ELECTRICITY MARKET DESIGN:
Coordination, Pricing and Incentives
William W. Hogan
Mossavar-Rahmani Center for Business and Government
John F. Kennedy School of Government
Harvard University
Cambridge, Massachusetts 02138
ERCOT Energized Conference
Austin, TX
May 2, 2008
ELECTRICITY MARKET
Electricity Restructuring
The case of electricity restructuring presents examples of fundamental problems that challenge
regulation of markets.
•
Marriage of Engineering and Economics.
o Loop Flow.
o Reliability Requirements.
o Incentives and Equilibrium.
•
Devilish Details.
o Retail and Wholesale Electricity Systems.
o Market Power Mitigation.
o Coordination for Competition.
•
Jurisdictional Disputes.
o US State vs. Federal Regulators.
o European Subsidiarity Principle.
1
ELECTRICITY MARKET
Energy Market Pricing
Consider three cases of interest that present difficult challenges for regulators. A focus on pricing
illustrates an important thread of modeling and analysis. Constrained optimization provides a
central organizing framework.
• Design Framework: “Locational Marginal Pricing”
LMP. Bid-based, security constrained economic dispatch.
• Design Implementation: Scarcity Pricing
Better scarcity pricing to support resource adequacy.
• Design Limitation: Uplift Payments
Unit commitment and lumpy decisions. Coordination and bid guarantees.
2
ELECTRICITY MARKET
Transmission Management
Defining and managing transmission usage is a principal challenge in electricity markets.
Transmission Capacity Definitions
Contract Path
Contract Path Fiction
OASIS Schedules
and TLR
Flow-Based Paths
Point-to-Point
Parallel Flows
Flows Implicit
Flowgate Rights
FGRs
Financial Transmission
Rights
FTRs
3
ELECTRICITY MARKET
Order 888 and the Contract Path
Under Order 888 the FERC made a crucial choice regarding a central complication of the electricity
system.
“A contract path is simply a path that can be designated to form a single continuous electrical path
between the parties to an agreement. Because of the laws of physics, it is unlikely that the actual
power flow will follow that contract path. … Flow-based pricing or contracting would be designed to
account for the actual power flows on a transmission system. It would take into account the
"unscheduled flows" that occur under a contract path regime.” (FERC, Order 888, April 24, 1996, footnotes 184185, p. 93.)
Why is this important? A quick tutorial follows.
4
NETWORK INTERACTIONS
Loop Flow
Electric transmission network interactions can be large and important.
•
Conventional definitions of network "Interface" transfer capacity depend on the assumed
load conditions.
•
Transfer capacity cannot be defined or guaranteed over any reasonable horizon.
POWER TRANSFER CAPACITY VARIES WITH LOAD
(WITH IDENTICAL LINKS, TRUE CONSTRAINT ON LINE FROM OLDGEN TO BIGTOWN)
Is The "Interface" Transfer Capacity
900 MW?
Or
OLDGEN
NEWGEN
0 MW
900 MW
0
30 W
M
600
=m
ax
600 MW
600
=m
ax
BIGTOWN
1800 MW
INTERFACE
0 MW
OLDGEN
INTERFACE
300 MW
900 MW
1800 MW?
M
00
12
1800 MW
W
BIGTOWN
NEWGEN
5
NETWORK INTERACTIONS
Loop Flow
There is a fatal flaw in the old "contract path" model of power moving between locations along a
designated path. The network effects are strong. Power flows across one "interface" can have a
dramatic effect on the capacity of other, distant interfaces.
Transmission Impacts Vary Across the Eastern System
Transfer Interface Impact (1000 MW)
Transfer Capability Impacts
1000 MW from VACAR to BG&E/PEPCO
0.2
Contract Path
Assumption
(Impact = 0)
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
-1.8
-2.0
-2.2
-2.4
-2.6
EC
A
R
to
M
EC
AR
AA
to
VP
C
DU
TV
MA
A
KE
EC
W
N
to
AC
/C
.E
DU YPP
AR
P&
CA
to
KE
to
to
VP
Lt
R
M
DU
/C
oV
to
P& AA
OH
KE
P
C
L
/C
P&
L
Interface in Eastern Interconnected System
Source: VEM, Winter Operating Study, December 1993.
