ECE 476 Power System Analysis

Lecture 4: Three-Phase, Power System Operations

Prof. Tom Overbye

Dept. of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

overbye@illinois.edu

Announcements

• Please read Chapter 4• HW 1 is due now• HW 2 is 2.44, 2.48, 2.49, 2.51

• It does not need to be turned in, but will be covered by an in-class quiz on Sept 10

• San Diego Gas & Electric is on campus for the ECE Career Fair on 9/9) (ARC Gym) and then for interviews on 9/10

Three-Phase - Wye Connection

• There are two ways to connect 3 systems– Wye (Y)– Delta ()

an

bn

cn

Wye Connection Voltages

V

V

V

V

V

V

3

Wye Connection Line Voltages

Van

Vcn

Vbn

VabVca

Vbc

-Vbn

(1 1 120

3 30

3 90

3 150

ab an bn

bc

ca

V V V V

V

V V

V V

Line-to-line

voltages are

also balanced

(α = 0 in this case)

4

Wye Connection, cont’d

• Define voltage/current across/through device to be phase voltage/current

• Define voltage/current across/through lines to be line voltage/current

6

*3

3 1 30 3

3

j

Line Phase Phase

Line Phase

Phase Phase

V V V e

I I

S V I

5

Delta Connection

IcaIc

IabIbc

Ia

Ib

a

b

*3

For the Delta

phase voltages equal

line voltages

For currents

I

3

I

I

3

ab ca

ab

bc ab

c ca bc

Phase Phase

I I

I

I I

I I

S V I

6

Three-Phase Example

Assume a -connected load is supplied from a 3 13.8 kV (L-L) source with Z = 10020W

13.8 0

13.8 0

13.8 0

ab

bc

ca

V kV

V kV

V kV

13.8 0138 20

138 140 138 0

ab

bc ca

kVI amps

I amps I amps

7

Three-Phase Example, cont’d

*

138 20 138 0

239 50 amps

239 170 amps 239 0 amps

3 3 13.8 0 kV 138 amps

5.7 MVA

5.37 1.95 MVA

pf cos 20 lagging

a ab ca

b c

ab ab

I I I

I I

S V I

j

8

Delta-Wye Transformation

Y

phase

To simplify analysis of balanced 3 systems:

1) Δ-connected loads can be replaced by 1

Y-connected loads with Z3

2) Δ-connected sources can be replaced by

Y-connected sources with V3 30Line

Z

V

9

Delta-Wye Transformation Proof

From the side we get

Hence

ab ca ab caa

ab ca

a

V V V VI

Z Z Z

V VZ

I

10

Delta-Wye Transformation, cont’d

a

From the side we get

( ) ( )

(2 )

Since I 0

Hence 3

3

1Therefore

3

ab Y a b ca Y c a

ab ca Y a b c

b c a b c

ab ca Y a

ab caY

a

Y

Y

V Z I I V Z I I

V V Z I I I

I I I I I

V V Z I

V VZ Z

I

Z Z

11

Three Phase Transmission Line

12

Per Phase Analysis

• Per phase analysis allows analysis of balanced 3 systems with the same effort as for a single phase system

• Balanced 3 Theorem: For a balanced 3 system with– All loads and sources Y connected– No mutual Inductance between phases

13

Per Phase Analysis, cont’d

• Then– All neutrals are at the same potential– All phases are COMPLETELY decoupled– All system values are the same sequence as sources. The

sequence order we’ve been using (phase b lags phase a and phase c lags phase a) is known as “positive” sequence; later in the course we’ll discuss negative and zero sequence systems.

