An NSF Industry / University Cooperative Research Center · An NSF Industry / University Cooperative Research Center PSERC 2 PSERC ... via TLR, or via prices) 7 13 PS ... Economics

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Power Systems Engineering Research Center (PSERC )

An NSF Industry / University Cooperative Research Center

PSERC

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PSERCMission

Universities working with industry and government to find innovative solutions to challenges facing a restructured electric power industry.• Multi-disciplinary (engineering, economics, operations research, etc.)

• Multi-university• Collaborative• Research and education activities

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PSERCPSERC Universities

• Cornell University (lead university)• Arizona State University• University of California at Berkeley• Carnegie Mellon University• Colorado School of Mines• Georgia Institute of Technology• The University Of Illinois at Urbana• Iowa State University• Texas A&M University• Washington State University• University of Wisconsin-Madison

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PSERCResearch Program

• Three research stems• Markets• Transmission and distribution technologies• Systems

• Leveraged research (such as Consortium for Electric Reliability Technology Solutions)

• Public documents: www.pserc.wisc.edu

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Electric Service Reliability

Fernando L. AlvaradoProfessor, University of WisconsinInvited PresentationInvited PresentationInvited PresentationInvited Presentation43434343rdrdrdrd NARUC ProgramNARUC ProgramNARUC ProgramNARUC ProgramEast Lansing, Michigan, August 15, 2001East Lansing, Michigan, August 15, 2001East Lansing, Michigan, August 15, 2001East Lansing, Michigan, August 15, 2001

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PSERCOutline

• Traditional reliability concepts• LOLP• n-1 security• Reserve margins

• Reliability in a market context• The Value Of Lost Load (VOLL)

• Some market power issues

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Traditional reliability concepts

• Loss of load probability (LOLP)• Expected Demand Not Served (EDNS)

• n-1 security• Reserve margins

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PSERCElectric service reliability

• End-user perspective:• Any involuntary loss of power is a reliability event

• Bulk system perspective:• Any system condition leading to loss of load is a reliability event

• Only those leading to widespread or extended outages are considered true reliability events

• The outage of a component is not an event

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PSERCReliability Time Frames

• The planning time frame• The operations time frame

• Reliability in this timeframe is sometimes called security

• In this talk we will emphasize the operations time frame

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PSERCLoss of load probability

• A “planning” concept• Based on random outage of generators, what is the probability that the available generators will be insufficient to meet the anticipated load

• Measured in frequency of expected outages

• EDNS extends the concept to consider energy “not served”

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PSERCThe n-1 security criterion

• “The outage of any single piece of equipment shall not result in an uncontrolled loss of load”• A pretty universal and fundamental way of operating the system

• Cost in not in the equation• Sometimes n-2 and n-3 criteria are used

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PSERCApplying the n-1 criterion

• Outage of any generator does not cause overloads or other problems• n-1 criterion used to establish reserve requirements

• Outage of any line or transformer should not cause any other overloads• If a potential problem exists, system is redispatched for “security reasons” (either via CED, via TLR, or via prices)

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PSERCWhy do systems fail?

• Cascading overloads • A simple line or transformer outage is not enough except in radial situations

• Most distribution systems are radial• Loss of system stability

• Transient or dynamic• Voltage collapse• Insufficiency of generation

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PSERCReserves

• The loss of any generator shall not cause an uncontrolled loss of load

• The “area control error” (ACE) must be brought under control• NERC has well-defined rules for this• At present the rules are “voluntary”

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PSERCWhat is the ACE?

• To facilitate control, the power system is divided into control areas• All exports and imports are monitored• Every area balances its energy to attain the desired exports or imports

• It also contributes to frequency control• The ACE is the deviation between the intended frequency+exports and the actual values

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PSERCMore on reserves

• Reserves may have to be locational• They must consider time of response

• Reserves are often classified this way• “Sustainability” attribute of reserves has been underconsidered to date

• The cost of procuring reserves can be quite important

• Reactive reserves are important

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PSERCReserve margins

• “How far are we from a failure under normal conditions”• And how about under contingency conditions

• A contingency is the loss of a component• You must also ask “in what direction”

• How far is the nearest gas station is different from how far is the next gas station

• Often the direction is “total system load”

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PSERCChoosing reserve margins

• Depends on “largest credible event”• Sometimes the probability of a triggered event is factored in• Play it more conservative during bad weather

• Margins often expressed in terms of size of largest generator or loss of biggest import

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PSERCTemporal classification

• Spinning reserves• Fast-responding, usually instantaneously

• Supplemental reserves• You can bring resources on-line quickly

• Backup reserves• They can be brought on line after some time

Reliability in a market context

• Reliability event occurs when demand exceeds supply• The supply and demand curves do not intersect!

