque lookup tables, or
- Stator current and torque lookup tables.
The lookup tables should be provided either as nested Python lists or 2-dimensional numpy arrays. For the flux linkage and the torque tables, the numbers of elements in the inner lists must match the number of elements in the stator current vector, while the number of elements in the outer list must match the number of elements in the machine mechanical angle vector. For the stator current table, the numbers of elements in the inner lists must match the number of elements in the flux linkage vector, while the number of elements in the outer list must match the number of elements in the machine mechanical angle vector. This is summarized in Figure 1, Figure 2, and Figure 3.
Mechanical
symbol | description |
---|---|
Nr | The number of rotor teeth |
Jm | Combined rotor and load moment of inertia [kgm2] |
Friction coefficient | Machine viscous friction coefficient [Nms] |
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] |


Snubber
All machines with current source based circuit interfaces have the Snubber tab in the properties window where the value of snubber resistance can be set. Snubbers are necessary in the cases when an inverter or a contactor is directly connected to the machine terminals. This value can be set to infinite (inf), but it is not recommended when a machine is directly connected to the inverter since there will be a current source directly connected to an open switch. In this case, one of each switch pairs S1 and S2, S3 and S4, and S5 and S6 will be forced closed by the circuit solver in order to avoid the topological conflicts. On the other hand, with finite snubber values, there's always a path for the currents Ia and Ib, so all inverter switches can be open in this case. Circuit representations of this circuit without and with snubber resistors are shown in Figure 4 and Figure 5 respectively. Snubbers are connected across the current sources.


symbol | description |
---|---|
Rsnb stator | Stator snubber resistance value [Ω] |
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 phase A flux | Stator phase A magnetic flux [Wb] |
Stator phase B flux | Stator phase B magnetic flux [Wb] |
Stator phase C flux | Stator phase C magnetic flux [Wb] |
Phase a torque component | Electric torque developed in phase a [Nm] |
Phase b torque component | Electric torque developed in phase b [Nm] |
Phase c torque component | Electric torque developed in phase c [Nm] |