6
ELECTRICITY MARKET
Order 888 and the Contract Path
Under Order 888 the FERC made a crucial choice regarding a central complication of the electricity
system.
“A contract path is simply a path that can be designated to form a single continuous electrical path
between the parties to an agreement. Because of the laws of physics, it is unlikely that the actual
power flow will follow that contract path. … Flow-based pricing or contracting would be designed to
account for the actual power flows on a transmission system. It would take into account the
"unscheduled flows" that occur under a contract path regime.” (FERC, Order 888, April 24, 1996, footnotes 184185, p. 93.)
“We will not, at this time, require that flow-based pricing and contracting be used in the electric
industry. In reaching this conclusion, we recognize that there may be difficulties in using a
traditional contract path approach in a non-discriminatory open access transmission environment,
as described by Hogan and others. At the same time, however, contract path pricing and
contracting is the longstanding approach used in the electric industry and it is the approach familiar
to all participants in the industry. To require now a dramatic overhaul of the traditional approach
such as a shift to some form of flow-based pricing and contracting could severely slow, if not derail
for some time, the move to open access and more competitive wholesale bulk power markets. In
addition, we believe it is premature for the Commission to impose generically a new pricing regime
without the benefit of any experience with such pricing. We welcome new and innovative proposals,
but we will not impose them in this Rule.” (FERC, Order 888, April 24, 1996, p. 96.)
Hence, although the fictional contract path approach would not work in theory, maintaining the
fiction would be less disruptive in moving quickly to open access and an expanded competitive
market!
7
ELECTRICITY MARKET
Pool Dispatch
An efficient short-run electricity market determines a market clearing price based on conditions of
supply and demand. Everyone pays or is paid the same price.
SHORT-RUN ELECTRICITY MARKET
Energy Price
Short-Run
Marginal
Cost
(¢/kWh)
Price at
7-7:30 p.m.
Demand
7-7:30 p.m.
Price at
9-9:30 a.m.
Price at
2-2:30 a.m.
Demand
9-9:30 a.m.
Demand
2-2:30 a.m.
Q1
Q2
Qmax
MW
8
NETWORK INTERACTIONS
Locational Spot Prices
The natural extension of a single price electricity market is to operate a market with locational spot
prices.
•
It is a straightforward matter to compute "Schweppe" spot prices based on marginal costs
at each location.
•
Transmission spot prices arise as the difference in the locational prices.
LOCATIONAL SPOT PRICE OF "TRANSMISSION"
Energy Price
Short-Run
Marginal
Cost
(¢/kWh)
Price differential =
Demand
MW
A Pa = 51
Marginal losses
+ Constraint prices
Constraint
B
Energy Price
Pb = 66
C
(¢/kWh)
Short-Run
Marginal
Cost
Demand
Energy Price
Pc = 55
Short-Run
Marginal
Cost
(¢/kWh)
MW
Demand
MW
Price of "Transmission" from A to B = Pb - Pa = 15
Price of "Transmission" from A to C = Pc - Pa = -4
9
NETWORK INTERACTIONS
Locational Spot Prices
Locational prices ($/MWh) arise from the standard formulation of security constrained economic
dispatch to balance generation and load at each location. For instance, in PJM there are several
thousand locations with thousands of constraints for each of thousands of contingencies.
Bid-Based, Security-Constrained, Economic Dispatch
Max
d ,g ,x, y
B(d ) − C ( g )
subject to
d−g = y
K ( x, y ) ≤ 0.
