SYNCHRONOUS GENERATOR.pptx

SYNCHRONOUS
GENERATORS
EE 3824 ENERGY CONVERSION
Class on 11-19-2013
1/12/2023 Prof. Z. Jan Bochynski 1

INTRODUCTION TO AC AND DC MACHINES
AC Machines
Synchronous Machines and Induction Machines

4.1 ROTATING MACHINES CONCEPT
Horizontal
axis
Magnetic
Field
e(t)
Electromechanical energy conversion occurs when changes in the flux linkages λ resulting from
mechanical motion.
dt
d
t
e


)
(
•Rotating the winding in magnetic field
•Rotating magnetic field through the winding
•Stationary winding and time changing magnetic field (Transformer
action)
Producing voltage in the coil
eind = (v x B) • I
v = rω
Θ = ωt

Schematic two-phase,
salient-pole
synchronous machine
eind = NcΦω cos ωt

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
4-6
(a) Space distribution of flux density and
(b) corresponding waveform of the generated voltage
for the single-phase generator.
Synchronous
Machines
•Two-pole, single phase machine
•Rotor rotates with a constant speed
•Constraction is made such that air-gap flux density is
sinusoidal
•Sinusoidal flux distribution results with sinusoidal induced
voltage

CASE 1: Machine armature (stator) winding to carry ac
current in
A. Synchronous machine In both the armature winding is on
B. Induction machine the stator (stationary winding)
C. DC machine Armature winding is on the rotor then ac is rectified

DC machine Field winding is on the stator
Synchronous machine Field winding is on the rotor
Note: Permanent magnets produce DC magnetic flux and are used in the place of field
windings in some machines.
VRM (Variable Reluctance Machines) No windings on the rotor
Stepper Motors (non-uniform air-gaps)
CASE 2: DC current winding for magnetic field production is placed

Cross section of a two-pole dc
machine.
DC Machines
Rms voltage in one phase

Elementary two-pole cylindrical-rotor field
winding
Field winding is a two-pole distributed winding
Winding distributed in multiple slots and
arranged to produce sinusoidal distributed air-
gap flux.
Why some synchronous generators have
salient-pole rotor while others have cylindirical
rotors?
Answer: In salient-pole machines the number
of poles can be large therefore they will be able
to operate in slow speed to produce 50 Hz
voltage.

Hydroelectric power plant (D. Yıldırım, İTÜ Lecture Notes)

generator sets
giant shaft
connecting turbine
to generator
generato
r
turbine
hydropower-plant-generator.swf
Hydroelectric power plant

Diameter of rotor:
16 meters
Rotating mass:
2650 ton
715 MW Generator

Four-pole, single phase machine
•a1,-a1 and a2,-a2 windings connected in series
•The generator voltage goes through two complete cycles per revolution of
the rotor.
•The frequency in hertz will be twice the speed in revolutions per second.
a
ae
p


2
 nm: rpm; fe:
Hz
Magnitude voltage in one phase:
EA = NcΦ ω

Cross-sectional view of
an elementary three-
phase ac machine

Schematic views of three-phase generators: (a) two-pole, (b) four-pole,
and (c) Y connection of the windings.

The production of a rotating magnetic field by means of three-phase
currents

Instantaneous phase currents under balanced three-phase
conditions

Simplified two-pole three-
phase stator winding.
MMF Wave of a
Polyphase Winding
t
I
i e
m
a 
cos

)
120
cos( 0

 t
I
i e
m
b 
)
120
cos( 0

 t
I
i e
m
c 

Typical induction-motor speed-torque characteristic.
Induction Machines
•The stator winding excited by ac
current. The current produces a
rotating magnetic field which in
turn produces currents in rotor
conductors due to induction.
•These machines mostly used as
motors.
•Rotor windings are short circuited
(electrically) and frequently have no
external connections.
•Stator and rotor fluxes rotate in
synchronism with each other and
that torque is related to the relative
displacement between them.
•Rotor does not rotate
synchronously

Windings placed in stator slots

Inside View of An Induction Motor

Elementary dc machine with commutator
DC Machines
Armature winding on the rotor with current
conducted from it by means of carbon
brushes

Flux distribution in a 4-pole
salient-pole generator
Colors represent the strength of B.
Blue to Red : The flux density
increases

Finite-element solution of the magnetic field distribution in a salient-pole dc
generator. Field coils excited; no current in armature coils. (General Electric
Company.)

Finite-element
solution for the flux
distribution around
a salient pole.
(General Electric
Company.)

Flux created by a
single coil side in a
slot

Voltage between the brushes in the elementary dc machine

Elementary two-pole machine with smooth air gap:
(a) winding distribution and (b) schematic representation

(a) Full-pitch coil and (b) Fractional-pitch coil.

