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A CPS1-driven market for Clearing/Settling
Inadvertent InterchangeSimulation from an 11-Day period of
17-control-area Western-Interconnection Jan/’02 hourly data
presented to
Inadvertent Interchange Payback Taskforce
North American Energy Standards Board
by Robert Blohm
Houston
December 10, 2003
Slide #
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Inadvertent Interchange is more than just energy
at the price of scheduled energy.
It’s also unscheduled contribution or correction
to frequency error.
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energy
transmission loading component
frequency control contribution
Inadvertent is a vector in a state space
FCCTLC,energy,
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Dual pricing of unscheduled energy
Ambiguity along the diagonal.Diagonal occurs only when frequency is high.
Off-diagonals occur only when frequency is low.
Revenue/Expense Unscheduled
part 0 good bad receive
energy part 0U
sold pUpe pUpe pay
bought pUpe pUpe
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Four possible combinations of Priced Energy Component
and Priced
Frequency Control Contributionof Inadvertent Interchange
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Case 1: Frequency High and Control Area A “Leaning” on Rest of Interconnection for 200 MWh
A pays the Interconnection $10/MWh energy price for 200 MWh = -$ 2000
A receives from the Interconnection $15* of FCCp per MWh of Inadvertent = +$ 3000 for 200 MWh of Inadvertent Interchange that is opposite to the frequency error.*FCCp per MWh would be less than $15 if the average frequency error were smaller.
A receives from the Interconnection a net total of $ 1000*.*The net result could be a payment if the average frequency error is small enough.
2. Frequency Control Contribution:
3. Net Result:
1. Energy Component:
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Case 2: Frequency High and Rest of Interconnection “Leaning” on Control Area A for 200 MWh
A receives from the Interconnection $10/MWh energy price for 200 MWh = +$ 2000
A pays the Interconnection $15* of FCCp per MWh of Inadvertent = -$ 3000 for 200 MWh of Inadvertent Interchange that is contributing to the frequency error.*FCCp per MWh would be less than $15 if the average frequency error were
smaller.
A pays the Interconnection a net total of $ 1000*.*The net result could be a receipt if the average frequency error is small enough.
2. Frequency Control Contribution:
3. Net Result:
1. Energy Component:
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Case 3: Frequency Low and Control Area A “Leaning” on Rest of Interconnection for 200 MWh
A pays the Interconnection $20/MWh energy price for 200 MWh = -$ 4000
A pays the Interconnection $15 of FCCp per MWh of Inadvertent = -$ 3000 for 200 MWh of Inadvertent Interchange that is contributing to the frequency error.
A pays the Interconnection a combined total of -$ 7000.
2. Frequency Control Contribution:
3. Net Result:
1. Energy Component:
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Case 4: Frequency Low and Rest of Interconnection “Leaning” on Control Area A for 200 MWh
A receives from the Interconnection $20/MWh energy price for 200 MWh = +$ 4000
A receives from the Interconnection $15 of FCCp per MWh of Inadvertent = +$ 3000 for 200 MWh of Inadvertent Interchange that is opposite to the frequency error.
A receives from the Interconnection a combined total of +$ 7000.
2. Frequency Control Contribution:
3. Net Result:
1. Energy Component:
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Case 1A receives $1000
Case 2A pays $1000
Case 3A pays $7000
High LowFrequency:
“Leaning”by:
Control Area A
Rest ofInterconnectio
n
Summary of the 4 cases
Case 4A receives $7000
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Animation of the Clearing/Settlement
of
Frequency Control Contributionbased on data of an 11-day period in January 2002
on 17 control-area Western Interconnection:
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Normal distribution of frequency errors
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Frequency error in Hertz
Nu
mb
er o
f h
ou
rs/e
rro
rs11
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iI
1 4
4
8
4 F
2
1F
4
1F
4
1tt
4
9I
4
1I
4
1tt,ii
2
9
F
Ii
Slope is "2-dimensional average"of Inadvertent & Frequency-error
Average Frequency-error
i's Average Inadvertent
A Balancing Authority i's Frequency Control Contribution is a "2-dimensional average" of Inadvertent and Frequency-error each weighted by Frequency error.
A "2-dimensional average" is the slope of a line from the origin through the intersection ofthe lines intercepting the two averages.
4-period scatter of Balancing Authority i's<Frequency-error, Inadvertent>
points
denoted by the 4 red dots t,it I,F
Drawing preparedby Robert Blohm
July 5, 2003
tF t,iIPeriod t 1 4 -2 2 1 -1 3 -4 4 4 1 8 Sum = 2 9
12
I t,i
Ft
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iI
2 8
8
8 F
8
-4¼
F
I i,t
A Balancing Authority i's Frequency Control Contribution is a "2-dimensional average" of Inadvertent and Frequency-error each weighted by Frequency error.
A "2-dimensional average" is the slope of a line from the origin through the intersection ofthe lines intercepting the two averages.
