Y - Delta Connections in 3 Phase Systems Power Calculations

23-Sep-11

1Lecture 03 Power Engineering - Egill Benedikt Hreinsson

Y - Delta Connections in 3 Phase Systems

Power Calculations

23-Sep-11


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

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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

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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

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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


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


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


“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

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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..

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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


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


One-line Diagrams and

One-phase Equivalents

23-Sep-11


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


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


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

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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

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“Reykjavik Energy” Power System

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Orkubú Vestfjarða

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Example One Line Diagram: Sweden (Geographical)

Generation in the north

Load in the south

Transmission from north to south

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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

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K E Y S T O N E

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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

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8 L O U D O N0 8 M D W B R K

8 M O R R S V L

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8 V A L L E Y

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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

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8 P A R K W O D

8 W A K E

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8 C U M B E R L

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8 J O C A S S E

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8 O C O N E E

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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

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8 R O A N E

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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

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K I N T I 3 4 5

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N A N T I C O K

M I D D 8 0 8 6

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T R A F A L H 1T R A F A L H 2

C L A I R V I L

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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 .

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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

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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


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


23-Sep-11

25Lecture 03 Power Engineering - Egill Benedikt Hreinsson 25The Integration of Weather Data and the Power System


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

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23-Sep-11


The Layers of a Power System

• From: Understanding Electric Utilities and De-Regulation, LorrinPhilipson, H. Lee Willis

23-Sep-11


Example 5

23-Sep-11


Example 5 - solution

Y - Delta Connections in 3 Phase Systems Power Calculations

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