3.EIR221_Transfor. & Elec. Machines R3.pdf

8/14/2019 3.EIR221_Transfor. & Elec. Machines R3.pdf

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EIR 211 /221

TRANSFORMERS & ELECTRICALMACHINES - NOTES

2013

Wilhelm Leuschner Pr Eng D Eng

DEPT. OF ELECTRICAL, ELECTRONIC &COMPUTER ENG.


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TRANSFORMERS (Zekavat Chapter 12)

ELECTRICAL MACHINES (Zekavat Chapter 13)(+ Notes / Summary)

1. Transformer Principles: Ideal & Practical Transformers1.1 Equivalent circuits1.2 Voltage, Current & Power Transformation1.3 Impedance transformation1.4 Regulation & Efficiency1.5 Types of transformers

2. Electrical Machines (Motors & Generators)2.1 DC Machines (Linear and Rotating)2.2 AC Machines

I Induction AC MachinesII Synchronous AC Machines

2.3 Electric Vehicles (cars)


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1. SINGLE & THREE PHASE TRANSFORMERS


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Impedance transformation through a transformer:Load impedance Z L as seen from the input V 1


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THREE PHASE TRANSFORMERS

The three phase transformer is connected to a three phase power source (e.g.power station or transmission line) on the Primary (input) side and to a threephase load (e.g. three phase motor, transmission line or any other threephase load on the Secondary (output) side.

A1 A1

a1 a1

Transformer A (same for B and C)

How to construct a three phase transformer in principle:

Take three single phase transformers A, B and C:

Xformer A: Primary connection: A1 a1 and Secondary Connection: A1 a1

Xformer B: Primary connection: B1 b1 and Secondary Connection: B1 b1

Xformer C: Primary connection: C1 c1 and Secondary Connection: C1 c1


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Three phase transformer connections:

1. Star Star Connection:

Primary (input to transformer): Connect a1, b1, and c1 together and call itN1

Secondary (output of transformer): Connect a1, b1 and c1 together andcall it N1

2. Delta Star Connection:Primary: Connect a1 and B1 together and call it B1, connect a2 to C1 andcall it C1, connect c1 and A1 together and call it A1Secondary: See 1. above

3. Star Delta Connection:Primary: See 1. aboveSecondary: : Connect a1 and B1 together and call it B1, connect a2 to

C1 and call it C1, connect c1 and A1 together and call it A1

Assignment: Show the schematic diagram of the complete three phasetransformer for 1. to 3. above.


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Practical Transformer


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Transformer Assignments

1. For an ideal transformer: Supply voltage v 1 = 230V 50Hz and primarywindings N 1 = 1000 and v 2 = 12V and i 2 = 6A:Calculate the number of secondary windings. 53 wCalculate the primary current. 318mA

Calculate the input and output power. 72VAWhat is the output frequency? 50Hz

2. For an ideal transformer: Supply voltage v 1 = 110V 60Hz and primarywindings N 1 = 500 and v 2 = 230V and i 2 = 10A:

Calculate the number of secondary windings. 1045 wCalculate the primary current. 20.9ACalculate the input and output power. 2300VAWhat is the output frequency? 50Hz

3. For an ideal transformer: Supply voltage v 1 = 48V 60Hz and i 2 = 5A:Primary windings = 100 and secondary windings is 50, calculate the loadimpedance as seen from the source. 19.2 Ohm


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4. For a practical transformer operating at input voltage of 200V and 50Hz we have:R

1= 10

, R

2= 2

L1 = 10mH, L 2 = 1mHLm = H, R c = 150k Load resistance = 100 N1 = 1000 windingsN2 = 100 windingsDraw the equivalent circuit and calculate Input and Output current; as well as theTransformer Efficiency and Load Voltage Regulation.


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2. AC & DC MACHINESDC MACHINES (MOTOR OR GENERATOR)

DC Linear Machine: Fundamentals for all electrical machines.

DC linear Generator:

Fixed homogeneous magnetic field B in a specific direction.Copper conductor cuts through the magnetic field in a directionperpendicular to the field, by a mechanical force f.

An e.m.f. is induced in the conductor, which creates a voltage if the

conductor is extended to form a continuous loop (with a load resistance orbattery in series.

The current in the loop induces a magnetic field around the conductor(right hand thumb rule).

The two magnetic fields interact to obtain a steady-state condition.The moving coil forms the armature of a linear DC Generator and themagnetic field is called the field of the generator.


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DC LINEAR MOTOR

The same construction as in 1.2 but now the supply a current to the coil(linear conductor).

This current induces a magnetic field around the conductor which reacts withthe static magnetic field B.

This creates a force on the conductor f in a specific direction.

The moving conductor is part of the armature of a linear DC Motor

Important equations: e = Blu -1. and f = Bli -2.Where: e is the e.m.f. (Voltage produced

f is the force in a specific direction

B is the magnetic field strength (which can be produced by a permanentmagnetic or electro-magnet)

l is the length of the conductor moving through the magneticfield

u is the speed of the conductor moving through the fieldi is the current flowing through the conductor


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ROTATING DC MACHINES

Important equations:

E = k - 3. and T = k Ia - 4.

Note: Rotational speed and torque T (i.s.o. u and f )

Two mechanical components: Stator (standing still) and Rotor (rotating

output shaft for driving something)Rotational movement. N r.p.m. ( N x 2 ) / 60 radians per second.

