Brushless DC Machine
Description of the Brushless DC Machine component in Schematic Editor.
component | component dialog window | component parameters |
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A, B, and C are the stator winding terminals. The stator winding uses the voltage behind reactance interface.
Electrical sub-system model
The electrical part of the machine is represented by the following system of equations:
where: ψa=fa(θe) , ψb=fb(θe), ψc=fc(θe)
Ideal trapezoidal waveforms are assumed for the phase fluxes. The starting angle value is given in the moment when the flux of phase A changes its sign from a negative to positive value. Thus, trapezoidal flux waveforms are defined in Table 2.
Electrical angle(deg) | 0 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 | 330 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
ψa | 0 | ψmax | ψmax | ψmax | ψmax | ψmax | 0 | -ψmax | -ψmax | -ψmax | -ψmax | -ψmax |
ψb | -ψmax | -ψmax | -ψmax | -ψmax | 0 | ψmax | ψmax | ψmax | ψmax | ψmax | 0 | -ψmax |
ψc | ψmax | ψmax | 0 | -ψmax | -ψmax | -ψmax | -ψmax | -ψmax | 0 | ψmax | ψmax | ψmax |
symbol | description |
---|---|
ψa | Stator phase A magnetic flux [Wb] |
ψb | Stator phase B magnetic flux [Wb] |
ψc | Stator phase C magnetic flux [Wb] |
ia | Stator phase A current [A] |
ib | Stator phase B current [A] |
ic | Stator phase C current [A] |
va | Stator phase A voltage [V] |
vb | Stator phase B voltage [V] |
vc | Stator phase C voltage [V] |
Ea | Stator phase A induced back emf [V] |
Eb | Stator phase B induced back emf [V] |
Ec | Stator phase C induced back emf [V] |
Rs | Stator phase resistance [Ω] |
Ls | Stator phase inductance [H] ( ) |
ωm | Rotor mechanical speed [rad/s] |
p | Machine number of pole pairs |
Te | Machine developed electromagnetic torque [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] |
Ls | Stator phase inductance [H] |
Vpk/krpm | Peak line-to-line back emf developed at a mechanical speed of 1000 rpm [V/krpm] |
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] |
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 phase A emf | Stator phase A induced back emf [V] |
Stator phase B emf | Stator phase B induced back emf [V] |
Stator phase C emf | Stator phase C induced back emf [V] |
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] |
Stator phase A current | Stator phase A current [A] |
Stator phase B current | Stator phase B current [A] |