This document provides an overview of synchronous generator models for power system analysis. It discusses the steady-state model of synchronous generators, including their cylindrical and salient pole rotor constructions. Equivalent circuits are presented showing the generator internal voltage and synchronous reactance. Per-unit calculations and phasor diagrams are used to explain generator operation at different power factors and reactive power control via field excitation.

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EEE 471 Power System Analysis-I
Chapter 3: Models for Power System Analysis
1
Assist. Prof. Dr. A. Mete VURAL
E-mail: mete.vural@gaziantep.edu.tr
Web: www.gantep.edu.tr/~mvural
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CONTENTS:
 STEADY-STATE MODEL OF GENERATOR
 STEADY-STATE MODEL OF TRANSFORMER
 PER-UNIT CALCULATIONS

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Cylindrical-Rotor synchronous generator
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The photo represents 15 MW 11 KV 3000 RPM 2 Pole cylindrical-rotor
Source:http://www.rkeww.com/gallery.html

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Salient-pole Synchronous Generator
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Source: http://processmodeling.org/theory/electronics/emf/electric_machinery3.html

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For the simple models of generators for steady-state balanced operation
generators, (like transformers and transmission lines), are represented with
lumped elements on substation buses.
SYNCHRONOUS GENERATORS
Large-scale power is generated by three-phase synchronous generators driven
either by steam turbines, hydroturbines, or gas turbines (prime movers).
The armature windings are placed on the stationary part called stator.
 The armature windings are designed for generation of balanced three-phase
voltages and are arranged to develop the same number of magnetic poles as the
field winding that is on the rotor.
Cross-sectional view of a
two-pole, salient-rotor,
three-phase synchronous
machine
Ref:http://www.ewh.ieee.org/soc/es/Nov1998/08/SYNCMACH.HTM
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 The field which requires a relatively small power (0.2-3 percent of the
machine rating) for its excitation is placed on the rotor.
 The rotor is also equipped with one or more short-circuited windings known
as damper windings.
The rotor is driven by a prime mover at constant speed and its field circuit is
excited by direct current.
 The excitation may be provided through slip rings and brushes by means of
dc generators (referred to as exciters) mounted on the same shaft as the rotor
of the synchronous machine.
 In modern excitation systems usually use ac generators with rotating
rectifiers, and are known as brushless excitation.
 The generator excitation system maintains generator voltage and controls
the reactive power flow.

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 The rotor of the synchronous machine may be of cylindrical
or salient construction.
 The cylindrical type of rotor, also called round rotor, has one
distributed winding and a uniform air gap. These generators
are driven by steam turbines and are designed for high
speed 3600 or 1800 rpm (two- and four-pole
machines,respectively) operation.
 The rotor of these generators has a relatively large axial
length and small diameter to limit the centrifugal forces.
 Roughly 70 percent of large synchronous generators are
cylindrical rotor type ranging from about 150 to 1500 MVA.
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Source: http://www.ge-energy.com/
A steam turbine which drives the rotor of a synchronous generator

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The salient type of rotor has concentrated
windings on the poles and nonuniform air
gaps. It has a relatively large number of
poles, short axial length, and large
diameter. The generators in hydroelectric
power stations are driven by hydraulic
turbines, and they have salient-pole rotor
construction.
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 Normally synchronous machines are built as internal-field machines.
 Machines with poles 2p = 2 have a round rotor (cylindrical/turbo-rotor)
because of high centrifugal forces, while those with 2p = 4; 6; 8 and more
poles mostly have a salient-pole rotor.
 The stator carries the three phase winding and must be made of laminated
iron sheets in order to reduce eddy currents. Since the flux in the rotor is
constant with time at a particular place on the rotor, the rotor can be built
from massive steel.
 The excitation winding is generally supplied with DC through the slip rings.
In order to reduce oscillations in case of a network fault, the machine has a
damper winding.

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 Damper or amortisseur windings are basically extra bars or coils added to
a synchronous machine rotor to 'damp' speed deviations.
 The windings behave in the same fashion as the squirrel cage of an induction
machine. When rotor speed differs from the stator-side electrical speed,
currents are induced in the damper windings. These currents set up a torque
that has the effect of pulling the rotor back toward synchronous speed. This is
true whether the rotor is spinning above synchronous or below synchronous
speed.
 When the rotor is spinning at synchronous speed (i.e. zero slip), no currents are
induced in the damper windings.
 Damper windings are commonly found on large, low-speed, salient pole
machines.
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Source: http://www.industrial-electronics.com/images/elec4_20-2.jpg

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Source: http://www.electrotechnik.net/2010/11/amortisseur-windings.html
Amortisseur windings as bars
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GENERATOR MODEL for STEADY-STATE ANALYSIS
The voltage induced in one-phase is:







2
cosmax

wtEea
where
Emax=w N =2f N
The rms value of induced voltage in one-phase is:
ea(rms)=4.44 f N

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 In actual AC machine windings, the armature coil of each phase is distributed
in a number of slots.
 Thus, a reduction factor Kw, called the winding factor, must be applied.
 Generally winding factor is Kw= 0.85-0.95
 Finally, the rms value of the generated voltage in one-phase is
ea(rms)=4.44 f N
ea(rms)=4.44 Kw f N
Important remark: Multiply above with sqrt(3) to obtain
line-to-line generated voltage if stator is Y-connected.
o f: electrical frequency (Hz)
o Kw: winding factor
o N: winding turns number per phase
o ϕ: flux in the machine
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 The frequency of the induced armature voltages depends on the speed at which
the rotor runs and the number of poles for which the machine stator is wound.
602
nP
f 
o f: electrical frequency (Hz)
o P: pole number on the stator
o n: synchronous speed of the stator shaft
 During normal conditions, the generator operates synchronously with the
power grid. This results in three-phase balanced currents in the armature.
 















