Power Systems Engineering
Research Center (PSERC )
An NSF Industry / University
Cooperative Research Center
PSERC
1
Mission
PSERC
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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PSERC Universities
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PSERC
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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Research Program
PSERC
• 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. Alvarado
Professor, University of Wisconsin
Invited Presentation
43rd NARUC Program
East Lansing, Michigan, August 15, 2001
5
Outline
PSERC
• Traditional reliability concepts
• LOLP
• n-1 security
• Reserve margins
• Reliability in a market context
• The Value Of Lost Load (VOLL)
• Some market power issues
6
3
Traditional reliability concepts
• Loss of load probability (LOLP)
• Expected Demand Not Served (EDNS)
• n-1 security
• Reserve margins
Electric service reliability
PSERC
• 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
8
4
Reliability Time Frames
PSERC
• 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
9
Loss of load probability
PSERC
• 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”
10
5
The n-1 security criterion
PSERC
• “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
11
Applying the n-1 criterion
PSERC
• 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)
12
6
Why do systems fail?
PSERC
• 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
13
Reserves
PSERC
• 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”
14
7
What is the ACE?
PSERC
• 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
15
More on reserves
PSERC
• 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
16
8
Reserve margins
PSERC
• “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”
17
Choosing reserve margins
PSERC
• 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
18
9
Temporal classification
PSERC
• 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
19
Reliability in a market context
• Reliability event occurs when demand
exceeds supply
• The supply and demand curves do not
intersect!
10
What is reliability anyway? PSERC
• 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
21
Economics 101
PSERC
Price
Demand function
(value of electricity
to customers)
Consumer
surplus
Total consumer
surplus (area)
Price
Equilibrium
Quantity
11
Economics 101
Price
PSERC
Production function
(cost of electricity
to producers)
Price
Producer
surplus
Equilibrium
Total producer
surplus (area)
Quantity
Economics 102
Price
PSERC
Total consumer
surplus (area)
Price
Equilibrium
Total producer
surplus (area)
Quantity
12
Some realities
PSERC
• Demand function is closer to vertical
• Supply function tends to have steps
• Supply function does not extend to
infinity
25
A market problem
Price
PSERC
Price
No Equilibrium?
Quantity
13
A market failure
Price
PSERC
Inelastic
demand
No Equilibrium
Quantity
Reliability & market failure PSERC
• 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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14
Assumptions
PSERC
• Exactly two technologies
• Each technology has a known price
• No market power
• Inelastic demand
29
Deterministic Demand and Supply, low demand case
Available supply
Quantity (power)
Demand (inelastic)
Price
Security Margin
Maximum
available
power
Clearing
price
15
Deterministic Demand and Supply, high demand case
Available supply
Demand (inelastic)
Price
Clearing
price
Maximum
available
power
Quantity (power)
Unfeasible case, no demand elasticity
No intersection
16
The effect of demand elasticity
Demand elasticity makes case feasible
Greater elasticity does not help
much more (price is still high)
Interruptible demand
Interruptible demand also helps
17
Probabilistic Demand, high demand case
Probability of low prices
Outage
probability
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
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 1A
Generator 2A
Generator 5A
Generator 6A
System A
Generator 4A
Low price
Secure
System A
Low price
n-1 secure
Generator 3A
Generator 1B
Generator 4B
Generator 5B
System B
Generator 3B
High price
n-1 insecure
High price
n-1 secure
System B
Generator 2B
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Flow
System A
System B
Low price
n-1 secure
Low price
n-1 secure
Temptation: construct a composite supply curve
unnecessary
Low price
n-1 secure
+
21
Situation with line transmission limits
System A
Max
flow
Flow
System B
Low price
n-1 insecure
Low price
n-1 secure
Outaged
generator
Normal conditions
Max
flow
Unable
to clear
Use of distributed reserves
System A
Low price
n-1 secure
Max
flow
Flow
System B
Low price
n-1 secure
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Reality
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Many flowgates
Networked sysyem
Demand can be elastic
Time delays important
Generators have fixed
(investment) costs and
restrictions
• Load is uncertain
PSERC
• Transmission outages
exacerbate problems
• If one firm dominates
a technology, market
power occurs (next)
• If one firm dominates
a location, market
power results
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The effect of congestion
Price
PSERC
Total consumer
surplus (area)
Equilibrium
point
Equilibrium
region
Total producer
surplus (area)
Price
Congestion
level
Surplus
net loss
Quantity
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Who gets what
PSERC
Price
Producer
surplus
loss
Producer
surplus
gain
Price
Congestion
level
Quantity
Who gets what, part II
Price
“Only under monopsony or regulated conditions” PSERC
Price
Consumer
surplus gain
Congestion
level
Quantity
24
Price
The incentive to congest
Producer
surplus
gain
Producer
surplus
loss
PSERC
Gain: ∆p*C
Loss: ∆C*p
Price
p
Congestion
level
C
Quantity
Equilibrium with congestion
Price
Gain: ∆p*C
Loss: ∆C*p
Price
p
C
Equilibrium when:
∆p*C = ∆C*p, or
∆p/ ∆C=p/C
Quantity
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The effect of congestion
PSERC
• 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
Additional remarks
PSERC
• 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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Features of the example
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PSERC
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
53
Observations
PSERC
• 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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Reliability and price spikes*PSERC
• What has happened in California?