PJM
:p
:μ
Real Time Hourly LMP Values for 20080224
Range
Max
Average
Min
Node
1
2
3
4
Start of Real Time LMP Data
Date
PnodeID
Name Voltage Equipm Type Zone
20080224
1 PJM-RTO
ZONE
20080224
3 MID-ATL/APS
ZONE
20080224
51291 AECO
ZONE
20080224
8445784 AEP
ZONE
551.94 550.57
516.16 434.34
69.79
-5.18
-35.78 -116.23
23.80
16.38
-0.53
-7.42
127.90
142.74
66.17
14.84
126.10
71.28
-4.88
-54.82
21.06
14.18
-0.53
-6.88
138.60
166.06
48.86
27.46
137.61
109.89
-2.22
-27.72
16.42
11.13
-0.44
-5.29
100
100
100
1200
1200
1200
1800
1800
1800
TotalLM CongestioMarginalLossPricTotalLMP CongestioMarginalLossPriceTotalLMP CongestioMarginalLossPrice
75.90
0.34
0.06
71.84
0.20
0.06
51.63
0.07
0.04
97.78
19.30
2.97
90.79
16.52
2.69
60.51
6.89
2.11
46.33 -33.86
4.69
91.28
15.17
4.53
48.86
-6.21
3.55
43.55 -28.48
-3.47
32.42
-35.94
-3.22
37.52
-11.51
-2.49
…
424
425
426
20080224
20080224
20080224
32406789 107 DIX138 KV TR76 34LOAD COMED 41.23
32406793 109 APT138 KV TR72 12LOAD COMED 42.72
32406795 109 APT138 KV TR73 12LOAD COMED 42.69
-28.37
-28.66
-28.66
-5.90
-4.12
-4.15
32.16
33.46
33.43
-34.15
-34.39
-34.39
-5.27
-3.73
-3.76
35.61
36.73
36.71
-11.59
-11.74
-11.74
-4.32
-3.05
-3.07
15.14
15.14
-31.29
1.93
1.93
-3.64
93.33
93.33
32.11
19.83
19.83
-36.24
1.92
1.92
-3.23
59.47
59.47
36.19
6.41
6.41
-12.85
1.54
1.54
-2.48
…
8075
8076
8077
20080224
49498 ZIONSV115 KV 1B12
20080224
49499 ZIONSV115 KV 2B12
20080224 32413125 ZUBER 138 KV T1
End of Real Time LMP Data
LOAD METED
LOAD METED
LOAD AEP
92.57
92.57
40.57
10
NETWORK INTERACTIONS
Locational Spot Prices
Locational spot prices for electricity exhibit substantial dynamic variability and persistent longterm average differences.
From MISO-PJM Joint and Common Market, http://www.jointandcommon.com/ for March 3, 2008, 9:55am. Projected 2011 annual average from 2006
Midwest ISO-PJM Coordinated System Plan.
11
NETWORK INTERACTIONS
Financial Transmission Rights
A mechanism for hedging volatile transmission prices can be established by defining financial
transmission rights to collect the congestion rents inherent in efficient, short-run spot prices.
NETWORK TRANSMISSION FINANCIAL RIGHTS
A Pa = 51
Constraint
B
Pb = 66
C
Pc = 55
Price of "Transmission" from A to B = Pb - Pa = 15
Price of "Transmission" from A to C = Pc - Pa = -4
DEFINE TRANSMISSION CONGESTION CONTRACTS BETWEEN LOCATIONS.
FOR SIMPLICITY, TREAT LOSSES AS OPERATING COSTS.
RECEIVE CONGESTION PAYMENTS FROM ACTUAL USERS; MAKE
CONGESTION PAYMENTS TO HOLDERS OF CONGESTION CONTRACTS.
TRANSMISSION CONGESTION CONTRACTS PROVIDE PROTECTION
AGAINST CHANGING LOCATIONAL DIFFERENCES.
12
ELECTRICITY MARKET
A Consistent Framework
The example of successful central coordination, CRT, Regional Transmission Organization (RTO)
Millennium Order (Order 2000) Standard Market Design (SMD) Notice of Proposed Rulemaking
(NOPR), “Successful Market Design” provides a workable market framework that is working in
places like New York, PJM in the Mid-Atlantic Region, New England, and the Midwest.
The RTO NOPR Order SMD NOPR "Successful Market Design"
Contains a Consistent Framework
Bilateral Schedules
Coordinated
Spot Market
Bid-Based,
Security-Constrained,
Economic Dispatch
with Nodal Prices
Financial Transmission Rights
(TCCs, FTRs, FCRs, CRRs, ...)
