Unit 4

Contents

Electrical Machines

Consider a stator of an electric motor where three-phase winding is physically distributed in the stator core in such a manner that winding of each phase is separated from other by 120o in space.

Although the vector sum of three currents in a balanced three-phase system is zero at any instant, but the resultant of the magnetic fields produced by the currents is not zero rather it will have a constant non-zero value rotating in space in respect to time.

The magnetic flux produced by the current in each phase can be represented by the equations given below. This is a similar representation of current is a three-phase system as the flux is phasal with the current.

ɸ R = ɸ m sin(wt)

ɸ Y = ɸ m sin(wt -120 0 )

ɸ B = ɸm sin(wt – 240 0 )

Where, φR, φY and φB are the instantaneous flux of corresponding Red, Yellow and Blue phase winding, φm amplitude of the flux wave. The flux wave in the space can be represented as shown below.

First consider the point 0.

ɸ R = ɸ m sin(0) = 0

The value of

ɸ Y = ɸ m sin(0 – 120 0) = ɸ m sin(-1200) = - ɸ m

The value of φB is

ɸ B = ɸm sin(0 – 240 0 )= ɸm sin (-240 0 ) = ɸ m

The resultant of these fluxes at that instant (φr) is 1.5φm which is shown in the figure below.

From the graphical representation of flux waves, consider the point 1, where ωt = π / 6 or 30o.

ɸ R = ɸ m sin(30) = ½ ɸ m

The value of

ɸ Y = ɸ m sin(30 – 120 0) = ɸ m sin (-90) = -ɸm.

The value

ɸ B = ɸm sin(30 – 240 0 ) = ɸ m sin (-210) = ½ ɸ m

The resultant of these fluxes at that instant (φr) is 1.5φm which is shown in the figure below. Here it is clear the resultant flux vector is rotated 30o further clockwise without changing its value.

Now, on the graphical representation of flux waves, we will consider the point 2, where ωt = π / 3 or 60o.

ɸ R = ɸ m sin(60) = ɸ m

The value of

ɸ Y = ɸ m sin(60 – 120 0) = ɸ m sin (-60) = - ɸm.

The value of

ɸ B = ɸ m sin(60 – 240 0) = ɸ m sin (-180) = 0

The resultant of these fluxes at that instant (φr) is 1.5φm which is shown in the figure below. It shows that the resultant flux vector is rotated 30° further clockwise without changing its value.

Now, consider the point 3, where ωt = π / 2 or 90o.

ɸ R = ɸ m sin(90) = ɸ m

The value of

ɸ Y = ɸ m sin(90 – 120 0) = ɸ m sin (-30) = - ɸm.

The value of

ɸ B = ɸ m sin(90 – 240 0) = ɸ m sin (-150) = -1/2 ɸ m.

The resultant of these fluxes at that instant (φr) is 1.5φm which is shown in the figure below. The resultant flux vector is rotated 30o further clockwise without changing its value.

In this way we can prove that the due to balanced supply applied to the three phase stator winding a rotating or revolving magnetic fields is established in the space.

Principle of operation of induction motor:

- When the 3Ф A.C supply is connected across the stator of induction motor, the current starts flowing through the stator wdg. i.ethe stator condition.
- Due to this current of flux (Ф) is established in the stator wdg. This flux (Ф) is alternating (changing) in nature. Thus this flux links with the rotor also, and a a Rotating Magnetic Field(RMF) is produced.
- This flux (Ф) induces emf in the rotor also. The RMF is produced in the air gap between stator and rotor.
- The rotor is rotating part which is till stationary, show the rotating magnetic field is cut by stationary rotor and an EMF is induced in the rotor winding. According to faraday's law of EMI the rotor EMF gives the rise to rotor current which opposes the main cause producing it according Lenz's law.

A Single-Phase Induction Motor consists of a single phase winding which is mounted on the stator of the motor and a cage winding placed on the rotor. A pulsating magnetic field is produced, when the stator winding of the single-phase induction motor shown below is energized by a single phase supply.

The word Pulsating means that the field builds up in one direction falls to zero and then builds up in the opposite direction. Under these conditions, the rotor of an induction motor does not rotate. Hence, a single-phase induction motor is not self-starting. It requires some special starting means.

If the 1 phase stator winding is excited and the rotor of the motor is rotated by an auxiliary means and the starting device is then removed, the motor continues to rotate in the direction in which it is started.

The performance of the single-phase induction motor is analysed by the two theories. One is known as the Double Revolving Field Theory, and the other is Cross Field Theory. Both the theories are similar and explain the reason to produce torque when the rotor is rotating.

Double Revolving Field Theory of Single- Phase Induction Motor

The double revolving field theory of a single- phase induction motor states that a pulsating magnetic field is resolved into two rotating magnetic fields. They are equal in magnitude but opposite in directions. The induction motor responds to each of the magnetic fields separately. The net torque in the motor is equal to the sum of the torque due to each of the two magnetic fields.

The equation for an alternating magnetic field is given as

b(α) = β max sin w t cos α -----------------------(1)

Where βmax is the maximum value of the sinusoidally distributed air gap flux density produced by a properly distributed stator winding carrying an alternating current of the frequency ω, and α is the space displacement angle measured from the axis of the stator winding.

