The Squirrel-Cage Induction Machine model implements a three-phase induction machine (asynchronous machine) with a squirrel-cage rotor model with resolvers and encoders. The machine can operate in both motoring mode, when the mechanical torque is positive, and generating mode when the mechanical torque is negative.

SCIM Configuration Page

In the System Explorer window configuration tree, expand the Power Electronics Add-On custom device and select Circuit Model >> SCIM to display this page.  Use this page to configure the SCIM machine model.

This page includes the following components:

Machine Model Settings
NameSpecifies the name of the machine model.
DescriptionSpecifies a description for the machine model.
Motor Configuration

SymbolUnitsDefaultDescription
Motor Type

Squirrel-Cage Induction Machine

Choose from one of the following types:

    • Squirrel Cage Induction Machine
Enable

True

Indicates whether this model is currently enabled. When a motor model is enabled, the machine outputs are made available at the specified Solver Timestep.

Because this model can simulate up to four machines at once, the number of enabled machines impacts the minimum achievable time step of each machine.

Stator ResistanceRsOhm0.6Stator winding phase resistance
Stator Leakage InductanceLlsH0.00035Stator winding leakage inductance
Mutual InductanceLmH0.62Magnetizing inductance
Rotor ResistanceRr'Ohm0.62Specifies the equivalent rotor winding resistance of phases A, B, and C, as seen from the stator.
Rotor Leakage Inductance

Llr'

H0.00547Specifies the equivalent rotor winding leakage inductance of phases A, B, and C, as seen from the stator.
Pole PairsPP
2Number of machine pole pairs
Initial Speedω0RPM0Describes the initial speed of the machine
Solver TimestepTss4.81E-7

Describes the execution timestep of the machine model. The minimum timestep is a function of how many SCIM machines are enabled in the application.

When all four machines are enabled, the minimum achievable timestep is 4.81E-7s, which is also the default value.

Zero Sequence

Don't Include

When Include is selected, the Zero-Sequence Resistance and Zero-Sequence Inductance parameters are enabled to include a Zero Sequence Model. See Including a Zero Sequence Model for more information.

Zero-Sequence ResistanceR0Ohm0.0029069Describes the zero-sequence stator winding resistance. This component is enabled when Zero Sequence is set to Included.
Zero-Sequence InductanceL0H0.00030892Describes the zero-sequence stator winding inductance. This component is enabled when Zero Sequence is set to Included.
Input Mapping Configuration
Use the Input Mapping Configuration to route signals to the Voltage Phase A, Voltage Phase B, and Voltage Phase C inputs of the machine model.  Available routing options may vary depending on the selected Hardware Configuration.

Group

Specifies the group that will be routed to the input voltages of the machine. The available routing options are defined by the selected Hardware Configuration, however it is typical to see the following options by default:

  • Measurements - eHS circuit model measurements

Element

Specifies the index of the measurement in the group that has been selected as the input voltage of the machine.


SCIM Section Channels

This section includes the following custom device channels:

Channel NameSymbolTypeUnitsDefault ValueDescription
Stator Current Phase AIaOutputA0 APhase A current measured at the stator terminal
Stator Current Phase BIbOutputA0 APhase B current measured at the stator terminal
Stator Current Phase CIcOutputA0 APhase C current measured at the stator terminal
Stator Direct Axis CurrentIrdsOutputA0 ADirect-axis current measured at the stator in the reference frame aligned with the rotor
Stator Quadrature Axis CurrentIrqsOutputA0 AQuadrature-axis current measured at the stator in the reference frame aligned with the rotor
Stator Direct Axis VoltageVrdsOutputV0 VDirect-axis voltage measured at the stator in the reference frame aligned with the rotor
Stator Quadrature Axis VoltageVrqsOutputV0 VQuadrature-axis voltage measured at the stator in the reference frame aligned with the rotor
Stator Direct Axis FluxΦrdsOutputWb0 WbDirect-axis flux measured at the stator in the reference frame aligned with the rotor
Stator Quadrature Axis FluxΦrqsOutputWb0 WbQuadrature-axis flux measured at the stator in the reference frame aligned with the rotor
Rotor Current Phase AIar'OutputA0 APhase A current measured at the rotor as seen from the stator
Rotor Current Phase BIbr'OutputA0 APhase B current measured at the rotor as seen from the stator
Rotor Current Phase CIcr'OutputA0 APhase C current measured at the rotor as seen from the stator
Rotor Direct Axis CurrentIdrr'OutputA0 ADirect-axis rotor current in the reference frame aligned with the rotor as seen from the stator
Rotor Quadrature Axis CurrentIqrr'OutputA0 AQuadrature-axis rotor current in the reference frame aligned with the rotor as seen from the stator
Rotor Direct Axis VoltageVdrr'OutputV0 VDirect-axis rotor voltage in the reference frame aligned with the rotor as seen from the stator
Rotor Quadrature Axis VoltageVqrr'OutputV0 VQuadrature-axis rotor voltage in the reference frame aligned with the rotor as seen from the stator
Rotor Direct Axis FluxΦdrr'OutputWb0 WbDirect-axis rotor flux in the reference frame aligned with the rotor as seen from the stator
Rotor Quadrature Axis FluxΦqrr'OutputWb0 WbQuadrature-axis rotor flux in the reference frame aligned with the rotor as seen from the stator


SCIM Model Description

Squirrel-Cage Induction Machines are common electrical machines in the the automotive and transportation industry. AC Induction Motors are usually chosen because they are relatively low cost in terms of production and maintenance, and are self-starting. However, compared to Permanent Magnet Synchronous Machines, they are typically less efficient and larger in size. 

