8. alternator stand alone
TRANSCRIPT
-
8/18/2019 8. Alternator Stand Alone
1/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
1
The Synchronous generatoroperating alone
Effects of load changes
increase in the load is anincrease in the real and!orreacti"e power drawn from the
generator#Since the field resistor is unaffected$ the field current is constant and$ therefore$ theflu%φ is constant too# Since the speed is assumed as constant$ the magnitude ofthe internal generated "oltage is constant also#
ssuming the same power factor of the load$ change in load will change the
magnitude of the armature current I A# &owe"er$ the angle will 'e the same (for aconstant PF)# *hus$ the armature reaction "oltage jX SI A will 'e larger for theincreased load# Since the magnitude of the internal generated "oltage is constant
A S A E V jX I φ = + (+#34#1)
rmature reaction "oltage "ector will ,mo"e parallel- to its initial position#
-
8/18/2019 8. Alternator Stand Alone
2/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
2
The Synchronous generatoroperating alone
.ncrease load effect on generators with
Lagging PF
Leading PF
/nit PF
-
8/18/2019 8. Alternator Stand Alone
3/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
3
The Synchronous generatoroperating alone
1# For lagging (inducti"e) loads$ the phase (and terminal) "oltagedecreases significantl #
2# For unit power factor (purel resisti"e) loads$ the phase (andterminal) "oltage decreases slightl #3# For leading (capaciti"e) loads$ the phase (and terminal) "oltage rises#
enerall $ when a load on a s nchronous generator is added$ the followingchanges can 'e o'ser"ed
Effects of adding loads can 'e descri'ed ' the "oltage regulation
100%nl fl
fl
V V VRV
−= (+#3 #1)
here V nl is the no5load "oltage of the generator and V fl is its full5load "oltage#
-
8/18/2019 8. Alternator Stand Alone
4/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
4
The Synchronous generatoroperating alone
s nchronous generator operating at a lagging power factor has a fairl large positi"e "oltage regulation# s nchronous generator operating at a unit powerfactor has a small positi"e "oltage regulation# s nchronous generator operatingat a leading power factor often has a negati"e "oltage regulation#
Normall $ a constant terminal "oltage supplied ' a generator is desired# Since thearmature reactance cannot 'e controlled$ an o'"ious approach to ad6ust theterminal "oltage is ' controlling the internal generated "oltage E A = K φω # *hisma 'e done ' changing flu% in the machine while "ar ing the "alue of the fieldresistance R F $ which is summari7ed
1# ecreasing the field resistance increases the field current in the generator#2# n increase in the field current increases the flu% in the machine#3# n increased flu% leads to the increase in the internal generated "oltage#4# n increase in the internal generated "oltage increases the terminal "oltage of
the generator#
*herefore$ the terminal "oltage of the generator can 'e changed ' ad6usting the
field resistance#
-
8/18/2019 8. Alternator Stand Alone
5/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
9
The Synchronous generatoroperating alone: Example
E%ample +#2 480 :$ 0 &7$ ;5connected si%5pole s nchronous generator has aper5phase s nchronous reactance of 1#0 Ω # .ts full5load armature current is 0 at0#8 PF lagging# .ts friction and windage losses are 1#9 < and core losses are 1#0< at 0 &7 at full load# ssume that the armature resistance (and$ therefore$ the I 2 R losses) can 'e ignored# *he field current has 'een ad6usted such that the no5load
terminal "oltage is 480 :#a# hat is the speed of rotation of this generator='# hat is the terminal "oltage of the generator if
1# .t is loaded with the rated current at 0#8 PF lagging>2# .t is loaded with the rated current at 1#0 PF>
3# .t is loaded with the rated current at 0#8 PF leading#c# hat is the efficienc of this generator (ignoring the un
-
8/18/2019 8. Alternator Stand Alone
6/15
ELEN 3441 Fundamentals of Power Engineering Spring 2008
The Synchronous generatoroperating alone: Example
Since the generator is ;5connected$ its phase "oltage is
3 277T V V V φ = =
t no load$ the armature current I A @ 0 and the internal generated "oltage is E A @
2++ : and it is constant since the field current was initiall ad6usted that wa #a# *he speed of rotation of a s nchronous generator is
120 12060 1200
6m en f rpm
P = = =
which is
1200
2 125.760m rad sω π = =
'#1# For the generator at the rated current and the 0#8PF lagging$ the phasor diagram is shown# *he phase"oltage is at 0 0$ the magnitude of E A is 2++ :$