Market-Driven Investment
License Plate Access Charges
at Difference in Nodal Prices
07/05
07/02
12/99
5/99
Poolco…OPCO…ISO…IMO…Transco…RTO… ITP…WMP…: "A rose by any other name …"
13
ELECTRICITY MARKET
Path Dependence
The path to successful market design can be circuitous and costly. The FERC “reforms” in Order
890 illustrate “path dependence,” where the path chosen constrains the choices ahead. Can Order
890 be reformed to overcome its own logic? Or is FERC trapped in its own loop flow?
Paths to Successful Market Design
SMD
t
rke
a
M
Bilateral Schedules
License Plate Access Charges
at Difference in Nodal Prices
Coordinated
Spot Market
Bid-Based,
Security-Constrained,
Economic Dispatch
with Nodal Prices
Financial Transmission Rights
(TCCs, FTRs, FCRs, CRRs, ...)
888
Standardization
Transparency
"Simple,
Quick"
Market-Driven Investment
ed
niz
ing
ga
r
nc
O
a
l
ion
Ba
iss
m
ns hts
Tra Rig
C
AT
"Last
Resort"
890
Reform
Rules
Explode
ISO
PX
Zonal
Contract
Path
TLR
Flowgate
14
ELECTRICITY MARKET
A Consistent Framework
Regional transmission organizations (RTOs) and independent system operators (ISOs) have grown
to cover 75% of US economic activity.
Bilateral Schedules
Market-Driven Investment
License Plate Access Charges
at Difference in Nodal Prices
Coordinated
Spot Market
Bid-Based,
Security-Constrained,
Economic Dispatch
with Nodal Prices
Financial Transmission Rights
(TCCs, FTRs, FCRs, CRRs, ...)
PJM Locatinal Prices 1/15/08
700
600
Price ($/MWh)
500
400
300
200
Max
Min
100
0
-100
1
3
5
7
9
11
13
15
17
19
21
23
-200
-300
Hour
15
ELECTRICITY MARKET
Resource Adequacy
There is a simple stylized connection between reliability standards and resource economics.
Defining expected load shedding duration, choosing installed capacity, or estimating value of lost
load address different facets of the same problem.
A Simple Reliability Model
MW
Curtailment
Capacity
Load Duration
Duration
Optimal Duration ≈
Peaker Fixed Charge
Value Lost Load
(Steven Stoft, Power System Economics, IEE Press, Wiley Interscience, 2002, p. 138)
16
ELECTRICITY MARKET
Resource Adequacy
The simple connection between reliability planning standards and resource economics illustrates a
major disconnect between market pricing and the implied value of lost load.
Reliability Planning Standard
and Value of Lost Load
Implied Average Value of Lost Load
Average Value of Load Load ($/MWh)
$80,000
Twenty Four Hours in Ten Years
$70,000
$60,000
$50,000
Optimal Duration ≈
$40,000
Peaker Fixed Charge
Value Lost Load
$30,000
$20,000
$10,000
$0
0
5
10
15
20
25
Annual Duration of Load Curtailm ent (Hours)
Peaker fixed charge at $65,000/MW-yr.
17
ELECTRICITY MARKET
Reliability Standards
There is a large disconnect between long-term planning standards and market design. The
installed capacity market analyses illustrate the gap between prices and implied values. The larger
disconnect is between the operating reserve market design and the implied reliability standard.
Reliability Standard and Market Disconnect
Implied Average Value of Lost Load
Average Value of Load Load ($/MWh)
$80,000
One Event in Ten Years
$70,000
$60,000
Twenty Four Hours in Ten Years
$50,000
$40,000
Optimal?
$30,000
Price Cap
$20,000
$10,000
$0
0
5
10
15
20
25
Annual Duration of Load Curtailm ent (Hours)
Peaker fixed charge at $65,000/MW-yr.
Implied prices differ by orders of magnitude.
( Price Cap ≈ $10 ; VOLL ≈ $10 ; Reliability Standard ≈ $10 )
3
4
5
18
ELECTRICITY MARKET
Pricing and Demand Response
Early market designs presumed a significant demand response. Absent this demand participation
most markets implemented inadequate pricing rules equating prices to marginal costs even when
capacity is constrained. This produces a “missing money” problem. The big “R” regulatory
solution calls for capacity mandates. The small “r” approach addresses the pricing problem.
SHORT-RUN ELECTRICITY MARKET
Energy Price
Short-Run
Marginal
Cost
(¢/kWh)
Price at
7-7:30 p.m.
