A CPS1driven market for Clearing/Settling Inadvertent Interchange Simulation from an 11Day period of 17controlarea WesternInterconnection Jan/’02 hourly data. presented to Inadvertent Interchange Payback Taskforce North American Energy Standards Board by Robert Blohm Houston
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A CPS1driven market for Clearing/Settling Inadvertent InterchangeSimulation from an 11Day period of 17controlarea WesternInterconnection Jan/’02 hourly data
presented to
Inadvertent Interchange Payback Taskforce
North American Energy Standards Board
by Robert Blohm
Houston
December 10, 2003
Slide #
1
Inadvertent Interchange is more than just energy
at the price of scheduled energy.
It’s also unscheduled
contribution or correction
to frequency error.
Inadvertent is a vector in a state space
2
transmission loading component
energy
frequency control contribution
3
b
>
0
>
U
0
+
10 b

10b
p
U
p
p
U
p
b
b
e
e

+
10 b


10 b
p
U
p
p
U
p
b
b
e
e
Dual pricing of unscheduled energy
Ambiguity along the diagonal.
Diagonal occurs only when frequency is high.
Offdiagonals occur only when frequency is low.
Revenue/Expense
Unscheduled
receive
good bad
part
energy part
sold
pay
bought
4
Four possible combinations of
Priced Energy Component
and
Priced
Frequency Control Contribution
of Inadvertent Interchange
5
Case 1: Frequency High and Control Area A “Leaning” on Rest of Interconnection for 200 MWh
1. Energy Component:
A pays the Interconnection $10/MWh energy price for 200 MWh =
$ 2000
2. Frequency Control Contribution:
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.
3. Net Result:
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.
6
Case 2: Frequency High and Rest of Interconnection “Leaning” on Control Area A for 200 MWh
1. Energy Component:
A receives from the Interconnection $10/MWh energy price for 200 MWh = +$ 2000
2. Frequency Control Contribution:
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.
3. Net Result:
A pays the Interconnection a net total of $ 1000*.
*The net result could be a receipt if the average frequency error is small enough.
7
Case 3: Frequency Low and Control Area A “Leaning” on Rest of Interconnection for 200 MWh
1. Energy Component:
A pays the Interconnection $20/MWh energy price for 200 MWh =
$ 4000
2. Frequency Control Contribution:
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.
3. Net Result:
A pays the Interconnection a combined total of $ 7000.
8
Case 4: Frequency Low and Rest of Interconnection “Leaning” on Control Area A for 200 MWh
1. Energy Component:
A receives from the Interconnection $20/MWh energy price for 200 MWh = +$ 4000
2. Frequency Control Contribution:
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.
3. Net Result:
A receives from the Interconnection a combined total of +$ 7000.
9
Summary of the 4 cases
Frequency:
High
Low
“Leaning”
by:
Case 3
A pays $7000
Case 1
A receives $1000
Control Area A
Rest of
Interconnection
Case 2
A pays $1000
Case 4
A receives $7000
10
Animation of the Clearing/Settlement of
Frequency Control Contribution
based on data of an 11day period in January 2002
on 17 controlarea Western Interconnection:
11
12
A Balancing Authority i's Frequency Control Contribution is a "2dimensional average"
of Inadvertent and Frequencyerror each weighted by Frequency error.
A "2dimensional average" is the slope of a
line
from the
origin
through the
intersection
of
the
lines
intercepting the two averages.
I
4period scatter of Balancing Authority i's
i
<Frequencyerror, Inadvertent>
8
points
I
9
<
D
>
F
,
I
i
=
=
t
i
,
t
D
denoted by the 4 red dots
F
2
Slope is "2dimensional average"
of
Inadvertent
&
Frequencyerror
Drawing prepared
by Robert Blohm
4
July 5, 2003
i's Average Inadvertent
4
1
9
=
=
=
å
I
I
I
i
i
,
t
i
,
t
4
4
=
t
1
D
I
F
Period t
D
i
,
t

F
t
4
1
4
1 4 2
2 1 1
3 4 4
Average Frequencyerror
4
1
8
4
1
1
Sum = 2 9
D
D
=
D
=
=
å
F
F
F
t
t
4
2
=
t
1
13
2
D
I
D
I
D
F
F
F
Period t
,
t
i
i
,
t
t
t
t
1 4 2 8 16
2 1 1 1 1
3 4 4 16 16
1
4
1
8
8
Sum = 2 9 17 32
Slope is "2dimensional average"
of
Inadvertent
&
Frequencyerror
weighted by Frequencyerror
i's Average Inadvertent
weighted by Frequencyerror
4
1
17
(
´
)
=
4¼
=
=
=
å
I
I
D
F
I
D
F
i
i
,
t
t
,
t
i
t
4
4
=
t
1
A Balancing Authority i's Frequency Control Contribution is a "2dimensional average"
of Inadvertent and Frequencyerror each weighted by Frequency error.
A "2dimensional average" is the slope of a
line
from the
origin
through the
intersection
of
the
lines
intercepting the two averages.
4period scatter of Balancing Authority i's
<Frequencyerror, Inadvertent>
points
<
D
>
F
,
I
t
i
,
t
denoted by the 4 red dots
Average Frequencyerror
weighted by Frequencyerror
I
i
4
1
(
´
)
2
D
D
=
D
=
=
D
8
å
F
F
F
F
8
t
t
t
4
=
t
1
DF
4¼
I
t
i,t
=
=
8
2
D
F
t
D

