Three Phase Wound Rotor Synchronous Machine

A, B, and C are stator winding terminals. The stator winding uses the current source interface. R1 and R2 represent field winding terminals. The rotor winding uses the single phase variant of the current source interface.

Electrical sub-system model

The electrical part of the machine is represented by the following system of equations, modeled in the rotating dq reference frame. The dq reference frame is attached to the rotor, and the direct axis is aligned with the field winding. The modeled dynamics can be represented with the following equations:

[\begin{matrix} v_{d s} \\ v_{q s} \\ v_{k d} \\ v_{k q} \\ v_{f d} \\ v_{k q 2} \end{matrix}] = [\begin{matrix} R_{s} \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix} \begin{matrix} 0 \\ R_{s} \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix} \begin{matrix} 0 \\ 0 \\ R_{k d} \\ 0 \\ 0 \\ 0 \end{matrix} \begin{matrix} 0 \\ 0 \\ 0 \\ R_{k q} \\ 0 \\ 0 \end{matrix} \begin{matrix} 0 \\ 0 \\ 0 \\ 0 \\ R_{f d} \\ 0 \end{matrix} \begin{matrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ R_{k q 2} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ i_{k d} \\ i_{k q} \\ i_{f d} \\ i_{k q 2} \end{matrix}] + \frac{d}{d t} [\begin{matrix} ψ_{d s} \\ ψ_{q s} \\ ψ_{k d} \\ ψ_{k q} \\ ψ_{f d} \\ ψ_{k q 2} \end{matrix}] + ω_{r} [\begin{matrix} {- ψ}_{q s} \\ ψ_{d s} \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix}]

[\begin{matrix} ψ_{d s} \\ ψ_{q s} \\ ψ_{k d} \\ ψ_{k q} \\ ψ_{f d} \\ ψ_{k q 2} \end{matrix}] = [\begin{matrix} L_{l s} + L_{m d} \\ 0 \\ L_{m d} \\ 0 \\ L_{m d} \\ 0 \end{matrix} \begin{matrix} 0 \\ L_{l s} + L_{m q} \\ 0 \\ L_{m q} \\ 0 \\ L_{m q} \end{matrix} \begin{matrix} L_{m d} \\ 0 \\ L_{c} + L_{l k d} + L_{m d} \\ 0 \\ L_{m d} \\ 0 \end{matrix} \begin{matrix} 0 \\ L_{m q} \\ 0 \\ L_{l k q} + L_{m q} \\ 0 \\ L_{m q} \end{matrix} \begin{matrix} L_{m d} \\ 0 \\ L_{m d} \\ 0 \\ L_{c} + L_{l f d} + L_{m d} \\ 0 \end{matrix} \begin{matrix} 0 \\ L_{m q} \\ 0 \\ L_{m q} \\ 0 \\ L_{l k q 2} + L_{m q} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ i_{k d} \\ i_{k q} \\ i_{f d} \\ i_{k q 2} \end{matrix}]

T_{e} = \frac{3}{2} p (ψ_{d s} i_{q s} - ψ_{q s} i_{d s})

If the saturation effects are considered, the equations have the same form, but in that case fluxes are functions of stator currents:

ψ_{m d} = f_{d} (i_{m d}, i_{m q})

ψ_{m q} = f_{q} (i_{m d}, i_{m q})

where:

ψ_{m} = \sqrt{{ψ_{m d}_{}}^{2} + {ψ_{m q}_{}}^{2}}

ψ_{m d} = {ψ_{d s} + ψ_{k d} + ψ_{f d}}^{}^{}

ψ_{m q} = {ψ_{q s} + ψ_{k q} + ψ_{k q 2}}^{}^{}

and:

i_{m} = \sqrt{{i_{m d}_{}}^{2} + {i_{m q}_{}}^{2}}

i_{m d} = {i_{d s} + i_{k d} + i_{f d}}^{}^{}

i_{m q} = {i_{q s} + i_{k q} + i_{k q 2}}^{}^{}

All rotor variables and parameters are referred to the stator with an appropriate turns ratio. To illustrate this, if you apply voltage v_fd^r at the field winding terminals, it is transformed to the stator value v_fd with the following equation:

v_{f d} = \frac{N_{s}}{N_{f d}} v_{f d}^{r}

Similarly, calculated rotor currents: field winding current i_fd, and damper winding currents i_kd and i_kq, are referred back to the real rotor windings values i_fd^r, i_kd^r, and i_kq^r, through the following equations:

i_{f d}^{r} = \frac{3}{2} \frac{N_{s}}{N_{f d}} i_{f d} i_{k d}^{r} = \frac{3}{2} \frac{N_{s}}{N_{k d}} i_{k d} i_{k q}^{r} = \frac{3}{2} \frac{N_{s}}{N_{k q}} i_{k q}