Demand
7-7:30 p.m.
Price at
9-9:30 a.m.
Price at
2-2:30 a.m.
Demand
9-9:30 a.m.
Demand
2-2:30 a.m.
Q1
Q2
Qmax
MW
19
ELECTRICITY MARKET
Generation Resource Adequacy
A variety of market rules for spot markets interact to create de jure or de facto price caps. The
resulting “missing money” reduces payments to all types of generation.
A Market Price Duration Curve
P($/MWh)
A Price Cap Results in "Missing Money"
P($/MWh)
Missing Money
Returns for Peak Generator
Returns for Mid-Range Generator
Price Cap
A
A
Returns for Base Load Generator
$85
$85
B
$35
B
$35
C
$15
$15
8760 (Hours)
C
8760 (Hours)
Missing money reduces the payments to all types of generation.
If market prices do not provide adequate incentives for generation investment, the result is a
market failure. The market design defect creates the pressure for regulators to intervene to
mandate generation investment.
20
ELECTRICITY MARKET
Generation Resource Adequacy
A workable “energy only” market would eliminate the “missing money” problem and provide an
alternative to the growing prescriptions of installed capacity markets. The concept is not that there
should be no market interventions. But the interventions should not overturn the market.
An “Energy Only” Market Outline
•
Implicit demand for inflexible load would define the opportunity costs as the average value
of lost load (VOLL).
An Illustrative Demand for Electricity
Price
Responsive
Demand
Inflexible
Demand
Total
Demand
P ($/MWh)
P ($/MWh)
P ($/MWh)
$20,000
$20,000
$20,000
+
=
$10,000
$10,000
$10,000
$30
$30
30,000
Q (MW)
$30
15,000
Q(MW)
Demand
45,000
Q(MW)
Involuntary curtailment of inflexible demand has an opportunity cost at
the average value of lost load (VOLL).
21
ELECTRICITY MARKET
Generation Resource Adequacy
… An “Energy Only” Market Outline
•
Operating reserve demand curve would reflect capacity scarcity.
Illustrative Reserve Demand
P ($/MWh)
$20,000
Reserve
Demand
3%
$10,000
$30
Energy
Demand
7%
Q(MW)
There is a minimum level of operating reserve (e.g., 3%) to protect
against system-wide failure. Above the minimum reserve, reductions
below a nominal reserve target (e.g., 7%) are price senstive.
22
ELECTRICITY MARKET
Generation Resource Adequacy
… An “Energy Only” Market Outline
•
Market clearing eliminates the “missing money.”
Normal "Energy Only" Market Clearing
P ($/MWh)
$20,000
$10,000
Scarcity "Energy Only" Market Clearing
P ($/MWh)
Generation
Supply
Energy +
Reserves
$30
$20,000
$10,000
$7,000
Generation
Supply
Energy +
Reserves
$30
Q(MW)
When demand is low and capacity available,
reserves hit nominal targets at a low price.
Q(MW)
When demand is high and reserve reductions apply,
there is a high price.
23
ELECTRICITY MARKET
Operating Reserve Demand
Operating reserve demand is a complement to energy demand for electricity. The probabilistic
demand for operating reserves reflects the cost and probability of lost load. Pricing operating
reserves could provide the missing money.
Example Assumptions
Expected Load (MW)
Std Dev %
Expected Outage %
Std Dev %
34000
1.50%
0.45%
0.45%
Expected Total (MW)
Std Dev (MW)
VOLL ($/MWh)
153
532.46
10000
Operating Reserve Demand
7,000
6,000
Under
the
simplifying
assumptions, if the dispersion of
the
LOLP
distribution
is
proportional to the expected load,
the operating reserve demand is
proportional to the expected load.
Total value is of same magnitude
as the cost of meeting load.
P ($/MWh)
5,000
Marginal VEUE
4,000
3,000
2,000
1,000
0
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
Q (% of load)
24
ELECTRICITY MARKET
Operating Reserve Demand
Existing market designs underprice scarcity and provide poor signals for investment. Hence we
have the resource adequacy debate. A market approach would be reinforced by adopting an
explicit operating reserve demand curve.