14

Per Phase Analysis Procedure

• To do per phase analysis

1. Convert all load/sources to equivalent Y’s

2. Solve phase “a” independent of the other phases

3. Total system power S = 3 Va Ia*

4. If desired, phase “b” and “c” values can be determined by inspection (i.e., ±120° degree phase shifts)

5. If necessary, go back to original circuit to determine line-line values or internal values.

15

Per Phase Example

Assume a 3, Y-connected generator with Van = 10 volts supplies a -connected load with Z = -j through a transmission line with impedance of j0.1 per phase. The load is also connected to a -connected generator with Va”b” = 10 through a second transmission line which also has an impedance of j0.1 per phase.Find

1. The load voltage Va’b’

2. The total power supplied by each generator, SY and S

16

Per Phase Example, cont’d

First convert the delta load and source to equivalent

Y values and draw just the "a" phase circuit

17

Per Phase Example, cont’d

' ' 'a a a

To solve the circuit, write the KCL equation at a'

1(V 1 0)( 10 ) V (3 ) (V j

3j j

18

Per Phase Example, cont’d

' ' 'a a a

'a

' 'a b

' 'c ab

To solve the circuit, write the KCL equation at a'

1(V 1 0)( 10 ) V (3 ) (V j

310

(10 60 ) V (10 3 10 )3

V 0.9 volts V 0.9 volts

V 0.9 volts V 1.56

j j

j j j j

volts

19

Per Phase Example, cont’d

*'*

ygen

*" '"

S 3 3 5.1 3.5 VA0.1

3 5.1 4.7 VA0.1

a aa a a

a agen a

V VV I V j

j

V VS V j

j

20

Power System Operations Overview

• Goal is to provide an intuitive feel for power system operation

• Emphasis will be on the impact of the transmission system

• Introduce basic power flow concepts through small system examples

21

Power System Basics

• All power systems have three major components: Generation, Load and Transmission/Distribution.

• Generation: Creates electric power.• Load: Consumes electric power.• Transmission/Distribution: Transmits electric power

from generation to load. – Lines/transformers operating at voltages above 100 kV are

usually called the transmission system. The transmission system is usually networked.

– Lines/transformers operating at voltages below 100 kV are usually called the distribution system (radial).

22

Simulation of the Eastern Interconnect

Bloomington

Peoria

RockfordWaukegan

Zi on

Pl easant

Des Pl ai nes

El mhurst

I t asca

Tol l w ay

W407 ( Fermi )

Cherry Val ley

Wempleton

Paddock

Cl inton

Powerton

Ipava

D uck Creek

Brai dw ood

Shefi eld

Chiave

Munster

El ect r i c Junct i on

Pl ano

La Sal le

Lombard

Li sle

Col l ins

D resden

Lockport

East Frankfort

Goodings Grove

Tazwel l

Lake George

D unacr

Green Acres

Schahfer

Tower Rd

Babcock

Prai ri e

Racine

Michi gan Ci ty

El wood

Gulon

Sti l lwel l

O l i ve

Sycamore

Bondurant

Motezuma

Arnold

Se Pol k

H azel ton

Burr Oak

Pl ai sades

Benton Harbor

RN TOUL J

PERKN SRD

CH AMP ECH AMP W

LEVER RD

RISIN G

CH AMP TP

MAHOMET

WEED MAN

N LEROY

PAXTON E

RANTOUL

GIBSON C

GIBSONCP

H OOPESTN

VERMILON

TILTN EC

BUNSONVL

W TILTON

VERML 1

VERMILON

GILMAN

WATSEKA 17GOD LN D

CLTN TAP

CLT RT54

S CLN TN

R FAL; R

1346A TP

H OLLAND

MACOMB WH AMLTNAM

H AVAN A

IPAVA

CANTON

CUBA

KICKAPOO

MASON

H AVAN A SMASON CY

TAZEWELL

H ALLOCK

ED WARD S3

CAT MOSSFARGO

KEYSTONE

E PEORIA

RSW EAST

CAT SUB2

H INES

PION EERC

RAD N OR

CAT TAP

CAT MAP

CAT SUB1

EASTERNBURLIN 1G

MACOMBN E

N IOTA

N IOTA

BRLGTN 5

SB 18 5

E MOLIN E

SB 43 5

SB 112 5

KPECKTP5

SO.SUB 5

SB 85 5

SB 31T 5

SB 28 5

SB 17 5

SB 49 5

SB 53 5

SB 47 5SB 48 5

SB A 5

SB 70 5

SB 79 5

SB 88 5

SB 71 5

BVR CH 65 BVR CH 5 ALBAN Y 5

YORK 5

SAVAN NA5

GALEN A 5

8TH ST.5

LORE 5

SO .GVW.5

SALEM N5

ALBAN Y 6

GARD E;