Table 1. Three Phase Wound Rotor Synchronous Machine electrical subsystem model variables
Symbol	Description
ψ_ds	Direct axis component of the stator flux [Wb]
ψ_qs	Quadrature axis component of the stator flux [Wb]
ψ_kd	Direct axis component of the damper winding flux, referred to the stator [Wb]
ψ_kq	Quadrature axis component of the damper winding flux, referred to the stator [Wb]
ψ_fd	Field winding flux, referred to the stator [Wb]
ψ_kq2	Second quadrature axis component of the damper winding flux, referred to the stator [Wb]
i_ds	Direct axis component of the stator current [A]
i_qs	Quadrature axis component of the stator current [A]
i_kd	Direct axis component of the damper winding current, referred to the stator [A]
i_kd^r	Direct axis component of the damper winding current [A]
i_kq	Quadrature axis component of the damper winding current, referred to the stator [A]
i_kq^r	Quadrature axis component of the damper winding current [A]
i_fd	Field winding current, referred to the stator [A]
i_fd^r	Field winding current [A]
i_kq2	Second quadrature axis component of the damper winding current, referred to the stator [A]
v_ds	Direct axis component of the stator voltage [V]
v_qs	Quadrature axis component of the stator voltage [V]
v_kd	Direct axis component of the damper winding voltage, referred to the stator [V]
v_kq	Quadrature axis component of the damper winding voltage, referred to the stator [V]
v_fd	Field winding voltage, referred to the stator [V]
v_fd^r	Field winding voltage [V]
v_kq2	Second quadrature axis component of the damper winding voltage, referred to the stator [V]
i_md	Direct axis component of the magnetizing current [A]
i_mq	Quadrature axis component of the magnetizing current [A]
ψ_md	Direct axis component of the magnetizing flux [Wb]
ψ_mq	Quadrature axis component of the magnetizing flux [Wb]
i_m	Magnetizing current [A]
ψ_m	Magnetizing flux [Wb]
R_s	Stator phase resistance [Ω]
R_kd	Direct axis damper winding resistance, referred to the stator [Ω]
R_kq	Quadrature axis damper winding resistance, referred to the stator [Ω]
R_kq2	Second quadrature axis damper winding resistance, referred to the stator [Ω]
R_fd	Field winding resistance, referred to the stator [Ω]
L_ls	Stator phase leakage inductance [H]
L_md	Direct axis magnetizing (mutual, main) inductance [H]
L_mq	Quadrature axis magnetizing (mutual, main) inductance [H]
L_lkd	Direct axis damper winding leakage inductance, referred to the stator [H]
L_lkq	Quadrature axis damper winding leakage inductance, referred to the stator [H]
L_lkq2	Second quadrature axis damper winding leakage inductance, referred to the stator [H]
L_lfd	Direct axis field winding leakage inductance, referred to the stator [H]
L_c	Canay leakage inductance, referred to the stator [H]
ω_r	Rotor electrical speed [rad/s] ( $= p ω_{m}$ )
p	Machine number of pole pairs
T_e	Machine developed electromagnetic torque [Nm]
N_s/N_fd	Turns ratio between the stator phase winding and the field winding used for transforming field winding variables to the stator-side
N_s/N_kd	Turns ratio between the stator phase winding and the direct axis damper winding used for transforming damper winding variables to the stator-side
N_s/N_kq	Turns ratio between the stator phase winding and the quadrature axis damper winding used for transforming damper winding variables to the stator-side

Mechanical sub-system model

Motion equation:

\frac{{d ω}_{m}}{d t} = \frac{1}{J_{m}} (T_{e} - T_{l} - b ω_{m})

θ_{m} = \int ω_{m} d t

Table 2. Mechanical sub-system model variables
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]

Note: Motion equation is the same for all of the rotating machine models.

Saturation effects

The Three Phase Wound Rotor Synchronous Machine machine model can include magnetic saturation effects. In that case, fluxes are defined as functions of magnetizing currents i_md and i_mq. These functions are represented in the form of lookup tables. The lookup tables use linear interpolation and linear extrapolation.