3
4
sin
3
2
sin
sin
max
max
max





wtIi
wtIi
wtIi
c
b
a
o İa, ib, ic: phase currents of armature
o w: angular frequency = 2*pi*f
o ψ: phase angle difference between ea and ia

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Source: http://www.youtube.com/watch?v=tiKH48EMgKE
How does alternator (synchronous generator) work ?
How does Alternator Work.mp4 (5:19 mins)
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A simple per-phase model for a cylindrical rotor generator is
E=V + [Ra+ j Xs ]Ia
o V: per-phase syn. gen. Voltage after its impedance
o Ia: Per-phase armature current
o E: Per-phase internal generated voltage
o Ra: per-phase armature resistance
o Xs: Synchronous reactance

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 The armature resistance is generally much smaller than the synchronous
reactance and is often neglected.
 The equivalent circuit of a synchronous generator connected to an infinite bus is
infinite bus
infinite bus: is the bus in a power system where the voltage and the frequency
are always constant.
?
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 The phasor diagrams of the generator with terminal voltage as reference for
excitations corresponding to lagging, unity, and leading power factors.

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 The voltage regulation of an alternator is used for
comparison with other machines. It gives an indication of the
change in field current required to maintain system voltage
when going from no-load to rated load at some specific
power factor.
The no-load voltage Vnl for a specific power factor may be
determined by operating the machine at rated load
conditions and then removing the load and observing the
no load voltage.
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POWER FACTOR CONTROL
Cylindrical Rotor
 Most synchronous machines are connected to large
interconnected electric power networks.
These networks have the important characteristic that
the system voltage at the point of connection is constant
in magnitude, phase angle, and frequency.
Such a point in a power system is referred to as an infinite
bus.That is, the voltage at the generator bus will not be
altered by changes in the generator's operating condition.

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The ability to vary the rotor excitation is an important
feature of the synchronous machine,
The effect of rotor excitation a variation
When the machine operates as a generator with constant
mechanical input power. neglecting the armature
resistance, the output power is equal to the power
developed, which is assumed to remain constant given by
   cos333 aa IVP  
IV
where V is the phase-to-neutral terminal voltage assumed
to remain constant. Here, for constant developed power at
a fixed terminal voltage V Ia cos  must be constant.
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 Thus, the tip of the armature current phasor must fall on a
vertical line as the power factor is varied by varying the
field current as shown in the figure.

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The variation in the magnitude of armature current as the
excitation voltage is varied is best shown by a curve.
 Keeping the field current as the abscissa the curve of the
armature current as the function of the field current
resembles the letter V and is often referred to as the V
curve of synchronous machines.
These curves constitute one of the generator's most
important characteristics.
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POWER ANGLE CHARACTERISTICS
The three-phase complex power at the generator terminal is

 aIVS 33
Expressing the phasor voltages in polar form, the
armature current is





s
a
Z
VE 0
I
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Substituting for results in

aI
 
ss Z
V
Z
VE 2
3 3)(3S
Thus, the real power P3 and reactive power Q3 are
 cos3)cos(3
2
3
ss Z
V
Z
VE
P 
 sin3)sin(3
2
3
ss Z
V
Z
VE
Q 

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If Ra is neglected, then Zs=jXs and =90o then these equations
can be written as
 VE
Z
V
Q
Z
VE
P
s
s






cos3
sin3
3
3
If E and V are held fixed and the power angle  is
changed by varying the mechanical driving torque, the
power transfer varies sinusoidally with the angle . The
theoretical maximum power occurs when =90o
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The limit beyond which the excitation cannot be reduced.
when  = 90o.
Any reduction in excitation below the stability limit for a
particular load will cause the rotor to pull out of synchronism.
V
E
Ia

0 90o 180o
Pmax
P
 sin33
sZ
VE
P 

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for small , cos is nearly unity and the reactive power can
be approximated to
 VE
Z
V
Q
s
  cos33
)(33 VE
x
V
Q
s

-When E>V the generator delivers reactive power to the bus,
and the generator is said to be overexcited.
-When E<V, the reactive power delivered to the bus is
negative; that is, the bus is supplying positive reactive power
to the generator.
Control of the reactive power;
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 Generators are normally operated in the overexcited mode
since the generators are the main source of reactive power
for inductive load throughout the system.
 The flow of reactive power is governed mainly by the
difference in the excitation voltage E and the bus bar
voltage V.
The adjustment in the excitation voltage E for the control of
reactive power is achieved by the generator excitation
system.

