# Three Phase Induction Motors Engineering Essay

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Published: *Mon, 5 Dec 2016*

Three phase induction motors are one of the most widely used industrial machines. This is mainly due to their simplicity, high reliability and robustness. Although three phase induction motors have the same physical stator as a synchronous machine, they do have different rotor constructions. In addition, three phase induction motors are divided into two groups: squirrel-cage and wound rotor. The magnitude of the flux in the quadrature axis in the stator diminishes, so that the flux will be zero, but the speed is increased above the synchronous speed. The rotor current comes from rotor voltage, so the resultant backward rotating for the flux component provides the magnetomotive force (mmf) so the flux is positive in the quadrature axis. So, the speed at which the magnetic field rotates can be determined. If the motor is connected to rated frequency, the speed of the magnetic field is called the synchronous speed (Ns).

The following table shows the relationship between number of poles and synchronous speed when the frequency equals 50HZ.

Pole pairs

1

2

3

4

6

Number of poles

2

4

6

8

12

Synchronous speed

3000

1500

1000

750

500

Table (3.1) relationship between number of poles and synchronous

The relationship between number of poles and synchronous speed is inversely proportional.

3.2 Equivalent circuit of an induction motor.

The per phase equivalent circuit is very important for induction motors and can be used to provide a great deal of understanding and prediction of performance of the induction motor in a stable state. The induction motor needs to provide for operation on the induction voltage and current in the rotor circuit from the stator circuit (transformer action); this is because the voltage and current in the rotor circuit of an induction motor is basically a transformer operation. So the equivalent circuit of the induction motor is similar to the equivalent circuit of the transformer. (In the transformer, primary like the stator in the induction motor, secondary in the transformer like the rotor in the induction motor.

In an equivalent circuit per phase of an induction motor, as shown in figure (3.1), Rs and Rr are the stator and rotor winding resistance per phase. Ls and Lr are stator and rotor leakage inductance per phase. However, the aim of test and analysis is to be able to refer the rotor resistance and reactance to the stator circuit and thereby to drive an equivalent circuit referred to the stator.

Figure (3.1) induction motor per-phase equivalent circuits.

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

(3.12)

(3.13)

In this circuit between a and b apply Thevenin

Figure (3.3) Simplification of equivalent circuits of an induction motor

Open Circuit voltage” at ab

(3.14)

“Short Circuit supply”

(3.15)

(3.16)

(3.17)

(3.18)

Maximum occurs:

(3.19)

(3.20)

## .

## 3.3 Overview on control of Induction motors.

Induction motors with squirrel-cage motors are used in industry because the advantage of these types of motors is their relatively low cost and simple construction. Induction motors always work at a nearly constant speed. However, power electronic converts; it can work to vary the speed of an induction motor. The induction motor drives can be divided into groups based on their applications: (a) “Adjustable-speed drive. One important application of this drive is in process control by controlling the speed of fans, compressors, pumps”. (b) “Servo drive: by means of sophisticated control, induction motors can be used as servo drives in computer peripherals, machine tools, and robotics” [reference].

I would like to give a brief explanation of two methods that are used in the control of induction motors and I will go into more detail about these methods later. Vector control is a method of control of induction motors so the stator current is controlled in the field rotating reference using PWM inverter [Reference]. The rotor flux and stator flux linkages are represented by Î»ar (t) and Î»as(t) depends on the angle of the rotor Ó¨m because the mutual inductance between the stator windings and rotor windings position is connected. However, “the main reason for the q and d axis analysis in machines like the induction machines is to control them properly, for example: vector control [reference], the method of vector control of induction motor drives produces better dynamic performance than scalar control [reference]. The following block diagram shows the direct torque control system of an induction motor.

Figure (3.4) shows direct torque control of induction motors.

This alternative type of control of an induction motor is very simple and basic in terms of construction. It consists of a switch table, hysteresis controllers, flux estimator and torque. It is much easier to represent in a block diagram compared to the block diagram representing the vector control system due to the absence of coordinate transformation between the synchronous frame and stationary frame and also it does not need a pulse width. Direct torque control drives are controlled by the method of a close loop system without using a current regulation loop and are also related to use of a stationary d-q reference frame as well as having the d-axis aligned with the stator q axis. Moreover, “the flux and torque are controlled by the stator voltage space vector defined in this reference frame”[reference]. Scalar control is another method of control of induction motors and is also the first method of control before the vector control method. The advantage of this method is simple control and ease of use. The motor drive is described by three factors: (a) frequency (b) voltage (c) parameters of the motor and its power supply [reference]. The scalar variable is strictly one represented by magnitude alone. This method uses either close loop or open loop control and any feedback loop such as that for speed. This use of scalar quantities gives the basic characteristics of satisfactory steady state behaviour, but poorly controlled transient response.