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PSERCWhat is reliability anyway?

• The CAISO just disconnected you as a result of insufficient reserves• This is an example of a reliability event

• You had vountarily signed up for an interruptible program and got cut off• This is not a reliability event

PSERCEconomics 101

Quantity

Pric

e

Equilibrium

PriceConsumer

surplus

Demand function(value of electricity

to customers)

Total consumersurplus (area)

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PSERCEconomics 101

Quantity

Pric

e

Equilibrium

Price

Producersurplus

Production function(cost of electricity

to producers)

Total producersurplus (area)

PSERCEconomics 102

Quantity

Pric

e

Equilibrium

Price



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PSERCSome realities

• Demand function is closer to vertical• Supply function tends to have steps• Supply function does not extend to infinity

PSERCA market problem

Quantity

Pric

e

No Equilibrium?

Price

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PSERCA market failure

Quantity

Pric

e

No Equilibrium

Inelasticdemand

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PSERCReliability & market failure

• Market failure ⇒⇒⇒⇒ Reliability event

• Reliability event ⇒⇒⇒⇒ Market failure?

• Certain reliability events are not the result of market failure

• There must have been a market in the first place

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PSERCAssumptions

• Exactly two technologies• Each technology has a known price

• No market power• Inelastic demand

Quantity (power)

Pric

e

Dem

and

(inel

astic

)

Available supply

Clearingprice

Maximumavailable

power

Deterministic Demand and Supply, low demand case

Security Margin

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Quantity (power)

Pric

e

Dem

and

(inel

astic

)

Available supply

Clearingprice

Maximumavailable

power

Deterministic Demand and Supply, high demand case

Unfeasible case, no demand elasticity

No intersection

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The effect of demand elasticity

Demand elasticity makes case feasible

Greater elasticity does not helpmuch more (price is still high)

Interruptible demand

Interruptible demand also helps

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Probabilistic Demand, high demand case

Outageprobability

Probability of low prices

The piece-wise nature of the supply curve

Gen

erat

or 1

Gen

erat

or 2

Gen

erat

or 3

Gen

erat

or 4 G

ener

ator

5

Gen

erat

or 6

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The effect of a generator outage

Outagedgenerator

Oldsupply

limit

Newsupplylimit

Effect of demand uncertainty and generator outage

n-1 secure

insecure

Probabilityp2

Outage probability is p1*p2

Probability p1

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System B

System A

Generator 1A

Generator 2A

Generator 3A

Generator 4AGenerator 5AGenerator 6A

Generator 1B

Generator 2B

Generator 3B

Generator 4B

Generator 5B

High price

n-1 insecureLow

priceSecure

System B

System A

High price

n-1 secureLow

pricen-1 secure

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System BSystem A

Low pricen-1 secureLow price

n-1 secure

Flow

Temptation: construct a composite supply curve

+

Low pricen-1 secure

unnecessary

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Flow

Normal conditions

System BSystem A

Low pricen-1 insecureLow price

n-1 secure

Situation with line transmission limitsMaxflow

Maxflow

Outagedgenerator

Unableto clear

System BSystem A

Flow

Maxflow

Use of distributed reserves

Low pricen-1 secureLow price

n-1 secure

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PSERCReality

• Many flowgates• Networked sysyem• Demand can be elastic• Time delays important• Generators have fixed

(investment) costs and restrictions

• Load is uncertain

• Transmission outages exacerbate problems

• If one firm dominates a technology, market power occurs (next)

• If one firm dominates a location, market power results

PSERCThe effect of congestion

Quantity

Pric

e

Price



Congestionlevel Surplus

net loss

Equilibriumregion

Equilibriumpoint

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PSERCWho gets what

Quantity

Pric

e

Price

Congestionlevel

Producersurplus

gain

Producersurplusloss

PSERCWho gets what, part II

Quantity

Pric

e

Price

Consumer surplus gain

Congestionlevel

“Only under monopsony or regulated conditions”

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PSERCThe incentive to congest

Quantity

Pric

e

Price

Congestionlevel

Producersurplus

loss

Producersurplus

gain

Gain: ∆p*CLoss: ∆C*p

p

C

Equilibrium with congestion

Quantity

Pric

e

Price

Gain: ∆p*CLoss: ∆C*p

Equilibrium when: ∆p*C = ∆C*p, or

∆p/ ∆C=p/C

p

C

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PSERCThe effect of congestion

• Congestion creates “gaming” opportunities• Producers have an incentive to congest

• (Up to a point)• The only unambiguous way to characterize the effect of congestion is to look at net surplus loss• Translated: when we compute congestion costs, we do not care who incurs them

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PSERCAdditional remarks

• Two-technology suppliers can lead to higher than marginal prices as the knee of the supply curve is approached

• Larger number of suppliers reduces this effect

• Market power studies should consider investment recovery issues

• Transmission congestion makes matters worse!!

