# Brushless DC Machine

Description of the Brushless DC Machine component in Schematic Editor.

Table 1. Brushless DC Machine component in Typhoon HIL Schematic Editor
component component dialog window component parameters
• Property tabs:

A, B, and C are the stator winding terminals. The stator winding uses the voltage behind reactance interface.

Note: Brushless DC Machine component uses nonlinear machine solver unit because its flux values are dependent on rotor electrical angle. That dependency is implemented by using lookup tables. List of the HIL device configurations which are supporting nonlinear machines can be found in Device Configuration Table.

## Electrical sub-system model

The electrical part of the machine is represented by the following system of equations:

$\left[\begin{array}{c}{v}_{a}\\ {v}_{b}\\ \begin{array}{c}{v}_{c}^{}\\ \end{array}\end{array}\right]=\left[\begin{array}{ccc}{R}_{s}& 0& 0\\ 0& {R}_{s}& 0\\ 0& 0& {R}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ \begin{array}{c}{i}_{c}^{}\\ \end{array}\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\psi }_{a}\\ {\psi }_{b}\\ \begin{array}{c}{\psi }_{c}^{}\\ \end{array}\end{array}\right]+\left[\begin{array}{c}{E}_{a}\\ {E}_{b}\\ \begin{array}{c}{E}_{c}^{}\\ \end{array}\end{array}\right]$

$\left[\begin{array}{c}{E}_{a}\\ {E}_{b}\\ \begin{array}{c}{E}_{c}\\ \end{array}\end{array}\right]=p{\omega }_{m}\left[\begin{array}{c}{\psi }_{a}\\ {\psi }_{b}\\ \begin{array}{c}{\psi }_{c}\\ \end{array}\end{array}\right]$

$\left[\begin{array}{c}{\psi }_{a}\\ {\psi }_{b}\\ \begin{array}{c}{\psi }_{c}^{}\\ \end{array}\end{array}\right]=\left[\begin{array}{ccc}{L}_{s}& 0& 0\\ 0& {L}_{s}& 0\\ 0& 0& {L}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ \begin{array}{c}{i}_{c}^{}\\ \end{array}\end{array}\right]$

${T}_{e}=p\left({\psi }_{a}{i}_{a}+{\psi }_{b}{i}_{b}+{\psi }_{c}{i}_{c}\right)$

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.

Table 2. Flux waveform dependence on rotor electrical angle
Electrical angle(deg) 0 30 60 90 120 150 180 210 240 270 300 330
ψa 0 ψmax ψmax ψmax ψmax ψmax 0 max max max max max
ψb max max max max 0 ψmax ψmax ψmax ψmax ψmax 0 max
ψc ψmax ψmax 0 max max max max max 0 ψmax ψmax ψmax
Table 3. Electrical sub-system model variables
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] ( $={L}_{ls}+{L}_{m}$ )
p Machine number of pole pairs
Te Machine developed electromagnetic torque [Nm]

## Mechanical sub-system model

Motion equation:

Table 4. Mechanical sub-system model variables
symbol description
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]
Note: Motion equation is the same for all of the rotating machine models.

## Electrical

Table 5. Electrical parameters
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

Table 6. Mechanical parameters
symbol description
pms Machine number of pole pairs
Jm Combined rotor and load moment of inertia [kgm2]
Friction coefficient Machine viscous friction coefficient [Nms]

symbol description
Load source Load can be set from SCADA/external or from model (in model case, one signal processing input will appear)
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:

${T}_{l}=load_ai_gain·\left(AI\left(load_ai_pin\right)+load_ai_offset\right)$

Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. For instance, if both the load and the resolver carrier signal use the same analog input pin, the signal value will only be applied only to one of these.

## Feedback

Table 8. Feedback parameters
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:

$res_carr_src=res_ai_gain·\left(AI\left(res_ai_pin_1\right)+res_ai_offset\right)$

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:

$res_carr_src=res_ai_gain·\left(\left(AI\left(res_ai_pin_1\right)-AI\left(res_ai_pin_2\right)\right)+res_ai_offset\right)$
Note: Differential external resolver signal support is available from the 2023.1 software version. Only the single ended external resolver option was available in previous software versions.
Note: In order to get a resolver signal with an amplitude of 1 when using an external carrier signal, the offset and the gain should be chosen in such a way that the resolver carrier signal has an amplitude of 1 after the adjustment. As shown in Figure 1, the sinusoidal signal used to generate external resolver carrier source is fed to HIL analog input 1. The analog input signal is scaled in order to get the resolver signals with an amplitude of 1.
Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. E.g. if both the load and the resolver carrier signal use the same analog input pin, the signal value will be applied only to one of these.

The following expression must hold in order to properly generate the encoder signals:

$4·enc_ppr·{f}_{m}{·T}_{s}\le 1$
Table 9. Variables in the encoder limitation expression
symbol description
enc_ppr Encoder number of pulses per revolution
fm Rotor mechanical frequency [Hz]
Ts Simulation time step [s]
Note: While the machine speed is positive, the encoder channel B signal leads the encoder channel A signal.
Note: Absolute encoder protocol is not supported on HIL402 (configurations: 1, 2, 3, and 4).

## 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.

Note: All machine components have the Execution rate, Electrical torque, Mechanical speed, and Mechanical angle, but the rest of the signals differ from component to component.
Table 10. Output parameters
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]