in the name of god the most compassionate, the most...

Electric Machines I

In The Name of God The Most Compassionate, The Most Merciful

2017 Shiraz University of Technology Dr. A. Rahideh

2

Table of Contents1. Introduction to Electric Machines

2. Electromagnetic Circuits

3. Principle of Electromechanical Energy Conversion

4. Principle of Direct Current (DC) Machines

5. DC Generators

6. DC Motors


3

Chapter 5Direct Current (DC) Generators

5.1. Different Types of DC Machines

5.2. Basic Relations

5.3. Armature Reaction

5.4. Operating Characteristics of DC Generators

5.5. Parallel Connection of DC Generators


4

Different Types of DC GeneratorsBase on the magnetic field production, DC generators are classified as1. Separately excited DC generators: a separate voltage source

(from the generator terminal) is required for field production.2. Shunt DC generators: field winding is connected in parallel to

the generator terminal (armature winding).3. Series DC generators: field winding is connected in series with

the armature winding.4. Cumulative compound DC generators: both series and parallel

field windings are used and their magnetic fields are added together. It is further divided as long shunt and short shunt.

5. Differential compound DC generators: both series and parallel field windings are used and their magnetic fields are subtracted from each other. It is divided as long shunt and short shunt.2017 Shiraz University of Technology Dr. A. Rahideh

5

Specifications of DC GeneratorsDC generators have the following specifications:

1. Nominal terminal voltage

2. Nominal power (nominal terminal current can be obtained from the first two items)

3. Efficiency

4. Nominal rotational velocity

5. Voltage regulation (VR) 100

fl

flnl

VVV

VR


6

Prime movers• The mechanical power to a DC generator can be provided by a

prime mover.

• The prime movers can be 1. Steam turbines2. Gas turbines3. Hydro turbines4. Diesel engines5. Electric motors

• In this chapter, it is assumed that the rotational velocity of the generators is constant, unless otherwise mentioned.


7

Separately Excited DC GeneratorsThe schematic diagram of the separately excited dc generator:

The simplified schematic diagram:

fV

aI

+

_

tV

fI

+ _

Field winding

Armature circuit

IL

N S +

Ia

Field winding Armature winding

_

+

_

If


8

Separately Excited DC GeneratorsThe equivalent circuit of the separately excited dc generator:

ra is the armature winding resistancerf is the field winding resistanceIa is the armature currentIf is the field currentIL is the load currentVt is the generator terminal voltage (load voltage)Vf is the field winding voltageEa is the induced voltage in the armature winding

fV

aI

+

_

tV fI

+ _

LI

aE

ar fr

La II aaat rIEV kEa fff rIV fI


9

Armature Induced VoltageInduced voltage in a single loop is expressed as:

is the rotational velocity in rad/s is the magnetic flux of each polep is the number of poles

The induced voltage in the armature winding having N turns and aparallel paths is obtained as:

Z is the total number of conductorsN is the total number of turnsa is the number of parallel paths

plrplr

lrA

lrBlvBE

/22

222

apZE

aZE

aNEa 22

apZk2

kEa


10

Shunt DC GeneratorsThe schematic diagram of the shunt dc generator:


IL

N S

Ia


+

_

If

aI

+

_

tV

fI

LI


11

Shunt DC GeneratorsThe equivalent circuit of the shunt dc generator:

aI

+

_

tV

fI

LI aI

+

_

tV

fI LI

aE

ar

fr

fLa III

aaat rIEV kEa

f

tf r

VI

fI


12

Voltage-Making of Shunt DC Generators

• Assume a shunt DC generator is rotated using a prime mover under no‐load condition.

• In the starting point (when the rotational speed is still zero) the terminal voltage is zero;

• Therefore, the field current ( If ) is zero and no field can be produced.

