Brushless DC Machine
Description of the Brushless DC Machine component in Schematic Editor.
component  component dialog window  component parameters 


A, B, and C are the stator winding terminals. The stator winding uses the voltage behind reactance interface.
Electrical subsystem model
The electrical part of the machine is represented by the following system of equations:
$\left[\begin{array}{c}{v}_{a}\\ {v}_{b}\\ \begin{array}{c}{v}_{c}^{}\\ \end{array}\end{array}\right]=\left[\begin{array}{ccc}{R}_{s}& 0& 0\\ 0& {R}_{s}& 0\\ 0& 0& {R}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ \begin{array}{c}{i}_{c}^{}\\ \end{array}\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\psi}_{a}\\ {\psi}_{b}\\ \begin{array}{c}{\psi}_{c}^{}\\ \end{array}\end{array}\right]+\left[\begin{array}{c}{E}_{a}\\ {E}_{b}\\ \begin{array}{c}{E}_{c}^{}\\ \end{array}\end{array}\right]$$\left[\begin{array}{c}{E}_{a}\\ {E}_{b}\\ \begin{array}{c}{E}_{c}\\ \end{array}\end{array}\right]=p{\omega}_{m}\left[\begin{array}{c}{\psi}_{a}\\ {\psi}_{b}\\ \begin{array}{c}{\psi}_{c}\\ \end{array}\end{array}\right]$
$\left[\begin{array}{c}{\psi}_{a}\\ {\psi}_{b}\\ \begin{array}{c}{\psi}_{c}^{}\\ \end{array}\end{array}\right]=\left[\begin{array}{ccc}{L}_{s}& 0& 0\\ 0& {L}_{s}& 0\\ 0& 0& {L}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ \begin{array}{c}{i}_{c}^{}\\ \end{array}\end{array}\right]$
${T}_{e}=p({\psi}_{a}{i}_{a}+{\psi}_{b}{i}_{b}+{\psi}_{c}{i}_{c})$where: ψ_{a}=f_{a}(θ_{e}) , ψ_{b}=f_{b}(θ_{e}), ψ_{c}=f_{c}(θ_{e})
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 

ψ_{a}  0  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  0  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max} 
ψ_{b}  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  0  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  0  ψ_{max} 
ψ_{c}  ψ_{max}  ψ_{max}  0  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  ψ_{max}  0  ψ_{max}  ψ_{max}  ψ_{max} 
symbol  description 

ψ_{a}  Stator phase A magnetic flux [Wb] 
ψ_{b}  Stator phase B magnetic flux [Wb] 
ψ_{c}  Stator phase C magnetic flux [Wb] 
i_{a}  Stator phase A current [A] 
i_{b}  Stator phase B current [A] 
i_{c}  Stator phase C current [A] 
v_{a}  Stator phase A voltage [V] 
v_{b}  Stator phase B voltage [V] 
v_{c}  Stator phase C voltage [V] 
E_{a}  Stator phase A induced back emf [V] 
E_{b}  Stator phase B induced back emf [V] 
E_{c}  Stator phase C induced back emf [V] 
R_{s}  Stator phase resistance [Ω] 
L_{s}  Stator phase inductance [H] ( $={L}_{ls}+{L}_{\mathrm{m}}$ ) 
ω_{m}  Rotor mechanical speed [rad/s] 
p  Machine number of pole pairs 
T_{e}  Machine developed electromagnetic torque [Nm] 
Mechanical subsystem model
Motion equation:
$\frac{{d\omega}_{m}}{dt}=\frac{1}{{J}_{m}}({T}_{e}{T}_{l}b{\omega}_{m})$ ${\theta}_{m}=\int {\omega}_{m}dt$symbol  description 

ω_{m}  Rotor mechanical speed [rad/s] 
J_{m}  Combined rotor and load moment of inertia [kgm2] 
T_{e}  Machine developed electromagnetic torque [Nm] 
T_{l}  Shaft mechanical load torque [Nm] 
b  Machine viscous friction coefficient [Nms] 
θ_{m}  Rotor mechanical angle [rad] 
Electrical
symbol  description 

R_{s}  Stator phase resistance [Ω] 
L_{s}  Stator phase inductance [H] 
V_{pk/krpm}  Peak linetoline back emf developed at a mechanical speed of 1000 rpm [V/krpm] 
Mechanical
symbol  description 

pms  Machine number of pole pairs 
J_{m}  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:
${T}_{l}=load\_ai\_gain\xb7\left(AI\right(load\_ai\_pin)+load\_ai\_offset)$
Feedback
symbol  description 

Encoder ppr  Incremental encoder number of pulses per revolution 
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:
$res\_carr\_src=res\_ai\_gain\xb7\left(AI\right(res\_ai\_pin\_1)+res\_ai\_offset)$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:
$res\_carr\_src=res\_ai\_gain\xb7\left(\right(AI(res\_ai\_pin\_1)AI(res\_ai\_pin\_2))+res\_ai\_offset)$The following expression must hold in order to properly generate the encoder signals:
$4\xb7enc\_ppr\xb7{f}_{m}{\xb7T}_{s}\le 1$symbol  description 

enc_ppr  Encoder number of pulses per revolution 
f_{m}  Rotor mechanical frequency [Hz] 
T_{s}  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] 