Saturation can be parametrized in the following ways:

no load curve
flux vs current

In the first case when the magnetizing curve is defined as no load curve, variables must be defined as Python lists. In the second case, when the magnetizing curve is defined as flux vs current, the magnetizing current components imd vector and imq vector must be defined as Python lists, while the magnetizing flux components psimd table and psimq table should be defined as nested Python lists. The number of inner lists must be equal to the number of elements in imd vector and the number of elements in each inner list must also be equal to the number of elements in the imq vector.

Figure 2. Nonlinear Model Type: no load curve v_s=f(i_f)

if_vector = [0, 4514.0, 9498.0, 13260.0, 15260.0, 16710.0, 18200.0, 19210.0, 21340.0, 23650.0, 25930.0]
vs_vector = [0.0, 4986.55, 10388.65, 14313.256, 16298.64, 17637.6, 18884.26, 19623, 20915.82, 22116.28, 23224.4]

Figure 3. Nonlinear Model Type: fluxes as functions of stator currents, ψ_md=f_d(i_md) , ψ_mq=f_q(i_mq)

imd_vector = [-9498.0, -8548.2, -7598.4, -6648.6, -5698.8]
imq_vector = [-9498.0, -8548.2, -7598.4, -6648.6, -5698.8]
psimd_table = [-22.46306805, -20.2273073, -17.99014399, -15.75121391, -13.51008229]
psimq_table = [-11.07784855, -9.9724961, -8.86656821, -7.76004375, -6.65291642]

Figure 4. Nonlinear Model Type: fluxes as functions of stator currents, ψ_md=f_d(i_md , i_mq) , ψ_mq=f_q(i_md , i_mq)

imd_vector = [-9498.0, -8548.2, -7598.4, -6648.6, -5698.8]
imq_vector = [-9498.0, -8548.2, -7598.4, -6648.6, -5698.8]
psimd_table = [[-22.46306805, -22.46854837, -22.47394023, -22.47914448, -22.48404604],
               [-20.2273073, -20.23340111, -20.23948657, -20.24544982, -20.25115112],
               [-17.99014399, -17.99688273, -18.00373418, -18.01057435, -18.01723878],
               [-15.75121391, -15.75858553, -15.7662438, -15.77406724, -15.78187459],
               [-13.51008229, -13.51799327, -13.52642503, -13.53528506, -13.54440031]]
psimq_table = [[-11.07784855, -9.9724961, -8.86656821, -7.76004375, -6.65291642],
               [-11.08362731, -9.97826979, -8.87224078, -7.765498, -6.65801557],
               [-11.08998614, -9.9847262, -8.87869102, -7.77180627, -6.6640132],
               [-11.09691706, -9.99189941, -8.88600464, -7.77911226, -6.67111073],
               [-11.10434879, -9.99976596, -8.89422511, -7.7875446, -6.67953349]]

Ports

A (electrical)
- Stator winding phase A port.

B (electrical)
- Stator winding phase B port.

C (electrical)
- Stator winding phase C port.

R1 (electrical)
- Field winding port 1.

R2 (electrical)
- Field winding port 2.

in
- Available if Model Load source is selected

Electrical (Tab)

Model Type
- Specifies machine model implementation.
- Two levels of model fidelity are available - linear and nonlinear
rated speed
- Available if Model Type is set to nonlinear.
- Machine mechanical rated speed used in the nonlinear model for the magnetizing curve defined as the no load curve [rpm]
Mag. Curve Type
- Available if Model Type is set to nonlinear.
- Following saturation types can be specified - no load curve and flux vs current
Number of damper windings
- Changes the number of damper windings on the q-axis
Rs
- Stator phase resistance [Ω]

Lls
- Stator phase leakage inductance [H]

Lmd
- Direct axis magnetizing (mutual, main) inductance [H]

Lmq
- Quadrature axis magnetizing (mutual, main) inductance [H]

Rf
- Field winding resistance, referred to the stator [Ω]
Llfd
- Direct axis field winding leakage inductance, referred to the stator [H]