• Consequently no emf is induced.• The question is how the terminal voltage can be made?• Residual flux is behind the voltage‐making.• Residual flux produces a small emf.• Small emf causes small terminal voltage.• Small terminal voltage flows small field current.• Small field current increases the flux and so on.

aI

+

_

tV

fI

LI

kEa

resa kE


13

Series DC GeneratorsThe schematic diagram of the series dc generator:


If

IL

N S

Ia


+

_

aI

+

_

tV

fI

LI


14

Series DC GeneratorsThe equivalent circuit of the series dc generator:

Lfa III

saaat rrIEV

kEa

af II

aI

+

_

tV

fI

LI aI

+

_

tV

fI LI

aE

arsr


15

Compound DC GeneratorsShort-shunt

The simplified schematic diagram of the short‐shunt compound dc generator:

aI

+

_

tV fI

LI

Series field Shunt field

Cumulative Differential


16

Compound DC GeneratorsShort-shunt

The equivalent circuit of the short‐shunt compound dc generator:

faL III

Lsaaat IrIrEV

kEa

alDifferenti

CumulativeLsfsh IkIk

aI

+

_

tV

fI

LI

aE

ar

fr

sr

f

aaaf r

IrEI


17

Compound DC GeneratorsLong-shunt

The simplified schematic diagram of the long‐shunt compound dc generator:

aI

+

_

tV fI

LI

Series field Shunt field

Cumulative Differential


18

Compound DC GeneratorsLong-shunt

The equivalent circuit of the long‐shunt compound dc generator:

faL III

saaat rrIEV

kEa

alDifferenti

Cumulativeasfsh IkIk

f

tf r

VI

aI

+

_

tV

fI

LI

aE

ar

fr

sr


19

Cumulative vs. Differential Compound DC Generators

• If the direction of the fields produced by the series and shunt field windings are the same, the generator is cumulative;

• Otherwise it is differential.

• Effective magneto‐motive force (MMF) is calculated as

whereThe number of turns of shunt field windingThe number of turns of series field winding

ATD Ampere turn demagnetizing

alDifferenti

CumulativeATDININMMF ssffeffective

fNsN


20

Power Flow in DC Generators• In dc generators the input power is mechanical (torque

multiplied by rotational speed)

• In dc generators the output power is electrical (voltage multiplied by current)

aaIEPP lossesmechmech

TPP mechin

LtLelecout IVPPP

Input mechanical power Mechanical losses

elecaa PPPPPIE lossesfieldlossescorelossesbrushlosses armature

Ohmic losses due to armature winding

Brushes losses Ohmic losses due to field windings

Core losses


21

DC GeneratorsExample 1: Consider a separately excited DC generator with

a) If the field current is reduced to 2.4 A, but the rotational velocity remains unchanged, calculate the emf ( Ea ).

b) If the field current is reduced to 2.1 A, and the rotational velocity is increased to 1600 rpm, calculate the emf ( Ea ).

c) If at the rotational velocity of 1200 rpm, the emf is 120 V, calculate field current ( If ).

d) If emf is 160 V and field current is 2.2 A, calculate the rotational velocity ( n ).

V151aE rpm1450n A8.2fI

Separately Excited


22

DC GeneratorsSolution 1: separately excited DC generator

a) If the field current is reduced to 2.4 A, but the rotational velocity remains unchanged, calculate the emf ( Ea ).

considering the linear core.


kEaˆ nIkE fa

11

22

1

2

nIknIk

EE

f

f

a

a 1

2

1

212 n

nII

EEf

faa

V4.12914501450

8.24.21512 aE


Separately Excited

23


b) If the field current is reduced to 2.1 A, and the rotational velocity is increased to 1600 rpm, calculate the emf ( Ea ).

Note that emf is directly proportional with the field current and rotational velocity.


1

2

1

212 n

nII

EEf

faa V125

14501600

8.21.21512 aE


Separately Excited

24


c) If at the rotational velocity of 1200 rpm, the emf is 120 V, calculate field current ( If ).

Note that field current is directly proportional with the emf but inversely proportional with the rotational velocity.


