7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 1/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
1
Lecture VI: Per Unit System (P.U.)
Instructor: Dr. John N. Jiang
MWF 09:30am - 10:20am
Carso E!"##r"! C#$#r: Room 001%
S&r"! 2010
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 2/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
2Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Summary: A more complicated example
• Example: A simple power system shown in i!ure "elow:
• #ontains a $%& V !enerator connected to an ideal ':'& step uptransormer a transmission line an ideal &:' step*down transormerand a load
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 3/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
3Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
E,#$r"a, Po.#r S*s$#m
500 kV TransmissionPower Pant
+eneration
,ransmission
System
-istri"ution
System('.V)
!n"ergroun"
Distri#ution Trans$omer
%esi"entia
&ustomer
&ommercia'
In"ustria
&ustomer
%esi"entia
&ustomer
()erhea"
Distri#ution
Trans$ormer
!r#an
&ustomers
*+ kV ,u#-transmission
230 kV
Transmission
Distri#ution ,u#station
*+'12 kV/
igh-Votage ,u#station
230'*+ kV/
tra-igh-Votage ,u#station
500'230 kV/
Distri#ution ine
!n"ergroun" &a#e
To (ther
igh-Votage
,u#stations
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 4/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
4Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Per Unit System
• Simpliy the analysis o power/ener!y system
with dierent 0olta!e le0els "y a0oidin! the
impudence con0ersion
• Easy to 0eriy the answers (since they all all
into a small ran!e)
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 5/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
5Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
T/# P#r-'"$ S*s$#m
• I$ "s 's$omar* $o s#,#$ $.o as# 'a$"$"#s $o #("#a !"+# &#r-'"$ s*s$#m – o,$a!# a Po.#r 4A&&ar#$ Po.#r5
• O# $/#s# as# 'a$"$"#s /a+# ## s#,#$#) a,,
$/# o$/#r as# +a,'#s a # o$a"# * $/# 's'a,#,#$r"a, ,a.s
• T/# as# a&&ar#$ &o.#r r#ma"s os$a$ ./# "$
!o#s $/ro'!/ a $ras(orm#r) o $/# o$/#r /a)+o,$a!# /a!#s a$ #+#r* $ras(orm#r " $/# s*s$#maor"! $o $/# $'rs ra$"o
basebasebasebasebase I V S or Q P =
( )
base
basebase
base
basebase
base
basebase
S
V Z and
V
I Y
I
V Z
2
===
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 6/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
*Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
T/# P#r-'"$ S*s$#m
• I( a &#r-'"$ s*s$#m as# o a #+"#6s 4$ras(orm#r) "'$"omo$or) or s*/roo's !##ra$or5 o. ra$"!s "s 's#) "$s
/ara$#r"s$" .",, o$ +ar* m'/ o+#r a ."# ra!# o( +o,$a!#
a &o.#r ra$"!s7
– S#r"#s r#s"s$a# o( a Tr7 : 0701 &7'7
– S#r"#s r#a$a# o( a Tr7 : 070280710 &7'7
• #a's# &#r-'"$ +a,'#s &ro+"# a o+#"#$ a m#a"!(',
.a* $o om&ar# $ras(orm#r /ara$#r"s$"s ./# $/#* ar# o(
"((#r#$ s"#s) Tr7 Im&#a#s ar# orma,,* !"+# " &#r-'"$ or
as a &#r#$a!# o $/# Tr76s am#&,a$#7
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 7/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
6Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
• T/# #$"r# s*s$#m m's$ /a+# $/# sam# as# &o.#r) a $/# as#+o,$a!#s a$ +ar"o's &o"$s " $/# s*s$#m m's$ # r#,a$# * $/#+o,$a!# ra$"os o( $/# $ras(orm#rs7
• O# ommo r',# "s $o /oos# $/# s*s$#m as# 'a$"$"#s $o ##'a, $o $/# as# o( $/# ,ar!#s$ om&o#$ " $/# s*s$#m7
•
P#r-'"$ +a,'#s !"+# $o ao$/#r as# a # o+#r$# $o $/##. as# * o+#r$"! $/#m $o $/#"r a$'a, +a,'#s 4+o,$s)am&#r#s) o/ms) #$75 A,$#ra$"+#,*) $/#* a # o+#r$#"r#$,* * $/# #'a$"os :
( ) ( )2
1/1/2
base
basebase pubase pu
S
S S Q P S Q P =
2
1/1/2
base
basebase pubase pu
V
V V V =
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) pri
basebase
basebasebase pubase pu
Z X Ra
Z X R Z X Ra Z X R
S V
S V Z X R Z X R
1
2sec
2
12
2
22
1/1/2
=″
=′
=
,he Per*unit System
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 8/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
7Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Summary PU System and 1ther 2orms
Quantity Base
Quantity Actual Value PU
[ ]
[ ]
[ ] [ ] [ ]
[ ]
[ ]
[ ] [ ]
[ ]
[ ]
[ ]
base
ohm
PU
base
basebase
base
basebasebase
base
basebasebasebase
basebasebasebasebasebase
base
basebase
Z
Z Z
V
I Y
VA
V
S
V
I
V Z X R
I V VAS Q P
V
VA I
=
=
=====
====
=
22
Per unit s8stem a s8stem o$ "imensioness 9arameters is use" $or
com9utationa con)enience an" $or rea"i8 com9aring the 9er$ormance
o$ a set o$ trans$ormers or a set o$ eectrica machines.
here ;actua <uantit8= an" >#ase <uantit8? are )aues in )ots am9eres ohms etc.@VAAbase an" @V Abase are chosen $irst.