Elementary cylindrical-rotor, two-
phase synchronous machine

Simplified two-pole machine: (a) elementary model and (b) vector diagram of
mmf waves. Torque is produced by the tendency of the rotor and stator
magnetic fields
to align. Note that these figures are drawn with ẟsr positive, i.e., with the rotor
mmf wave Fr leading that of the stator.

Generators in a Power Plant

Large Generator Stator

STATOR WIRES
Insulated copper bars are
placed in the slots to form
the three-phase winding
Laminated iron
core with slots
Metal frame

WIRING LARGE GENERATOR

SILENT POLES LARGE ROTOR

LARGE HYDRO GENERATOR
View of
conductors
and
spacers

ASSEMBLING SYNCHRONOUS
GENERATOR

TURBO GENERATOR

SMALL SILENT 4-POLES ROTOR
Excitation
Coil
Excitation
Pole
Fan

SMALL SYNCHRONOUS MACHINE
ROTOR is producing magnetic field
STATOR with three-phase armature windings is
generating emf

TURBO GENERATORS
Steam Turbines in thermal or nuclear power stations
Hydro Turbines in hydroelectric power stations
Diesel Engines in diesel stations with lower speed
Gas Turbines in power plants for rotate medium size
generators

NUCLEAR POWER PLANT

HYDROPOWER PLANT

THERMAL POWER PLANT

GENERATING PRINCIPLES
Horizontal
axis
Magnetic
Field
e(t)
https://www.youtube.com/watch?v=tiKH48EMgKE

Generator with Two-poles Salient Rotor

Cylindrical Two-Poles Rotor of A
Synchronous Generator

Synchronous Generator with
Two- and Four-Poles Silent Rotor

Flux Inside a Silent 4-Poles Machine
From Blue color to the Red
the magnetic field density
B increases
Bnet = Brot + Barm
The net magnetic field is the sum of the rotor and the
stator magnetic fields.

Synchronous Generator Circuit
External source to power the rotor for producing
magnetic field carried to the shaft

INDUCED VOLTAGE IN FOUR-POLE,
SINGLE PHASE MACHINE

SYNCHRONOUS GENERATOR FULL
EQUIVALENT CIRCUIT

MAGNITUDE OF INDUCED VOLTAGE IN
THE STATOR
Number of conductors Z = 2 N in series :
N – number of turns in a coil
f - frequency of induced emf in Hz
Φ - flux per pole in Wb
K – machine construction constant
In the short pitched and distributed stator the voltage
per phase of winding is:
Vϕ =4.44 K Φ f N
Vϕ = 2.22 K Φ f Z

GENERATOR CIRCUIT
The phase voltage is:
Vϕ = Eg – j X Ia
Armature reaction is:
Estator = - j X Ia
EA = K φ ω
K is a machine construction constant

GENERATOR EQUIVALENT CIRCUITS
Synchronous reactance is XS = Xa + X
X is a constant of proportionality
Armature reaction voltage is Ea = - j X Ia

POWER GRID PHASORS DIAGRAM
Vt is voltage of the grid
Ef is function of current If

SIMPLIFIED CIRCUIT
In practice R << XS
Than the circuit can be
Where equivalent excitation
voltage Ef is:
The generated voltage is :
Eg = Vt + Ia (R +jX)
Vt is a phase voltage across the load
Ia is the armature current

GENERATOR CIRCUIT SIMPLIFIED

POWER EQUATIONS FOR 3-PHASE SYSTEM
jQ
P
I
V
S a
a 

 *
3
The apparent power delivered by
the generator to the power grid:

sin
3 0
S
f
X
V
E
P 
The real power (active power)
This equation is called power-angle equation
It shows the influence of the power angle δ
The reactive power
for an inductor Q > 0
for a capacitor Q < 0
)
cos
(
3 O
f
S
O
V
E
X
V
Q 
 

GENERATOR MAXIMUM POWER
Pm
opt
Actual δ
Pullover power
The maximum power produced by the generator is when δ = 900
Pmax~ Ef

POWER CONTROL
Power Variables: Excitation current If and Reactance XS

sin
3
X
E
V
P
f
o

• Increasing excitation current the maximum power Pmax increases
• The input mechanical power Pm that is equal to the electrical power P delivered to the
infinite bus is unchanged
• The power angle δ decreases

EXAMPLE 1
A 3-phase 11-kV, 11 MW, Y-connected synchronous
generator has a synchronous reactance of 9 Ω.
The generator is connected to an infinite bus.
a. Calculate the excitation voltage for a maximum
generation of 11 MW.
b. If the mechanical power is unchanged, calculate the
current when the excitation increases by 10%

SOLUTION EXAMPLE 1
a) b)

GENERATOR ON THE GRID
Terminal bus Infinite bus
P & Q
Qt
Qo
Ef is the equivalent field voltage
Vo is the infinite bus voltage
Vt is the terminal voltage
Xl is the transmission line reactance
XS is the stator reactance
P is the real power
Q is the reactive power
Xl >> Rl

