Transcript Document

Reliability concepts and market power
Fernando L. Alvarado
Professor, The University of Wisconsin
Invited Seminar at the U. S. Department of Energy
December 4, 2000
December 4, 2000
© 2000 Fernando L. Alvarado
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Outline
• Reliability basics overview
• Some market power issues
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© 2000 Fernando L. Alvarado
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Basics overview (assumptions)
• Exactly two technologies
– Each technology has a known price
• No market power
• Inelastic demand
• Reliability event occurs when demand
exceeds supply
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Available supply
Demand (inelastic)
Price
Deterministic Demand and Supply, low demand case
Quantity (power)
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Maximum
available
power
Clearing
price
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Deterministic Demand and Supply, high demand case
Available supply
Demand (inelastic)
Price
Clearing
price
Maximum
available
power
Quantity (power)
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Probabilistic Demand, high demand case
Probability of low prices
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© 2000 Fernando L. Alvarado
Outage
probability
6
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Generator 6
Generator 5
Generator 4
Generator 3
Generator 2
Generator 1
The piece-wise nature of the supply curve
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The effect of a generator outage
Outaged
generator
Old
supply
limit
New
supply
limit
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Effect of demand uncertainty
and generator outage
Probability
p2
Probability p1
n-1 secure
insecure
Outage probability is p1*p2
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Generator 5B
Generator 4B
Low price
Secure
Generator 3B
Generator 2B
Generator 1B
Generator 5A
Generator 6A
Generator 4A
Generator 3A
Generator 2A
Generator 1A
System B
System A
High price
n-1 insecure
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System B
System A
High price
n-1 secure
Low price
n-1 secure
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System A
Flow
Low price
n-1 secure
Low price
n-1 secure
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System B
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Temptation: construct a composite supply curve
unnecessary
Low price
n-1 secure
+
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Situation with line transmission limits
System A
Max
flow
Flow
System B
Low price
n-1 insecure
Low price
n-1 secure
Outaged
generator
Unable
to clear
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© 2000 Fernando L. Alvarado
Normal conditions
Max
flow
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Use of distributed reserves
System A
Max
flow
Flow
Low price
n-1 secure
Low price
n-1 secure
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System B
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Features 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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Observations
• 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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Reality
•
•
•
•
•
Many flowgates
Networked sysyem
Demand can be elastic
Time delays important
Generators have fixed
costs and restrictions
• Load is uncertain
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• Transmission outages
exacerbate problems
• If one firm dominates
a technology, market
power occurs (next)
• If one firm dominates
a location, market
power results
© 2000 Fernando L. Alvarado
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Market Power?
• The ability to raise
prices significantly
above the efficient
economic equilibrium
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• 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.
© 2000 Fernando L. Alvarado
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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 to recover
• Demand is inelastic
– First deterministic, then probabilistic
• All suppliers but a schedule all their cheap power
• Supplier 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
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Demand
If generators bid marginal price,
the generators surplus is zero
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Supplier a generator 1
Other suppliers
Supplier a generator 2
The piece-wise nature of the supply curve revisited
Clearing
price
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Red generator decides to withhold one generator
Red supplier now
has large surplus
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Surplus for
red supplier
Surplus for
blue supplier
Clearing
price
Withheld
generator
Of course blue supplier
has even LARGER surplus!
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If margins are increased
Question: and how are the
expensive technology units
supposed to recover their
fixed costs if they always
clear at their marginal cost?