11

22

1

2

nIknIk

EE

f

f

a

a 2

1

1

212 n

nEEII

a

aff

A7.212001450

1511208.22 fI


Separately Excited

25


d) If emf is 160 V and field current is 2.2 A, calculate the rotational velocity ( n ).

Note that rotational velocity is directly proportional with the emfbut inversely proportional with the field current.


11

22

1

2

nIknIk

EE

f

f

a

a 2

1

1

212

f

f

a

a

II

EEnn

rpm19552.28.2

15116014502 n


Separately Excited

26

DC GeneratorsExample 2: Consider a separately excited DC generator with the following values for nominal power, nominal terminal voltage and armature resistance:

a) If the generator supplies the nominal load under the nominal voltage, calculate the emf ( Ea ) and the armature current ( Ia ).

b) If the voltage terminal remains 250 V but the load decreases to 40 kW, calculate the emf ( Ea ).

c) If the load is 40 kW and emf is 255 V, calculate the terminal voltage( Vt ).

d) If the terminal voltage is 253 V and emf is 257 V, calculate load power ( PL ).

kW50nP V250ntV 025.0ar


Separately Excited

27

DC GeneratorsSolution 2: a separately excited DC generator with

a) If the generator supplies the nominal load under the nominal voltage, calculate the emf ( Ea ) and the armature current ( Ia ).


fV

aI

+

_

tV

fI

+ _

LI

aE

arfr

Load

V250 ntt VV

kW50 nL PP

A200250

50000 aL II

V255200025.0250 aata IrVE


Separately Excited

28


b) If the voltage terminal remains 250 V but the load decreases to 40 kW, calculate the emf ( Ea ).


fV

aI

+

_

tV

fI

+ _

LI

aE

arfr

Load

V250tV

kW40LP

A160250

40000 aL II

V254160025.0250 aata IrVE


Separately Excited

29


c) If the load is 40 kW and emf is 255 V, calculate the terminal voltage( Vt ).


fV

aI

+

_

tV

fI

+ _

LI

aE

arfr

Load

V255aE

kW40LP

taL V

II 40000

aata IrVE t

t VV 40000025.0255

010002552 tt VV

accepted)(NotV4

(Accepted)V251tV


Separately Excited

30


d) If the terminal voltage is 253 V and emf is 257 V, calculate load power ( PL ).


fV

aI

+

_

tV

fI

+ _

LI

aE

arfr

Load

V257aE

V253tV

a

taaL r

VEII aata IrVE

W40480160253 LtL IVPA160025.0

253257

LI


Separately Excited

31

DC GeneratorsExample 3: Consider a series DC generator with the following values for nominal power, nominal terminal voltage and series field resistance:

a) If the armature current is the nominal current and the terminal voltage is also nominal and emf is 137 V, calculate the armature resistance ( ra ).

b) If the terminal voltage is nominal but the load is 75% of nominal load, calculate the emf ( Ea ).

c) If the load is 8 kW and emf is 136 V, calculate the terminal voltage ( Vt ).

kW10nP V125ntV 05.0sr

Series


32

DC GeneratorsSolution 3: a series DC generator

a) If the armature current is the nominal current and the terminal voltage is also nominal and emf is 137 V, calculate the armature resistance ( ra ).


aI

+

_

tV

fILI

aE

arsr

Load

A80125

10000

nt

nna V

PI

15.080

125137

a

tasa I

VErr

1.015.0 sa rr


Series

33


b) If the terminal voltage is nominal but the load is 75% of nominal load, calculate the emf ( Ea ).


aI

+

_

tV

fILI

aE

arsr

Load

A60125

1000075.0

t

La V

PI

saata rrIVE

V13405.01.060125 aE


Series

34


c) If the load is 8 kW and emf is 136 V, calculate the terminal voltage ( Vt ).


