23-Sep-11
1Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Y - Delta Connections in 3 Phase Systems
Power Calculations
23-Sep-11
2Lecture 03 Power Engineering - Egill Benedikt Hreinsson
A 3 phase system - drawn like phasors - Star (Y)configuration
Z
Z
Z
Ic
Ib
Vaf
Vcf
Z
Z
Vbf
Ia
Neutral grounding
Neutral grounding
23-Sep-11
3Lecture 03 Power Engineering - Egill Benedikt Hreinsson
A 3 phase system – with neutral return
Z
Z
Ic
Ib
Vaf
Vcf
Z
Z
Vbf
Ia
Zn
+
– +
+n2
n1
The neutrals are labeled n1 and n2 respectively
I
23-Sep-11
4Lecture 03 Power Engineering - Egill Benedikt Hreinsson
A 3 phase system - drawn like phasors - Delta(D) connection
Z ZZ
Ic
Ib
Vaf
Vcf
Z
Z
Vbf
Ia
Z
The Delta connection has never any neutral!
Neutral grounding
23-Sep-11
5Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Y-Δ connections (or Y-D)• Impedances, reactances, loads and transformer windings
may be connected either as Y (Star) or Δ (Delta or D)– Y connection makes it possible to ground the neutral, but has
inferior performance in an unbalanced situation– Δ (D) connection has no neutral but performs better for
unbalanced currents.
23-Sep-11
6Lecture 03 Power Engineering - Egill Benedikt Hreinsson
A Star - Delta (Y-Δ) comparison
Z
Z’’
Z’’
Z’’Z’
Z’
Z’
ab
c
B
A
C
2
' ''' 2 '''' 2 ''
2 123 3
ab
AB
ab AB
Z Z ZZ ZZZ Z
ZZ Z Z Z ZZ
= +⋅
=+
′′′ ′ ′′= → = → =
′′
When are these 2 circuits equivalent?
23-Sep-11
7Lecture 03 Power Engineering - Egill Benedikt Hreinsson
2 Methods of Total Power Calculations in a 3 Phase System
• Method A: Total power (P, Q or S) in a 3 phase system can be determined by calculating the power in 1 phase by using phase voltages and currents and then multiplying by 3!
• Method B: Total power (P, Q or S) in a 3 phase system can be determined directly by using “line-to-line” voltages and currents
23-Sep-11
8Lecture 03 Power Engineering - Egill Benedikt Hreinsson
“Line to Line” and “Phase” Quantities
fV
fI
3L fV V= ⋅
3L fI I= ⋅
Phase and line-to-line voltages:(Note. These quantities are physical
and measurable)
Phase current(Note. This quantity is physical and
measurable)
“Line-to-line current” Note: This quantity is NOT physical and measurable. It is defined for the purpose of the direct method (B) of power calculation
LI
fI
fV LV
23-Sep-11
9Lecture 03 Power Engineering - Egill Benedikt Hreinsson
The 2 Methods of Calculating Total 3 Phase Power
Method A: (1 phase calculation) Method B: (The direct method)Use phase voltages and currents as given:
1 cosf f fP I V φ= ⋅
fV fI
Calculate 1 phase power:
2
1 *f
f
VS
Z=
21 f fS Z I=
Finally, calculate 3 phase power by multiplying by 3:
3 13f fS S= ⋅3 13f fP P= ⋅
Define and use “line to line” voltages/currents:
3L fV V= ⋅ 3L fI I= ⋅
Calculate 3 phase power directly:
1
3
3 3 cos
3 cos 3
cosf L L
f f
f f f
P
V
V
V
I
I
I
P
φ
φ
φ
= ⋅
= ⋅ ⋅ = ⋅
= ⋅
2
3
2
13 3**
fLff
VSS
ZVZ
= ⋅ = ⋅=
23
23f L fIS Z I Z= ⋅= etc.etc.
or.. or..
or..
or..