-
8/18/2019 8. Alternator Stand Alone
7/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
+
The Synchronous generatoroperating alone: Example
1 60 36.87 60 53.13S A jX I j= × × ∠ − ° = ∠ °and that
*wo un
-
8/18/2019 8. Alternator Stand Alone
8/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
8
The Synchronous generatoroperating alone: Example
'#2# For the generator at the rated current andthe 1#0 PF$ the phasor diagram is shown#*hen
( ) 22 cos sin 270.4
A S A S AV E X I X I V φ θ θ = − − =
3 468.4T
V V V φ
= =and
'#3# For the generator at the rated current and the0#8 PF leading$ the phasor diagram is shown#*hen
( ) 22 cos sin 308.8
A S A S AV E X I X I V φ θ θ = − − =
3 535T
V V V φ
= =and
-
8/18/2019 8. Alternator Stand Alone
9/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
A
The Synchronous generatoroperating alone: Example
c# *he output power of the generator at 0 and 0#8 PF lagging is
3 cos 3 236.8 60 0.8 34.1out A P V I kW φ θ = = × × × =
*he mechanical input power is gi"en '
34.1 0 1.0 1.5 36.6in out elec loss core loss mech loss P P P P P kW = + + + = + + + =
*he efficienc is34.1
100 % 100% 93.2%36.6
out
in
P P
η = × = × =
d# *he input tor?ue of the generator is
36.6291.2
125.7in
appm
P N mτ
ω = = = -
-
8/18/2019 8. Alternator Stand Alone
10/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
10
The Synchronous generatoroperating alone: Example
*he induced countertor?ue of the generator is
e# *he "oltage regulation of the generator is
34.1271.3
125.7conv
appm
P N mτ
ω = = = -
Lagging PF480 410
100% 17.1%410
VR−
= × =
/nit PF
Lagging PF
480 468100% 2.6%
468VR
−= × =
480 535100% 10.3%
535VR
−= × = −
-
8/18/2019 8. Alternator Stand Alone
11/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
11
Terminal characteristics ofsynchronous generators
ll generators are dri"en ' a prime mo"er $ such as a steam$ gas$ water$ windtur'ines$ diesel engines$ etc# Begardless the power source$ most of prime mo"erstend to slow down with increasing the load# *his decrease in speed is usuallnonlinear 'ut go"ernor mechanisms of some t pe ma 'e included to lineari7e thisdependence#
*he speed drop (S ) of a prime mo"er is defined as
100%nl fl
fl
n nSD
n
−= ×
Cost prime mo"ers ha"e a speed drop from 2D to 4D# Cost go"ernors ha"e amechanism to ad6ust the tur'ine s no5load speed (set5point ad6ustment)#
(+#44#1)
-
8/18/2019 8. Alternator Stand Alone
12/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
12
Terminal characteristics ofsynchronous generators
t pical speed"s# power plot
Since the shaft speed is lin
-
8/18/2019 8. Alternator Stand Alone
13/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
13
Terminal characteristics ofsynchronous generators
similar relationship can 'e deri"ed for the reacti"e power Q and terminal "oltageV T # hen adding a lagging load to a s nchronous generator$ its terminal "oltagedecreases# hen adding a leading load to a s nchronous generator$ its terminal"oltage increases#
*he plot of terminal "oltage "s#
reacti"e power is not necessarillinear#
Goth the fre?uenc 5power andterminal "oltage "s# reacti"e powercharacteristics are important forparallel operations of generators#
hen a generator is operating alone suppl ing the load1#*he real and reacti"e powers are the amounts demanded ' the load#2#*he go"ernor of the prime mo"er controls the operating fre?uenc of the s stem#3#*he field current controls the terminal "oltage of the power s stem#
-
8/18/2019 8. Alternator Stand Alone
14/15ELEN 3441 Fundamentals of Power Engineering Spring 2008
14
Terminal characteristics ofsynchronous generators: Example
E%ample +#3 generator with no5load fre?uencof 1#0 &7 and a slope s p of 1 C !&7 isconnected to Load 1 consuming 1 C of realpower at 0#8 PF lagging# Load 2 (that is to 'econnected to the generator) consumes a real
power of 0#8 C at 0#+0+ PF lagging#a# Find the operating fre?uenc of the s stem 'efore the switch is closed#'# Find the operating fre?uenc of the s stem after the switch is closed#c# hat action could an operator ta
-
8/18/2019 8. Alternator Stand Alone
15/15ELEN 3441 F d t l f P E i i
19
Terminal characteristics ofsynchronous generators: Example
a# *he fre?uenc of the s stem with one load is
161 60
1 s s nl p
P f f !"
s= − = − =
'# *he fre?uenc of the s stem with two loads is1.8
61 59.21 s s nl
p
P f f !"
s= − = − =
c# *o restore the s stem to the proper operating fre?uenc $ the operator shouldincrease the go"ernor no5load set point ' 0#8 &7$ to 1#8 &7# *his will restorethe s stem fre?uenc of 0 &7#