per unit system pp

7/24/2019 Per Unit System PP

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Per Unit System

Simplifying Calculations on anElectric Power System

James A. Schreiber December 17 !""#


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Per Unit System !

$hy Use Per Unit%

& $here 'oing analysis of a system with multiple (oltagesPer Unit ma)es calculations easier.

& 1amp *+), - 1amp ! "),

& /y using Per Unit rather than actual (alues electricalparameters at 'iffering (oltage le(els can be 'irectly

use'.


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Per Unit System

$hat is Per Unit%

& A Per Unit (alue is a ratio0 Per Unit actual number 2base number

& Compare to Percent (a more familiar concept) Per Cent Per hun're'31"" 21"" 4ne hun're' Percent 1""563 #721"" Eighty se(en Percent #756

Per Unit Per unit of base number Per Cent 21""31"" 21"" 4ne Per Unit 1."" p.u.63#721"" ".#7 Per Unit ".#7 p.u.63#72#7 4ne Per Unit 1."" p.u.6


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Per Unit System 8

E9amples of Per Unit

Choose a /ase ,alue that has some meaning in your calculations. E9ample0 Eggs

Choose 1! eggs 3one 'o:en6 as the base (alue. /ase ,alue 1! eggs 1 'o:en 1""5 1 Per Unit

;umber


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Per Unit System =

>ow 'o we get Per Unit ,alues%

&


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Per Unit System *

Selecting Per Unit /ase ,alues

& $e choose 1""@,A as our /ase @,A./ase @,A 1""@,A/ase B,A 1"" """B,A

& $e choose the (arious line to line (oltage le(els use' onour system for /ase ,oltages0

="" ! " 11= *+ * 1 .# 8. ),


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Per Unit System 7

Deri(ing Con(ersion


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Per Unit System #


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Per Unit System +

4ther mportant


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Per Unit System 1"

Per Unit Constants on a 1""@,A /ase

/ase ,oltage /ase /ase Amps 3B,6 4hms 3per phase6="" !=""."" 11=.87! " =!+."" !=1."1 # 1+".88 81#. #11= 1 !.!= ="!."* *+ 87.*1 # *.7* * 1!.+* 1*" .#" 1 .# 1.+" 81# .#!

8. ".1+ 1 8.1!(N T " T#is is t#e most important pa$e of t#e presentation! %now t#is pa$e and &ou're $olden )


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Per Unit System 11

E9ample of Using Per UnitCon(ert 1" @,A to actual amps per phase at 1 .#),0

Using actual (alues0 1" @,A 23F 6 31 .#),6

1" """ B,A

23F 6 31 .#),6(Requires calculator) 81# Amps 1 .#),

Using Per Unit0 31" @,A 6 381#8A base J1 .#), 21""@,A 6 3".16 381#8A6 (Simple arit#metic)

81# Amps 1 .#),


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Per Unit System 1!

Con(erting from Per Unit to Actual ,alues

Actual Value = (Per Unit Value) (Base Value) Actual Amps 3Per Unit Amps6 3/ase Amps6

Actual 4hms 3Per Unit 4hms6 3/ase 4hms6 Actual ,olts 3Per Unit ,olts6 3/ase ,olts6

Koing bac) to our Egg E9ample01! eggs 1 Per Unit

f you ha(e ".*7 per unit eggs you ha(e0 Actual eggs 3Per Unit eggs6 3/ase eggs6

3".*76 31! eggs6 # eggs


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Per Unit System 1

Uses of Per Unit System

Performing System Analysis Calculationsmpe'ances of system e9presse' in per unit 3or 56oa' flows 3System Planning6

Short circuit stu'ies 3System Protection6E?uipment si:ing 3Substation Engineering6 "@,A transformer carries how many amps%

3 "@,A21""@,A63/ase Amps6 3". 6381#8A 1 .#),6 1!==A 1 .#), 3". 63 # *A *+),6 !=1A *+),


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Per Unit System 18

Uses of Per Unit System 3conLt6

Ihe per unit system is goo' for 'etermining transformerparalleling suitability.

f you are paralleling transformers with 'iffering @,Aratings they will share the loa' properly if they ha(e thesame per unit impe'ance on their own base.E9ample0 Iransf A 1!5 "@,A Iransf / 1!5 ="@,A Iransf C 185 .*@,A

Iransfs A an' / can be parallele' an' will each loa' up toits appropriate rating.f Iransf C is parallele' with either A or / it will be carryingless than full loa' when A or / reach full loa'.


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Per Unit System 1=

Con(ersion

per unit system pp

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