The Characteristic of Control Algorithms for an Induction Electromotor by the Parameters Change in Stator Winding Voltage

In this paper we study various control algorithms of electromagnetic torque and rotor rotation speed by parameters change in stator voltage for an induction electromotor.


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Abstract-In this paper we study various control algorithms of electromagnetic torque and rotor rotation speed by parameters change in stator voltage for an induction electromotor.

I. INTRODUCTION
The induction motors are very common because they are inexpensive and robust, finding use in everything from industrial applications such as pumps, fans and blowers to home appliances.Traditionally, induction motors have been run at a single speed, which was determined by the frequency of the main voltage and the number of poles in the motor.Controlling the speed of an induction motor is far more difficult than controlling the speed of a DC motor since there is no linear relationship between the motor current and the resulting torque as there is for a DC motor [1].Moreover, in contrast to dc motors, induction motors can be used for a long time without maintenance because of their brushless structures.
The least expensive and most widely spread induction motor is the squirrel cage motor.There is no current supply needed from outside the rotor to create a magnetic field in the rotor.This is the reason why this motor is so robust and inexpensive [2].
The technique called Vector control or Field Oriented Control can be used to vary the speed of an induction motor over a wide range.It was initially developed by Blaschke (1971Blaschke ( -1973) ) [3].In the vector control scheme, a complex current is synthesized from two quadrature components, one of which is responsible for the flux level in the motor, and another which controls the torque production in the motor.
The field Oriented Control was originally developed for high-performance motor applications that are required to operate smoothly over the full speed range, generate full torque at zero speed, and have high dynamic performance including fast acceleration and deceleration.However, it is becoming increasingly attractive for lower performance applications as well due to FOC's motor size, cost and power consumption reduction superiority [4].The vector control algorithm is based on two fundamental ideas.The first is the flux and torque producing currents [5].An induction motor can be modelled most simply (and controlled most simply) using two quadrature currents rather than the familiar three phase currents actually applied to the motor.These two currents called direct (id) and quadrature (iq) are responsible for producing flux and torque respectively in the motor.By definition, the Iq current is in phase with the stator flux, and Id is at right angles.Of course, the actual voltages applied to the motor and the resulting currents are in the familiar three-phase system.The move between a stationary reference frame and a reference frame, which is rotating synchronous with the stator flux, becomes then the problem.This leads to the second fundamental idea behind vector control.The second fundamental idea is that of reference frames.The idea of a reference frame is to transform a quantity that is sinusoidal in one reference frame, to a constant value in a reference frame, which is rotating at the same frequency.Once a sinusoidal quantity is transformed to a constant value by careful choice of reference frame, it becomes possible to control that quantity with traditional proportional integral (PI) controllers.

II. THE INFLUENCE OF STATOR VOLTAGE PARAMETERS ON MECHANICAL CHARACTERISTIC OF INDUCTION ELECTROMOTOR
The parameters of stator sinusoidal voltage are the active value U1 and the angular frequency  1 .Thus we can control the electromagnetic torque by the change of U1 and (or)  1 .
With the change of stator voltage active value U1 and constant angular frequency  1 , the induction electromotor critical torque MK varies proportionally to the voltage square U1 with a constant value of critical slip SK.The variation of angular frequency  1 with constant voltage value U1 will provoke the variation of critical torque but just a bit influences on the rotor current frequency critical value.
The induction electromotor mechanical characteristics in per-units system with separate variation of active voltage U1 and angular frequency  1 are represented in figure 1.

The Characteristic of Control Algorithms for an Induction Electromotor by the Parameters Change in Stator Winding Voltage
Frederic B. Motto, Roger Tchuidjan, Benoît Ndzana, Colince Tatsa Tchinda The deep regulation of induction electromotor speed by voltage reduction on stator winding will lead to the increase of rotor current frequency.With high rotor current frequency, the power losses will increase.(Figure 2) The deep regulation of induction electromotor speed by reduction of stator winding voltage frequency will lead to the increase of magnetization current and energy losses in stator windings.
Thus, to ensure high energy efficiency of induction electromotor control, with squirrel-cage rotor, it is necessary to have a mutual control of voltage amplitude and frequency on stator winding.

Control Algorithm with Maximal Energy Efficiency
In stationary functioning regime, the total electrical power losses in electromotor stator and rotor winding: From that equation, the active losses depend on angular rotor currents frequency.They have a minimum value: For The maximal factor value of energy efficiency for an induction electromotor with squirrel-cage rotor is expressed as follows: It is proved that the maximal possible value of energy efficiency of induction electromotor is: Thus, the maximal possible value of energy efficiency coefficient is: If we consider that the magnetic circuit of the machine is linear, then  2 is a constant value, and does not depend on the load.If we consider the non-linearity, then the main time constant value  0 is to be studied as a function of magnetization current.
The plot of dependence for power electric losses on rotor frequency current is shown in figure 2.
Finally, the construction algorithm of electromagnetic torque ensuring maximal energy efficiency is as follows: 1. We stabilize angular rotor currents frequency at the level  2 by varying the angular frequency of voltage such that  1 =  +  2 ; 2. We ensure the given electromagnetic torque by varying the voltage amplitude in stator winding.We shall express the condition of minimal losses in a different manner: Magnetization currents are: Consequently,  2 = √. 01 . 2 . 0 By replacing the expression  2 =  2 = 1/(√2. 0 ), we have the second condition: The electromagnetic torque of induction electromotor with stabilization of angular rotor currents frequency at the level  2 is defined by the expression: The set of mechanical characteristics with stabilization of angular rotor currents frequency at level  2 will have the aspect represented in figure 3. The active voltage value that can ensure the given electromagnetic torque is found by using the formula ( 2 The plots of stator voltage dependence on angular frequency  1 with  2 =  2 and various torque values are shown on figure 4. Finally, for the realization of control from the power losses point of view it is necessary to maintain the stator voltage less than nominal value   .
The plot of dependence that characterizes the decrease of energy efficiency of squirrel-cage induction electromotor with reduction of rotor currents frequency from  2 is shown in figure 5. Finally, the use of such control algorithm ensures minimal and constant electrical losses value is possible only for little rotor rotation frequencies or for little values of electromagnetic torque.That is why this control mode is not often applied.

III. THE CONTROL ALGORITHM WITH CONSTANT MAGNETIZATION CURRENT
This control algorithm has received a great expansion: 1) We stabilize the stator magnetization current at the level of nominal value by acting on voltage vector  ̇1; 2) We ensure the given torque by acting on angular voltage frequency  1 .
We study in details this mutual control of amplitude and voltage frequency in stator.For a fixed magnetization current value at  01 , the winding stator voltage is  1 =  01 .( 1 ,  2 ).
If we replace ( The induction electromotor mechanical characteristics with voltage variation according to (3) are shown in figure 7.

Fig. 1
Fig. 1 Mechanical Characteristics, obtained by varying voltage parameters windings a) amplitude; b) frequency

Fig. 4 .
Fig. 4. Stator Voltage dependences on stator currents frequency for fixed rotor currents frequency