H 71 ;BTH 71 ; B

H 71 ; R

R FAL; B

N ELSO; R

N ELSO;RT

STERL; B

D IXON;BT

MECCORD 3

CORD O;

LEECO;BP

MARYL; B

MEND O; T

STILL;RT

B427 ;1T

LANCA; R

PECAT; B

FREEP;

ELERO;BT ELERO;RT

LENA ; RLENA ; B

H 440 ;RT

H 440 ; R

STEWA; B

H 445 ;3B

Roscoe

Pi erpont

S PEC; R

FORD A; R

H arlem

Sand Park

N WT 138

BLK 138

ROR 138

JAN 138

ALB 138

N OM 138

D AR 138

H LM 138

POT 138 MRE 138

COR 138 D IK 138

BCH 138

Sabrooke

Bl awkhawk

Al pine

E. Rockford

Charles

Belvidere

B465

Marengo

WIB 138

WBT 138 ELK 138

N LG 138

N LK GV T

SGR CK5

BRLGTN 1

BRLGTN 2

SGR CK4

UN IVRSTY

UN IV NEU

WHTWTR5

WHTWTR4

WHTWTR3

SUN 138

VIK 138

LBT 138

TICH IGN PARIS WE

ALBERS-2

Green Lake

Sand Ridge

Chicago H eights

Burnham

Lansing

F-575

F-503Gl enwood

Bl oomPark ForestMatteson

Country Cl ub H i l l s

Woodhi l lU. Park

Bl ue Island

Wi lmington

Wi l ton Center

Frankfort

N Len

Brigg

D owners Groove

N Aurora

Hanover

Bart l et t

Church

Addi son

NordiG l endal e

Romeo

Wayne

Wi l l Co.