SinA cosB = ½ sin(A-B) + ½ sin(A+B)

So, the equation (1) becomes

b(α) =1/2 β max sin (w t- α) + ½ β max sin (w t+ α) ------------(2)

The first term of the right-hand side of the equation (2) represents the revolving field moving in the positive α direction. It is known as a Forward Rotating field. Similarly, the second term shows the revolving field moving in the negative α direction and is known as the Backward Rotating field.

The direction in which the single -phase motor is started initially is known as the positive direction. Both the revolving field rotates at the synchronous speed. ωs = 2πf in the opposite direction. Thus, the pulsating magnetic field is resolved into two rotating magnetic fields. Both are equal in magnitude and opposite in direction but at the same frequency.

At the standstill condition, the induced voltages are equal and opposite as a result; the two torques are also equal and opposite. Thus, the net torque is zero and, therefore, a single- phase induction motor has no starting torque.

Separately excited dc motor has field coils similar to that of shunt wound dc motor. The name suggests the construction of this type of motor. Usually, in other DC motors, the field coil and the armature coil both are energized from a single source. The field of them does not need any separate excitation. But, in separately excited DC motor, separate supply Provided for excitation of both field coil and armature coil. Figure below shows the separately excited dc motor.

Here, the field coil is energized from a separate DC voltage source and the armature coil is also energized from another source. Armature voltage source may be variable but, independent constant DC voltage is used for energizing the field coil. So, those coils are electrically isolated from each other, and this connection is the specialty of this type of DC motor

In a separately excited motor, armature and field windings are excited form two different dc supply voltages. In this motor,

• Armature current Ia = Line current = IL = I

• Back emf developed , Eb = V – I Ra

where V is the supply voltage and Ra is the armature resistance.

• Power drawn from main supply , P = VI

• Mechanical power developed ,

Pm = Power input to armature – power loss in armature

Operating characteristics of Separately excited dc motor

Both in shunt wound dc motor and separately excited dc motor field is supplied from constant voltage so that the field current is constant. Therefore, these two motors have similar speed -armature current and torque – armature current characteristics. In this type of motor flux is assumed to be constant.

• Speed – armature current (N – Ia) characteristics: We know that speed of dc motor is proportional to back emf / flux i.e Eb / φ . When load is increased back emf Eb and φ flux decrease due to armature resistance drop and armature reaction respectively .However back emf decreases more than φ so that the speed of the motor slightly decreases with load.

• Torque – armature current ( τ – Ia) characteristics : Here torque is proportional to the flux and armature current . Neglecting armature reaction, flux φ is constant and torque is proportional to the armature current Ia . τ – Ia characteristics is a straight lien passing through the origin. From the curve we can see that huge current is needed to start heavy loads. So this type of motor do not starts on heavy loads.

Speed control of separately excited DC motor

Speed of this type of dc shunt motor is controlled by the following methods:

I. Field control methods: Weakening of field causes increase in speed of the motor while strengthening the field causes decreases the speed. Speed adjustment of this type of motor is achieved from the following methods:

II. Field rheostat control: – Here a variable resistance is connected in series with the field coil. Thus the speed is controlled by means of flux variation.

Reluctance control involving variation of reluctance of magnetic circuit of motor.

Field voltage control by varying the voltage at field circuit while keeping armature terminal voltage constant.

III. Armature control methods: Speed adjustment of separately excited DC motor by armature control may be obtained by any one of the following methods :

i. Armature resistance control: – Here, the speed is controlled by varying the source voltage to armature. Generally, a variable resistance is provided with the armature to vary the armature resistance.

ii. Armature terminal voltage control involving variation of variation of voltage in armature circuit.

Applications OF DC Motors

Separately excited dc motors have industrial applications. They are often used as actuators. This type of motors is used in trains and for automatic traction purposes.

The synchronous generator or alternator is an electrical machine that converts the mechanical power from a prime mover into an AC electrical power at a particular voltage and frequency.

The synchronous motor always runs at a constant speed called synchronous speed.

It works on the principle of Faraday laws of electromagnetic induction. The electromagnetic induction states that electromotive force induced in the armature coil if it is rotating in the uniform magnetic field.

The EMF will also be generated if the field rotates and the conductor becomes stationary. Thus, the relative motion between the conductor and the field induces the EMF in the conductor. The wave shape of the induces voltage always a sinusoidal curve.

Construction of Synchronous Generator

The rotor and stator are the rotating and the stationary part of the synchronous generator. They are the power generating components of the synchronous generator.

The rotor has the field pole, and the stator consists the armature conductor. The relative motion between the rotor and the stator induces the voltage between the conductor.

Applications of Synchronous Generator

- The three-phase synchronous generators have many advantages in generation, transmission and distribution.
- The large synchronous generators use in the nuclear, thermal and hydropower system for generating the voltages.
- The synchronous generator with 100MVA power rating uses in the generating station. The 500MVA power rating transformer use in the super thermal power stations.
- The synchronous generators are the primary source of the electrical power. For the heavy power generation, the stator of the synchronous generator design for voltage ratings between 6.6 kV to 33 kV.

References:

Getting Started in Electronics Book by Forrest Mims

Practical Electronics for Inventors, Fourth Edition Book by Paul Scherz and Simon Monk

Electronics for dummies Book by Cathleen Shamieh and Gordon McComb