## 3.4 Description of the Induction motor drive

Since a motor drive plays a big part in the control system, it is necessary to have some background information about it. In a typical induction motor drive, power electronic devices are used to operate AC motors at frequencies other than the supply one. It consists of two main sections, a controller to set the operating frequency and a three-phase inverter to generate the required sinusoidal three-phase system from a DC bus voltage.

Therefore, an induction motor requires a variable-frequency three-phase source for variable speed operation by using a power converter system consisting of a rectifier connected to an inverter through a DC link. The next figure shows a block diagram of the power circuit of a typical variable-frequency induction motor drive.

Figure (3.5) shows Variable-Frequency Induction Motor Drive

The rectifier converts the power grid AC voltage into a fixed DC voltage. An LC filter to provide a smooth DC voltage, which is then applied to the inverter input, filters out the harmonics.

## 3.5 Induction Motor Control Methods

## 3.5.1 Vector control

The vector control of induction motors has been widely used for high performance drives. There have been many studies developed and presented which allow an overview of vector control (reference). Many proposals for the theory of electric machines discuss using space vector control to represent sinusoidal distribution in the air gap and they also discuss types of control of ac drives including induction motor drives, permanent-magnet ac drives and switched reluctance drives (reference).

Induction motor drives have performance control as the same high performance four-quadrant DC drive. In 1960 field-oriented control (FOC) was used in the area of induction motors, but in the past decades, induction motors have been controlled by using scalar control methods like the voltage/hertz. However, this manner is an old way used before vector control in the area of induction machines, but it was an easy method of controlling an induction motor (Reference).

3.5.1.2 Concept of vector control

The concept of vector control of AC drives is related to a space phaser which provides a means of representing three phase variables in a machine, voltage, current and flux (Reference). Both flux and torque (DTC) are basically controlled by methods of closed loop; so are methods of control of an induction motor, using closed loop without current loop, similar to the conventional vector control drives (Reference). So the stator current will be utilizing transformation to the d q synchronize system and direct axis with the rotor flux space factor; therefore, the stator d q – axis current is controlled dependently and the d q-axis for rotor flux will be zero.

(3.21)

The relationship between the stator current, rotor flux and electromagnetic are shown by this equation:

(3.22)

Where

Is rotor flux linkage, Rr , Lr , Lr are rotor resistance, and Lm magnetizing inductance. (Reference).

However, the space vector in the three phase inverter will produce eight output states [1 0 0] switch states, upper in switch phase is represented by á and b- is closed and c are open. The eight space vector represented by V0 [ 0 0 0] and V7 [ 1 1 1 ] are null and continuing six are of equal magnitude and arranged 600 part in space diagram as shown in figure. (Reference).

Figure (3.6) shows witching voltage space vectors.

3.5.1.3 Control Characteristics

Vector control has allowed the dynamic performance of AC drives so that they better DC drives; the flux and the torque can be controlled separately by using vector control producing components of the supply current. The terminal voltage cannot be directly monitored, but can be using the dc link voltage and switching function of the inverter supplying the motor. Currently, the drive dynamic is largely used with the inverter control of the stator current of the induction machines; this in turn is determined by the supply voltage and inductance of the machine. The main features of the direct torque control (DTC) are direct control of the torque and flux, and indirect main control of voltages and currents. This type of control has a number of advantages: sinusoidal stator current and reduced torque oscillations; excellent torque dynamics; and the main advantage of (DTC) direct torque control, absence of coordinate transformations which related to vector control implementations. However, in this type of control there are some disadvantages: possible problems during starting and low speed operation and also during change in torque command; it also requires flux and torque estimators (Reference).

The vector control theory provides independent control between torque and flux; torque is controlled by the q-axis component of current if the flux is constant and oriented along the d-axis of the referred frame. The referred frame can be rotor flux-oriented control, stator flux-oriented control or air gap flux-oriented control. Thus, the phase angle and the modulus of the current or current vector have to be controlled. Figure 2.1(a), [Reference], shows the rotor angle ±r with respect to the stator. Since the vector control is to be implemented in the rotor flux oriented reference frame, the induction machine is fixed in that reference frame by rotating the variable as appropriate. Figure (3.7) shows that the rotor flux reference frame rotates at speed (angle ±e) with respect to the stator reference and the d-q axes are fixed to the rotor flux space phasor. This results in decoupling of the flux and torque which are separately controlled by stator direct-axis current ids and quadrature-axis current iqs. [Reference]

(B) Vector rotation Figure (3.7) (A) Rotor angle

## 3.5.2 Direct and Indirect Rotor Flux-Oriented Control

The vector controls can be divided into two groups, indirect and direct, for the indirect (slip frequency controlled) and the direct (field oriented). The characteristics of these two controllers have been considered to be the same, but there are some differences between these methods. However, the direct control type is a modern control theory and also has high performance and it is more well-known than indirect control (Reference).