The maximum generation outage
contingency quantity provides a
vertical demand curve that adds
horizontally to a probabilistic
operating reserve demand curve.
Operating Reserve Demand
12,000
10,000
Security Minimum
8,000
P ($/MWh)
If the security minimum will
always be maintained over the
monitored period, the VEUE price
at r=0 applies. If the outage
shocks allow excursions below
the security minimum during the
period, the VEUE starts at the
security minimum.
A realistic operating reserve
demand curve would address the
missing money problem and help
jump start greater demand
participation.
6,000
Demand=Minimum + Marginal VEUE
4,000
2,000
Marginal
VEUE
0
0
500
1000
1500
2000
2500
Q (MW)
25
ELECTRICITY MARKET
Better Scarcity Pricing
Improved pricing through an explicit operating reserve demand curve raises a number of issues.
Demand Response: Better pricing implemented through the operating reserve demand curve would provide an
important signal and incentive for flexible demand participation in spot markets.
Price Spikes: A higher price would be part of the solution. Furthermore, the contribution to the “missing money” from
better pricing would involve many more hours and smaller price increases.
Practical Implementation: The NYISO and ISONE implementations dispose of any argument that it would be impractical
to implement an operating reserve demand curve. The only issue is the level of the appropriate price.
Operating Procedures: Implementing an operating reserve demand curve does not require changing the practices of
system operators. Reserve and energy prices would be determined simultaneously treating decisions by the operators as
being consistent with the adopted operating reserve demand curve.
Multiple Locations: Transmission limitations mean that there are locational differences in the need for and efficacy of
operating reserves. This would continue to be true with different demand curves for different locations.
Multiple Reserves: The demand curve would include different kinds of operating reserves, from spinning reserves to
standby reserves.
Reliability: Market operating incentives would be better aligned with reliability requirements.
Market Power: Better pricing would remove ambiguity from analyses of high prices and distinguish (inefficient) economic
withholding through high offers from (efficient) scarcity pricing derived from the operating reserve demand curve.
Hedging: The Basic Generation Service auction in New Jersey provides a prominent example that would yield an easy
means for hedging small customers with better pricing.
Increased Costs: The higher average energy costs from use of an operating reserve demand curve do not automatically
translate into higher costs for customers. In the aggregate, there is an argument that costs would be lower.
26
ELECTRICITY MARKET
Energy Pricing and Uplift Payments
Energy dispatch is continuous but unit commitment requires discrete decisions. Bid-based,
security constrained, combined unit commitment and economic dispatch presents a challenge in
defining market-clearing prices.
• Continuous convex economic dispatch
o System marginal costs provide locational, market-clearing, linear prices
o Linear prices support the economic dispatch
• Discrete, economic, unit commitment and dispatch
o Start up and minimum load restrictions enter the model
o System marginal costs not always well-defined
o There may be no linear prices that support the commitment and dispatch solution
27
ELECTRICITY MARKET
Energy Pricing
Energy dispatch is continuous, convex and yields linear prices.1 A simplified example with two
generating units illustrates the total and marginal costs.
Marginal Cost Illustration
Aggregate Cost Illustration
Marginal Variable Cost
Total Variable Cost
120
35000
Marginal Cost ($/MWh)
A&B
Total Cost
30000
25000
A
20000
15000
B
10000
5000
A
100
A&B
B
80
60
40
20
0
0
0
100
200
300
Load
400
500
0
100
200
300
400
500
Load
1
Paul R. Gribik, William W. Hogan, and Susan L. Pope, “Market-Clearing Electricity Prices and Energy Uplift,” Harvard University, December 31,
2007, available at www.whogan.com.
28
ELECTRICITY MARKET
Energy Pricing and Uplift
Unit commitment requires discrete decisions. Now the second unit (B) has a startup cost.
Aggregate Cost: Two Generator Example
Marginal Cost: Two Generator Example
Total Commitment and Dispatch Cost
Marginal Cost
40000
120
MC v
Marginal Cost ($/MWh)
35000
V
Total Cost
30000
25000
20000
A
15000
A&B
10000
5000
0
100
80
60
40
20
0
0
100
200
300
Load
400
500
0
100
200
300
400
500
Load
Marginal cost-based linear prices cannot support the commitment and dispatch. The solution has
been to make “uplift” payments to assure reliable and economic unit commitment.