Jol i et

D umont 345 D umont 765

Kenzie Creek

JackSr

Cook - 345 kV

Cook - 765 kV

Twin Branch

BAIN 4

SOMERS

ST RITA

BIG BEND

MUKWON GO

N ED 138

N ED 161

LAN 138

EEN 138

CASVILL5TRK RIV5D UND EE 5

LIBERTY5

ASBURY 5

CN TRGRV5

JULIAN 5

MQOKETA5

E CALMS5

GR MN D 5

D EWITT 5

SBHYC5

SUB 77 5

SB 74 5SB 90 5

SB 78 5D AVN PRT5

SB 76 5

SB 58 5

SB 52 5

SB 89 5

IPSCO 5

IPSCO 3

D ENMARK5

N EWPORT5

H WY61 5

WEST 5

9 SUB 5

H ENRYCO5

VIELE 5

TRIVERS5

CARBID E5

TRIPP

Kenda

MPWSPLIT

WYOMIN G5

MT VERN5

BERTRAM5

H AZL S 5

BLKHAWK5

ED WARD S1

JEFF 5

WAPELLO5

APANOSE5

AD AIR

H ILLSIE5

PCI 5

BEVERLY5

FAIRFAX5

H ILLS 5PARNEL 5POWESHK5

BEACON 5

EIC 5

BRD GPRT5

LUCAS 5

CRLRID G5

SB PIC 5

SB J IC 5

SB EIC 5

SB YIC 5

SB GIC 5

SB UIC 5

WASH BRN 5

UN IONTP5

EL FARM5

D R EN G 5

WTWEST 5

D RFN D RY5

MID PORT5

6 ST 5

VINTON 5

H IAWATA5

D YSART 5

TRAER 5

D R N E 5

LUND QST5

D RCOMP 5

H AMPTON 5

FRANKLN5BUTLER 5

M-TOWN 5

REASN OR5

N EWTON 5

JASPER 5

TIMBRCK5

McCook

Covert

93%B

MVA105%

B

MVA

23

Small PowerWorld Simulator Case

Bus 2 Bus 1

Bus 3Home Area

204 MW

102 MVR

150 MW

150 MW 37 MVR

116 MVR

102 MW 51 MVR

1.00 PU

-20 MW 4 MVR

20 MW -4 MVR

-34 MW 10 MVR

34 MW-10 MVR

14 MW -4 MVR

-14 MW

4 MVR

1.00 PU

1.00 PU

106 MW 0 MVR

100 MWAGC ONAVR ON

AGC ONAVR ON

Load withgreenarrows indicatingamountof MWflow

Usedto controloutput ofgenerator

Direction of arrow is used to indicatedirection of real power (MW) flow

Note thepower balance ateach bus

24

Power Balance Constraints

• Power flow refers to how the power is moving through the system.

• At all times in the simulation the total power flowing into any bus MUST be zero!

• This is know as Kirchhoff’s law. And it can not be repealed or modified.

• Power is lost in the transmission system.

25

Basic Power Control

• Opening or closing a circuit breaker causes the power flow to instantaneously(nearly) change.

• No other way to directly control power flow in a transmission line.

• By changing generation or load, or by switching other lines, we can indirectly change this flow.

26

Modeling Consideration – Change is Not Really Instantaneous!

• The change isn’t really instantaneous because of propagation delays, which are near the speed of light; there also wave reflection issues– This will be addressed more in Chapters 5 and 13

Red is the vs end, green the v2 end

27

Transmission Line Limits

• Power flow in transmission line is limited by heating considerations.

• Losses (I2 R) can heat up the line, causing it to sag.• Each line has a limit; Simulator does not allow you

to continually exceed this limit. Many utilities use winter/summer limits.

28

Overloaded Transmission Line

29

Interconnected Operation

• Power systems are interconnected across large distances. For example most of North America east of the Rockies is one system, with most of Texas and Quebec being major exceptions

• Individual utilities only own and operate a small portion of the system, which is referred to an operating area (or an area).

30

Operating Areas

• Transmission lines that join two areas are known as tie-lines.

• The net power out of an area is the sum of the flow on its tie-lines.

• The flow out of an area is equal to

total gen - total load - total losses = tie-flow

31

Area Control Error (ACE)

• The area control error is the difference between the actual flow out of an area, and the scheduled flow.– There is also a frequency dependent component that we’ll

address in Chapter 12

• Ideally the ACE should always be zero.• Because the load is constantly changing, each

utility must constantly change its generation to “chase” the ACE.

32

Automatic Generation Control

• Most utilities use automatic generation control (AGC) to automatically change their generation to keep their ACE close to zero.

• Usually the utility control center calculates ACE based upon tie-line flows; then the AGC module sends control signals out to the generators every couple seconds.

33

Three Bus Case on AGC

Bus 2 Bus 1

Bus 3Home Area

266 MW

133 MVR

150 MW

250 MW 34 MVR

166 MVR

133 MW 67 MVR

1.00 PU

-40 MW 8 MVR

40 MW -8 MVR

-77 MW 25 MVR

78 MW-21 MVR

39 MW-11 MVR

-39 MW

12 MVR

1.00 PU

1.00 PU

101 MW 5 MVR

100 MWAGC ONAVR ON

AGC ONAVR ON

Net tie flow is close to zero

Generationis automaticallychanged to matchchange in load

34

MISO Real-Time ACE

https://www.misoenergy.org/MARKETSOPERATIONS/REALTIMEMARKETDATA/Pages/ACEChart.aspx

Previouslyindividualutilities didtheir ownACE calculations;now we arepart of MISO,which doesone for the

region

MISO Real-Time ACE

• MISO's real-time ACE is available online (along with lots of other data)

https://www.misoenergy.org/MARKETSOPERATIONS/REALTIMEMARKETDATA/Pages/ACEChart.aspx