Rkd
- Direct axis damper winding resistance, referred to the stator [Ω]
Rkq
- Quadrature axis damper winding resistance, referred to the stator [Ω]
Rkq2
- Available if Number of damper windings is set to 2.
- Second quadrature axis damper winding resistance, referred to the stator [Ω]
Llkd
- Direct axis damper winding leakage inductance, referred to the stator [H]
Llkq
- Quadrature axis damper winding leakage inductance, referred to the stator [H]
Llkq2
- Available if Number of damper windings is set to 2.
- Second quadrature axis damper winding leakage inductance, referred to the stator [H]
if vector
- Available if Model Type is set to nonlinear - no load curve
- List of no load excitation currents, referred to the field winding [A]
vs vector
- Available if Model Type is set to nonlinear - no load curve
- List of no load stator line-to-line RMS voltages [V]
imd vector
- Available if Model Type is set to nonlinear - flux vs current
- List of magnetizing current direct axis component values [A]
imq vector
- Available if Model Type is set to nonlinear - flux vs current
- List of magnetizing current quadrature axis component values [A]
psimd table
- Available if Model Type is set to nonlinear - flux vs current
- Table of magnetizing flux direct axis component values [Wb]
psimq table
- Available if Model Type is set to nonlinear - flux vs current
- Table of magnetizing flux quadrature axis component values [Wb]
Ns/Nfd
- Turns ratio between the stator phase winding and the field winding used for transforming field winding variables to the stator-side
Ns/Nkd
- Turns ratio between the stator phase winding and the direct axis damper winding used for transforming damper winding variables to the stator-side
- Ns/Nkd turns ratio is not supported in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Ns/Nkq
- Turns ratio between the stator phase winding and the quadrature axis damper winding used for transforming damper winding variables to the stator-side
- Ns/Nkq turns ratio is not supported in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Lc
- Canay leakage inductance, referred to the stator [H]

Mechanical (Tab)

pms
- Machine number of pole pairs
Star/delta
- Stator winding connection (star or delta)
- Stator winding connection option is not supported in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
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 (Tab)

Load source
- Load source can be set from SCADA/external or from model (in model case, one signal processing input will appear).
- In TyphoonSim, if SCADA/external is chosen as Load source, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
External/Model load type
- Load type: torque or speed
Load ai pin
- Load ai pin for external torque/speed command.
- In real-time/VHIL simulation, Load ai pin represent HIL analog input address for external torque command.
- In TyphoonSim, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
- Available only if SCADA/external is set as Load source.
Load ai offset
- Assigned offset value to the input signal representing external torque command.
- Available only if SCADA/external is set as Load source.
Load ai gain
- Assigned gain value to the input signal representing external torque command.
- Available only if SCADA/external is set as Load source.

External load enables you to use an analog input signal from a HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) 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:

$T_{l} = l o a d_a i_g a i n \cdot (A I (l o a d_a i_p i n) + l o a d_a i_o f f s e t)$

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 (Tab)

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)
Resolver carrier frequency
- Resolver carrier signal frequency (internal carrier) [Hz]
- Available only if the Resolver carrier source property is set to internal
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 ai pin 1
- Resolver carrier input channel 1 address (external carrier)
- Available only if the Resolver carrier source property is set to external
- In TyphoonSim, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
Resolver ai pin 2
- Resolver carrier input channel 2 address (external carrier)
- Available only if the Resolver carrier source property is set to externaland External resolver carrier source type property is set to differential
- In TyphoonSim, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
Resolver ai offset
- Resolver carrier input channel offset (external carrier)
- Available only if the Resolver carrier source property is set to external
- In TyphoonSim, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
Resolver ai gain
- Resolver carrier input channel gain (external carrier)
- Available only if the Resolver carrier source property is set to external
- In TyphoonSim, analog signals are read from the internal virtual IO bus. Hence, if some signal is sent to analog ouput 1, it will appear on analog input 1.
Absolute encoder protocol
- Standardized protocol providing the absolute machine encoder position.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Singleturn bits
- Number of machine absolute encoder singleturn bits.
- Available only if Absolute encoder protocol is not None.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Enable multiturn
- Enables multiturn absolute encoder support.
- Available only if Absolute encoder protocol is not None.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Multiturn bits
- Number of machine absolute encoder multiturn bits.
- Available only if Enable multiturn is checked.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
EnDat/SSI/BiSS clock DI pin
- Clock digital input pin for the chosen absolute encoder protocol type.
- Available only if Absolute encoder protocol is not None.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Clock DI logic
- Clock DI pin logic: active high/active low.
- Available only if Absolute encoder protocol is not None.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
EnDat data DI pin
- EnDat data digital input pin.
- Available only if Absolute encoder protocol is EnDat.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.
Data DI logic
- EnDat data DI pin logic: active high/active low.
- Available only if Absolute encoder protocol is EnDat.
- Absolute encoder protocol is ignored in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all.

