# Squirrel Cage Induction Machine

## Description

Squirrel Cage Induction Machine

A three-phase Squirrel Cage Induction Machine (IM). In this model, the parameter slip dependency can be modeled using a piecewise linear approximation. Often two-axis rectangular coordinate is employed to represent the machine dynamics. When the coordinate is fixed on the stator, it is called being in a stationary reference frame (αβ reference frame). Meanwhile, when the coordinate rotates in the synchronized speed with the excitation from the stator, it is called being in a synchronous reference frame (dq reference frame). All equations in this document are also expressed in the stationary reference frame.

### Electrical model and equations

Where v_sαis α-axis stator voltage [V], v_sβ is β-axis stator voltage[V], i_sα is α-axis stator current[A], i_sβ is β-axis stator current[A], i_rα is α-axis rotor current[A], i_rβ is β-axis rotor current[A], R_s is Stator resistance[Ω], R_r is Rotor resistance[Ω], ω is Rotor speed in electrical angle[rad / sec], ϕ_sα is α-axis stator flux[Wb], ϕ_sβ is β-axis stator flux[Wb], ϕ_rα is α-axis rotor flux[Wb], ϕ_rβ is β-axis rotor flux[Wb],

The magnetic flux in induction motors can be represented using the inductance as follows. $$ \phi_{s\alpha} = L_s i_{s\alpha} + L_m i_{r\alpha} $$

Where L_s is Stator self-inductance[H], L_r Rotor self-inductance[H], L_m is Mutual inductance across from the stator to the rotor[H]

### Electromechanical equations

Electro-magnetic torque:

Mechanical rotational speed \Omega:

## Library

Electrical > Motors

## Pins

Name | Description |
---|---|

Pin_A | Phase A (Electrical) |

Pin_B | Phase B (Electrical) |

Pin_C | Phase C (Electrical) |

Pin_R | Rotor (Rotational Mechanical) |

Pin_Angle | Rotor Angle in radians (Control) |

## Parameters

Name | Description |
---|---|

Rs | Stator Winding Resistance [Ohm] |

Ls | Stator winding leakage inductance [H] |

Rr | Rotor resistance [Ohm] |

Lr | Rotor leakage inductance [H] |

Lm | Magnetizing inductance [H] |

J | Rotor Inertia [kg.m²] |

B | Rotor Friction Coefficient [N.m/(rad/s)] |

InitialCurrent | Initial Current Vector [IA IB IC] |

NPP | Number of pole pairs |