23-Sep-11
10Lecture 03 Power Engineering - Egill Benedikt Hreinsson
A Delta Connected Load, Delta Currents and phasor Diagram
ab bc caI I I IΔ= = = a b c fI I I I= = =
3fI IΔ= ⋅ 3L fI I= ⋅
“delta currents”
phase currents
From previous slide:
23-Sep-11
11Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Delta Currents - Line to Line Currents
• The delta currents (IΔ ) flowing in a delta connected load (or windings) should not be confused with the fictiousconcept: line to line current (IL)
• The magnitude of the fictious line to line current (IL) is 3 times (or √3 x √3 ) the magnitude of the delta current (IΔ )
• The magnitude of the phase current (If) is √3 times the magnitude of the delta current (IΔ )
23-Sep-11
12Lecture 03 Power Engineering - Egill Benedikt Hreinsson
One-line Diagrams and
One-phase Equivalents
23-Sep-11
13Lecture 03 Power Engineering - Egill Benedikt Hreinsson
One-line Diagram
• Most power systems are balanced three phase systems.
• A balanced three phase system can be modeled as a single (or one) line.
• One-lines show the major power system components, such as generators, loads, transmission lines.
• Components join together at a bus.
23-Sep-11
14Lecture 03 Power Engineering - Egill Benedikt Hreinsson
One Line Diagram - One Phase Equivalent, etc.
Consider a simple balanced 3 phase system:
Since all phases are identical (voltages, currents, impedance except for a 120° phase difference) the system can be represented by a one phase equivalent:
IaVa
Vb
Vc
IbIc
+
+
+-
--
ZLine
ZLine
ZLine
ZLoad
ZLoad
ZLoad
Generator Transmission line Load
Bus 1 Bus 2
Vf If+
-
ZLine ZLoad
Generator Transmission line Load
Bus 1 Bus 2
…or a one-line diagram:Bus 1 Bus 2
23-Sep-11
15Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example One-line Diagram: Iceland
Sog 132 kV
Sog 220 kV
Geitháls
Geitháls 220 kV Búrfell1
Hrauneyjarfoss
Sigalda
Krafla
Hryggstekkur
Varmahlíð
Blanda
MjólkáGeiradalurGlerárskógar Laxá 66 kVRangárvellir 66 kV
Rangárvellir
Laxárvatn
Hrútatunga
Vatnshamrar
Brennimelur 132 kV
Hamra-nes
Brennimelur 220 kV
Sigalda 132 kV
Prestbakki Hólar
Teigar-horn
23-Sep-11
16Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example One Line Diagram: Iceland (Geographical)
Laxá28 MW
Sog90 MW
Blanda150 MW
60 MWKrafla
Hryggstekkur
Teigar-horn
Hólar
VarmahlíðLaxárvatn
Hrútatunga
Vatnshamrar Brenni-melur
Glerárskógar
Prestbakki
Geiradalur
Mjólká Rangárvellir
Power-IntensiveIndustry
Substation
132/220 kV Transmissionline
GeothermalPower generation:
Hydro power
BúrfellHamranes270 MW
Bjarnarflag3 MW
Nesjavellir60 MWKorpa
Sultartangi120 MW
210 MWHrauneyjafoss
Nordic Aluminum
FeSi
Sigalda 150 MWISAL
23-Sep-11
17Lecture 03 Power Engineering - Egill Benedikt Hreinsson
“Reykjavik Energy” Power System
23-Sep-11
18Lecture 03 Power Engineering - Egill Benedikt Hreinsson
“Reykjavik Energy” Power System
23-Sep-11
19Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Orkubú Vestfjarða
23-Sep-11
20Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example One Line Diagram: Sweden (Geographical)
Generation in the north
Load in the south
Transmission from north to south
23-Sep-11
21Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Eastern North American High Voltage Transmission Grid
8 2 8 M W2 9 3 M V R2 7 3 M V R8 2 9 M W
2 5 0 M V R1 0 9 3 M W
1 0 9 4 M W2 5 0 M V R
9 M V R3 0 0 M W 9 M V R3 0 0 M W 9 M V R3 0 0 M W
3 0 0 M W 9 M V R3 0 0 M W 9 M V R3 2 0 M W 9 M V R
- 1 1 4 M V R8 9 3 M W
8 9 7 M W- 1 1 0 M V R
- 1 2 7 M V R8 0 1 M W
0 M V R
0 M V R1 1 2 9 M W 1 8 3 M V R
0 M V R
0 M V R
3 4 0 M V R
1 4 3 M V R
2 9 4 M V R
3 4 8 M W 2 6 2 M V R
0 M W 0 M V R
2 8 6 M V R
1 4 5 M V R
2 5 0 M W 4 5 M V R
0 M W 0 M V R
4 5 M V R 2 5 0 M W
0 M V R 0 M W
2 9 4 M V R
- 2 0 2 M V R
- 2 1 0 M V R
1 4 6 M V R
6 7 6 M W 5 0 M V R 6 7 6 M W 5 0 M V R
R i v e r h e a dW i l d w o o d
S h o r e h a m
B r o o k h a v e n
P o r t J e f f e r s o n
H o l b r o o k
H o l t s v i l l e
N o r t h p o r t
P i l g r i mS y o s s e t
B e t h p a g eR u l a n d R d .N e w b r i d g e
L c s t . G r v .