aI

+

_

tV

fILI

aE

arsr

Load

tt

La VV

PI 8000

saata rrIVE

15.08000136 t

t VV

012001362 tt VV

accepted)(NotV5.9

(Accepted)V5.126tV


Series

35

DC GeneratorsExample 4: Consider a shunt DC generator with the following values for nominal power, nominal terminal voltage armature resistance and field resistance:

An electrical load under nominal voltage is connected to the generator and emf is 267 V. Calculate the load power and the efficiency of the machine.

kW30nP V250ntV 12.0ar 40fr


Series

36

DC GeneratorsSolution 4: Consider a shunt DC generator with


Shunt

40fr

V250 ntt VV V267aE

aI

+

_

tV

fI

LI

aE

ar

fr

Load

A7.14112.0

250267

a

taa r

VEI

A25.640250

f

tf r

VI

A45.135 faL III

?LP ?

W5.3386245.135250 LtL IVP


37

DC GeneratorsSolution 4: Consider a shunt DC generator with

Neglecting the mechanical losses,the input power is calculated as

kW30nP V250ntV 12.0ar 40fr

V250 ntt VV V267aE

aI

+

_

tV

fI

LI

aE

ar

fr

Load

?LP ?

W5.33862 Lout PP

W9.378337.141267 aain IEP

%5.899.37833

33862.5100% in

out

PP


Shunt

38

DC GeneratorsExample 5: Consider a cumulative long‐shunt compound DC generator with the following values for nominal power, nominal terminal voltage series field resistance and shunt field resistance:

At the nominal condition (load power and terminal voltage are nominal), the input power to the generator is 103.5 kW. Calculate the armature resistance.


Cumulative compound

200fr


39

DC GeneratorsSolution 5: Consider a cumulative long‐shunt compound DC generator with

kW100nP V600ntV 02.0sr 200fr

kW100 nL PP V600 ntt VV kW5.103inP ?ar

aI

+

_

tV

fI

LI

aE

ar

fr

sr

Load

A7.166600

100000

t

LL V

PI

A3200600

f

tf r

VI

A7.169 fLa III


Cumulative compound

40

DC GeneratorsSolution 5: Consider a cumulative long‐shunt compound DC generator with

kW100nP V600ntV 02.0sr 200fr

kW100 nL PP V600 ntt VV kW5.103inP ?ar

aI

+

_

tV

fI

LI

aE

ar

fr

sr

Load

A7.166LI A3fI A7.169aI

aain IEP V6107.169

103500

a

ina I

PE

059.07.169600610

a

tasa I

VErr

039.0059.0 sa rr


Cumulative compound

41

Armature Reaction (AR)• The influence of the magnetic field due to armature current on

the main field due to field winding current is called armature reaction.

• Assume there is no current in the armature winding (no‐load condition), therefore the field is only produced by the field winding current.

If

N S Bf


42

Armature Reaction (AR)• Now assume armature winding carrying currents, therefore the

field due to armature current interferes with that due to field winding current.

If

Bf Ba


43

Armature Reaction (AR)

N S Ba

Bf

Ba Bf

Bf + Ba

Neutral axis

New neutral

axis


44

Armature Reaction (AR)There are two armature reactions:1. Latitudinal armature reaction:

It means the neutral axis displacement. The displacement in the generating mode is in the direction of motion and in the motoring mode is in the opposite direction of motion.

2. Longitudinal armature reaction: The flux density under one edge of each pole increases and under the other edge decreases. The increase may saturate one edge of the pole and this effect is known as longitudinal AR or armature reaction demagnetization.

N S Ba

Bf

Ba Bf

Bf + Ba

Neutral axis

New neutral

axis


45

Methods to Improve Commutation1. Brushes displacement

(load dependent)

2. Increase in the brush connection resistance (higher ohmic loss)

3. Using inter‐poles (higher cost)

4. Using compensating windings (higher cost)

Field

windingArmature winding

Rotor

Stator

Inter-pole

Commutator

Compensating winding

Pole-shoe

Brush


46

Compensating Windings• Compensating windings reduce the

armature reaction.