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SALIENT-POLE SYNCHRONOUS GENERATORS
The salient-pole rotor results in nonuniformity of the
magnetic reluctance of the air gap.
The reluctance along the polar axis  the rotor direct axis
is less than that along the interpolar axis  the quadrature
axis.
Therefore, the reactance has a high value Xd along the
direct axis, and a low value Xq along the quadrature axis
Xd>Xq
These reactances produce voltage drop in the armature
and can be taken into account by resolving the armature
current Ia into two components Iq, in phase, Id in time
quadrature, with the excitation voltage.
36

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The phasor diagram with the armature resistance neglected
is
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It is no longer possible to represent the machine by a
simple equivalent circuit. The excitation voltage magnitude
is
The three-phase real power at the generator terminal is
dd IXVE  cos
cos3 aIVP 
The power component of the armature current can be
expressed in terms of Id and Iq as follows:
Ia cos  = ab + de
= Iq cos  + Id sin 

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)sincos(3  dq IIVP 
or the real power can be rewritten as
V sin  = Xq Iq
q
q
X
V
I
sin
or
Xd
VE
Id
cos

from Id is given bydd IXVE  cos
The real power equation contains an additional term known
as the reluctance power.
For short circuit analysis, assuming a high X/R ratio, the
power factor approaches zero, and the quadrature
component of current can often be neglected. In such a
case, Xd merely replaces the Xq used for the cylindrical
rotor machine. Generators are thus modeled by their direct
axis reactance in series with a constant-voltage power
source.
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Substituting for Id and Iq into
the real power with armature current neglected becomes
)sincos(3  dq IIVP 
 2sin
2
3sin3 2
3
qd
qd
d XX
XX
V
X
VE
P



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POWER TRANSFORMER
Power transformers are essential in power systems.
They are used to increase voltage level for transmission.
They are used to decrease voltage level for distribution and consumer use.
In modern utility systems there are five or more voltage transformations.
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A single voltage level is obtained by Referring
Referring is done either primary or secondary side
This simplifies analysis of systems with transformers

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EFFICIENCY and VOLTAGE REGULATION of POWER TRANSFORMER
Referred to primary side
Referred to secondary side
No referring
efficiency 95% - 99% in real transformers
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A typical 50 MVA three-phase power transformer
Ref: http://www.energy.siemens.com/hq/en/power-transmission/transformers/power-transformers/#content=Power%20Transformer%2050%20MVA

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45Source: http://www.trcamerica.com/IMG_2719.JPG
850 MVA three-phase power transformer
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50

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51
Source: http://www.youtube.com/watch?v=6LLVWzh47CY
Power Transformer Drying (Siemens).mp4
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THREE-PHASE TRANSFORMER CONNECTIONS
WYE-WYE
WYE-DELTA DELTA-WYE
DELTA-DELTA
No phase-shift between
HV side and LV side
30-degrees phase-shift
between HV side and LV
side: HV side is leading

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COMMON CONNECTION CONFIGURATIONS
Advantages:
 High voltage side is grounded so the insulation requirements for
the high-voltage transformer windings are reduced
 One advantage of the Δ winding is that the undesirable third harmonic magnetizing current, caused by
the nonlinear core B-H characteristics, remains trapped inside the Δ winding.
WYE-DELTA DELTA-WYE
for step-down for step-up

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VOLTAGE CONTROL OF TRANSFORMERS
Voltage control is required for
o To compensate voltage drops
o To control reactive power flow over transmission line
TAP CHANGING TRANSFORMERS
 Off-load tap changing transformers
 Requires disconnection of transformer
 infrequent change in voltage ratio due to load growth or seasonal change
 Typically 4-taps each has 2.5 %, a total regulation of ±5 % of the nominal voltage
 TAP CHANGING UNDER LOAD (TCUL) TRANSFORMERS
 No requirement of disconnection of transformer
 frequent change in voltage ratio
 HV side: Typically 4-taps each has 2.5 %, a total regulation of ±5 % of the nominal voltage
 LV side: Typically 32-incremental step of 5/8 each, giving an automatic range of ±10 % of the
nominal voltage
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Tap setting (in pu)
for sending-end side
Tap setting (in pu)
for receiving-end side
Transmission Line
P: real power flow per phase
Q: reactive power flow per phase
TAP SETTING EQUATION:

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PER-UNIT (PU) SYSTEM
Advantages of PU system:
o Different voltage levels are disappeared to reduce a single level,
so the analysis of power system becomes easy.
o Physical quantities of the power system (voltage,power,current,impedance) are represented
as percentage or decimal fraction of base quantites.
Actual value
Base value

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PER-UNIT (PU) SYSTEM
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CHANGE OF BASE:
 required to match different base values on a common base value

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2-machine 6-bus system
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Thank you
End of Chapter 3
Questions and Discussion ?
Assist. Prof. Dr. A. Mete VURAL
E-mail: mete.vural@gaziantep.edu.tr
Web: www.gantep.edu.tr/~mvural