a cps1-driven market for the frequency control contribution of inadvertent interchange presented to...

A CPS1-Driven Market for the Frequency Control Contribution

of Inadvertent Interchange

presented to

Inadvertent Interchange Payback Taskforce

North American Energy Standards Board

by Robert Blohm

Austin

September 15/16, 2003

From The New York Times, August 19, 2003

Managing

Inadvertent

or

Tie-Line Error:

Primary Response Stabilizes Frequency

Secondary Response Restores Frequency

Hz

15

6059.925

1

Hz

59.925

60

10

Seconds

Minutes

Secondary Response (should be made by the BA who caused the disturbance)

(Shared)Primary Response

Generator slows down while governor opens steam-control valve to stop the slow-down. Interconnection’s Overall Primary Response offsets Intcrconn.’s Overall Scheduling Error.

Operator raises steam-control valve set-point to increase the steam flow to speed up generator.

As generator speeds back up to normal, the governor closes-back steam-control valve. Balancing Authority’s Secondary Response to his own error

replaces Interconnection’s Shared Primary Response to that error.

A BA has Inadvertent* whenever the BA’s share of the Interconnection’s overall Scheduling Error doesn’t match the BA’s required share of the Interconnection’s overall Primary Response to that Scheduling Error

Numbers in 10s Mw

100 100

75 75

100

100

75 25 50 50

25 5075 50

75 25

5050 50

BalancingAuthority A

BalancingAuthority B

B’s Inadvertentof -25

Outage of 50 inBalancing Authority B

Replacement by 50 from Balancing Authority A

PRIMARY RESPONSE of50 in load reduction,25 each in A and B

Load

Generation

SECONDARY RESPONSE of50 in generationincrease in A

A’s Inadvertentof 50

A’s Inadvertentof 25

B’s Inadvertentof -50

Inadvertent always

sums to zero

between intercon-

nected entities.

* or tie-line error

Ancillary Service Dispatch Decision• Three 500 MW Units with 5% Droop.

5 % Droop means

- 100 % of capacity needed to arrest freq. drop of 5 % of 60 Hz = 3 Hz - Response Requirement of 10 % of capacity (= 150 MW = 50MW per gen.) to

arrest .3 Hz freq. drop (= 0.5% of 60 Hz).

• Each Loaded to 425 MW

• Unit 1 – Incremental Price = $30/MWh



• How should a 75 MW increase in balancing energy be delivered?

Marginal-Energy-Cost May Not be the Most Economic Basis for Reliability

• Alternative 1: Variable-cost Based Decision - load Unit 1 an additional 75 MW.– Cost $ 2,250– Remaining resp. to next .3Hz drop: 100 MW

only 2 available generators left @ 50 MW per generator = 1/3rd shortfall from response needed to arrest next frequency drop. Need to have bought 500 MW of new excess capacity to get the extra 50 MW of response

• Alternative 2: Capacity-cost Reliability Based Decision - load each unit an additional 25 MW.– Cost $ 3,000– Remaining resp. to next .3Hz drop 150 MW

all 3 generators available @ 50 MW per generator = No shortfall from the response needed to arrest next frequency drop

energy

transmission loading component

frequency control contribution

Inadvertent is a vector in a state space

FCCTLC,energy,

Dual pricing of unscheduled energyAmbiguity along the diagonal

Revenue/Expense

Unscheduled

part 0 good bad receive

energy part 0U sold pUpe

pUpe pay

bought pUpe pUpe

Animation of the Mechanism for

Determining and Settling

Frequency Control Contribution:

iI

1 4

4

8

4 F

2

1FF

4

1F

4

1tt

4

9II

4

1I i

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 frequency-error-weighted"2-dimensional average" of Inadvertent and 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

hFhF

iI

iI

redBA ‘s hourly averages during a month

redBA

Scatter is horizontally normally distributed likehF

:i

hFhF

iI

iI

redBA ‘s hourly averages during a month

redBA

hi ,10Closest line estimate of the scatter

:i

hFhF

iI

iI

blueBA ‘s hourly averages during a month

blueBA


:i

hFhF

iI

iI


blueBA

Closest line estimate of the scatter

hi ,10

:i

hFhF

iI

iI


blueBA:i

hFhF

iI

iI

blueBAredBA

‘s scatter combined with‘s

Combined scatter is horizontally normally distributed like hF

hFhF

iI

iI

blueBAredBA


Closest line estimate of blueBA ‘sscatter and redBA ‘s scatter

hFhF

iI

iI

blackBA ‘s hourly averages during a month

blackBAi :


hFhF

iI

iI

‘s hourly averages during a month

blackBAi :

blackBA

Closest line estimate of the scatter

hi ,10

hFhF

iI

iI

blackBA ‘s hourly averages during a month

blackBAi :