The following figure illustrates the equivalent circuits of the SCIM motor model in the D-Q frame.

Figure 1.  Electrical Model for SCIM in the D-Q frame

DQ Transform

The D-Q transform and the inverse used for the model are:

\left[\begin{array}{l}
{V_{q}} \\
{V_{d}} \\
{V_{0}}
\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}
{\cos (\theta)} & {\cos \left(\theta-\frac{2 \pi}{3}\right)} & {\cos \left(\theta+\frac{2 \pi}{3}\right)} \\
{\sin (\theta)} & {\sin \left(\theta-\frac{2 \pi}{3}\right)} & {\sin \left(\theta+\frac{2 \pi}{3}\right)} \\
{\frac{1}{2}} & {\frac{1}{2}} & {\frac{1}{2}}
\end{array}\right]\left[\begin{array}{l}
{V_{a}} \\
{V_{b}} \\
{V_{c}}
\end{array}\right]


\left[\begin{array}{c}
{V_{a}} \\
{V_{b}} \\
{V_{c}}
\end{array}\right]=\left[\begin{array}{ccc}
{\cos (\theta)} & {\sin (\theta)} & {1} \\
{\cos \left(\theta-\frac{2 \pi}{3}\right)} & {\sin \left(\theta-\frac{2 \pi}{3}\right)} & {1} \\
{\cos \left(\theta+\frac{2 \pi}{3}\right)} & {\sin \left(\theta+\frac{2 \pi}{3}\right)} & {1}
\end{array}\right]\left[\begin{array}{l}
{V_{q}} \\
{V_{d}} \\
{V_{0}}
\end{array}\right]


θ required for the D-Q transform depends on the chosen reference frame as follows:

Because the Induction Machine is modeled in the rotor reference frame, the θ required for the dq0 transform is the rotor electrical angle (θr).


Induction Machine Electrical Model

Induction machine models in state space frameworks output winding currents and use magnetic fluxes as the state variables. They can be represented as follows:

\begin{aligned}
\phi[n+1] &=A_{d}[n] \phi(n)+B_{d}[n] u[n] \\
I[n+1] &=C[n+1] \phi[n+1]
\end{aligned}


where the coefficient matrices are defined as:


A_{d}=T_{s}\left(\text{-}R L^{-1}-\Omega\right)+I


B_{d}=T_s \times I


\boldsymbol{C}=\boldsymbol{L}^{-1}


and


\boldsymbol{u}=\left[\begin{array}{llll}
{V^r_{qs}} & {V^r_{ds}} & {V_{qr}^{r ^\prime}} & {V_{dr}^{r^\prime}}
\end{array}\right]^{t}


\boldsymbol{I}=\left[\begin{array}{llll}
{I^r_{qs}} & {I^r_{ds}} & {I_{qr}^{r ^\prime}} & {I_{dr}^{r^\prime}}
\end{array}\right]^{t}


\boldsymbol{\psi}=\left[\begin{array}{llll}
{\phi^r_{qs}} & {\psi^r_{ds}} & {\psi_{qr}^{r^\prime}} & {\psi_{dr}^{r^\prime}}
\end{array}\right]^{t}


\boldsymbol{R}=\left[\begin{array}{llll}
{R_{s}} & {R_{s}} & {R_{r}^{\prime}} & {R_{r}^{\prime}}
\end{array}\right]^{t}


L=\left[\begin{array}{cccc}
{L_{ls}} & {0} & {L_{m}} & {0} \\
{0} & {L_{ls}} & {0} & {L_{m}} \\
{L_{m}} & {0} & {L_{lr}^{\prime}} & {0} \\
{0} & {L_{m}} & {0} & {L_{lr}^{\prime}}
\end{array}\right]


\Omega=\left[\begin{array}{cccc}
{0} & {\omega} & {0} & {0} \\
{-\omega} & {0} & {0} & {0} \\
{0} & {0} & {0} & {\omega-\omega_{r}} \\
{0} & {0} & {-\left(\omega-\omega_{r}\right)} & {0}
\end{array}\right]



The Induction Machine is modeled in the rotor reference frame, so ω=ωr.

In the model, all the rotor parameters and variables are seen from the stator, distinguished by a prime sign. Since the squirrel-cage rotor type is not supplied by an external source, then it is always the case that 

V_{qr}^{r^\prime} = V_{dr}^{r^\prime} = 0

The electrical torque can be calculated as follows:

T_{e}=\frac{3}{2} p p\left(\psi_{d} i_{q}-\psi_{q} i_{d}\right)


Including a Zero Sequence Model

The Zero Sequence option allows the user to add a zero-sequence resistance and zero-sequence inductance modeling the system as unbalanced, which allows for better fidelity. By enabling this option, the zero-sequence inductance and the zero-sequence resistance can be specified allowing a wye with neutral or delta connection to the stator side of the machine.

When enabling this option, the three stator currents should be mapped to eHS.


In order to do this, the machine can be connected in wye or in Delta as shown in the following circuits:

Connecting the SCIM in wye

Connecting the SCIM in Delta