• The armature current flows in the compensating windings.

• Ampere‐turn of compensating windings in each pole is expressed as:

(1)Where Zcw is the number of compensating conductors, Ia is the armature current.

Inter-pole


acw

cw IZAT2


47

Compensating Windings• The ampere‐turn of armature

windings under each pole is expressed as:

(2)

Where Z is the total armature conductors, a is the number of parallel paths and p is the number of poles.

Inter-pole


aa MMFATpitchPolearcPole

aI

pZAT a

a 2pitchPolearcPole


48

Compensating Windings• To minimize the armature reaction,

the ampere‐turn of compensating windings should be equal to that of armature windings but in opposite direction.

(1)

(2)

Inter-pole


aI

pZAT a

a 2pitchPolearcPole

acw

cw IZAT2

acw ATAT pa

ZZcw pitchPolearcPole


49

Compensating WindingsExample: Consider a DC machine with 14 poles, 400 V, 2000 kW, having lap winding and 1100 conductors. Pole arc per pole pitch ratio is 0.7. Calculate the number of compensating conductors in each pole to have a uniform air‐gap flux density under each pole.

paZZcw pitchPole

arcPole

14p 14aLap winding

1100Z

41414

11007.0

cwZ


50

Inter-polesExample: Consider a DC generator with 6 inter‐poles, 600 V, 600 kW, having lap winding and 696 conductors. Calculate the number of turns of each inter‐pole if the MMF of inter‐poles is 1.25 times higher than that of armature.

The current of inter‐poles is the same as armature current (Ia).

aMMFMMF 25.1poleinter

6p 6aLap winding

696Z

12662

69625.1poleinter

NaI

pZIN a

a 225.1poleinter


51

Operating Characteristics of DC Generators

1. No‐load Characteristics (Magnetic Characteristics): No load terminal voltage vs. field currentGenerator speed is kept constant.

2. Full‐load Characteristics: Full‐load terminal voltage vs. field currentGenerator speed and load current are kept constant.

3. External Characteristics: Terminal voltage vs. load currentGenerator speed and field current are kept constant.

4. Armature‐reaction CharacteristicsField current vs. load currentGenerator speed and terminal voltage are kept constant.

fa IE

ft IV

Lt IV

Lf II


52

Operating Characteristics of Separately Excited DC Generators

The following circuit is used to obtain the characteristics of a separately excited DC generator:

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR


53


1. No‐load Characteristics (Magnetic Characteristics): No load terminal voltage vs. field current

fa IE

)A(fI

(V)aE

Procedure: • Switches S1 and S2 are both open.• Generator is rotated at the nominal

speed.• Due to the residual flux, a small voltage

appears on the terminal.• Rf is set to its maximum value and S2 is

closed.• Rf is gradually and monotonically

decreased and the terminal voltage and field current are recorded.

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR

ctenr


54


2. Full‐load Characteristics: Full‐load terminal voltage vs. field current

ft IV

Procedure: • Switches S1 and S2 are both open.• Generator is rotated at the nominal speed.• Load resistance is set to its minimum (zero)

and Rf is set to its maximum value.• Switches S1 and S2 are closed.• Load resistance is increased and Rf is

gradually decreased so that the load current always remains at nominal value.

• The terminal voltage and field current are recorded.

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR

ctenr

)A(fI

(V)tV

cteIL


55


3. External Characteristics: Terminal voltage vs. load current

Lt IV

Procedure: • Switches S1 and S2 are both open.• Generator is rotated at the nominal speed.• S2 is closed and Rf is set so that to have

nominal terminal voltage.• Load resistance is set to its maximum value

and S1 is closed.• Load resistance is decreased and field current

is kept unchanged.• The terminal voltage and load current are

recorded.

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR

ctenr cteI f

(A)LI

(V)tV

Ohmic drop AR drop


56


4. Armature‐reaction CharacteristicsField current vs. load current

Lf II



and S1 is closed.• Load resistance is decreased and field current

is increased to keep the terminal voltage unchanged (always nominal value).

