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EEE 471 Power System Analysis-IChapter 3: Models for Power System Analysis

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Assist. Prof. Dr. A. Mete VURAL

E-mail: mete.vural@gaziantep.edu.trWeb: 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:

2cosmax

wtEea

where

Emax=w N =2f 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 factoro N: winding turns number per phaseo 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.

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nPf

o f: electrical frequency (Hz)o P: pole number on the statoro 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.

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4sin

3

2sin

sin

max

max

max

wtIi

wtIi

wtIi

c

b

a

o İa, ib, ic: phase currents of armatureo w: angular frequency = 2*pi*fo 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 currento E: Per-phase internal generated voltageo Ra: per-phase armature resistanceo 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 frequencyare 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

sa

Z

VE 0I

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Substituting for results inaI

ss Z

V

Z

VE 2

33)(3S

Thus, the real power P3 and reactive power Q3 are

cos3)cos(32

3ss Z

V

Z

VEP

sin3)sin(32

3ss Z

V

Z

VEQ

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If Ra is neglected, then Zs=jXs and =90o then these equations

can be written as

VEZ

VQ

Z

VEP

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

EI

a

0 90o 180o

Pmax

P

sin33sZ

VEP

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for small , cos is nearly unity and the reactive power can

be approximated to

VEZ

VQ

s

cos33

)(33 VEx

VQ

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.

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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

qq

X

VI

sinor

Xd

VEId

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.40

Substituting for Id and Iq into

the real power with armature current neglected becomes

)sincos(3 dq IIVP

2sin2

3sin3 23

qd

qd

d XX

XXV

X

VEP

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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 ReferringReferring is done either primary or secondary sideThis 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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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 foro To compensate voltage dropso 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 phaseQ: 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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612-machine 6-bus system

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Thank youEnd of Chapter 3

Questions and Discussion ?

Assist. Prof. Dr. A. Mete VURAL

E-mail: mete.vural@gaziantep.edu.trWeb: www.gantep.edu.tr/~mvural