Now it is not possible for red
supplier to withhold and gain
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© 2000 Fernando L. Alvarado
Answer: you may end
up with less capacity
than you thought
Raising prices
would require
collusion
Clearing
price
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Probability p that
withholding will
result in surplus
Price
If demand is uncertain
p2
P1
price p1
Quantity (power)
The expected surplus
gain is: p*(p2-p1)*P1
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Since p1 is cheap unit’s marginal
cost, there is no expected surplus loss
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Additional 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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Effect of “granularity”
Surplus is P*(p2-p1) for
demand above this level
With only one
generator, it is
impossible to
withhold and
benefit P
For two generators, surplus
is P*(p2-p1)/2 for demand
above this level
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Effect of “granularity,” three generator case
Surplus is P*(p2-p1)/3 for
demand above this level
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© 2000 Fernando L. Alvarado
Surplus is 2P*(p2-p1)/3 for
demand above this level
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With n=1, there is no surplus
Surplus
Effect of “granularity”
Surplus with n=2
Surplus with n=3
Surplus with n=4
Demand level
Surplus with n
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Observations and assumptions
• For “worst case” effect, assume n=
• Assume withholding will occur
– Withholding “softens” the supply curve
• High cost periods needed for fixed cost recovery
• Demand is probabilistic
• Suggestion: market power occurs if expected
surplus exceeds fixed cost recovery
– This is also a signal for system expansion
• This means that in the absence of uncertainty, expansion will
occur when expected profits exceed long run marginal costs
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Price
Effect of number of suppliers on supply curve
Demand
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Effect of demand uncertainty on fixed cost recovery
Price
Period during which
fixed cost recovery
can take place
Withholding increases the period during
which surplus accrues but reduces the
amount that accrues
Demand
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Price
The effect of demand uncertainty on fixed cost recovery
Period during which
fixed cost recovery
can take place
Demand
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Numerical studies
•
•
•
•
•
Demand is 60/70/80/90/95% of “knee”
s for demand varies from 0 to 20%
Demand probability distribution is normal
Supplier has  equal size units available
There are 3/6/10/15/ suppliers
We illustrate the fixed costs that can be recovered
for each of the case combinations above according
to our earlier withholding assumptions
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Fixed cost recovery without market power ( suppliers)
Thousands per year per MW
250
99%
200
Demand level as a percentage
of available capacity
150
95%
100
90%
50
80%
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Variance of demand (per unit)
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 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
200
60%
70%
80%
90%
95%
180
160
140
120
Even for high
demand levels, some
demand variance
is essential for
cost recovery
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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15 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
250
200
For high enough demand levels
cost recovery is possible
even without demand
variance
150
60%
70%
80%
90%
95%
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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10 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
300
250
For high demand levels
demand variance can become
irrelevant
200
150
60%
70%
80%
90%
95%
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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6 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
400
350
300
250
200
60%
70%
80%
90%
95%
For low demand levels it is
very difficult to recover
fixed costs
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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4 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
450
400
350
300
For high demand levels, high variance
can even be slightly detrimental to profits
250
200
60%
70%
80%
90%
95%
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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3 suppliers, demand level as a parameter
Fixed cost recovery (thousands per MW-year)
450
400
350
60%
70%
80%
90%
95%
300
250
200
With three or less suppliers, it becomes feasible
at high variances to recover fixed costs by
withholding at low demand
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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Demand level 60%, number of suppliers as a parameter
50
Fixed cost recovery (thousands per MW-year)
 suppliers
15 suppliers
10 suppliers
6 suppliers
4 suppliers
3 suppliers
45
40
35
30
25
At low demand and low
variance it is impossible
to recover fixed costs
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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Demand level 70%, number of suppliers as a parameter
Fixed cost recovery (thousands per MW-year)
120
 suppliers
15 suppliers
10 suppliers
6 suppliers
4 suppliers
3 suppliers
100
80
60
At higher demand with 3 suppliers
it is possible to recover
costs at low variance
40
20
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
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Demand level 90%, number of suppliers as a parameter
Demand level 80%, number of suppliers as a parameter
250
350
Fixed cost recovery (thousands per MW-year)
Fixed cost recovery (thousands per MW-year)
400
300
200
As demand increases, withholding becomes

profitable
even when there are many suppliers
250
suppliers
15 suppliers
10 suppliers
6 suppliers
4 suppliers
3 suppliers
150
200
150
 suppliers
15 suppliers
10 suppliers
6 suppliers
4 suppliers
3 suppliers
100
100
50
50
0
0
0
0
2
2
4
4
6
8
10
12
14
6 Demand
8 Variance
10 (percent)
12
16
14
18
16
20
18
20
Demand Variance (percent)
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Demand level 95%, number of suppliers as a parameter
Fixed cost recovery (thousands per MW-year)
450
400
350
300
250
200
150
100
50
0
 suppliers
Only in the case
of infinite suppliers is it
impossible to recover costs
0
2
4
6
8
10
12
14
15 suppliers
10 suppliers
6 suppliers
4 suppliers
3 suppliers
16
18
20
Demand Variance (percent)
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Comments on numeric results
• The number of suppliers has a strong influence on
cost recovery
– Below a certain number of suppliers, cost recovery by
withholding becomes easier
• There are demand threshold levels beyond which
there is a jump in the ability to recover costs
• All studies assume that supplier can adjust level of
withholding after learning the demand
– Lower returns when this is not true, study underway
• Demand variance has a strong influence on ability
to recover costs, sometimes with a threshold level
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Final 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 fixed
cost recovery issues
• We did not even look at congestion or voltage
problems!
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