• The load current and field current are recorded.

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR

ctenr cteVt

(A)LI

(A)fI


57

Operating Characteristics of Shunt DC Generators

The following circuit is used to obtain the characteristics of a shunt DC generator:

LIS1

_

tVfI Variable

load V

A+

S2 A

fR

aI


58

Starting of Shunt DC Generators• Shunt DC generators use the

terminal voltage to excite the field circuit.

• At starting situation there is a small terminal voltage due to residual flux which slightly excites the field circuit.

• The small voltage causes a small field current.

• The small field current in addition to residual flux increase the terminal voltage.

• It continues to reach to the normal operating point.

)A(fI

(V)aE cR fR

cf RR


59

Starting of Shunt DC GeneratorsA shunt DC generator may not make voltage due to one of the following reasons:1. Lack of residual flux. The shunt

generator should be started in separately excited mode.

2. The flux due to the field circuit is in opposite to the residual flux.

3. The field resistance is greater than critical resistance (Rc).

)A(fI

(V)aE cR fR

cf RR


60


1. No‐load Characteristics (Magnetic Characteristics): No load terminal voltage vs. field current

fa IE

)A(fI

(V)aE

Procedure: • Switches S1 and S2 are both open.• Generator is rotated at the nominal

speed.• Due to the residual flux, a small voltage

appears on the terminal.• Rf is set to its maximum value and S2 is

closed.• Rf is gradually and monotonically

decreased and the terminal voltage and field current are recorded. ctenr

LIS1

_

tVfI Variable

load V

A+

S2 A

fR

aISimilar to separately excited


61


2. Full‐load Characteristics: Full‐load terminal voltage vs. field current

ft IV

Procedure: • Since Vt and If are, respectively, the

voltage and current of the field resistance, this characteristics is a line with slope of Rf .

ctenr cteIL

)A(fI

(V)tV

LIS1

_

tVfI Variable

load V

A+

S2 A

fR

aI


62


3. External Characteristics: Terminal voltage vs. load current

Lt IV



and S1 is closed.• Load resistance is gradually decreased. Field

current cannot be kept constant.• The terminal voltage and load current are

recorded. ctenr

LIS1

_

tVfI Variable

load V

A+

S2 A

fR

aI

(A)LI

(V)tV

B

scI


63


4. Armature‐reaction CharacteristicsField current vs. load current

Lf II

• The generator is connected as separately excited and this characteristics is obtained.

fV

La II S1

_

tV

fI

+

_

Variable load

V

A+

S2

A

fR

ctenr cteVt

(A)LI

(A)fI


64

Operating Characteristics of Series DC Generators

The following circuit is used to obtain the characteristics of a series DC generator:

• No‐load characteristics is undefined for this generator because at no‐load the field current is zero.

• Armature reaction characteristics is meaningless here because.

LIS1

_

tV

fI

Variable load

V

A+ aI

Lf II 2017 Shiraz University of Technology Dr. A. Rahideh

65

Operating Characteristics of Series DC Generators

Full‐load and external Characteristics: Full‐load terminal voltage vs. field or load current

ft IV

Since load and field currents are identical full‐load and external characteristics are the same.

ctenr

Lf II

LIS1

_

tV

fI

Variable load

V

A+ aI

Lt IV

)A(fL II

(V)tV


66

Operating Characteristics of Compound DC Generators

1. Cumulative compoundi. Over Compound: series field MMF is significantly greater

than shunt field MMF.

ii. Flat compound: series and shunt MMFs are so that the terminal voltage at full‐load is the same as the terminal voltage at no‐load.

iii. Under compound: series field MMF is lower than shunt field MMF.

2. Differential compound


67

Operating Characteristics of Compound DC Generators

(A)LI

(V)tV

Flat compound

Over compound

LnI

Under compound Separately excited

Shunt Differential compound


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