In this two methods above are considered of voltage and current of a stator. The first method, indirect, is related to stator current control and the second method is related to stator voltage control. In both cases the system inputs are torque and flux reference which is required current values for isd and isq. Field oriented control to induction motor operation in a synchronously rotating d-q reference from that is aligned with one of the motor flux. So, control of the torque and flux is decoupled such as the d- axis component of the stator current and rotor flux magnitude and the q-axis component control , the output torque , where the ids stator current of d-axis component and is the rotor flux magnitude demand, so can be given in equation as

(3.23)

Where, Lm = magnetizing inductance.

For the q-axis component of the stator current iqs, the torque demand as

(T* em) so can be determined as the equation:

(3.24)

The d-axis of the synchronously rotating reference frame to be aligned with the rotor flux, the slip relation.

(3.25)

Direct rotor flux-oriented control (RFOC) has a control loop for flux where the measurement is performed using flux sensing coils (or Hall-effect devices) or by the flux model. In indirect rotor flux-oriented control (RFOC), the rotor flux angle is not measured but is estimated from the equivalent circuit model. One of the techniques for estimating the rotor flux angle (±e) is based on the slip relation, which requires measurement of the rotor speed () and slip frequency (). The slip frequency is dependant on rotor time constant (´r) and estimated rotor flux amplitude. This indicates that indirect methods are easier to implement since they do not require a flux model, but are less accurate. Nevertheless, if the model were perfect, the performance obtained would be identical to direct torque control. In [6], the relationships between direct and indirect approaches have been analyzed. It proves that they have the same control but have differences in coordinate of state variable, the rotor flux and stator currents. A new indirect vector control with an observer has been presented which has the same characteristic as the conventional direct torque control.

Figure (3.8) direct vector control

Figure (3.9) indirect vector control

3.5.3 Scalar control method

Scalar Control manner is related to AC machines and can use voltage fed-inverters. In addition, the scalar control is related to control of the magnitude of a variable only, also using of applications for constant voltage/hertz supply at the motor terminals are given constant air gap flux, so it could be that the stator voltage is dropped. (Reference) The scalar control methods are considered just for study state behaviour, but have poorly controlled transients. (Reference)

This method applies to use in either close loop or open loop, and in any feedback loop such as that of speed. The scalar control method was basically developed for study state operation. However, it is a method also used in variable speed applications. (Reference)

In this curve, the voltage and frequency are applied on the stator, therefore, when the supply frequency is constant, the speed will be constant, but the torque can be changing as the square of the applied voltage. I will give more details about scalar control in another chapter.

3.5.4 Comparison of vector control (VC) and scalar control (SC).

Induction machines are widely used in various industries as prime workhorses to produce rotational motions and forces. However, the squirrel-cage type is a simple and rugged electrical machine with low cost and minimal maintenance; this is reason that the squirrel-cage types are most widely used in industrial electrical motors [reference]. With regard to the scalar control methods for an induction machine, only the motor model is considered for steady state and the scalar control methods are controlled based of the induction motor, but this method will not give good performance transients for an induction motor and it is also poor in terms of dynamics; but the vector control methods considered above are valid for transient conditions and the vector control will give a dynamic performance far superior to that of scalar control [reference]. The scalar control method to control an induction motor is simple to execute and easy to programme, but the vector control is related to the varying magnitude and phase alignment of the vector quantities of the motor. Moreover, the scalar control is related to the voltage per hearts v/f control and is usually used for low cost drives where high dynamic performance is not a key requirement. The applications include fans, blowers and pumps where the applied load is known. In this method, the form is simple, the control does not require any sensors and the control algorithm can be implemented in a relatively low performance microprocessor. Vector control is related to a mathematical model which deals with voltage, current, flux torque and the motor parameters. We can control the instantaneous stator currents, control the magnitude and position is.

The following diagram shows a feedback control system for measuring currents.

When the controller has a fast response then is vector can be imposed on the stator rapidly.

Advantages and disadvantages of vector control and scalar control [reference]

Method

Advantages

Disadvantages

SC

Simplest method of obtaining variable speed.

Low cost and easy to implement solution.

Is widely used.

Is not as complicated as other control methods.

Poor transient performance and poor dynamic.

It cannot control torque directly.

The transit response such as control is not fast.

VC

For those d component and q component are two decouple components can be independently controlled by passing through separate PI controller.

This control method has an excellent torque and speed curve.

It has excellent dynamic performance.

Sensitive parameter variation use PI current regulators that decrease transient performance.

Is more complicated than any other control method.

Cannot control torque before transformation is done.

Table (3.2) advantages and disadvantages of scalar control and vector control

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