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/TyphoonSim (internal virtual IO bus in TyphoonSim) 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:

r e s_c a r r_s r c = r e s_a i_g a i n \cdot (A I (r e s_a i_p i n_1) + r e s_a i_o f f s e t)

The differential external resolver carrier source type enables use of two analog input signals from the HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) analog channels with the res_ai_pin_1 and the res_ai_pin_2 addresses. Analog signals from these HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) 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:

r e s_c a r r_s r c = r e s_a i_g a i n \cdot ((A I (r e s_a i_p i n_1) - A I (r e s_a i_p i n_2)) + r e s_a i_o f f s e t)

Note: In real-time/VHIL simulation, 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 5, the sinusoidal signal used to generate external resolver carrier source is fed to HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) 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 \cdot e n c_p p r \cdot f_{m} {\cdot T}_{s} \leq 1

Table 3. Variables in the encoder limitation expression
symbol	description
enc_ppr	Encoder number of pulses per revolution
f_m	Rotor mechanical frequency [Hz]
T_s	Simulation time step [s]

Figure 6. Machine encoder signals when *Full period* option is selected

Figure 7. Machine encoder signals when *Quarter period* option is selected

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).

Note: More information about absolute encoder protocol could be found here.

Advanced

Theta_ab
- Position of the stationary αβ reference frame, in respect to the stator phase a axis [rad]
Field Input
- Physical quantity applied to the field winding - voltage or current. It refers to the rotor-side.
- In order for the input field current to be referred to the stator parameter, N_s/N_fd in the Electrical Tab should be set to $\frac{3}{2}$
  
  Note: If field input is defined as current, the field winding equation is removed from the mathematical model. Instead, the field input current is used as the model's input. There is no support for 2 q-axis damper windings with current input as of yet. For linear machine models, you can choose whether to apply voltage or current to the field winding. Nonlinear machine models only allows voltage as a field input.
- Field Input option is not supported in TyphoonSim. Changing its value will not affect TyphoonSim simulation at all

The machine model output variables (currents, voltages and fluxes) can be observed from a stationary reference frame. There are two widely used approaches in electrical machine modeling: in the first, the alpha axis of the stationary reference frame lags by 90 degrees in regard to the stator phase a axis (used by default, and indicated in a) Figure 8. In the second one, the alpha axis is aligned with the stator phase a axis (indicated in b) Figure 8. The user can select between these two situations.

Figure 8. Selection of a stationary reference frame position: a) Theta_ab= -pi/2; b) Theta_ab= 0

It is important to know the value of Theta_ab when the rotor position feedback is necessary. As an example, if a model uses the mechanical angle as a feedback signal and feeds it to one of the abc to dq, alpha beta to dq, dq to abc, or dq to alpha beta transformation blocks, the same transformation angle offset value should be used in both components to ensure the expected simulation results.

Figure 9. Example of model containing abc to dq transformation component and chosen stationary reference frame position Theta_ab= -pi/2

Snubber (Tab)

Rsnb rotor
- Rotor snubber resistance value [Ω]
Rsnb stator
- Stator snubber resistance value [Ω]

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 10 and Figure 11 respectively. Snubbers are connected across the current sources.

Figure 10. Circuit representation of machine and inverter when all the switches are open without resistors (not recommended)

Figure 11. Circuit representation of machine and inverter when all the switches are open with resistors (recommended)

Note: Snubbers exist only in the machine components that have the current source based circuit interface.

Note: Snubbers are dynamic, which means that the snubber is dynamically added to circuit modes where topological conflicts are detected.

Output (Tab)

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.

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 current
- Alpha axis component of the stator current [A]
Stator beta axis current
- Beta axis component of the stator current [A]
Stator d-axis current
- Direct axis component of the stator current [A]
Stator q-axis current
- Quadrature axis component of the stator current [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]
Stator d-axis flux
- Direct axis component of the stator flux [Wb]
Stator q-axis flux
- Quadrature axis component of the stator flux [Wb]

Extras (Tab)

The Extras tab gives you the opportunity to set Signal Access Management for the component.

Signal visibility is calculated based on the 'signal_access' property and whether or not a parent component in its hierarchy is locked or not. Components that are not contained within locked components expose their signals regardless of the 'signal_access' property. The 'signal_access' property can have one of three values:

Public - Components marked as public expose their signals on all levels.
Protected - Components marked as protected will hide their signals to components outside of their first locked parent component.
Inherit - Components marked as inherit will take the nearest parent 'signal_access' property value that is set to a value other than inherit.