[ ] [ ]
[ ][ ]
[ ][ ] aratioturnsV
V
S S
base
pribase
base pribase
==
=
sec
sec
Bs ong as two si"es are consistent #ase )aue can #e an8thing.
&on)ention is to use rate" )aue
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 9/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
+Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
•Cin" #ase I #ase V #ase #ase , #aseE/
•a)e at east two known )aues
•&acuate P.!. )aue #ase" on the "e$inition o$ P.!. s8stem
•&acuate P.!. acti)e 9ower o$ oa" I2%/
•Cin" the actua 9ower o$ oa"
•Cin" the actua ine oss oa" I2%/
,F100GVB
2indin! Per*unit Value
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 10/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
10Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Solution
• Example: A simple power system shown in 2i!ure "elow:
• #ontains a $%& V !enerator connected to an ideal ':'& step uptransormer a transmission line an ideal &:' step*down transormerand a load
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 11/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
11Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Example (con3t)
• Impedance o line &456&7 and impedance o load
• #hose 8ase Values (I V 9 P) H +enerator: $%& V and '& VA
• I"aseS"ase/V"ase' '&&&&/$%&&.%; A
• 9"ase'V"ase'/I"ase'$%&/&.%;;.&$ 7
H ,ransmission line: '&VA and a+, ':'&. VT <• V"ase V"ase'/a$%&/&.' $%&& V
• S"ase'& VA• I"ase'&&&&/$%&&.&%; A
• 9"ase$%&& V/ .&%; A ;&$ 7
H Load: '&VA and a,L &:' V L <
• V"ase;V"ase/a $%&&/& $& V
• S"ase;'& VA
• I"ase;'&&&&/$&$'.6= A
• 9"ase;$&/$'.6= >.=6 7
• #on0ert this system to its p.u. e?ui0alent cct.
• Sol0e the pro"lems H 2ind power supplied to load in this system
H 2ind power lost in transmission line
• 2ind the true 0alue ("ased on the "ase 0alues)
Ω∠
3010
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 12/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
12Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Example (con3t)
(") to "uild the pu e?ui0alent cct. 1 power system each cct parameter
di0ided "y its "ase 0alue
• V+pu
• 9linepu(&456&)/;&$&.&&%=45&.&6& pu
• 9loadpu• Per unit e?ui0alent circuit can "e o"tained:
pu
00.1470'0470 ∠=∠
pu
063*.16*.5'3010 ∠=∠
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 13/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
13Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Example (con3t)
Acti0e Power• IpuVpu/9totpu
• Per unit acti0e power o load :
Ploadpu Ipu@pu(&.>6B)@('.>&;)&.$%= p.u.• actual power supplied to load:
PloadPloadpuS"ase&.$%= x '&&&&$%=& C
Line Loss• Pline losspu Ipu@ linepu(&.>6B)@(&.&&%=)&.&&%
• Pline Pline losspu S"ase (&.&&%)('&&&&)%. C
..*.305*+.07+4.0512.1
01
/3063*.1/02*.00076.0
01u p
j j
−∠=+
∠=
∠++
∠
7/23/2019 Energy Conversion VI
http://slidepdf.com/reader/full/energy-conversion-vi 14/14
The University of Oklahoma SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
14Co'rs# No$#s o( ECE 3113) E#r!* Co+#rs"o
Domewor 6
A &*VA %&&&:$%& V distri"ution transormer has the ollowin! resistances andreactance:
,he excitation "ranch impedances are reerred to the hi!h*0olta!e side.
a) 2ind the e?ui0alent circuit o the transormer reerred to the hi!h*0olta!e side aswell as the parameters (all con0erted to the primary side)
")
") 2ind the per unit e?ui0alent circuit o this transormer (you can use the simpliiede?ui0alent circuit).
c) #alculate ,ransormer3s eiciency at ull load (or ull power)a) 8ased on actual resistance
") 8ased on Per Unit Value
c) 2ind actual 0alue o the secondary side load resistanceF.
d) #alculate ,ransormer3s eiciency at G o ull load (or G ull power)a) 8ased on actual resistance
") 8ased on Per Unit Value
c) 2ind actual 0alue o the secondary side load resistanceF.
R P F 32 ohm X PF 45 ohm
RC F 250000 ohm
9rimar8/
RS F 0.05 ohm secon"ar8/ X S F 0.0* ohm
secon"ar8/
X M F 30000 ohm 9rimar8/
Iase"on,im9i$i e
"1<
&ircuit
int: the oa"' im9e"ances o$ the secon"ar8 is not gi)en see eam9es in Notes 22 $or how to "ea with 1'2oa"
Top Related