hFhF

iI

iI

blackBAredBA


hFhF

iI

iI

scatters combinedblackBA ‘s, redBA ‘s and blueBA ‘s

Combined scatter is horizontally normally distributed like hF

hFhF

iI

iI

scatters combinedblackBA ‘s, redBA ‘s and blueBA ‘s

Closest line estimate of blackBA ‘sscatter , blueBA ‘s scatter , and

redBA ‘s scatter

hFhF

iI

iI

greenBA ‘s hourly averages during a month

greenBAScatter is horizontally normally distributed likehF

:i

hFhF

iI

iI


greenBAClosest line estimate of the scatter

hi ,10

:i

hFhF

iI

iI


greenBA:i

hFhF

iI

iI

greenBAredBA


hFhF

iI

iI

scatters combinedgreenBA ‘s, redBA ‘s and blueBA ‘s

hFhF

iI

iI

‘s scatters combinedgreenBA ‘s, redBA ‘s, blueBA ‘s, and

blackBACombined scatter is horizontally normally distributed like hF

hF

iI

iI

‘s scatters combined.‘s, redBA ‘s, blueBA ‘s, and

blackBAgreenBA

hF

Vertical cross-section contains equal weight of points above & below axishF

hFhF

iI

iI

‘s scatters combined.greenBA ‘s, redBA ‘s, blueBA ‘s, and

blackBAVertical cross-section contains equal weight of points above & below axishF

hFhF

iI

iI


blackBAClosest line estimate of greenBA ‘sscatter , blackBA ‘s scatter ‘sblueBA,scatter, & redBA ‘sscatter

hFhF

iI

iI

‘s scatters combinedgreenBA ‘s, redBA ‘s, blueBA ‘s, and

blackBALine estimate of system’s scatter is horizontal line on

hF axis.Zero systeminadvertent.

010 , hI

hblack ,

hred ,hblue,

hgreen,

hctionInterconne ,

hblack ,

hred ,hblue,

hgreen,

hF

iI

iI


blackBALine estimate of system’s scatter is horizontal line on

hF axis.Zero system inadvertent.

010 , hI

hF

hFhF

iI

iI

Line estimate of system’s scatter is horizontal line on axis.hFZero system inadvertent.

is horizontally normally distributed

hF

• 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

Tiered real-time market

• Three tiered market for frequency control– NERC, Balancing Authorities, local entities.

• Frequency is a public good requiring an authority like NERC to drive the frequency-control 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

• 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)

• 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)

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

Possible portfolio of optionsPrice should arbitrage buyer's avoided cost of with supplier's opportunity cost

psupply:

demand:price:

q in order of size of unscheduled

Puts on generation Calls on generation Calls on loads

I n a c o m p l e t e o p t i o n s m a r k e t f o r f r e q u e n c y r e s p o n s et h e o p t i m a l s c h e d u l i n g p o i n t m i n i m i z e s t h e c o s t o f u n s c h e d u l e d B + C

P e r i o d

O v e r s c h e d u l i n g

A C M O p t i m a l l y w S c h e d u l i n g B D

U n d e r s c h e d u l i n g O r d e r o f s i z e o f u n s c h e d u l e d U n s c h e d u l e d

A B C D O v e r s c h e d u l e d O v e r s c h e d u l e d + U n d e r s c h e d u l e d U n d e r s c h e d u l e d d u e t o o v e r s c h e d u l i n g d u e t o o p t i m a l l y s c h e d u l i n g d u e t o u n d e r s c h e d u l i n g

)](),([)( DValueAValueMinCBMinValue

Relation between CPS1

and

Frequency Control Contribution

pFCC

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

boils down to

22

,

,,

t

ti

titi FAVGb

b

tib ,where is a least-squares estimator of

bias tiB ,

2,

2

,, tittiti bFAVGb

1CPS

02

, tti FAVG

0)(

)( 2

2

t

t

ti FAVGFAVG

FTAVG

0)( ti FTAVG

With bias , tolerance band and becomes

0, settiB

1CPS02

, tib

monetizes the part

of not being subject to compliance enforcement

because

since

and

p

n h

n hiFCCp

F

FI

102

1CPS

pFCC

0)( ti FTAVG

phi FCCFIAVGk )(

2?

10 hFAVGkp

10,10

10 ppFCChih

Trading/procurement of to get within the tolerance band

drives the price of all in

22

,

,,

t

ti

titi FAVGb

b

).10( ,1010 hih pFCCp

hi ,1CPS

• Marginal price of in terms of . hi , hF

2

• When it takes less response than regulation to avoid violation.

22

tF

ti ,

tib ,

1CPS

hi ,10

p

pFCC

provides a means for s to decentralize frequency control to entities by passing through the cost/benefit of s s’ compliance to the entities necessitating/causing it.

• to alleviate ‘s compliance, and

• to re-decentralize frequency control when

compliance is centralized into fewer and bigger s

pFCC

j

BA i 1CPS

1CPSBA i

BA i1CPS

BA i1CPSj

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

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

Tolerance band makes CPS1 control proactive:

a Balancing Authority becomes non-compliant before

the Interconnection becomes non-compliant.

BAs with different biases have different CPS1 cuts/bands, all pivoting around point . Tolerance band is proactive, enabling BA violations of CPS1 to be caught before

the Interconnection violates CPS1.

Slope of tangent

Slope of asymptote (ray from origin)

1

2

2,

,

1010

t

ti

tiF

BB

1

,10

tiB

tF

badiT ,

tF

goodiT ,

,0

A CPS1 band becomes the cut when bias is .0tblueB

,

tpurpleB,

tredB,

torangeB,

tgreenB,

toliveB,

tblueB,

0

pFCC

tpurpleB,

tredB,

torangeB,

tgreenB,

toliveB,

tblueB,

0

Room for BA violations before Interconnection is in violation

CPS1 makes control economically more efficient by enabling:

•avoidance of expensive “overcontrolling” to too-short deviations

that wears and tears generators.

•natural economic incentive to control just as effectively and compliantly

but more cheaplyto a longer-term sample average.

a cps1-driven market for the frequency control contribution of inadvertent interchange presented to...

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