4-period scatter of Balancing Authority i's<Frequency-error, Inadvertent>
points
denoted by the 4 red dots t,it I,F
13
4
-17I
4
1I
4
1tt,ii
i's Average Inadvertent weighted by Frequency-error
( Ft) Ii Ft, t -4¼
tF t,iIPeriod t 1 4 -2 -8 16 2 1 -1 -1 1 3 -4 4 -16 16
4 1 8 Sum = 2 9 -17 32
Ii Ft, t
8
F t2
1
Average Frequency-errorweighted by Frequency-error
) FF4
1F
4
1tt
t2F t( 8
t2
Ft Slope is "2-dimensional average"of Inadvertent & Frequency-errorweighted by Frequency-error
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1800 Megawatt-Hours of Inadvertent
+.01 +.02 +.03-.01-.02-.03
Frequency error in Hertz
Bad quadrant: Inadvertent and frequency error
in the same direction.
Bad quadrant: Inadvertent and frequency error
in the same direction.
Good quadrant: Inadvertent and frequency error
in opposite directions.
Good quadrant: Inadvertent and frequency error
in opposite directions.
Bad quadrant: Inadvertent and frequency error
in the same direction.
Bad quadrant: Inadvertent and frequency error
in the same direction.
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Line is in the good quadrants: so red control area gets paid for his Frequency Control Contribution for
helping frequency.
Slope of line is red control area’s Frequency Control Contribution. It is the two-dimensional average of red control area’s frequency-error-weighted Inadvertent and frequency-error-weighted frequency error.
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Red control area’s 264 hourly-average Inadvertent and frequency
error
Control Area 1 (CA 1)
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Slope of the black line is two-dimensional average of the combined control areas’ frequency-error-weighted Inadvertent and frequency-error-weighted frequency error.
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CA 5
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CA 6
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CA 10CA 10
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Lines’ slopes add up to zero slope of horizontal line.
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Positive slopes pay Positive slopes pay Positive slopes pay
Bad quadrant: Inadvertent and frequency error
in the same direction.
Bad quadrant: Inadvertent and frequency error
in the same direction.
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Good quadrant: Inadvertent and frequency error
in opposite directions.
Good quadrant: Inadvertent and frequency error
in opposite directions.
Positive slopes pay to the negative slopes
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Positive slopes pay to the negative slopes and Frequency Control Contribution always clears.
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• Real-time transactions cannot be done moment-by-moment deterministically/deliberately– Time is too short
• Real time performance must be managed, measured and valued as a statistical distribution– Classical physics versus quantum mechanics
• joint-indeterminacy of position and momentum
– Joint-indeterminacy of time-quantity and reliability-pricing• reliability pricing of a time average
Market price of a distribution of points over time, not of a sharp point in time
“Computational Equivalence” (Wolfram/Mathematica): computational limitations in humans & physical nature
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Tiered real-time market
• Three tiered market for frequency contribution
– NERC, Balancing Authorities, local entities.• Frequency is a public good requiring an authority like NERC
to drive the frequency-contribution markets by the threat of penalty.
– This meets both a reliability and a markets objective
• Balancing Authorities must settle their FCC monthly– Since inadvertents sum to zero by definition, Balancing
Authorities always clear
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• Balancing Authorities must also comply with CPS frequency targeting, acting as agents subject to NERC penalty– FCC does not target frequency – NERC CPS penalty will prompt Balancing Authorities to trade
their CPS rights instead of paying the penalty, the way DOE pollution penalties prompted the market for pollution rights.
• To meet their monthly CPS scores, Balancing Authorities will trade their frequency control contributions as an alternative to buying options on frequency support
Tiered real-time market (cont.d)55
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• FCC is open and scalable to a market below Balancing Authorities– Balancing Authorities can apply FCC to their constituent
entities to incent entities’ self-provision and good performance, thereby minimizing the Balancing Authority’s own local intervention
Tiered real-time market (cont.d)
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Ancillary services markets
• Ancillary services markets need to be developed as robust options markets– The option price is driven by volatility which is
another way to capture/express Frequency Control Contribution
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Relation between CPS1
and
Frequency Control Contribution
pFCC
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extends to all inadvertent the price of the trading & procurement of
residual inadvertent done to get compliant with .
The tolerance band limits and drives .
pFCC
1CPSp
FCC
1CPS
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boils down to
22
,
,,
t
ti
titi FAVGb
b
tib
,where is a least-squares estimator of bias
tiB,
2,
2
,, tittiti bFAVGb
1CPS
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02
, tti FAVG
0)(
)( 2
2
t
t
ti FAVGFAVG
FTAVG
0)( ti FTAVG
With bias , tolerance band and becomes
0, settiB
1CPS02
,
tib
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monetization is equivalent to without bias obligation/tolerance: . monetization makes this equation hold because
since
and
p
h
hi FCCpFAVG
FIAVG
102
1CPSp
FCC
0)( ti FTAVG
phi FCCFIAVGk )(
2?