0 7 M E R O M 5
K E Y S T O N E
0 1 Y U K O N
C O N E M - G H
J U N I A T A
S U N B U R Y
S U S Q H A N A
W E S C O V L E
A L B U R T I SH O S E N S A K
B R A N C H B G
E L R O Y
W H I T P A I NL I M E R I C K
D E A N SS M I T H B R G
3 M I L E I
R A M A P O 5
H U N T E R T N
C N A S T O N E
P E A C H B T M
K E E N E Y
B R I G H T O N
W C H A P E L
C L V T C L F
C H A L K 5 0 0
B U R C H E S
8 P O S S U M
8 O X
8 C L I F T O N
8 L O U D O N0 8 M D W B R K
8 M O R R S V L
8 M T S T M
8 V A L L E Y
8 D O O M S
8 B A T H C O
8 L E X N G T N
8 N O A N N A8 L D Y S M T H
8 E L M O N T
8 M D L T H A N
8 C H C K A H M
8 C A R S O N8 S E P T A
8 Y A D K I N8 F E N T R E S
8 S U R R Y
8 P E R S O N 8 M A Y O 1
8 P A R K W O D
8 W A K E
8 P L G R D N
8 C U M B E R L
8 R I C H M O N
8 M C G U I R E
8 J O C A S S E
8 B A D C R K
8 O C O N E E
8 N O R C R O S
8 B U L L S L U8 B I G S H A
8 B O W E N
8 K L O N D I K
8 U N I O N C T
8 V I L L A R
8 W A N S L E Y
8 S N P
8 W B N P 1
8 R O A N E
8 B U L L R U
8 V O L U N T E
8 S U L L I V A
8 P H I P P B
0 5 N A G E L
8 W I L S O N
8 M O N T G O M
8 D A V I D S O
8 M A R S H A L
8 S H A W N E E
8 J V I L L E
8 W E A K L E Y
8 J A C K S O N
8 S H E L B Y
8 C O R D O V A
8 F R E E P O R
W M - E H V 8
8 U N I O N
8 T R I N I T Y
8 B F N P8 L I M E S T O
8 B N P 2
8 M A D I S O N 8 B N P 1
8 W I D C R K
8 R A C C O O N
8 F R A N K L I
8 M A U R Y
8 M I L L E R
8 L O W N D E S
8 W P O I N T
M C A D A M 8
8 S . B E S S
8 F A R L E Y
8 S C H E R E R
8 H A T C H 8
8 A N T I O C H
8 C L O V E R
R O C K T A V
C O O P C 3 4 5R O S E T O N
F I S H K I L L
P L T V L L E Y
H U R L E Y 3
L E E D S 3
G I L B 3 4 5
F R A S R 3 4 5
N . S C O T 9 9
A L P S 3 4 5
R E Y N L D 3
E D I C
M A R C Y T 1
M A S S 7 6 5
O A K D L 3 4 5
W A T E R C 3 4 5
S T O L E 3 4 5
L A F A Y T T E
D E W I T T 3
E L B R I D G E
C L A Y
V O L N E Y
S C R I B A
J A P I T Z P9 M I P T 1I N D E P N D C
O S W E G O
P A N N E L L 3R O C H 3 4 5
K I N T I 3 4 5
N I A G 3 4 5
B E C K A
B E C K B
N A N T I C O K
M I D D 8 0 8 6
M I L T O N
T R A F A L H 1T R A F A L H 2
C L A I R V I L
H A W T H O R N
E S S A
B R U J B 5 6 1
B R U J B 5 6 9
B R U J B 5 6 2
L O N G W O O D
B a r r e t t
E . G . C .