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PSERCFeatures of the example

• Only two areas (one flowgate)• Radial• Demand is inelastic• Time delays are not an issue• Generators have no startup/shutdown costs or restrictions or minimum power levels

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PSERCObservations

• Demand elasticity is important• Locational aspects of reserves matter

• LMP for reserves• Ramping rates matter• In deregulated markets only units explicitly

committed to reserves are available• In regulated markets and in PJM all units are

• Reliability requires that we increase supply• Standby charges tend to reduce supply (Tim

Mount)

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PSERCReliability and price spikes*

• What has happened in California?• Price caps have come down• Average prices have increased• Price volatility has decreased• There have been involuntary curtailments

(*) Some of this material comes from Tim Mount at Cornell

PJM daily average on-peak spot price and max load

-800.00

-600.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

4/97 6/97 8/97 10/97 12/97 2/98 4/98 6/98 8/98 10/98 12/98 2/99 4/99 6/99 8/99 10/99 12/99 2/00 4/00

date

22000

30000

38000

46000

54000

62000

70000

78000PriceMaxload

$/MWh MW

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PJM Offer Curves at 5pm from April to August (last Tuesday)

April (4/27/99) : $29.4/MWh 28.2GW/h

0200400600800

10001200

0 10 20 30 40 50 60 70

Offer Price

May (5/25/99) : $25.9/MWh 30.3GW/h

0200400600800

10001200

0 10 20 30 40 50 60 70

Offer Price

June (6/29/99) : $59.5/MWh 48.1GW

0200400600800

10001200

0 10 20 30 40 50 60 70

Offer Price

July (7/27/99) : $935.0/MWh 49.2GW

0200400600800

10001200

0 10 20 30 40 50 60 70

Offer Price

August (8/24/99) : $33.7/MWh 38.5GW

0200400600800

10001200

0 10 20 30 40 50 60 70

Offer Price

Assorted PJM offer curves

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PSERCObservations

• Price spikes have developed not so much under high load conditions as under tight reserve conditions

• For suppliers that own more than one technology, there are strong incentives to withhold capacity

• There is a strong connection between reserves and reliability (and market power)

Market Power?

• The ability to raise prices significantly above the efficient economic equilibrium

• Disclaimer: the slides that follow are not really a market power study but rather they represent a simplified illustration of how higher prices could result as a result of market concentration.

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Market Power: Assumptions• There are exactly two technologies

• Each technology has a fixed marginal price• ∞∞∞∞ availability of the expensive technology• Limited availability of the cheap technology• Cheap technology has fixed costs (investments) to recover

• Demand is inelastic• All suppliers but a schedule all their cheap power• a owns P MW in n≥≥≥≥1 equal-sized generators

• Supplier a can “withhold” one or more generators• Bidding above marginal cost is not allowed, withholding is

The piece-wise nature of the supply curve revisited

Oth

er su

pplie

rs

Supp

lier a

gene

rato

r 1Dem

and

Clearingprice

If generators bid marginal price,the generators surplus is zero

Supp

lier a

gene

rato

r 2

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Red generator decides to withhold one generator

Withheldgenerator

Clearingprice

Surp

lus f

orre

d su

pplie

rRed supplier nowhas large surplus

Of course blue supplierhas even LARGER surplus!

Surp

lus f

orbl

ue su

pplie

r

If margins are increased

ClearingpriceNow it is not possible for red

supplier to withhold and gain

Raising priceswould requirecollusion

Question: and how are theexpensive technology units

supposed to recover theirinvestment if they always

clear at their marginal cost?