10 hFAVGkp
10,10
10 ppFCChih
pFCC
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Trading/procurement of to get within the tolerance band drives the price of all
hi ,1CPS 2
hi ,10
p
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CPS1
(mHz)+
+
FB i 10
-
MW, or
Control area i's maximum allowed 1-minute average tie-lineerror (plus response obligation) in direction of the frequency error:
:
:
: One-year target probability density of 1-minuteaverages of frequency error, adjusted for deviation of
the mean from 0
FBi 10
F
F
:
: InstantaneousProbability
"No inadvertent allowedin the direction of
Frequency error when"
F :
On average over the past year:Approximate
0iB :
F
FBT
ii
10
1-minute average ofFrequency error
- + F
50-50
Annual standarddeviation of F
Year's Mean of F
Control area i's bias
F 22 TargetRMS:
: in same direction as+ F
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CPS1
++
++-
-
-
-
Vertical cut Horizontal band
hF tF
hF tF
goodiI , goodiT ,badiI , badiT ,
Isoquants
2
t
i
ti FB
FTAVG
: buys FCC or response: buys regulation
Isoquants hi FIAVG
pFCC
‘s cut is perpendicular to CPS1's cut/band.Payments for traded s would sum to zero around CPS1's cut/band when .
There is excess demand for traded s outside CPS1's cut/band when whence receipt of reduces CPS1 penalty to incent BAs to get back inside.
tF
tF
pFCC
hFCC
hFCC
pFCC
's vertical cut gets stretched right from the middle into CPS1's horizontal band.BA outside his CPS1 cut/band buys enough from BAs & to get inside his CPS1
cut/band & avoid CPS1 penalty, and thereby helps set the settlement price .
pFCC
hFCChFCC 10
p
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To GetHourly Decomposition of
Frequency Control Contribution:
Interpret Frequency Control Contribution as an 11-day average of 1-hour Frequency
Control Contributions
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h
h
hi FCCFAVG
FIAVG
2
1264
1
2
1
)264/1(FCC
F
FI
hh
i
1264
1
2
1264
FCCF
FI
hh
i
FCCh (11 day* average): *264 hours
FCCh (hour 1):
h
hh
hi FCCF
FIAVG
264
1
2)264/1(
h
h
hi FCCFAVG
FIAVG
2
(Column K of spreadsheet)
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17
1264
1
2
117
11
)264/1(i
hh
i
i F
FIFCC
264
1
2
17
11
)264/1(h
h
ii
F
FI
264
1
2
1
17
1
)264/1(h
h
ii
F
FI
0
1-hour FCCh sum to 0 across control areas i
017
1
i
iIsince
because Ii sum to 0 across the i’s.
|| 0
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17
1,1
iiFCC
Because 1-hour FCCh sum to 0 across the control areas i,
•••
1,1FCC 2,1FCC 17,1FCC 0
17
1,2
iiFCC 1,2FCC 2,2FCC 17,2FCC
17
1,264
iiFCC 1,264FCC 2,264FCC 17,264FCC
0
0
•••
264/1 264/1 264/1
|| || ||
1,hFCC 2,hFCC 17,hFCC
the 264-hour averages of 1-hour FCCh sum to 0 across the i’s.
0
•••
•••
•••
17
1,
iihFCC
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Marginal FCC Cost of
Inadvertent as
Amount of Frequency Control Contribution per
MWh of Inadvertent
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1264
1
2
1264
FCCF
FI
hh
i
FCCh (hour 1):
iI
hh
MCFCCF
F1264
1
2
1264
Marginal FCC cost (in units of FCC1) of Inadvertent Ii: (Column F of spreadsheet)
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To avoid economic gaminga continuous
Frequency Control Contribution value of Inadvertent Interchange is needed because the
hourly Frequency Control Contribution of Inadvertent Interchange
is often very big relative to the Energy Component of
Inadvertent Interchange.
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Inadvertent Payments by/to (Green) Control Area 3Assuming price of 10¢/MWh/Hz of FCC
For Energy + For FCC ==FCCt¢/MWh/Hz
Day 1: Hour 4
Day 6: Hour 2
Day 1: Hour 11
Day 6: Hour 12
Receive $950 @$10/MWh $481 @ $5.06/MWh
=FCC4MCI3
Pay $722 @$20/MWh $4314 @ $11.95/MWh
=FCC12MCI3
Receive $1350 @$10/MWh $2324 @ $17.21/MWh
=FCC146MCI3
Pay $2420 @$20/MWh $1767 @ $14.60/MWh
=FCC156MCI3
11-day Average $2.06/MWh
Net
Receive$469
Receive$3592
Pay$974
Pay$4197
(Row 277 Column X of spreadsheet)
Pay
Pay
Receive
Pay
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