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 ()
Wye Connection Voltages
Van
 V  
Vbn
 V   
Vcn
 V   
2
Wye Connection Line Voltages
Vca
Vcn
Vab
-Vbn
Van
Vbn
Vbc
Vab
(α = 0 in this case)
 Van  Vbn  V (1  1  120

3 V   30
Vbc

3 V   90
Vca

3 V   150
Line-to-line
voltages are
also balanced
3
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
VLine  3 VPhase 130  3 VPhase e
j
6
I Line  I Phase
S3
*
 3 VPhase I Phase
4
Delta Connection
For the Delta
phase voltages equal
line voltages
Ica
For currents
Ia  I ab  I ca
Ic

Ib
Ibc
Iab
Ia
3 I ab   
I b  I bc  I ab
Ic  I ca  I bc
*
S3  3 VPhase I Phase
5
Three-Phase Example
Assume a -connected load is supplied from a 3
13.8 kV (L-L) source with Z = 10020W
Vab  13.80 kV
Vbc  13.8 0 kV
Vca  13.80 kV
13.80 kV
I ab 
 138  20 amps
 W
I bc  138  140 amps
I ca  1380 amps
6
Three-Phase Example, cont’d
I a  I ab  I ca  138  20  1380
 239  50 amps
I b  239  170 amps I c  2390 amps
*
S  3  Vab I ab
 3  13.80kV  138 amps
 5.7 MVA
 5.37  j1.95 MVA
pf  cos 20   lagging
7
Delta-Wye Transformation
To simplify analysis of balanced 3 systems:
1) Δ-connected loads can be replaced by
1
Y-connected loads with ZY  Z 
3
2) Δ-connected sources can be replaced by
VLine
Y-connected sources with Vphase 
330
8
Delta-Wye Transformation Proof
From the  side we get
Vab Vca
Vab  Vca
Ia 


Z Z
Z
Hence
Vab  Vca
Z 
Ia
9
Delta-Wye Transformation, cont’d
From the Y side we get
Vab
 ZY ( I a  I b )
Vca  ZY ( I c  I a )
Vab  Vca  ZY (2 I a  I b  I c )
Since
Ia  I b  I c  0  I a   I b  I c
Hence
Vab  Vca  3 ZY I a
3 ZY
Vab  Vca

 Z
Ia
Therefore
ZY
1
 Z
3
10
Three Phase Transmission Line
11
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
12
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.
13
Per Phase Analysis Procedure
•
1.
2.
3.
4.
To do per phase analysis
Convert all  load/sources to equivalent Y’s
Solve phase “a” independent of the other phases
Total system power S = 3 Va Ia*
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.
14
Per Phase Example
Assume a 3, Y-connected generator with Van = 10
volts supplies a -connected load with Z = -jW
through a transmission line with impedance of j0.1W
per phase. The load is also connected to a
-connected generator with Va”b” = 10 through a
second transmission line which also has an impedance
of j0.1W per phase.
Find
1. The load voltage Va’b’
2. The total power supplied by each generator, SY and
S
15
Per Phase Example, cont’d
First convert the delta load and source to equivalent
Y values and draw just the "a" phase circuit
16
Per Phase Example, cont’d
To solve the circuit, write the KCL equation at a'
1
'
'
'
(Va  10)(10 j )  Va (3 j )  (Va 
   j  
3
17
Per Phase Example, cont’d
To solve the circuit, write the KCL equation at a'
1
'
'
'
(Va  10)(10 j )  Va (3 j )  (Va 
   j  
3
10
(10 j 
60)  Va' (10 j  3 j  10 j )
3
Va'  0.9  volts
Vb'  0.9  volts
Vc'  0.9 volts
'
Vab
 1.56 volts
18
Per Phase Example, cont’d
*
Sygen  3Va I a
*
'
 Va  Va 
 3Va 
  5.1  j 3.5 VA
 j 0.1 
"

V
"
Sgen  3Va  a
' *
 Va
  5.1  j 4.7 VA
 j 0.1 
19
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
20
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).
21
Simulation of the
Eastern Interconnect
VIK 138
BIG BEN D
WH TWTR3
EEN 138
SUN 138
ST RITA
M UKWO N GO
WH TWTR4
TRIPP
WH TWTR5
UN IVRSTY
Raci ne
JAN 138
Pl ai sades
SGR CK4
UN IV N EU
LBT 138
N5
SGR CK5
LAN 138
BRLGTN 2
SO M ERS
Covert
ALB 138
RO R 138
N LK GV T
H azel ton
BRLGTN 1
ALBERS-2
PO T 138
BUTLER 5
H AZL S 5
UN IO N TP5
M RE 138
Pl easantPrai ri e
N WT 138
N ED 161
BCH 138
TRK RIV5
CASVILL5
BLK 138
CO R 138
DRNE 5
LEN A ; B
WBT 138
ELK 138
D IK 138
LEN A ; R
8TH ST. 5
D R EN G 5
LO RE
WASH BRN 5
Zi on
5
ELERO ; BT
ASBURY 5
EL FARM 5
Benton H arbor
BAIN 4
N LG 138
LIBERTY5
D UN D EE 5
LUN D Q ST5
D RCO M P 5
PARIS WE
TICH IGN
WIB 138
D AR 138
N ED 138
M ID PO RT5
D RFN D RY5
WTWEST 5
Paddock
N O M 138
H LM 138
BLKH AWK5
ELERO ; RT
SO . GVW. 5
Wempl eton
PECAT; B
Rockford
Waukegan
CN TRGRV5
LAN CA; R
JULIAN 5
SALEM N 5
H arl em
FREEP;
Bel vi dere
M arengo
Roscoe
GALEN A 5
Sand Park
Pi erpont
B465
FO RD A; R
S PEC; R
E. Rockf ord
Al pi ne
Cook - 345 kV
Charl es
B427 ; 1T
Sabrooke
Cherry Val l ey
Cook - 765 kV
Bl aw khaw k
Kenzi e Creek
SAVAN N A5
Arnol d
TRAER 5
STILL; RT
M Q O KETA5
WYO M IN G5
VIN TO N 5
Tol l w ay
D YSART 5
FAIRFAX5
PCI
M T VERN 5
5
Hanover
BEVERLY5
H IAWATA5
6 ST
Tw i n Branch
BERTRAM 5
5
Bar t l et t
Des Pl ai nes
YO RK
5
O l i ve
M ARYL; B
Wayne
JackSr
I t asca
Nor di
G l endal e
M i chi gan Ci ty
W407 ( Fer m i )
LEECO ; BP
Addi son
Chur ch
H 445 ; 3B
H 440 ; R
El m hur st
Lom bar d
GR M N D 5
ALBAN Y 6
E CALM S5
BVR CH 65
D EWITT 5
BVR CH 5
M EN D O ; T
D IXO N ; BT
GARD E;
ALBAN Y 5
H 71 ; BT
H 440 ; RT
H 71 ; B
H 71 ; R
N Aurora
STEWA; B
D umont 345
El ect r i c Junct i on
STERL; B
D umont 765
D unacr
Li sl e
M cCook
Sti l l w el l
D ow ners Groove
CRLRID G5
Chi ave
M ECCO RD 3
SB PIC 5
CO RD O ;
N ELSO ; RT
SB YIC 5
Lake George
Bl ue Isl and
Goodi ngs Grove
SB 71 5
Green Lake
SB 78 5
Kenda
Green Acres
SB 76 5
SB 89 5
Tow er Rd
M unster
Burnham
Lockport
SB 17 5
SUB 77 5
D AVN PRT5
Romeo
SB 49 5
SB 74 5
SB 90 5
H ILLSIE5
Shef i el d
Wi l l Co.
R FAL; R
SB 79 5
SBH YC5
SB UIC 5
Pl ano
N ELSO ; R
R FAL; B
SB GIC 5
JASPER 5
Babcock
Sand Ri dge
SB 88 5
SB EIC 5
IPSCO
SB JIC 5
M otezuma
3
IPSCO
Lansi ng
Jol i et
SB 58 5
5
Gl enw ood
SB 70 5
Bri gg
SB A 5
PO WESH K5
H ILLS 5
PARN EL 5
SB 28 5
SB 52 5
SB 48 5
R5
SB 85 5
SB 47 5
Frankf ort
El w ood
East Frankf ort
M atteson
U. Park
Burr O ak
Chi cago H ei ghts
F-503
Country Cl ub H i l l s
N Len
SB 31T 5
Park Forest
F-575
Bl oom
