# Practical Work of Three-Phased Induction Motor Modeling in a Classical Spreadsheet Software
## 2 Three-Phased Induction Motor  
### Composition and General Principles  
An induction motor is composed of two major components. 1. The **stator** of a three-phase motor (the most common in medium and high power motors) is, as its name suggests, _the static part_ of the induction motor. It mainly consists of the frame, bearings, bearing flanges, the fan cooling the motor, and the cover protecting the fan. 2. The **rotor** is the _moving part_ of the induction motor. Mechanically coupled to the mechanical load of the motor (an elevator lift, for example), it will create a torque capable of providing work for raising and lowering the elevator car. It mainly consists of a stack of thin discs insulated from each other and keyed to the rotor shaft in order to channel and facilitate the passage of the magnetic flux, as well as rotor electrical windings that \"watch\" the flux passing through them. Electrical windings can either take the form of a cast aluminum squirrel cage whose bars are trapezoidal in shape for standard asynchronous motors and closed laterally by two conductive \"flanges\", or three copper wire windings similar to those found in stator windings. These lead to more expensive motors, but they offer wider starting solutions. The stator currents create a rotating magnetic field in the stator. The rotational frequency of this field is determined by the frequency of the stator currents. Its rotational speed is proportional to the power supply frequency. The speed of this rotating field is called _synchronous speed_\(\Omega_{\mathrm{s}}\) and is expressed in rad/s. The synchronous speed is a function of the electrical network frequency \(f\) and the number of pairs of poles \(p\). The synchronousspeed is then always an integer sub-multiple of the power supply frequency. At 50 Hz, it is a sub-multiple of 3000 rpm: 3000, 1500, 1000, 750, etc. At 60 Hz, it is a sub-multiple of 3600 rpm: 3600, 1800, 1200, 900, etc. It is expressed by the following relationship:  
\[\Omega_{s}=\frac{60f}{p}\frac{2\pi}{60}=\frac{2\pi f}{p}. \tag{1}\]  
The rotor winding is therefore subject to the flux variations of the magnetic field. An induced electromotive force appears in the rotor windings and then creates rotor currents. The induced currents in the rotor are responsible for the appearance of a torque that tends to set the rotor in motion. This torque opposes the load torque, which is consistent with [PERSON]'s law and states that the induced EMF and current in the circuit oppose the change in magnetic flux, thus giving it the name of \"induction\" motor. The rotor therefore begins to rotate in an attempt to \"follow\" the stator field. The rotor rotational speed is denoted \(\Omega_{r}\) and is expressed in rad/s. This machine can also be said to be asynchronous because it is impossible, without the presence of an external drive, to reach the same speed as the stator field. In fact, there must be a difference in speed for this type of machine to work because it is the difference between the rotor and the stator field that causes the appearance of currents induced in the rotor--currents that create the rotor field. The speed difference between the rotor and the stator field is called _slip_. The division of this difference by the synchronous speed gives the slip \(s\). Slip is then the difference in speed between the rotor and the synchronous speed of the stator field, which is expressed as a relative quantity (in per unit, p.u.). It is given by the following:  
\[s=\frac{\Omega_{s}-\Omega_{r}}{\Omega_{s}}. \tag{2}\]  
When measurements are carried out to identify the characteristics of the machine, it is possible to reach the synchronous speed using a device comprising at least a second machine (a synchronous machine used as a motor, for example), which ensures the production of the necessary torque to maintain the rotation. This is what is performed in the _synchronism test_ or no-load test, which will be dealt with later in this paper.