REACTIVE POWER
The reactive power depends on the level of the
synchronous generator excitation level.
Qt > 0
Qt = 0
Qt < 0

OVER EXCITED GENERATOR
The generator is consuming reactive power Q

EXACTLY EXCITED GENERATOR
The generator produces no reactive power Q = 0.
Ef cos δ =Vo

UNDER EXCITED GENERATOR
The generator is producing reactive power Q

INCREASING TRANSMISSION LINE CAPACITY
Usually in the transmission system current is lower
than the wires capacity. We can add to the system
more power increasing the mechanical power of the
turbine.
• This can be done by reducing inductive reactive
power (adding in series a capacitor to balance
reactive inductance)
• Connecting generators in parallel

GENERATORS IN PARALLEL
Total transmission line reactance
2
1
2
1
l
l
l
l
S
total
X
X
X
X
X
X




ADDING CAPACITY TO TL
Adding capacity to the
transmission line we
reducing the line
inductive reactance.
As the result reactive
power Q decreases
giving space in the
cables for more active
power P
𝑋 = 𝑋𝑠 + (X l – X c )

EXAMPLE 2
A synchronous generator is connected to an infinite bus
through a transmission line.
The infinite bus voltage Vo = 230 kV. The transmission line’s
inductive reactance is 10 Ω, and the synchronous reactance of
the machine is 2 Ω.
1) Compute the capacity of the system
2) If a capacitor is connected in series with the transmission
line to increase the transmission capacity by 25%, compute
its reactance.

mF
C
X
MW
X
X
X
kV
kV
MW
X
X
X
E
V
MW
MW
x
P
capacity
New
C
C
l
s
C
l
s
f
o
1
4
.
2
5031
210
230
5031
3
5031
4025
25
.
1
:
_
max












SOLVING EXAMPLE 2
1. The system capacity is
MW
kV
kV
X
E
V
P
l
S
f
o
4025
2
10
210
230
max 







2. The system capacity increases by 25% with added reactive capacitance XC
Very large

EXAMPLE 3
A synchronous generator is connected to an infinite bus
through a transmission line.
The infinite bus voltage Vo = 230 kV. The equivalent field
voltage of the machine Vt =210 kV, the transmission line’s
inductive reactance is Xl = 10 Ω, and the synchronous
reactance of the machine XS = 2 Ω.
1) Compute the capacity of the system
2) Compute the capacity of the system if the second
transmission line with Xl2 =10Ω (inductive reactance) is
connected in parallel with the first line.

SOLVING EXAMPLE 3
1. The system capacity is:
GW
kV
kV
X
E
V
P
l
S
f
o
025
.
4
2
10
210
230
3
max 







2. After the second line is added, the system capacity is:
2
1
2
1
max
3
3
l
l
l
l
S
f
o
new
f
o
X
X
X
X
X
E
V
X
E
V
P




MW
kV
kV
Pnew 6900
7
48300
20
100
2
)
210
230
(
max
1









SYNCHRONOUS GENERATOR
POWER FLOW

POWER AND TORQUE EQUATIONS
Pout = √3 Vll Ill cos θ
Pout = 3 Vph Iph cos θ
Qout = √3 Vll Ill sin θ
Qout = 3 Vph Iph sin θ
Induced torque:
S
m
A
ph
m
A
A
m
e
m
conv
ind
X
E
V
I
E
P






sin
3
cos
3




S
A
ph
e
m
out
X
E
V
P
P conv

sin
3

 

VOLTAGE REGULATION
%
100



fl
fl
nl
V
V
V
VR
• Decreasing the field resistance increases generator
field current.
• An increase in the field current increases the flux in
the machine.
• An increase in the flux increases the internal generated
voltage EA = K ϕ ω.
• An increase in EA increases Vph and the generator
terminal voltage Vll.

EXAMPLE 4
A 120 MW synchronous generator is
connected to an infinite bus through two
parallel 3-phase transmission lines each
having a reactance of XS =6 Ω (including
transformers).
The synchronous reactance of the generator is
9 Ω. The infinite-bus voltage is Vll= 110 kV.
Assume that the power factor at the infinite
bus is unity.
Determine the equivalent excitation voltage to
deliver 120 MW to the infinite bus.

SOLVING EXAMPLE 4
A
I
I
kV
MW
I
V
P
a
a
o
o
84
.
629
110
3
120
cos
3






 2
2
)
5
.
0
( l
S
a
o
f X
X
I
V
E 

 
 
phase
kV
E
kA
E
f
f
/
64
)
6
5
.
0
9
(
63
.
0
3
110 2
2














HOMEWORK
Due day next Tuesday class on 11-18-2013
El-Sharkawi Chapter 12
Exercises 12.17 to 12.21

SYNCHRONOUS MOTOR
https://www.youtube.com/watch?v=Vk2jDXxZIhs

SYNCHRONOUS GENERATOR.pptx

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