CHAPTER-FIVESynchronous

Machines

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 2

Introduction A synchronous machine is an ac rotating machine

whose speed under steady state condition is proportional to the frequency of the current in its armature.

The magnetic field created by the armature currents rotates at the same speed as that created by the field current on the rotor, which is rotating at the synchronous speed, and a steady torque results.

Synchronous machines are commonly used as Generators especially for large power systems, such as turbine generators and hydroelectric generators in the grid power supply.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 3

Synchronous Generator

Facts Used principally in large power applications because of their

High operating efficiency Reliability Controllable power factor

Rotates at constant speed in the steady state

i.e. The rotating air gap field and the rotor rotate at the same speed.

It is a doubly excited machine

i.e. Rotor poles are excited by a DC current

Stator are connected to the ac supply It can draw leading or lagging reactive current from the ac

supply system.

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 4

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 5

Stator

Rotor+

Vf

-

If

If

If

N

RS

DC Machines

The DC excitation current in the stator generates a Resultant flux. and induced voltage in the rotor.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 6

Synchronous machines

Stator

Rotor+Vf-

If

If

N

RS

The DC excitation current in the rotor generates a flux. The turbine drives the rotor and produces a rotating flux The rotating flux induce AC three phase voltage in the

stator winding. The generated power of a synchronous machine can be

adjusted by controlling the magnitude of the rotor field current.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 7

Synchronous Machine StructuresStator and Rotor

1. The stator is termed as stationary armature where the generated power can be easily taken out. The armature winding of a conventional synchronous machine is almost invariably on the stator and is usually a three phase winding.

2. The rotor is the rotating member of the machine The field winding is usually on the rotor and excited

by dc current, or permanent magnets. The dc power supply required for excitation usually

is supplied through a dc generator This dc generator known as exciter, which is

often mounted on the same shaft as the synchronous machine.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 8

Rotor structures:There are two types of rotor structures 1. Salient pole rotor For low speed applications, such as hydroelectric

generators, Diesel Generator etc.2. Non-Salient pole (cylindrical) rotor

For high speed synchronous machines, such as steam turbine generators, Gas turbine, etc

Salient Pole rotor

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 9

Cont’d

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 10

Non-Salient(Cylindrical) Rotor

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 11

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 12

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 13

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 14

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 15

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 16

Mechanical and Electrical Angle1. Mechanical angle

Any angle Measured on the surface of a synchronous Machine is a Mechanical Angle.

Always the total Mechanical angle over the complete surface being 3600 or 2pi radian.

2. Electrical Angle The Generated Voltage depends on the number of

poles is called Electrical Angle.

MechElec

P2

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 17

Contd. Example, we consider a four pole machine. As the

rotor rotates for one revolution the induced

emf varies for two cycles and hence

For a general case, if a machine has P poles, the relationship between the electrical and mechanical units of an angle can be readily deduced as ,similarly,

Where is the angular frequency of electrical radians per second and the angular speed of the rotor in mechanical radians per second.

m

rotorofSpeedn

nandf m

:60

22

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 18

Synchronous Speed

The Synchronous speed defined as

It can be seen that the frequency of the induced emf is proportional to the rotor speed and this speed is called Synchronous speed

P

fN

NPf S

S 120

602

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 19

Distributed Three Phase Windings The stator of a synchronous

machine consists of a laminated electrical steel core and a three phase winding.

The stator lamination of a synchronous machine that has a number of uniformly distributed slots.

Coils are to be laid in these slots and connected in such a way that the current in each phase winding would produce a magnetic field in the air gap around the stator.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 20

Contd. Stator coils are connected to form a three phase

winding. Each phase is able to produce a specified number of magnetic poles.

The windings of the three phase are arranged uniformly around the stator periphery and are labeled in the sequence that phase ‘a’ is 120o(electrical) ahead of phase ‘b’ and 240o(electrical) ahead of phase ‘c’.

Phase a

Phase b

Phase c

120o

120o

120o

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 21

Contd. Stator windings are

sinusoidally distributed with Ns equivalent turns and their magnetic axes are displaced by 120o.

Where Ns: the number of turns of

the equivalent sinusoidally distributed stator windings.

s: the angular displacement about stator

as'

as

bs

bs'

as

bs

cs

cs' vas

vbs

vcscs

32

32

cos2

mmf

cos2

mmf

cos2

mmf

scss

cs

sbss

bs

sass

as

iN

iN

iN

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 22

Rotating Magnetic FieldsMagnetic Field of a Distributed Phase Winding The magnetic field distribution of a distributed phase winding can be

obtained by adding the fields generated by all the coils of the winding.

The mmf distribution along the air gap is a square wave. Because of the uniform air gap, the spatial distribution of magnetic field strength is the same as that of mmf.

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 23

Magnetic Field of Three Phase Windings

The resultant mmf generated by a three phase winding becomes

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 24

Graphical Analysis

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 25

Contd. The Resultant mmf wave has a constant

amplitude of 3/2 FM and rotates at constant Synchronous speed

Using Per-Phase Analysis the equivalent circuit of Synchronous Generator

DC

VtEsta Ista

Xsyn Rsta

Flux

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 26

Equivalent Circuit of Synchronous Machine

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 27

Contd. Consider the terminal

Voltage leads the current by Φ. Determine the Generated Voltage

Consider Triangle ONM

)(

0

Satg

t

jXRIVE

IIandVV

O

Vt

IaRa

IaXs

Eg

IaN

M

Φ

VtCos Φ IaRa

VtSinΦ

22

222

222

sincos

sincos

)()()(

Saaag

Saaag

XIVRIVE

XIVRIVE

NMONOM

ECEg3202:- Introduction to Electrical Machine By Dawit Habtu 28

Open- and Short-Circuit Characteristics The Short-Circuit -Ratio (SCR) is

the ratio of the field current Of ’=If1 needed to generate rated open-circuit Armature Voltage to the field current Of ’’=If2 needed to produce rated armature current

CSCR

Open- and short-circuit characteristics of a synchronous machine.

Ia1

Ia2=In

The SCR exactly equals the per unit synchronous reactance so that

2

1

f

f

I

ISCR

fISh

g

S

ups

I

E

phasepercurrentcctShort

phasepervoltagecctOpenZ

SCRX

0

..

1

ECEg3202:- Introduction to Electrical Machine By

Dawit Habtu 29