Stator coil on stator & Rotor coil on rotor

Note: Stator can be the Field or the Armatureand Rotor can be Field or Armature

The same DC machine can be used as Generator and Motor by changingthe field voltage or the torque direction

Series, Parallel, Series-Parallel connected DC machines(field relative to armature)

Data sheets: Torque as a function of Rotational Speed graphs


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AC MACHINES:

1. Induction Machine (Mainly used as AC motor)INDUCTION MOTOR: Two types - Manufactured differently

a. Squirrel cage induction motor: Field winding on the Stator & Armature

winding on the Rotor.The rotor conductors are solid copper or aluminium rods short-circuited atthe ends to look like a squirrel cage. No electrical connection to the Rotor(Stator) from outside.

Torque / Speed characteristic of the motor is fixed.Simple and inexpensive manufacturing.No wear on brushes or other components (only mechanical bearings).

b. Wound rotor induction motor: Field winding on the Stator - Armaturewindings on the Rotor.

The Armature resistance (windings on the rotor) can be varied as a functionof motor speed through external resistances connected via slip rings to therotor. The Torque / Speed curve of this induction motor can be varieddynamically.

More complex construction and therefore more expensive.


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Types of Induction Motors (Electrical supply to the motor):

Three phase - Most used machine in Industry:

Three phase electrical supply to the Field windings on the Stator produces afixed amplitude (constant) rotating Field i n the motor core to cut theArmature windings on the rotor.

Single phase induction motor has an oscillating field and needs an externalcapacitor to be switched into the circuit at zero speed to create a temporaryphase shift to create magnetic torque to start the rotor turning. After that thecapacitor has to be switched out.

This means a more expensive motor, limited life and oscillating magneticfield.

Mode of operation (see Characteristic Torque / speed diagram - specific for

each motor):Magnetic field of three phase motor rotates as a function of supplyfrequency and number of pole pairs (number of magnetic poles divide bytwo North & South): n = 60f / P p


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Example: 50 Hz supply and 2 pole pairs on the rotor (i.e. 2 North poles and 2South Poles) Then the rotating speed of the Field will be 1500rpm.

The rotating magnetic field on the Stator cuts the conductors when the supplyis switched ON. This induces e.m.f. in the rotor conductors and this in turncreates current to flow in the Armature (rotor) conductors/windings. Thesecurrents create magnetic fields that interact with the field of the fieldwindings on the Stator. The rotor starts moving but cannot reach thesynchronous speed of the field. This difference in speeds is called the slip ofthe motor. If the slip is zero i.e. speed of rotation of the Field and the speed ofthe rotor is the same and there is no field cutting the rotor coils/conductors,i.e. no Torque is produced. As the load Torque is increased the rotor will slowdown, slip increases and output torque increases.Torque/Speedcharacteristics of the Induction Motor and the load (pump, fan, hoist, etc.) hasto be super-imposed to determine the operating point and ascertain stableoperation (for increased or reduced load torque requirement).

Starting of induction motors: As the starting current in an induction motor is

very high (no field produced in the rotor yet to oppose the magnetic field inthe stator (Field) coils, one can use a Star/Delta starter to first switch thethree phase supply to a star connection to the motor (i.e. phase voltage to thefield coils) and the once it is running and creating sufficient rotor current, thesupply can be switched to a delta connection (i.e. line voltage across eachfield winding).


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2. SYNCHRONOUS MACHINES (Mainly used as AC Generators)2.1 Synchronous Motors: Always run at a constant speed

2.2 Synchronous Generators (alternators): Produce electrical power of a frequencydetermined by the speed of the generator and the number of pole pairs, e.g. ASynchronous generator used in a Hydro power station can run at low speed and stillproduce 50Hz by just increasing the number of magnetic polesf = ( P p x n ) / 60 For n = 750 rpm and P p = 4 pole pares we find f = 50 Hz (What happensif f = 60 Hz ?)

Operation of Synchronous generator (machine):The Armature windings (three phase mostly) are usually on the Stator The magnetic Field is usually produced by an electromagnet (DC supply) on the Rotorand can consist of 1,2, 3 or more pole pairs. The Field winding (magnet) on the rotor isthen rotated at a specific speed, called the synchronous speed (or close to it for agenerator)The current for the field winding on large generators is usually produced by a DCgenerator (Exciter) on the same shaft as the Synchronous Generator and connected tothe rotating field by slip rings and brushes.Torque/Speed characteristic of the Synchronous Motor:

As the speed is constant the motor can only produce output torque once it is running atconstant speed. The motor has to be brought to synchronous speed by other equipment.Over-excited synchronous motors: The phase angle of the supply current and the supplyvoltage can be made leading by supplying more field current to make E larger than Vfor the same mechanical output torque. This is equivalent to having a rotating

capacitor connected to the power system (power factor correction for many of theinduction motors on the system e.g. Sasol.


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Machine Analysis:DC MachinesEA = K m and T = K IA (for motor and generator action)

Figure: Generic Equivalent circuit for a separately excited DC machine (generator

and/or motor)


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The DC machine can change from a generator to a motor by simplychanging the direction of the torque (changing it from positive to negative)

in the diagram above.

Rotation direction is fixed:

Torque may be anti-clockwise: Then the machine acts as a DC Generator

and I A flows to the left (e.g. charging battery & E A > V or supplying power toa load))

Torque may be clock-wise: Then machine act as a DC Motor and I A flows tothe right. The supply voltage V is larger than E A

In both cases the electrical losses are I A 2 RA plus I F 2 RF

Note: I F does not change in value or directionNote: E A = K at all times

Note: For the Shunt DC machine: The field coil is connected inparallel with the supply voltage V


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3.EIR221_Transfor. & Elec. Machines R3.pdf