F
8
2
8
14
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.
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.
MegawattHours of Inadvertent
Frequency error in Hertz
.03
.02
.01
+.01
+.02
+.03
15
Slope of line is red control area’s Frequency Control Contribution. It is the twodimensional average of red control area’s frequencyerrorweighted Inadvertent and frequencyerrorweighted frequency error.
Red control area’s 264 hourlyaverage Inadvertent and frequency error
Line is in the good quadrants:
so red control area gets paid for his
Frequency Control Contribution for
helping frequency.
Control Area 1 (CA 1)
16
CA 2
17
Slope of the black line is twodimensional average of the combined control areas’ frequencyerrorweighted Inadvertent and frequencyerrorweighted frequency error.
18
CA 3
19
20
CA 4
21
22
CA 5
23
24
CA 6
25
26
CA 7
27
28
CA 8
29
30
CA 9
31
32
CA 10
33
34
CA 11
35
36
CA 12
37
38
CA 13
39
40
CA 14
41
42
CA 15
43
44
CA 16
45
46
CA 17
47
48
49
Lines’ slopes add up to zero slope of horizontal line.
50
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.
Positive slopes pay
51
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
52
Positive slopes pay to the negative slopes and Frequency Control Contribution always clears.
Market price of a distribution of points over time, not of a sharp point in time
53
“Computational Equivalence” (Wolfram/Mathematica): computational limitations in humans & physical nature
54
Tiered realtime market
55
Tiered realtime market (cont.d)
56
Tiered realtime market (cont.d)
57
Ancillary services markets
58
Relation between CPS1
and
Frequency Control Contribution
extends to all inadvertent the price of the trading & procurement of residual inadvertent done to get compliant with . The tolerance band limits and drives .
59
where is a leastsquares estimator of bias
60
With bias , tolerance band and becomes
61
monetization is equivalent to without bias obligation/tolerance: . monetization makes this equation hold because since and
62
63
Trading/procurement of to get within the tolerance band drives the price of all
p
64
CPS1
Approximate
Instantaneous
:
On average over the past year:
Probability
e
p
Annual standard
+
:
MW
, or
D
F
+
deviation of
D
F
:
in same direction as
(
)
Target
2
e
=
e
+
m
D
F
:
2
"No inadvertent allowed
RMS
(
)
D
F
D
F
m
:
Year's Mean of
in the direction of
D
F
:
1minute average of
Frequency error when
Frequency error
"

D
³
e
F
<
e
e
:
+
B
0
Control area
i's bias
i

D
F
+
50
50
(
mHz)

D
F
10
B
10
B
D
F
i
i
:
Control area
i's maximum allowed 1minute average
tieline
error (plus response obligation) in direction of the frequency error:
e
æ
ö
e
D
=


D
T
10
B
F
ç
÷
D
i
i
è
ø
F
:
Oneyear target probability density of 1minute
averages of frequency error, adjusted for deviation of
the mean from 0
65
‘scut is perpendicular to CPS1's cut/band.
Payments for traded s would sum to zero around CPS1'scut/band when .
There is excess demand for traded s outside CPS1's cut/band when
whence receipt ofreduces CPS1 penalty to incent BAs to get back inside.
CPS1
+
Isoquants
Isoquants
+




+
: buys FCC
or response
+
: buys
regulation
Vertical cut
Horizontal band
'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 .
66
To Get
Hourly Decomposition of
Frequency Control Contribution:
Interpret
Frequency Control Contribution as an 11day average of 1hour Frequency Control Contributions
67
FCCh(11 day* average):
*264 hours
FCCh(hour 1):
(Column K of spreadsheet)
68
because Ii sum to 0 across the i’s.

since
1hour FCCh sum to 0 across control areas i
69
the 264hour averages of 1hour FCCh sum to 0 across the i’s.
•
•
•
•
•
•
•
•
•



Because 1hour FCCh sum to 0 across the control areas i,
•
•
•
•
•
•
70
Marginal FCC Cost
of
Inadvertent
as
Amount of
Frequency Control Contribution per MWh of Inadvertent
71
FCCh(hour 1):
Marginal FCC cost
(in units of FCC1) of
Inadvertent Ii:
(Column F of spreadsheet)
72
To avoid economic gaming
a 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.
73
Inadvertent Payments by/to (Green) Control Area 3
Assuming price of 10¢/MWh/Hz of FCC
For Energy +
For FCC =
=FCCt´ 10¢/MWh/Hz
Net
Day 1: Hour 4
Receive
$950 @$10/MWh
Pay
Receive
$469
$481 @ $5.06/MWh
=FCC4MCI3
Day 1: Hour 11
Receive
$3592
Pay
$722 @$20/MWh
Receive
$4314 @ $11.95/MWh
=FCC12MCI3
Day 6: Hour 2
Pay
Pay
$974
Receive
$1350 @$10/MWh
$2324 @ $17.21/MWh
=FCC146MCI3
Day 6: Hour 12
Pay
$2420 @$20/MWh
Pay
Pay
$4197
$1767 @ $14.60/MWh
=FCC156MCI3
11day Average
$2.06/MWh
(Row 277 Column X of spreadsheet)