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.

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 | ||||

Name | Specifies the name of the machine model. | |||

Description | Specifies a description for the machine model. | |||

Motor Configuration | ||||
---|---|---|---|---|

Symbol | Units | Default | Description | |

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 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 Resistance | R_{s} | Ohm | 0.6 | Stator winding phase resistance |

Stator Leakage Inductance | L_{ls} | H | 0.00035 | Stator winding leakage inductance |

Mutual Inductance | L_{m} | H | 0.62 | Magnetizing inductance |

Rotor Resistance | R_{r}' | Ohm | 0.62 | Specifies the equivalent rotor winding resistance of phases A, B, and C, as seen from the stator. |

Rotor Leakage Inductance | L | H | 0.00547 | Specifies the equivalent rotor winding leakage inductance of phases A, B, and C, as seen from the stator. |

Pole Pairs | PP | 2 | Number of machine pole pairs | |

Initial Speed | ω_{0} | RPM | 0 | Describes the initial speed of the machine |

Solver Timestep | T_{s} | s | 4.81E-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 | ||

Zero-Sequence Resistance | R_{0} | Ohm | 0.0029069 | Describes the zero-sequence stator winding resistance. This component is enabled when Zero Sequence is set to Included. |

Zero-Sequence Inductance | L_{0} | H | 0.00030892 | Describes 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. | ||||

| 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
| |||

| 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 Name | Symbol | Type | Units | Default Value | Description |
---|---|---|---|---|---|

Stator Current Phase A | I_{a} | Output | A | 0 A | Phase A current measured at the stator terminal |

Stator Current Phase B | I_{b} | Output | A | 0 A | Phase B current measured at the stator terminal |

Stator Current Phase C | I_{c} | Output | A | 0 A | Phase C current measured at the stator terminal |

Stator Direct Axis Current | I^{r}_{ds} | Output | A | 0 A | Direct-axis current measured at the stator in the reference frame aligned with the rotor |

Stator Quadrature Axis Current | I^{r}_{qs} | Output | A | 0 A | Quadrature-axis current measured at the stator in the reference frame aligned with the rotor |

Stator Direct Axis Voltage | V^{r}_{ds} | Output | V | 0 V | Direct-axis voltage measured at the stator in the reference frame aligned with the rotor |

Stator Quadrature Axis Voltage | V^{r}_{qs} | Output | V | 0 V | Quadrature-axis voltage measured at the stator in the reference frame aligned with the rotor |

Stator Direct Axis Flux | Φ^{r}_{ds} | Output | Wb | 0 Wb | Direct-axis flux measured at the stator in the reference frame aligned with the rotor |

Stator Quadrature Axis Flux | Φ^{r}_{qs} | Output | Wb | 0 Wb | Quadrature-axis flux measured at the stator in the reference frame aligned with the rotor |

Rotor Current Phase A | I_{ar'} | Output | A | 0 A | Phase A current measured at the rotor as seen from the stator |

Rotor Current Phase B | I_{br'} | Output | A | 0 A | Phase B current measured at the rotor as seen from the stator |

Rotor Current Phase C | I_{cr'} | Output | A | 0 A | Phase C current measured at the rotor as seen from the stator |

Rotor Direct Axis Current | I_{dr}^{r'} | Output | A | 0 A | Direct-axis rotor current in the reference frame aligned with the rotor as seen from the stator |

Rotor Quadrature Axis Current | I_{qrr}' | Output | A | 0 A | Quadrature-axis rotor current in the reference frame aligned with the rotor as seen from the stator |

Rotor Direct Axis Voltage | V_{drr}' | Output | V | 0 V | Direct-axis rotor voltage in the reference frame aligned with the rotor as seen from the stator |

Rotor Quadrature Axis Voltage | V_{qrr}' | Output | V | 0 V | Quadrature-axis rotor voltage in the reference frame aligned with the rotor as seen from the stator |

Rotor Direct Axis Flux | Φ_{drr}' | Output | Wb | 0 Wb | Direct-axis rotor flux in the reference frame aligned with the rotor as seen from the stator |

Rotor Quadrature Axis Flux | Φ_{qrr}' | Output | Wb | 0 Wb | Quadrature-axis rotor flux in the reference frame aligned with the rotor as seen from the stator |

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

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:

- Rotor reference frame: θ=θ
_{r}, - Stationary reference frame: θ=0,
- Synchronous reference frame: θ=θ
_{e}.

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

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) |

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: