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[email protected]://www.powerworld.com
2001 South First StreetChampaign, Illinois 61820+1 (217) 384.6330
2001 South First StreetChampaign, Illinois 61820+1 (217) 384.6330
New PowerWorld Modal Analysis Tools
Tom OverbyeJune 19, 2018
2© 2018 PowerWorld Corporation
Aside: Synthetic Grids
3© 2018 PowerWorld Corporation
• PowerWorld Dynamics Studio (DS) provides an interactive simulation environment for doing transient stability level simulations
• It can be run either stand alone, or as a server as part of a multi‐user simulation
• Input cases are pwb/pwd• It can be also used as aC37.118 data source andis currently being updatedto support DNP3 control
Aside: PowerWorld Dynamics Studio
4© 2018 PowerWorld Corporation
DS Interactive Example
5© 2018 PowerWorld Corporation
• Frequency domain techniques can be quite helpful in providing information about power system dynamic performance
• With version 20 PowerWorld includes a growing array of tools– Fast Fourier Transform (FFT) and modal analysis using a variety of methods
• Tools are available both from transient stability and from the case info displays
• Goal is to provide insight into the power system results, either from studies like transient stability or from measurements (e.g., PMUs)
Overview
6© 2018 PowerWorld Corporation
• Small signal analysis has been used for decades to determine power system frequency response– It is a model‐based approach that considers the properties of a power system linearized about an operating point
– PowerWorld Simulator does single‐machine, infinite bus (SMIB) small signal analysis
• Measurement‐based modal analysis determines the dynamic properties of a system– Input can either be measurements from PMUs or transient stability results
Small Signal Analysis and Measurement‐Based Modal Analysis
7© 2018 PowerWorld Corporation
• Ring‐down analysis seeks to determine the frequency and damping of key power system modes following some disturbance
• There are several different techniques, with the Prony approach the oldest (from 1795)
• Regardless of technique, the goal is to represent the response of a sampled signal as a set of exponentially damped sinusoidals (modes)
Ring‐down Modal Analysis
( ) cosi
qt
i i ii 1
y t Ae t
Damping (%) i2 2i i
100
8© 2018 PowerWorld Corporation
Movie of 0.611 Hz ModeKeep in mind the mode data is being extracted from the full system response
9© 2018 PowerWorld Corporation
• PowerWorld has implemented several modal analysis techniques– Variable Projection Method (VPM); the VPM was first applied to power systems at UW‐Madison through BPA funding
– Matrix Pencil Method (MPM); the MPM is the first step in the VPM, but can be used independently
– Dynamic Model Decomposition (DMD); DMD is fast, but requires multiple signals
• For all, computation increases substantially with the number of sample points
PowerWorld Modal AnalysisTechniques
10© 2018 PowerWorld Corporation
• Our goal is to make modal analysis easy to use, and easy to visualize the results
• Goal is to provide a tool that could be used with either transient stability results or actual system signals (e.g., from PMUs)
• Two ways to access in PowerWorld– On the Transient Stability Analysis form left menu, Modal Analysis (right below SMIB Eigenvalues)
– By right‐clicking on a transient stability or plot case information display, and selecting Modal Analysis Selected Columns or Modal Analysis All Columns
Modal Analysis in PowerWorld
11© 2018 PowerWorld Corporation
• A short fault at t=0 gets the below three generator case oscillating with multiple modes (mostly clearly visible for the red and the green curves)– CaseB3_CLS_3Gen_Damped
Modal Analysis: Three Generator Example
GENCLS
slack
GENCLS X=0.2
X=0.2 X=0.2
GENCLS
Bus 1 Bus 2
0.00 Deg 3.53 Deg1.0000 pu1.0500 pu
-3.53 Deg 1.050 pu
200 MW 0 Mvar
Bus 3
54.543.532.521.510.50
60.0100
60.0090
60.0080
60.0070
60.0060
60.0050
60.0040
60.0030
60.0020
60.0010
60.0000
59.9990
59.9980
59.9970
Speed_Gen Bus 1 #1 Speed_Gen Bus 2 #1 Speed_Gen 3 #1
12© 2018 PowerWorld Corporation
• Run the transient stability for 5 seconds• One way to do modal analysis is on the Transient Stability Display select Modal Analysis, then Open Modal Analysis Form to display the Modal Analysis Form, load the data from the Gen_Speed Plot and click Do Modal Analysis– This does modal analysis simultaneously for all three generator speed curves (signals)
• Alternatively, select Results from RAM, view just the generator speed fields, right‐click and select Modal Analysis All Columns
Simple VPM Three Generator Example
13© 2018 PowerWorld Corporation
Transient StabilityModal Analysis Page
Key results are shown in the upper‐right of the form. There are two main models, one at 2.03Hz with 1.7% damping, and one at 1.51 with 1.1% damping. The bottom portion of the display provides a summary of how well each signal was matched, and by right‐clicking on the signal, provides more details
14© 2018 PowerWorld Corporation
Transient StabilityModal Analysis Page: Some Key Fields
When used with case infodisplays the data source is the existing data loaded from the case info
Select time and calculation method. Best to select the start time after the last event. The Maximum Hz field determines the highest frequency thatcan be determined. Higher values resultin more computation
Select signals to include in determining modesand the signals to include in the reproduced results
Right‐click on signal to view its dialog
15© 2018 PowerWorld Corporation
• The Signal Dialog provides details about each signal, including its modal components and a comparison between the original and reproduced signals (example for gen 3)
Three Generator Example: Signal Dialog
PWDVectorGrid Variables
Time (Seconds)543210
Valu
es
1.00006
1.000055
1.00005
1.000045
1.00004
1.000035
1.00003
1.000025
1.00002
1.000015
1.00001
1.000005
Original Value Reproduced Value
16© 2018 PowerWorld Corporation
• Assume the system is run with no disturbance for two seconds, and then the fault is applied– The incorrect approach would be to try to match the entire signal; rather just match from after the fault
Caution: Setting in Time Incorrectly Can Result in Unexpected Results!
PWDVectorGrid Variables
Time (Seconds)76543210
Valu
es
1.000065
1.00006
1.000055
1.00005
1.000045
1.00004
1.000035
1.00003
1.000025
1.00002
1.000015
1.00001
1.000005
1
0.999995
Original Value Reproduced Value
PWDVectorGrid Variables
Time (Seconds)765432
Valu
es
1.00006
1.000055
1.00005
1.000045
1.00004
1.000035
1.00003
1.000025
1.00002
1.000015
1.00001
1.000005
Original Value Reproduced Value
Requiredten modes! Just three
modes
17© 2018 PowerWorld Corporation
• The individual modes (or any combination) can also be viewed
Three Generator Example: Looking at Selected Modes
Allows theremoval of the detrend
Allows inclusionof selectedmodes in thereproducedsignals
Select to updatethe reproducedsignals
View the reproducedsignals with just theselected modes
18© 2018 PowerWorld Corporation
Three Generator Example: Looking at Selected Modes
PWFullMatrixBasicGrid Variables
Time (sec)543210
Valu
es
0.000010.0000090.0000080.0000070.0000060.0000050.0000040.0000030.0000020.000001
0-0.000001-0.000002-0.000003-0.000004-0.000005-0.000006-0.000007-0.000008-0.000009-0.00001
Gen Bus 1 #1 Speed Gen Bus 2 #1 Speed Gen 3 #1 Speed
PWFullMatrixBasicGrid Variables
Time (sec)543210
Valu
es
0.000120.000110.0001
0.000090.000080.000070.000060.000050.000040.000030.000020.00001
0-0.00001-0.00002-0.00003-0.00004-0.00005-0.00006-0.00007-0.00008-0.00009-0.0001
-0.00011
Gen Bus 1 #1 Speed Gen Bus 2 #1 Speed Gen 3 #1 Speed
1.51 Hz Mode: Generators1 and 2 are In Phase
2.03 Hz Mode: Generators2 and 3 are In Phase
19© 2018 PowerWorld Corporation
• The magnitude and angle of the contribution of a mode in each signal can be viewed by right‐clicking on the desired mode
Mode Analysis Mode Details Dialog
Right‐click and selectShow Dialog
Notice for the 2.03 Hz Modethe bus 2 and 3 generatorsare in phase
20© 2018 PowerWorld Corporation
• This a 22,000 bus case with 8400 substations. Contingency is the double Palo Verde outage
• Goal is to provideinsight into thesystem response
• Focus is on beingable to handlemany signals,which requiresvisualization
Larger Case Example
Figure shows theaverage frequencyfor all the substations
21© 2018 PowerWorld Corporation
• With one signal used (sub 18004 freq) to get the modes, there are four: 0, 0.029, 0.21, 0.42Hz
Modal Analysis With Many Signals: The Best and The Worst
PWDVectorGrid Variables
Time (Seconds)2015105
Valu
es
60
59.99
59.98
59.97
59.96
59.95
59.94
59.93
59.92
59.91
59.9
59.89
59.88
59.87
59.86
59.85
Original Value Reproduced Value
PWDVectorGrid Variables
Time (Seconds)2015105
Valu
es
60.03
60.02
60.01
60
59.99
59.98
59.97
59.96
59.95
59.94
59.93
59.92
59.91
59.9
59.89
59.88
59.87
59.86
59.85
Original Value Reproduced Value
Best Match Worst Match
The robustness of this process can be quantified by looking at both the averagecost function and the maximum over all 8400 signals (0.008 and 0.028 here)
22© 2018 PowerWorld Corporation
• The modal analysis can be improved by including more signals in the calculation of the modes. Yet only a small number need to be included
• For example, by just adding the signal with the highest cost function we now get a total of five modes and reduce average cost function from 0.008 to 0.0054, with the largest value reduced from 0.028 to 0.02
• The Iterative Matrix Pencil optimizes this process by iteratively adding more signals
Improving Modal Analysis With Many Signals
23© 2018 PowerWorld Corporation
• This approach iteratively adds the signal with the highest cost function– Usually about ten gives quite good results; this gives 8 modes, and reduces the average error to 0.0025 and the maximum to 0.0088
Iterative Matrix Pencil Approach
24© 2018 PowerWorld Corporation
• The below figures should an average signal reproduction and the worst signal reproduction
Modal Analysis With Many Signals: The Average and The Worst
PWDVectorGrid Variables
Time (Seconds)2015105
Valu
es
60
59.99
59.98
59.97
59.96
59.95
59.94
59.93
59.92
59.91
59.9
59.89
59.88
59.87
59.86
59.85
Original Value Reproduced Value
PWDVectorGrid Variables
Time (Seconds)2015105
Valu
es
60
59.99
59.98
59.97
59.96
59.95
59.94
59.93
59.92
59.91
59.9
59.89
59.88
59.87
59.86
59.85
Original Value Reproduced Value
Average Match Worst Match
25© 2018 PowerWorld Corporation
• Modal analysis can be quickly done on a large number of signals– Computationally is an O(N3) process where N is the number of sample points and varies linearly with the number of included signals
– Number of sample points is automatically determined from the highest desired frequency (The Nyquist‐Shannon sampling theory requires sampling at twice the highest desired frequency)
– Determining how signals are manifested in modes is extremely fast
PowerWorld Modal Analysis: Takeaways So Far
26© 2018 PowerWorld Corporation
Mode Details
Lots of detailsare easily available, including being able to visualizeindividual modes
27© 2018 PowerWorld Corporation
Visualization of 0.611 Mode
Gr
an
d
Co
ul
ee
Mesq ui te Powe r
McNary
C o p p er M o u n t
a in
Chi
ef
Jos
eph
Drew
Pinnacle Peak APS
Avenue/Kingbird
The Geysers
Br
idg
e R
ive
r T
erm
in
al
Klondike
Wind Farm
Brilliant
C l a rk ( N E V P )
Powell River Dam
Ro
ck
y
Re
ac
h
Janet
Priest
Rapid
s
Devers
Como Lake
Colo rado Ri ver
The Dalle
s Ph
Va
nc
ou
ve
r I
sla
nd
T
er
min
al
Cholla
Randolph
Mir
a L
om
a
Kyrene
Bonn
eville
Keephills
Tracy & Clark M
ountain
California Valley Solar Ranch
Dunsmuir
Clayburn
Semitropic
Su
nd
an
ce
Su
mm
erv
ie
w
Win
d
Fa
rm
Harew
ood
An
ac
on
da
M
ill
Cre
ek
Lethbridge
Wheatland
I vanpah
Avola
Empress
Ri
din
g R
ec
ei
vin
g
Pawnee
Newark
San J uan 345
P r es id e
n t e J u
a rez ( R
o s a rit o )
Freder
ickson (PS
PL)
Rossdale
Colst
rip
F o u r C o r n e rs ( A Z P S )
Nicola
Moss Landing (DUENNO)
Yu cca
EC O
Vale
mou
nt
Casper
Calpeak Power Panoche No. 2
Gonder
CSS
St
ate
lin
e
Win
d
Pr
oje
ct
-
Wa
sh
in
gt
on
Hi
gh
lan
d
Va
lle
y
Co
pp
er
.
Natal
Walnut Energy Center [Turlock]
Sc
ot
for
d
Co
ge
n
Keswick
Calpeak Vaca Dixon No. 1
Me
dic
ine
Ha
t (
CM
H)
Bl ack Me sa
Belridge 1A
Tale ga
Revelstok
e
Gates Peaker
Cranbro
ok
Mcl
ee
se
Ca
pa
cit
or
St
ati
on
Tracy
Fo
rt
Pec
k
Gi la Ri ver Power St ati on
Lib
by
-
PA
CI
F
Lo
gan
C
an
yo
n
ARD
Va ll e y
Co
ol
Wa
te
r
Wild
Horse
Proje
ct
Su
m
mi
t/W
es
twa
rd
En
er
gy
P
roje
ct
McCall
Vernon Terminal
Ju
dit
h
Ga
p
Au
to
Kerr
Santa Clara
Olympia
Bi
llin
gs
-
Ri
mr
oc
k
Midway
Broad
view
Table Mt.
Snohomish
Rattlesnake
Fre
do
nia
(P
SP
L)
Golden
Yavapai
Hopkins R
idge
Prospect 1
Mica B
at
tle
Riv
er
Teckl
a
Falcon
Gold River
Bell
Barriere
Naug
hton
Goshen
Edward Hyatt
Hayden
Vestal
Ca
ny
on
Fe
rr
y
Lower G
ranite
Great Falls
Cherokee (PSCO)
Hundred Mile House
Lower
Monu
ment
al
Mountai
n Home
Br
az
ea
u H
yd
ro
BEN
Thermo Cog
en Fort Lupton
Weed Junction
Im
p
eri
al
Va
lle
y
Ge
ot
he
rm
al
Or mes a 1 E F ac ili ty
Hope
French
C i m a r r o n
Fairm
ont
Machacek
Riverga
te
Balzac Cogen
Round Bu
tte
Granby PP
Drum 1Summit
Glenrock
Robert C Kirkwood
Alamosa
DS
RawhideHappy Jack W
ind Project
Ra
th
dr
um
We st Me sa
Drake
Bridg
er
Ca
sc
ad
e
He
rit
ag
e P
ow
er
Pa
rk
Cassia
Si lver King
Yellow
tail
Lamar
Bl
ac
ksp
ri
ng
Rid
ge
Foote
Creek I
Verde
G le n Ca nyo n
Pit 1
Little G
oose
Ph
Lon
g Lak
e
Osage (
BKH)
H il lto p
Misso
ulaMoss
yrock
COB Energy Facility
Santiam
Wild Horse Creek
Burlington IC (BURML)
Panoche (Los Banos Peaker)
Twin Falls
Fort Churchill
Fla
mi
ng G
org
e
Brownle
e
South Cut B
ank
Ashton
Creek
SEGS
VII
Craig (TSG
T)
Big Creek 1
Bickerdike
Hard
in Aut
o
So
ut
h
Bu
tte
Lo
we
r B
ak
er
Woss
Elkford
Dworsha
k
Humboldt
Tr
ea
sur
eto
n
Wi ll ard
Boise B
ench
A lamo
Goleta
Peter
son
Fuller
Rainbow
Nuc la
A.A. Lambert
Jordan R
iver
Pr eac her CanyonSp rin gervi l le
Guad al upe
Saltery
Bay
Headgate Rock
La Junta
Humboldt Bay
Morro Bay
Miracle Mile
Malin
Th
re
e
Riv
ers
New De
nver
Kelly Lak
e
Sandia
San Luis Valley
Primrose
Dixonville
BLM West
Blythe 2
Toketee Falls
Ke rmac
Al
b N
ew
s
Ra
ttl
es
na
ke
Sw
itc
hy
ar
d
Clearwa
ter
Aberde
en
Buffa
lo Bill
Luning
Condo
n Windpow
er LLC
Port McN
eill
Rowley
Mil
ne
r (
AB)
Quartz
Stettler
Ponderosa
Nakusp
Cleveland Avenue
Hyder
Lost R
iver
Cedar Mountai n
Laramie River
Mor enc i
Kinport
Palisa
des (U
SBRID)
Cascade (TAUC)
Sp
ion
Ko
p RE
A
Halsey
Ross Dam
Riverto
n
Sheerness
Muss
elshe
ll
Summit
Taft
HGTN W
IND
Barrick
Winston Ridddle
Whitn
ey
Anaconda
California
Monitor
Black Dog
Bonanza
Chevron
Bl ack P .
Leavitt
Upalco
High River
Wray
Pilot B
utte
Tuan
a Gu
lch
Win
d Pa
rk LL
C
Clearwa
ter
Zi a
Diablo Canyon
Newell
Coronado
I n d ia n S p r in g s
Spillim
acheen
Arvada
A ll iso n
Gosh County
Fort Bragg Western Wood Produc
McGiness
North Valmy
Havre
(WAPA)
Hazelton B Hydro
Cove
Langl
ey
ET A
Lumby No. 2
N M W
i n d E n e r g y Ce n te r
Jenner
R ed Mesa
Hu
ng
ry
Ho
rse
Hopkins
Hansman
Hill Top
Nightingale & Ngp
Conda
Painte
r
Nye R
EA
Ri
cha
rds
on
Cou
le
e
So corro
So
ut
h
Tro
na
Bagdad
Ba
rr
he
ad
Stillwater
1
Belle
Creek
Del Norte
Yuma
Walsenburg
Trinity (U
SBRCA)
Ca sa Di ab lo
Capitan
Willingdon
C hurch R ock
Centr a
Carter M
ounta
in
Bole
Tiber
Ta os
Bi
gh
orn
Da
m
Lincoln
El ep han t B utte
Elk Creek
Shushartie Wind Farm
Applegate Dam
Fort Rock Compensation Station
Roger s
Tract Ca
LaGra
nde
J.C. Boyle
I ron Mounta in
TUNGSTEN
Morrow Point
Eagle
Tap
Cadomin
Dersser Min Mtr'G
Lake
Fork
Redbox
Lewis
Pine
Creek
Springfield (ARPA)
Mile Hi
Windish
ar
Clatsop
Upton
Carlin (NEWM
NTM)
Cascade (IDPC
)
Vermilion
Buffa
lo
Toledo
Burdett
Winthro
p
Hanly Road
Bayfi el d
D os Co nd ado
Sheri
dan
Seventy Mile House
Pt.Arena
Fields
Big G
rassy
Ramon
Gal leg os
East Jac
kson
Minnkhat
Lampo
Ta
ma
ris
k
J ac k a s s F l a
t s
Great D
ivide
Quarry Gypsum
Oreana
Clipper
Ca
ve
nd
is
h
Ta
p
CheneyPlaza Sub
Duran
Hines
West Hill
Belle Fourche
Macks In
n
La Ja ra
Joes
Ukiah
Pinon Canyon
S t o c ka d e W
a sh
Hask
ill Harlem
Happy Ca
mp
Leupp J ct Sub
Mcdermitt
Tybo
Goldfield
Silver
Gasquet
Buffalo
Head
Beatt y
Dunn S i ding
But
ler
C
ree
k
Morison
Limestone
Cedar Cree
k
C aba ll o
Devils Lake
Bl ack water
Catlow
Riley
Se li gma n
Rudyard
Ro
un
du
p A
uto
Hoback
Podalak
Pisgah
Arlingto
n
Longhous e Val ley
Monarch
Mile
s
Cit
y
GT
Malta
Linden
Visualization of the magnitude and angle of the mode at different locations
Gran
d Cou
lee
Mesq ui te Powe r
McNa
ry
Chief Joseph
Dr ew
Pi nn acl e Pea k AP S
Avenue/Kingbird
The Geysers
Bridge River Te
rmin
al
Klondike Wind
Farm
Brilliant
Powell Rive
r Dam
Rocky
Rea
ch
Janet
Pries
t Rapid
s
Dev ers
Como Lake
Colo r ado Rive r
The Dalles Ph
Va
nc
ou
ve
r I
sla
nd
T
er
min
al
C hol la
Rand olph
Ky rene
Bonneville
Tracy & Clark M
ountain
California Valley Solar Ranch
Duns
muir
Clayburn
Semitropic
Su
mm
erv
ie
w
Win
d
Fa
rm
Harewood
An
ac
on
da
M
ill
Cre
ek
Lethbridge
Wheatland
I vanpah
Avola
Empress
Pawnee
Newark
San J uan 345
P r e sid e n t
e Ju a re
z ( Ro s a r
it o )
Frederickso
n (PSPL)
Colst
rip
F o u r C o r n e rs ( A Z P S )
Nicola
Moss Landing (DUENNO)
Yucca
ECO
Vale
mou
nt
Casper
Calpeak Power Panoche No. 2
CSS
St
ate
lin
e
Win
d
Pr
oje
ct
-
Wa
sh
in
gt
on
Highland
Valley Coppe
r.
Natal
Walnut Energy Center [Turloc
k]
Keswick
Calpeak Vaca Dixon No. 1
Me
dic
ine
Ha
t (
CM
H)
Blac k M es a
Belridge 1A
Ta lega
Revelstok
e
Gates Peaker
Cranbrook
Mcleese Capacito
r Statio
n
Tracy
G il a Ri ve r P ower Stat i on
Libby
- PAC
IF
Logan C
anyon
ARD
Vall e y
Co o l Wa ter
W
ild
Ho
rse
P
ro
je
ct
Su
mm
it/
We
stw
ar
d E
ne
rg
y
Pro
jec
t
McCall
Vernon
Terminal
Ju
dit
h
Ga
p
Au
to
Kerr
Olympia
Billing
s - R
imroc
k
No
va
J
of
fre
C
og
en
er
ati
on
Midway
Broad
view
Table Mt.
Snohomish
Rattlesnake
Fre
do
nia
(P
SPL
)
Golden
Ya vap ai
Hopk
ins Ri
dge
Prospec
t 1M
ica Battle River
Teckla
Falcon
Gold River
Bell
Barriere
Naug
hton
Goshen
Edward Hyatt
Hayden
Vestal
Cany
on Ferr
y
Lowe
r Gran
ite
Mo
un
ta
in
Win
d
En
er
gy
C
en
te
r
Cherokee (PSCO)
Hundred Mile
House
Lowe
r Monu
menta
l
Mountain Hom
e
Brazeau Hydro
BEN
Thermo Cog
en Fort Lupton
Weed Junction
Im
pe
ria
l V
al
ley
G
eo
th
er
ma
l
Or me s a 1 E Fa cili ty
Hope
French
Fairmont
Rivergate
Balzac Cogen
Round Bu
tte
Granby PP
Drum 1 Summit
Glenrock
Robert C Kirkwood
Alamosa
DS
Rawhide
Happy Jack Wind Project
Rathdru
m
W es t Mesa
Drake
Bridge
r
Ca
sc
ad
e
He
rit
ag
e P
ow
er
Pa
rk
Cassia
Si l ver Ki ng
Yellow
tail
Lamar
Blackspring Ridge
Foote Cree
k I
V erde
G le n Ca nyo n
Pit 1
Little
Goos
e Ph
Long Lake
Osage (BKH)
Hi llt op
Misso
ula
Mossyr
ock
COB Energy Facility
Santiam
Wild Horse Creek
Burlington IC (BURML)
Panoche (Los Banos Peaker)
Twin Falls
Fort Churchill
Flaming Gor
ge
Brown
lee
Ashton
Creek
SE GS V I I
Craig (TSGT)
Big Creek 1
Hard
in Aut
o
South
Butt
e
Lower BakerW
oss
Elkford
Dwor
shak
Humboldt
Treasure
ton
W ill ard
Boise Bench
A lamo
Peters
on
Fuller
Rainbow
Nuc la
A.A. Lambert
Jordan R
iver
Pre ache r C an yonSpr ingervil le
Guadalupe
Saltery B
ay
Headgate Roc k
La Junta
Humboldt Bay
Morro Bay
Miracle Mile
Malin
Three
Rive
rs
New Denve
r
Kelly Lake
Sandia
San Luis Valley
Dixonville
BL M W
est
Blythe 2
Toketee Fa
lls
Ker mac
Ra
ttl
es
na
ke
Sw
itc
hy
ar
d
Clear
water
Aberd
een
Buffa
lo Bill
Luning
Condon W
indpowe
r LLC
Port McN
eill
Quartz
Stettler
Ponderosa
Nakusp
Cleveland Aven
ue
H yde r
Lost River
Cedar Mountai n
Laramie River
More nci
Kinport
Pa
lisa
de
s
(US
BR
ID
)
Cascade (TAUC)
Spion Kop
REA
Rifle Generating Station
Halsey
Riverto
n
Sheerness
Muss
elshe
ll
Summit
Taft
HGTN WIND
Barrick
Winston Ri
dddle
Bo
ze
ma
n
Ea
st
Ga
lla
ti
n A
uto
Whitn
ey
Anaconda
California
Monitor
Black Dog
Bonanza
Black P.
Leavitt
Upalco
High River
Wray
Pilot B
utte
Tua
na G
ulch
Win
d Pa
rk LLC
Clearwater
Zia
Diablo Canyon
Newell
C oron ado
Spillimacheen
Arvad
a
All ison
Gosh County
Fort Bragg Western Wood Produc
McGiness
North Valmy
Hazelton B Hydro
Cove
Langley
ETA
Lumby N
o. 2
N M W
i n d E n e r g y Ce n te r
Jenner
Red M esa
Hung
ry Ho
rse
Hopkins
Hansman
Hill To
p
Nightingale & Ngp
Conda
Paint
er
Nye R
EA
Soc or r o
South
Trona
Ba gd ad
Stillwater 1
Belle Creek
Del Norte
Yuma
Walsenburg
Trinity (U
SBRCA)
Casa Diablo
C api tan
Chur ch Rock
C entral
Carte
r Mou
ntain
Taos
Bighorn Dam
Lincoln
Elephant Butt e
Elk Creek
Shushartie Wind Farm
Applegate D
am
Fort Rock Compensation Station
R oge rs
Tract Ca
LaGrande
J.C. Bo
yle
I ron Mountain
TUNGSTEN
Eagle
Tap
Dersser Min M
tr'G
Lake Fo
rk
Redbox
Lewis
Pine
Creek
Springfield (ARPA)
Mile Hi
Windishar
Clatsop
Upton
Carlin (NEWM
NTM)
Cascade (IDP
C)
Buffalo
Toledo
Burdett
Winthr
op
Hanly Road
Bayfi el d
Dos Co nd ado
Sherid
an
Seven
ty Mile House
Pt.Arena
Fields
Big Gr
assy
Ramon
Gall egos
East Ja
ckson
Minnkhat
Lamp
o
Grea
t Divide
Quarry Gypsum
Oreana
Clipper
Cavendish Tap
CheneyPlaza Sub
Dur an
Hines
West Hill
Belle Fourche
Macks Inn
La J ara
Joes
Ukiah
Pinon Canyon
Hask
ill
Happy Ca
mp
Le upp J ct S ub
Mcdermitt
Tybo
Goldfie
ld
Silver
Gasquet
Buffalo
Head
Dunn Si d ing
Butle
r Cree
k
Morison
Limestone
Cedar Creek
Caballo
Devils Lake
Blackwat er
Catlow
Riley
Seli gman
Roun
dup A
uto
Hoback
Podalak
Arlingto
n
Lo ngh ou se Va ll ey
Monarch
Miles
City G
T
Li nd en
And, of course, there are many ways to visualize the values
28© 2018 PowerWorld Corporation
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Grand
Co u
lee
Mesq
uite P
ower
Mc N
a ry
Copp
er Mo
untain
Chie
f Josep
h
Pinna
cle Pe
ak AP
S
Avenu
e/King
bird
The G
eyse
rs
Bridge River Terminal
K lo nd ik e W
i nd F
arm
Brilliant
Kitimat
Clark
(NEV
P)
Powell River Dam
Ro cky
Re a
ch
In
te
rmo
un
ta
in G
en
era
ti
ng
Glenannan
Harbo
r Gen
eratin
g Sta
tion
Janet
Pr ies t R ap id s
Deve
rs
Como Lake
Color
ado Ri
ver
T he D
all es Ph
Vanco
uver Islan
d Termina
lCh
olla
Rand
olph
Mira L
oma
Kyren
e
Bon n
e vi lle
Keephills
acito
r Sta
tion
Tr
ac
y
& C
lar
k M
ou
nt
ain
Ca
lif
or
nia
V
all
ey
S
ola
r
Ra
nc
h
Dunsmuir
Clayburn
Semi
tropic
Sundance
Summerview W
ind Farm
Harewood
MKL
Anaco
nda Mill Cre
ek
Lethbridge
Wheatland
Williston
Ivanpa
h
Avola
Empress
Kemano
a
Newa
rk
San J
uan 3
45
o)
Frederi ckso
n ( PSPL )
Rossdale
Colstrip
Four
Corne
rs (AZ
PS)
Nicola
Mo
ss
La
nd
in
g
(DU
EN
NO
)
Valemount
Ca
lp
ea
k P
ow
er
Pa
no
ch
e
No
.
2
Gond
er
CSS
St ateli ne Wi nd Pr ojec t - Wa shin gton
Hig
hland V
alley Co
pper.
Natal
Wa
lnu
t E
ne
rg
y
Ce
nt
er
[T
ur
loc
k]
Scotford Cogen
Medicine Hat (CMH)
Black
Mesa
Belrid
ge 1A
Taleg
a
wa
Revelstoke
Gates
Peak
er
Cranbrook
Mcleese
Cap
acitor S
tation
Tracy
Fort Peck
Statio
n
Libby - PAC
IF
ARD
Valley
Cool
Water
Wild
Hors
e Pro ject
Santa
Clar
a
Su mmit /W
e stw ar d E ne rgy Pro jec t
McCa
ll
Vernon Terminal
Judith
Gap
Auto
Bloom
ington
Kerr
Santa
Clara
Oly
mpia
Billings - Rim
rock
Nova Joffre Cogeneration
Broadview
Snohomish
Hicko
ry
Pinto
Fredonia (PSPL)
Golden
Yavap
ai
Hopk
ins Ridge
P rospect 1
Mica
Battle River
T eckl a
Falco
n
Gold River
Bell
Barriere
Pa
ro
wa
n (
Ce
nt
er
Cre
ek
)
Vesta
l
Canyo
n Ferry
Low
e r Gran
ite
Great Falls
Hundred Mile House
L ow
er Mo
num
en tal
Mo
un
ta
in
Ho
me
Brazeau Hydro
BEN
AES H
unting
ton Be
ach
We
ed
Ju
nc
tio
n
Impe
rial Va
lley G
eothe
rmal
Sturgeon (CUPCAN)
Facili
ty
Hope
Cimarr
on
Fairmont
Salmon Valley
Mach
acek
Riv e
r ga te
Balzac Cogen
Rou nd B utte
Drum
1
Summ
it
Ro
be
rt
C
Ki
rkw
oo
d
DS
Rathdrum
West M
esa
Cascad
e Heritag
e Powe
r Park
ilver
King
Y ellow
tail
Blackspring Ridge
Verde
e Prairie EcoPower Centre
Glen C
anyo
n
Li ttle Goo
se Ph
Long Lake
Hillto
p
Missoula
Mos s
y roc k
CO
B E
ne
rg
y
Fa
cil
ity
Sant ia
m
Edith Lake
Vanderhoof
Pa
no
ch
e (
Lo
s B
an
os
Pe
ak
er)
tGrain
Fort C
hurc
hill
Br ow nle e
South Cut Bank
Ashton Creek
SEGS
VII
Big C
reek 1
Bickerdike
Hardin Au
to
South B
utte
Lower Baker
Woss
Elkford
Dw
or shak
Willar
d
Boise Benc h
Golet
a
Peterson
Rainbow
Nucla
A.A. Lambert
Jordan River
Preach
er Ca
nyon
Sprin
gervil
le
Mitsue
Guad
alupe
Saltery Bay
Head
gate R
ock
Morro
Bay
Marguerite Lake
Hunt
er Pla
nt
Three R
ivers
New Denver
Kelly Lake
Quintette
ar Hill PowerElm
worth
Sand
ia
Primrose
Dixon ville
BLM W
est
Blythe
2
To ketee Fall s
Kerm
ac
Alb News
Rattlesnake Sw
itchyard
Clea
rwater
Abe rde
en
Buff alo Bill
Lunin
g
Con d
on Win d
po we
r LLC
Port McNeill
HR Milner (AB)
Hunt
ington
Q uar tz
Stettler
Pon derosa
Gr
an
d
Ju
nc
tio
n (
UT
E)
Nakusp
Clevela nd Avenue
er
Ceda
r Mou
ntain
Cascade (TAUC)
Spion Kop REA
Ha lsey
Ros s D
am
Riv erto n
Sheerness
Muss
elshell
Taft
H GTN WI ND
Barri
ck
Winston Rid ddle
McMillan
Bozem
an Eas
t Galla
tin Auto
Anac
onda
Califo
rnia
Monitor
Black Dog
Chevron
Black
P.
Milfor
d Sub
.
High River
P ilot Bu tte
Clearwater
Zia
Diabl
o Can
yon
Newell
Coron
ado
Indian
Sprin
gs
Spillimacheen
Ar va d a
Alliso
n
McGi
ness
North
Valm
y
Havre (WAPA)
Heart Lake
Co ve
La n gle y
ETA
Lumby No. 2
gyCe
nter
Jenner
Red M
esa
Equity Mining
Hung
ry Horse
Hansman
Hi ll To p
Kodiak
Ni
gh
tin
ga
le
& N
gp
Las V
egas
Nye R
EA
Richardson Coulee
Socor
ro
Bagd
ad
Barrhead
Stillw
ater 1
B ell e Cr eek
Del Norte
Casa D
iablo
an
Willingdon
Churc
h Rock
wn Lak
e Hydroelectric Plant
Burns Lake
Car ter M oun tain
Bole
Tiber
Taos
Bighorn Dam
Shushartie Wind Farm
Applegate Dam
Fo
rt
R
oc
k
Co
mp
en
sa
tio
n
St
at
ion
Roge
rs
L aGra nd e
J.C. Boy le
McElm
o Cre
ek
Isle Pierre
Iron M
ounta
in
TUNG
STEN
Morro
w Po
int
Eagle
Cadomin
De
rs
se
r M
in M
tr'
G
La ke F ork
Lewis
Pine C
reek
Wind
ishar
Clats o
p
Plamondon
Ca
rli
n
(NE
WM
NT
M)
C asca de (ID PC)
Swan Hill
Vermilion
Buff a lo
To ledo
Burdett
Wi nthro
pUpper Fraser
H anly Road
Bayfie
ld
S he ri da n
Seventy Mile House
Fie lds
Big Grassy
Galleg
os
Abajo
Jackas
s Flat
s
Qu
arr
y
Gy
ps
um
Orea
na
Saddle Hills
Clipper
Cavendish Tap
Duran
Hi nes
La Ja
ra
Ukia
h
Stocka
de W
ash
Haskill
Harlem
Happy Camp
Leupp
Jct S
ub
Mcde
rmitt
Tybo
Goldf
ield
Gasquet
Beatt
yDu
nn Si
ding
Butler Creek
Mor ison
Simone
Limestone
Devi ls
Lake
C atlowRiley
Seligm
an
Rudyard
Roun
dup Auto
Cotton R.E.A. (VLY)
Pisga
h
Utah-
Neva
da
Utah/
Neva
da
Hatch
High
Longh
ouse
Valley
Monarch
Miles
Cit y G
T
Malta
Linde
n
Grand Coulee
Mes q
uite P
owe r
McNary
Co
pp
er
M
ou
nta
in
Chief Joseph
Dre w
Pi
nn
ac
le
Pe
ak
A
PS
Aven
ue/Kin
gbi rd
The G
eys e
rs
Bridge River Terminal
wWind Farm
Brilliant
Kitimat
Clar k
( NE V
P)
Powell River Dam
Rocky Reach
Glenannan
Ha
rb
or
Ge
ne
ra
tin
g
Sta
ti
on
J anet
Priest Rapids
Deve
rs
Como Lake
Colo r
ado R
iver
Vancouver Is
land Terminal
Choll
a
Rand
o lph
Mira
Loma
Kyren
e
BonnevilleKe
ephil l s
Kennedy Capacitor Station
Ca
lif
orn
ia
Va
lle
y S
ol
ar
Ra
nc
h
Dunsmuir
Clayburn
Semi
tr op ic
Sund
ance
Su
mm
er
vie
w
Wi
nd
Fa
rm
Harewood
MKL
An
aco
nda
M
ill
Cre
ek
L ethb
r idge
Wh eatlan
d
Williston
Ivanp
ah
Avola
Emp res
s
Long La
k
Kemano
Skeena
Pawnee
Newa
rk
Ju
are
z
(R
os
ar
ito
)
Fre
der
icks
on
(PS
PL
)
R ossd ale
Colstrip
Nicola
Mo
ss
La
nd
in
g
(DU
EN
NO
)
Yuc caEC
O
Valemount
Casper
Ca
lp
ea
k P
ow
er
Pa
no
ch
e
No
. 2
CSS
Highland Valley Copper.
Scotf
ord Co
gen
Medic
i ne H
at ( C
MH)
Black
Mes a
Belr id
ge 1A
Taleg
a
Telkwa
Revelstoke
Gat es
Peak
er
Mcleese Capacitor Station
Trac y
Gi
la
Riv
er
Po
we
r
St
ati
on
Libby - PACIF
ARD
Vall e
y
Cool
Wat er
Wild
Ho
rse
Pr
oje
ct
McCa
ll
Vernon Terminal
Kerr
San ta
Cla r
a
Olympia
Billings - Rimrock
Nova Jo
ffre C og
enerat
io n
Midw
ay
Broadview
Snohomish
Rattlesnake
Fredonia (PSPL)
Yava
pai
Hopkins Ridge
Mica
Battl e
Rive
r
Teckla
Gold River
Bell
Barriere
Hayden
Ves ta
l
Lower Granite
Cherokee (PS
CO)
Hundred Mile House
Low
er
Mo
nu
me
nta
l
Brazea
u Hyd ro
BEN
AE
S
Hu
nti
ng
to
n B
ea
ch
Thermo Cogen Fort Lupton
Im
pe
ria
l V
all
ey
Ge
ot
he
rma
l
Sturg eo
n (CU
PCAN
)
Or
me
sa
1
E
Fa
cili
ty
Hope
French
Salmon Valley
We sle
Rivergate
Balz a
c Cog
en
Granby PP
Drum
1
Glenrock
Ro
be
rt
C
Ki
rkw
oo
d
Alamosa
DS
Rawhide
Happy Jack Wind Project
Rathdrum
Drake
Bridger
Cascade Heritage Pow
er Park
Silv er
Kin g
Yellowtail
Lamar
Blac k
s pri ng
Ridg
e
Foote Creek I
Ver de
G rand e P
rairie
E coPow
er Ce
ntre
Glen
Canyo
n
Little Goose Ph
Long Lake
Osage (BKH)
Hillt o
p
Missoula
Mossyrock
Edith
L ake
Wild Horse Cree
k
Burlington IC (BUR
ML)
Vanderhoof
Pa
no
ch
e
(Lo
s B
an
os
P
ea
ke
r)
Prince Rupert Grain
Flaming Gorge
Ashton Creek
SEGS
VII
Craig (TSGT)
Big C
reek
1
Bi cke
rdike
Hardin Auto
South Butte
Lower Baker
Woss
E lkf o
rd
Dworshak
Golet
a
Peterson
Fuller
Rainbow
Jordan River
Pr
ea
ch
er
Ca
ny
on
Mi tsue
Saltery Bay
Head
g ate
Rock
La Junta
Mor ro
Bay
Miracle Mile
Marguer
i te La
ke
Three Rivers
New Denver
Kelly Lake
Quintette Popla
r Hi ll
Powe
r
El mwort
h
San Luis Valley
Primrose
BLM
West
Blyt h
e 2
A lb New
s
Ra
tt
les
nak
e
Sw
itch
ya
rd
Clearwater
Aberdeen
Buffalo Bill
Port McNeill
HR Mi lne
r (AB)
Stettl e
r
Grand Junction (UTE)
Nakusp
Hyde
r
Ce
da
r
Mo
un
ta
in
Laramie
River
ci
Cas ca
de (T
AUC)
Rifle Generating Station
Ross Dam
Riverton
Sheer
n ess
Musselshell
Summ
it
Taft
McMilla
n
Bo
ze
ma
n
Ea
st
Ga
lla
ti
n A
uto
Monitor
Blac k
Dog
Bonanza
C hevro
n
Black
P .
Upalco
High
River
Wray
Pilot Butte
Clearwater
Diabl
o Can
yon
Newe
l lCo
r onad
o
I ndia
n Sp r
in gs
Arvada
Gosh County
Heart
Lake
Lumby No. 2
Jenner
Equity Mining
Hungry Horse
Hopkins
H ansman
Hill Top
Kodia
k
Nye REA
C
South Trona
Bagd
ad
Barrh
ead
Belle Creek
Yuma
Walse
nburg
Cas a
Diab l
o
Wi ll ingd
on
Van Buren
Brown Lake Hydroelectric Plant
Burns Lake
Carter Mountain
Bi gh orn
Dam
Lincoln
Shushartie Wind Farm
Roge
rs
Gladstone
Tract Ca
Isle Pierre
I ron
Moun
tain
Morrow Point
Eagle
Tap
C adomin
Redbox
Pine Creek
Springfie
ld (ARPA)
Windishar
Clatsop
Upton
Pl amo ndo
nSwa n H
i l l
V ermil io
n
Buffalo
Bur d
et t
Winthrop
Upper Fraser
Sheridan
Seventy Mile House
Pt.Ar
ena
Ramon
Minnkhat
Jacka
s s F la
t s
Great Divide
Saddl
e Hil ls
C li ppe r
Caven di s
h Ta p
Chen
ey
Plaza Sub
West Hill
Belle Fourche
Joes
Pinon Canyon
St
oc
ka
de
Wa
sh
Haskill
Leup
p Jct
Sub
Buffalo Head
Beatt
y
Br
Dunn
S id in
g
Butler Creek
Si mon
e
Li mest
o ne
Seli g
man
Roundup Auto
Podalak
Pisg a
h
Arlington
H ig h
Lo
ng
ho
us
e
Va
lle
y
Miles City GT
L inde
n
29© 2018 PowerWorld Corporation
Movie of 0.611 Hz ModeKeep in mind the mode data is being extracted from the full system response