Cage induction motor#

The Cage induction motor block implements a generalized unsteady model of asynchronous motor with short circuit rotor, without taking saturation into account. The calculation uses a fixed two-axis system \(\alpha\beta\). The Clarke transformation is used to move to the corresponding coordinates (1):

\[ {U_{\alpha}}\:= \frac{2 \cdot U_A}{3}\ -\ \frac{U_B + U_C}{3} \]

(1)#\[ {U_{\beta}}\:= \frac{U_B - U_C}{\sqrt{3}} \]

The basic equations for flux coupling and voltage are (2):

\[ \vec{U_S} = R_S\vec{i}_S + \frac{d\vec{\Psi}_S}{dt} \]

\[ \vec{U_R} = R_R\vec{i}_R + \frac{d\vec{\Psi}_R}{dt} - jp\omega_r\vec{\Psi}_R \]

\[ \vec{\Psi}_S = L_S\vec{i}_S + L_m\vec{i}_R \]

(2)#\[ \vec{\Psi}_R = L_R\vec{i}_R + L_m\vec{i}_S \]

where:

\(L_S = L_{1s} + L_m , L_R = L_{1R} + L_m \) - stator and rotor natural inductances;

\(L_m\) - mutual inductance between stator and rotor;

\(\omega_r\) - rotor rotation frequency;

\(p\) - number of pole pairs.

The current, voltage and flux coupling parameters in these equations are in the form of a spatial vector.

The coupling of moment, flux coupling and current is described by the following equation (3):

(3)#\[ \vec{M} = k(\vec{\Psi} X \vec{i}) \]

The basic equation of an asynchronous motor motion is described by the law of moments equilibrium on the machine shaft (4):

(4)#\[ {J\frac{d\omega_m}{dt}}\:= M - M_C \]

where:

\(J\) - inertia moment on the machine shaft, taking into account the inertia of both the machine and the inertia of the working mechanism and the gearbox reduced to the shaft;

\(\omega_m\) - angular speed of the machine shaft;

\(M_C\) - resistance moment of the working mechanism, driven to the shaft.

1. Properties#

Property	Default value	Description	Units of measurement
Source frequency	50	Frequency of the power supply	Hz
Stator resistance	500e-3	–	Ohm
Stator leakage inductance	1e-3	–	H
Rotor leakage inductance	1.8e-3	–	H
Magnetizing inductance	50e-3	–	H
Rotor resistance	1	–	Ohm
Friction coefficient	100e-3	–	–
Inertia moment	1	Rotor moment of inertia	kg\(\cdot\) m\(^2\)
Number of magnetic pole pairs	1	Number of pairs of magnetic poles for stator winding	–

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
A	Input	-	В	Electronics
B	Input	-	В	Electronics
C	Input	-	В	Electronics
Applied torque	Input	External resistance torque on the shaft	N\(\cdot\) m	Automation
Angular frequency	Output	Angular frequency of rotation of the shaft	rad/s	Rotational motion
Electromagnetic torque	Output	The moment of force on the shaft created by the electromagnetic field of the machine	N\(\cdot\) m	Automation
Phase A current	Output	I\(_a\)	A	Automation
Phase B current	Output	I\(_b\)	A	Automation
Phase C current	Output	I\(_c\)	A	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports