electrical power and machines- sync gen(2)

8/9/2019 Electrical Power and Machines- Sync Gen(2)

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Chapter 16: Synchronous

Generators (2)


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Generator under Load• The behavior of a synchronous

generator depends upon theconnected load

two basic load categorieso

isolated loadso infinite bus

isolated loads with a lagging pf o current lags the terminal voltage, E o the voltage drop across the

synchronous reactance, E X, leadsthe current by 90°

o the induced voltage, E 0, generated by the flux, Φ , is equal to the phasor sum of E and E X


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Generator under Load

• isolated loads with a leading pf current leads the terminal voltage, E the voltage drop across thesynchronous reactance, E X, leads the

current by 90°the induced voltage, E 0, generated bythe flux, Φ , is equal to the phasor sumof E and E X

•

note that E 0 always leads E by theangle dfor lagging loads E 0 is greater than E

for leading loads E is greater than E 0


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Generator under Load

Example !" #$ , %0&' ($, !)phase

generator – synchronous reactance is 9 ohms –

nominal current is *000 – no)load saturation curve is given

d+ust the excitation so that theterminal voltage is fixed at %* ($

i& calculate the excitation current

ii& draw the phasor diagrams for thefollowing load conditions

a& no)load b& resistive load of !" #c& capacitive load of *% #$ r


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Generator under LoadExample

!" #$ , %0&' ($, !)phase generator – synchronous reactance is 9 ohms – nominal current is *000 – no)load saturation curve is givend+ust the excitation so that the terminal voltage is fixed at %* ($i& calculate the excitation currentii& draw the phasor diagrams for the following load conditions



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Regulation Cur es• $oltage regulation is the behaviour of the generator-s terminal

voltage as the load varies• .egulation is a function of the load current

the regulation curve is a plot of the terminal voltage, V T, with respect toload current, I , ranging from no)load to full)load

o for a fixed field excitation currento for a given load power factor

family of curves are developed for various field excitation currents and

for different load power factors percent regulation is defined as/


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Regulation Cur es

Exampleonsider the regulation

curves for a !" #$ , %* ($generator& alculate the

percent regulationcorresponding to the unity

power factor curve


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Synchroni!ation o" aGenerator

• 1ften two or more generators are connected in parallel tosupply a common load in large utility systems

connecting a generator to other generators is called parallelingmany paralleled generators behaves li(e an infinite bus

o voltage and frequency are constant and can not be easily altered

before connecting a generator to an electrical grid, it must be synchronized

o the generator frequency is equal to the system frequencyo the generator voltage is equal to the system voltageo the generator voltage is in phase with the system voltageo the phase sequence of the generator is the same as that of the system


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Synchroni!ation o" a Generator

• To synchroni2e a generator ad+ust the speed regulator of the prime mover so that frequencies areclosead+ust the excitation so that generator voltage and system voltage are

equalobserve the phase angle by means of a synchroscope, which indicatesthe phase angle between two voltages

o the pointer rotates proportional to the frequency differenceo a 2ero mar( indicates a 2ero degree phase angleo the speed regulator is ad+usted so that the pointer barely creeps across the

dial

on the 2ero mar(, the line circuit brea(er is closed


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Connecting to an #n$nite%us

• n infinite bus system is so powerful that it imposes its ownvoltage magnitude and frequencyonce an apparatus is connected to an infinite bus, it becomes part of itfor a synchroni2ed generator, the operator can only vary two machine

parameterso the field excitation current, I Xo the prime)mover-s mechanical torque, T


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Connecting to an #n$nite %us

• $arying the exciting currentimpacts the induced voltage E 0causes a current to flow that is 90 degrees out)of)phase due to thesynchronous reactance

does not affect the flow of active 3real4 power does cause reactive power to flow


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Connecting to an #n$nite %us

• $arying the mechanical torque by opening up the control valve of the prime)mover, an increase torqueis developedthe rotor will accelerate, E 0 will increase in value and begin to slip

ahead of phasor E , leading by a phase angle δlthough both voltages have similar values, the phase angle produces a

difference of potential across the synchronous reactanceo a current will flow, but this time almost in phase with E o real 3active4 power will flow


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&cti e 'o er eli ered• The active power delivered by a synchronous generator is

given by

P E = !)phase power delivered by the generator

E = induced generator voltageV T = generator terminal voltage

X 5 6 synchronous reactance, per phaseδ 6 phase angle between E and V T


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&cti e 'o er eli ered


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&cti e 'o er eli ered

Example !" #$ , %* ($, *'00 rpm, !)phase, "0 72 generator is

connected to the power grid

synchronous reactance of 9 per phaseline)to)neutral exciting voltage is *% ($line)to)line system voltage is *8&! ($&

Calculate

a& the active power delivered when the power angle d is !0° b& the pea( power that the generator can deliver before losing

synchronism


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Example !" #$ , %* ($, *'00 rpm, !)phase, "0 72 generator is connected to the power grid

synchronous reactance of 9 per phaseline)to)neutral exciting voltage is *% ($

line)to)line system voltage is *8&! ($&Calculate

a& the active power delivered when the power angle d is !0° b& the pea( power that the generator can deliver before losing synchronism


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*ransient Reactance•

synchronous generatorconnected to a system is sub+ectto switching events

short)circuits, load energi2ation,etc&

• n many cases, the equivalentcircuit does not reflect the

behavior of the machinethe equivalent circuit is only valid

for steady)state operationfor sudden, large current changesanother reactance is needed

o reactance X' whose value varies as afunction of time

the reactance for a short circuito prior to the fault, the reactance

equals the synchronous valueo at the instant of fault, the

reactance falls to a much lowervalue, X' d


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*ransient Reactance

• The reactance X' d is called the transient reactancecan be as low as *:; of the synchronous reactanceconsequently, the initial short)circuit current is much higher than thatcorresponding to the synchronous reactance


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*ransient +odel

Example %:0 #$ , %: ($, !)phase generator delivers its rated output at

unity power factor a synchronous reactance of *&" pua transient reactance of 0&%! pu

short circuit suddenly occurs on the connecting transmissionline, close to the generator Calculatea& the induced voltage, E 0, prior to the short circuit

b& the initial value of the short)circuit currentc& the final value of the short)circuit current if the circuit brea(er should fail

to open


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*ransient +odel

%:0 #$ , %: ($, !)phase generatordelivers its rated output at unity powerfactor

a synchronous reactance of *&" pua transient reactance of 0&%! pu

short circuit suddenly occurs on the

connecting transmission line, close tothe generator

Calculatea& the induced voltage, E 0, prior to the

short circuit

b& the initial value of the short)circuitcurrent

c& the final value of the short)circuitcurrent if the circuit brea(er shouldfail to open


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*ransient +odel






short circuit




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*ransient +odel






short circuit




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'o er *rans"er•

e are often interested in the active power that can be transmitted betweensource and source <

using =irchhoff-s voltage law

the active power absorbed at source < is

applying the geometry law of the sines fora triangle

substitution results in


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'o er *rans"er

Example transmission line connects two generators

generator operates at E 6 %0 ($ ∠ :°generator < operates at E 6 *: ($ ∠ >%°the transmission line has a reactance of *> ohms

alculate the active power that flows over the line whichmachine is receiving the power


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'o er *rans"er

Example transmission line connects two generators

generator operates at E 6 %0 ($ ∠ :°

generator < operates at E 6 *: ($ ∠ >%°the transmission line has a reactance of*> ohms

alculate the active power that flows over theline which machine is receiving the power


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+achine E,ciency• The physical si2e of the synchronous machine has a profound

effect upon/efficiency, power output, relative cost, and temperature riselosses in the machine

o I % R losses in the stator windingso I dc % Rf losses in the rotor field windingo iron core losses and mechanical losses

(eeping all machine parameters and materials the sameo an increase in all linear dimensions causes

voltage increases by the squareoutput power increases by the >th power losses increase by the !rd power


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-ome or.• ?roblems *")%%, *")%!, and *")%>

electrical power and machines- sync gen(2)

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