Woodhi l l
SB 53 5
E M O LIN E
Col l i ns
Wi l ton Center
D resden
SB 18 5
B
SB 43 5
Schahf er
B
93%
105%
SB 112 5
MVA MVA
La Sal l e
Wi l mi ngton
KPECKTP5
WEST
5
SO . SUB 5
Br ai dw ood
H WY61 5
9 SUB 5
BEACO N 5
N EWPO RT5
EIC
5
BRD GPRT5
M PWSPLIT
H ALLO CK
LUCAS 5
Peoria
WATSEKA
17GO D LN D
GILM AN
FARGO
CAT M O SS
RSW EAST
RAD N O R
CAT SUB1
E PEO RIA
PIO N EERC
CAT TAP
CAT M AP
KEYSTO N E
H IN ES
WAPELLO 5
JEFF
5
ED WARD S3
ED WARD S1
H EN RYCO 5
CAT SUB2
EASTERN
BURLIN 1G
D EN M ARK5
BRLGTN 5
TAZEWELL
Tazw el l
GIBSO N C
PAXTO N E
H O O PESTN
N IO TA
Pow erton
N IO TA
GIBSO N CP
APAN O SE5
N LERO Y
Bloomington
CUBA
VIELE 5
WEED M AN
D uck Creek
M ACO M BN E
RN TO UL J
RAN TO UL
CAN TO N
H AM LTN AM
VERM ILO N
M ACO M B W
TRIVERS5
CLTN TAP
TILTN EC
VERM L 1
CARBID E5
VERM ILO N
CLT RT54
Ipava
M ASO N
W TILTO N
M AH O M ET
IPAVA
AD AIR
S CLN TN
M ASO N CY
H AVAN A S
H AVAN A
CH AM P TP
CH AM P W
1346A TP
H O LLAN D
KICKAPO O
Gul on
LEVER RD
Cl i nton
RISIN G
CH AM P E
BUN SO N VL
PERKN SRD
22
Small PowerWorld Simulator Case
Load with
green
arrows
indicating
amount
of MW
flow
Bus 2
20 MW
-4 MVR
Bus 1
1.00 PU
204 MW
102 MVR
1.00 PU
106 MW
0 MVR
150 MW AGC ON
116 MVR AVR ON
-14 MW
-34 MW
10 MVR
4 MVR
34 MW
-10 MVR
Home Area
Used
to control
output of
generator
-20 MW
4 MVR
100 MW
Note the
power
balance at
each bus
14 MW
-4 MVR
1.00 PU
Bus 3
102 MW
51 MVR
150 MW AGC ON
37 MVR AVR ON
Direction of arrow is used to indicate
direction of real power (MW) flow
23
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.
24
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.
25
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
26
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.
27
Overloaded Transmission Line
28
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).
29
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
30
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.
31
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.
32
Three Bus Case on AGC
Bus 2
-40 MW
8 MVR
40 MW
-8 MVR
Bus 1
1.00 PU
266 MW
133 MVR
1.00 PU
101 MW
5 MVR
150 MW AGC ON
166 MVR AVR ON
-39 MW
-77 MW
25 MVR
12 MVR
78 MW
-21 MVR
Home Area
Generation
is automatically
changed to match
change in load
100 MW
39 MW
-11 MVR
Bus 3
1.00 PU
133 MW
67 MVR
250 MW AGC ON
34 MVR AVR ON
Net tie flow is
close to zero
33
MISO Real-Time ACE
Previously
individual
utilities did
their own
ACE
calculations;
now we are
part of MISO,
which does
one for the
region
https://www.misoenergy.org/MARKETSOPERATIONS/REALTIMEMARKETDATA/Pages/ACEChart.aspx
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