V a l l e y S t r e a m
L a k e S u c c e s sR a i n e y
J a m a i c a
G r e e n w o o d
F o x H i l l sF r e s h K i l l sG o e t h a l s
C o g e n T e c hG o w a n u s
F a r r a g u tE 1 5 t h S t .
W 4 9 t h S t .
T r e m o n t
S h o r e R d .
D u n w o o d i eS p r a i n B r o o k
E a s t v i e wP l e a s a n t v i l l e
M i l l w o o d
B u c h a n a n
I n d i a n P o i n t
D v n p t . N KH m p . H a r b o r
V e r n o n
C o r o n a
G r e e l a w nE l w o o dFigure shows
transmission lines at 345 kV or above in Eastern
U.S.
23-Sep-11
22Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example Three Bus System
Bus 2 Bus 1
Bus 3
200 MW100 MVR
150 MWMW
150 MWMW 35 MVRMVR
114 MVRMVR
100 MW 50 MVR
1.00 pu
-17 MW 3 MVR
17 MW -3 MVR
-33 MW 10 MVR
33 MW-10 MVR
17 MW -5 MVR
-17 MW 5 MVR
1.00 pu
1.00 pu
100 MW 2 MVR
100 MWAGC ONAVR ON
AGC ONAVR ON
Generator
LoadBus
Circuit Breaker
Pie charts show
percentage loading of
lines
23-Sep-11
23Lecture 03 Power Engineering - Egill Benedikt Hreinsson 23
Power Density in the USA
The blue colorshows the energydensity in load, while red showsthe energy densityin generation.
Source:http://www.pserc.org/ecow/get/generalinf/presentati/psercsemin1/3psercsemin/
23-Sep-11
24Lecture 03 Power Engineering - Egill Benedikt Hreinsson 24
A Voltage Profile in the US grid
The figure show the voltage distribution prior to the collapse and blackout of August 2005
Source:http://www.pserc.org/ecow/get/generalinf/presentati/psercsemin1/3psercsemin/
23-Sep-11
25Lecture 03 Power Engineering - Egill Benedikt Hreinsson 25The Integration of Weather Data and the Power System
Source:http://www.pserc.org/ecow/get/generalinf/presentati/psercsemin1/3psercsemin/
23-Sep-11
26Lecture 03 Power Engineering - Egill Benedikt Hreinsson 26One line diagram of the IEEE standard 114 bus system
23-Sep-11
27Lecture 03 Power Engineering - Egill Benedikt Hreinsson 27Northeast Ohio 138 kV Voltage Contour: 15:00 EDT
http://www.ima.umn.edu/talks/workshops/3-8-13.2004/overbye/overbye.pdf
23-Sep-11
28Lecture 03 Power Engineering - Egill Benedikt Hreinsson 28Northeast Ohio 138 kV Voltage Contour: 15:33 EDT
http://www.ima.umn.edu/talks/workshops/3-8-13.2004/overbye/overbye.pdf
23-Sep-11
29Lecture 03 Power Engineering - Egill Benedikt Hreinsson 29Northeast Ohio 138 kV Voltage Contour: 15:46 EDT
http://www.ima.umn.edu/talks/workshops/3-8-13.2004/overbye/overbye.pdf
23-Sep-11
30Lecture 03 Power Engineering - Egill Benedikt Hreinsson 30Northeast Ohio 138 kV Voltage Contour: 16:05 EDT
http://www.ima.umn.edu/talks/workshops/3-8-13.2004/overbye/overbye.pdf
23-Sep-11
31Lecture 03 Power Engineering - Egill Benedikt Hreinsson
The Layers of a Power System
• From: Understanding Electric Utilities and De-Regulation, LorrinPhilipson, H. Lee Willis
23-Sep-11
32Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example 5
23-Sep-11
33Lecture 03 Power Engineering - Egill Benedikt Hreinsson
Example 5 - solution