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•
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
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PJM daily average on-peak spot price and max load
$/MWh
MW
800.00
78000
Price
Maxload
600.00
70000
400.00
62000
200.00
54000
0.00
46000
-200.00
38000
-400.00
30000
-600.00
-800.00
4/97
22000
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
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Assorted PJM offer curves
PJM Offer Curves at 5pm from April to August (last Tuesday)
Offer Price
1200
1000
800
600
400
200
0
0
April (4/27/99) : $29.4/MWh 28.2GW/h
10
20
0
10
20
0
10
20
Offer Price
1200
1000
800
600
400
200
0
0
0
50
60
70
30
40
50
60
70
30
40
50
60
70
50
60
70
50
60
70
July (7/27/99) : $935.0/MWh 49.2GW
10
20
30
40
August (8/24/99) : $33.7/MWh 38.5GW
Offer Price
1200
1000
800
600
400
200
0
40
June (6/29/99) : $59.5/MWh 48.1GW
Offer Price
1200
1000
800
600
400
200
0
30
May (5/25/99) : $25.9/MWh 30.3GW/h
Offer Price
1200
1000
800
600
400
200
0
10
20
30
40
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Observations
PSERC
• 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)
59
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
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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
If generators bid marginal price,
the generators surplus is zero
Supplier a generator 1
Demand
Supplier a generator 2
Other suppliers
The piece-wise nature of the supply curve revisited
Clearing
price
31
Red generator decides to withhold one generator
Surplus for
red supplier
Surplus for
blue supplier
Clearing
price
Red supplier now
has large surplus
Withheld
generator
Of course blue supplier
has even LARGER surplus!
If margins are increased
Question: and how are the
expensive technology units
supposed to recover their
investment if they always
clear at their marginal cost?
Now it is not possible for red
supplier to withhold and gain
Answer: you may end
up with less capacity
than you thought
Raising prices
would require
collusion
Clearing
price
32
Probability p that
withholding will
result in surplus
Price
If demand is uncertain
π2
P1
price π1
Quantity (power)
The expected surplus
gain is: p*(π2-π1)*P1
Since π1 is cheap unit’s marginal
cost, there is no expected surplus loss
Additional observations
PSERC
• 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*(π2-π1) for
demand above this level
With only one
generator, it is
impossible to
withhold and
benefit P
For two generators, surplus
is P*(π2-π1)/2 for demand
above this level
Effect of “granularity,” three generator case
Surplus is P*(π2-π1)/3 for
demand above this level
Surplus is 2P*(π2-π1)/3 for
demand above this level
34
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→∞
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
35
ers
10 suppli
2
On
lier
p
p
u
es
su
pp
lie
rs
3s
u pp
lier
s
Price
Effect of number of suppliers on supply curve
Demand
Effect of demand uncertainty on investment recovery
Price
Period during which
investment recovery
can take place
Withholding increases the period during
which surplus accrues but reduces the
amount that accrues
Demand
36
Price
The effect of demand uncertainty on investment recovery
Period during which
investment recovery
can take place
Demand
Numerical studies
•
•
•
•
•
PSERC
Demand is 60/70/80/90/95% of “knee”
σ 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 recovered
for each of the case combinations above according
to our earlier withholding assumptions
74
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Investment 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)
∞ suppliers, demand level as a parameter
Investment 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
Investment 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
18
20
Demand Variance (percent)
10 suppliers, demand level as a parameter
Investment 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
Demand Variance (percent)
39
6 suppliers, demand level as a parameter
Investment 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
investments
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Demand Variance (percent)
4 suppliers, demand level as a parameter
Investment 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)
40
3 suppliers, demand level as a parameter
Investment 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 investments by
withholding at low demand
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
18
20
Demand Variance (percent)
Demand level 60%, number of suppliers as a parameter
50
Investment 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 investments
20
15
10
5
0
0
2
4
6
8
10
12
14
16
Demand Variance (percent)
41
Dem and lev e l 70% , num ber of suppliers as a param e ter
120
Fixed cost recovery (thousands per MW-year)
∞ s upplie rs
15 s upplie rs
10 s upplie rs
6 s upplie rs
4 s upplie rs
3 s upplie rs
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
De m and Variance (pe rce nt)
Dem and lev e l 90% , num ber of suppliers as a param e ter
Fixed cost recovery (thousands per MW-year)
400
350
300
As demand increases, withholding becomes
profitable even when there are many suppliers
250
200
∞ s upplie rs
15 s upplie rs
10 s upplie rs
6 s upplie rs
4 s upplie rs
3 s upplie rs
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
De m and Variance (pe rce nt)
42
Dem and lev e l 95% , num ber of suppliers as a param e ter
Fixed cost recovery (thousands per MW-year)
450
400
350
300
250
200
150
100
∞ s upplie rs
Only in the case
of infinite suppliers is it
impossible to recover costs
50
0
0
2
4
6
8
10
12
14
15 s upplie rs
10 s upplie rs
6 s upplie rs
4 s upplie rs
3 s upplie rs
16
18
20
De m and Variance (pe rce nt)
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
43
Final remarks
PSERC
• 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
87
Reliability
Reserves
Price spikes
44