# Practical Work of Three-Phased Induction Motor Modeling in a Classical Spreadsheet Software
## 2 Three-Phased Induction Motor
### Speed Variation and Variable Frequency Drives
#### 2.6.2 Vector Control  
Vector control is a generic term that designates all the controls taking into account, in real time, the equations of the system it controls. The real-time aspect is possible thanks to the sensors (position, speed, and torque) installed on the system. The equations obtained are much more complex than those of the scalar controls, but, on the other hand, they give better performance in transient states. There are vector controls for all types of AC machines, induction, and synchronous motors.  
Vector control is also called field-oriented control because this control method consists of transforming the stator currents into two orthogonal components, which can be considered as vectors. The first vector allows the adjustment of the magnetic flux of the motor, while the second regulates the torque. Their decoupling makes the motor operation similar to that of a DC motor.  
There are several variations of vector control that are used for synchronous and asynchronous machines. It was originally designed for applications requiring good performance from the motor: smooth operation over the entire speed range, maximum torque at zero speed, and good dynamic performance combined with rapid acceleration and deceleration. Currently, this technique has been democatized because it reduces the size of the brushless motor used in a system, and therefore its cost, as well as its electrical consumption. The Park transform is the keystone of flux-oriented control and to analyze and model synchronous and asynchronous machines [16; 17]. Its major contribution was to allow the replacement of linear differential equations by constant coefficients over time [18].  
The **hypotheses** that must be satisfied to use the Park transform to simplify the equations and allow the use of flux-oriented control are as follows:  
1. The flux varies linearly with the current (the magnetic circuit of the machine is not saturated).
2. Eddy current losses are neglected.
3. Currents, voltages, and fluxes are sinusoidal.
4. Leakage reactances are independent of the position of the rotor and are homogeneous.
5. The machine must be powered, as is performed in practice, by a three-phase voltage system without neutral, so that the homopolar component is zero. Vector control has the following **advantages**:  
1. It is based on the transient model, and it deals with the transient regimes that the classic drive could not do.
2. It is precise and fast.
3. There is torque control at standstill.
4. Control is conducted in amplitude, as well as in phase. It also has some **disadvantages**:It is expensive (incremental encoder, speed estimator, or digital signal processor). The processor must be able to calculate the algorithm approximately every millisecond.
2. Weak robustness to parametric variations, and particularly to those of the rotor time constant.
3. Requires a modulator for close control of the inverter, which causes delays, especially at low modulation frequencies (high power). These delays are responsible for the torque response time increase, which penalizes the drives used in traction.
4. The coordinate transformations depend on an estimated angle \(\theta_{s}\).
5. The rotational speed \(\Omega\) explicitly affects the control algorithm. When this speed is not measured, errors in the estimation of this speed degrade the performance of the drive.
6. Wrong parameters lead to a torque error.