Answer: you may endup with less capacitythan you thought

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If demand is uncertain

The expected surplusgain is: p*(π2-π1)*P1

Probability p thatwithholding willresult in surplus

π2

P1

price π1

Quantity (power)

Pric

e

Since π1 is cheap unit’s marginalcost, there is no expected surplus loss

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PSERCAdditional observations

• If the margin to the “knee” is Pm, any supplier with a total ownership above Pm may profit from withholding• If more than one supplier meets this conditions, chances are that someone will withhold

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For two generators, surplusis P*(π2-π1)/2 for demandabove this level

Effect of “granularity”

With only onegenerator, it isimpossible towithhold andbenefit P

Surplus is P*(π2-π1) fordemand above this level

Effect of “granularity,” three generator case

Surplus is P*(π2-π1)/3 fordemand above this level

Surplus is 2P*(π2-π1)/3 fordemand above this level

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Effect of “granularity”

Surp

lus

With n=1, there is no surplus

Surplus with n=2

Surplus with n=3

Surplus with n=4

Surplus with n→∞

Demand level

Observations and assumptions

• For “worst case” effect, assume n=∞∞∞∞• Assume withholding will occur

• Withholding “softens” the supply curve• High cost periods needed for investment

recovery• Demand is probabilistic• Suggestion: market power occurs if expected

surplus far exceeds investment recovery• This is also a signal for system expansion

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Effect of number of suppliers on supply curve

One supplier

2 sup

pliers

3 su

pplie

rs

10 su

pplie

rs

Demand

Pric

ePr

ice

Demand

Period during whichinvestment recoverycan take place

Effect of demand uncertainty on investment recovery

Withholding increases the period duringwhich surplus accrues but reduces theamount that accrues

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Pric

e

Demand

Period during whichinvestment recoverycan take place

The effect of demand uncertainty on investment recovery

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PSERCNumerical studies

• Demand is 60/70/80/90/95% of “knee”• σσσσ for demand varies from 0 to 20%• Demand probability function is normal• Supplier has ∞∞∞∞ equal size units available• There are 3/6/10/15/∞∞∞∞ suppliers

We illustrate the investments that can be recoveredfor each of the case combinations above accordingto our earlier withholding assumptions

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

50

100

150

200

250

80%

Variance of demand (per unit)

Investment recovery without market power (∞ suppliers)

Thou

sand

s per

yea

r per

MW

90%

95%

99% Demand level as a percentageof available capacity

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

120

140

160

180

200

Demand Variance (percent)

Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)

∞∞∞∞ suppliers, demand level as a parameter

60%70%80%90%95%

Even for highdemand levels, somedemand varianceis essential forcost recovery

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0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)

15 suppliers, demand level as a parameter

60%70%80%90%95%

For high enough demand levelscost recovery is possibleeven without demand variance

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)


60%70%80%90%95%

For high demand levelsdemand variance can becomeirrelevant

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0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)


60%70%80%90%95%

For low demand levels it isvery difficult to recoverinvestments

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400

450


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)


60%70%80%90%95%

For high demand levels, high variancecan even be slightly detrimental to profits

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0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400

450


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)


60%70%80%90%95%

With three or less suppliers, it becomes feasibleat high variances to recover investments bywithholding at low demand

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50


Inve

stm

ent r

ecov

ery

(thou

sand

s pe

r MW

-yea

r)

Demand level 60%, number of suppliers as a parameter

∞ suppliers15 suppliers 10 suppliers 6 suppliers 4 suppliers 3 suppliers

At low demand and lowvariance it is impossibleto recover investments

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0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

120


Fixe

d co

st re

cove

ry (t

hous

ands

per

MW

-yea

r)


∞ s upplie rs15 s upplie rs 10 s upplie rs 6 s upplie rs 4 s upplie rs 3 s upplie rs

At higher demand with 3 suppliersit is possible to recovercosts at low variance

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400


Fixe

d co

st re

cove

ry (t

hous

ands

per

MW

-yea

r)



As demand increases, withholding becomesprofitable even when there are many suppliers

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0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400

450


Fixe

d co

st re

cove

ry (t

hous

ands

per

MW

-yea

r)



Only in the caseof infinite suppliers is it

impossible to recover costs

Comments on numerical results

• The number of suppliers has a strong influence on investment recovery• Below a certain number of suppliers, investment

recovery by withholding becomes easier• There are demand thresholds beyond which there

is a jump in the ability to recover investments• All studies have assumed that supplier adjusts

withholding after learning the demand• Demand variance affects reliability

• It also influences the ability to recover investments

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PSERCFinal remarks

• Reliability not decoupled from economics• Tight reliability precursor to price spikes

• The structure of two-technology suppliers can lead to higher prices as the “knee” of the supply curve is approached• More suppliers reduce this effect

• Market power studies should consider investment recovery, locational effects

• Congestion, loop flows, voltage, frequency are also important

Reliability

Reserves

Price spikes

Documents

An NSF Industry / University Cooperative Research Center · An NSF Industry / University Cooperative Research Center PSERC 2 PSERC ... via TLR, or via prices) 7 13 PS ... Economics