A CPS1-driven market for Clearing/Settling Inadvertent Interchange Simulation from an 11-Day period of 17-control-area Western-Interconnection Jan/02 hourly.

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 #

Inadvertent Interchange is more than just energy

at the price of scheduled energy.

It’s also unscheduled contribution or correction

to frequency error.

1

energy

transmission loading component

frequency control contribution

Inadvertent is a vector in a state space

FCCTLC,energy,

2

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

3

Four possible combinations of Priced Energy Component

and Priced

Frequency Control Contributionof Inadvertent Interchange

4

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:

5

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:

6

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:

7

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:

8

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

9

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:

10

Normal distribution of frequency errors

0

5

10

15

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25

30

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45

50

Frequency error in Hertz

Nu

mb

er o

f h

ou

rs/e

rro

rs11

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

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.

14

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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.

15

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.

17

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CA 8

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CA 10CA 10

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Lines’ slopes add up to zero slope of horizontal line.

49

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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.

50

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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

51

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Positive slopes pay to the negative slopes and Frequency Control Contribution always clears.

52

• 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

53

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

54

• 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

• 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)

56

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

57

Relation between CPS1

and

Frequency Control Contribution

pFCC

58

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

59

boils down to

22

,

,,

t

ti

titi FAVGb

b

tib

,where is a least-squares estimator of bias

tiB,

2,

2

,, tittiti bFAVGb

1CPS

60

02

, tti FAVG

0)(

)( 2

2

t

t

ti FAVGFAVG

FTAVG

0)( ti FTAVG

With bias , tolerance band and becomes

0, settiB

1CPS02

,

tib

61

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

62

Trading/procurement of to get within the tolerance band drives the price of all

hi ,1CPS 2

hi ,10

p

63

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

64

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

65

To GetHourly Decomposition of

Frequency Control Contribution:

Interpret Frequency Control Contribution as an 11-day average of 1-hour Frequency

Control Contributions

66

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)

67

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

68

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

69

Marginal FCC Cost of

Inadvertent as

Amount of Frequency Control Contribution per

MWh of Inadvertent

70

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)

71

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.

72

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

73