29
ELECTRICITY MARKET
Energy Pricing and Uplift
Selecting the appropriate approximation model for defining energy and uplift prices involves
practical tradeoffs. All involve “uplift” payments to guarantee payments for bid-based cost to
participating bidders (generators and loads), to support the economic commitment and dispatch.
Uplift with Given Energy Prices=Optimal Profit – Actual Profit
• Restricted Model (r)
o Fix the unit commitment at the optimal solution.
o Determine energy prices from the convex economic dispatch.
• Dispatchable Model (d)
o Relax the discrete constraints and treat commitment decisions as continuous.
o Determine energy prices from the relaxed, continuous, convex model.
• Convex Hull Model (h)
o Select the energy prices from the Lagrangean relaxation (i.e., usual dual problem for pricing
the joint constraints).
o Resulting energy prices minimize the total uplift.
30
ELECTRICITY MARKET
Minimum Uplift
Economic commitment and dispatch is a special case of a general optimization problem.
v ( y ) = Min
f ( x)
x∈ X
g ( x ) = y.
s.t.
From the perspective of a price-taking bidder, uplift is the difference between actual and optimal profits.
π ( p, y ) = py − v ( y )
Actual profits:
Optimal Profits: π * ( p ) = Max { pz − v ( z )}
Uplift ( p, y ) = π
z
*
( p ) − π ( p, y )
Classical Lagrangean relaxation and pricing creates a familiar dual problem.
L ( y , x, p ) = f ( x ) + p ( y − g ( x ) )
{
}
Lˆ ( y, p ) = Inf f ( x ) + p ( y − g ( x ) )
x∈ X
{
{
}}
L* ( y ) = Sup Lˆ ( y, p ) = Sup Inf f ( x ) + p ( y − g ( x ) )
p
p
x∈ X
The optimal dual solution minimizes the uplift, and the “duality gap” is equal to the minimum uplift.
v ( y ) − L* ( y ) = Inf Uplift ( p, y ) .
p
31
ELECTRICITY MARKET
Energy Pricing and Uplift
Comparing illustrative energy pricing and uplift models.
Comparison of Example Uplift Costs
Comparison of Example Marginal Costs
Implied Uplift
Implied Marginal Cost
35.00
MC d
120
MC r
30.00
MC h
100
Ur
25.00
Uplift ($/MWh)
Marginal Cost ($/MWh)
140
80
60
40
20.00
15.00
10.00
Ud
Uh
20
5.00
0
0.00
0
100
200
300
Load
400
500
0
100
200
300
400
500
-5.00
Load
Both the relaxed and convex hull models produce “standard” implied supply curve. The convex
hull model produces the minimum uplift.
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ELECTRICITY MARKET
Energy Pricing and Uplift
Alternative pricing models have different features and raise additional questions.
• Computational Requirements. Relaxed model easiest case, convex hull model the hardest. But
not likely to be a significant issue.
• Network Application. All models compatible with network pricing and reduce to standard LMP in
the convex case.
• Operating Reserve Demand. All models compatible with existing and proposed operating reserve
demand curves.
• Solution Independence. Restricted model sensitive to actual commitment. Relaxed and convex
hull models (largely) independent of actual commitment and dispatch.
• Day-ahead and real-time interaction. With uncertainty in real-time and virtual bids, expected realtime price is important, and may be similar under all pricing models.
33
ELECTRICITY MARKET
Electricity Restructuring Summary
With current technology, property rights are difficult to define and there is a continuing need for
coordination to support markets. Regulation must adapt to the requirements of hybrid markets.
•
Little “r’ regulation: Design rules and policies that are the “best possible mix” to support
competitive wholesale electricity markets.
o Necessary functions for energy markets.
ƒ Real-time, bid-based, security constrained economic dispatch with locational prices.
o Necessary functions for energy markets with effective long-term hedges.
ƒ Financial transmission rights (FTRs).
o Valuable functions for energy markets with effective long-term hedges.
ƒ Day-ahead energy market with associated reliability unit commitment.
ƒ Transmission planning and investment protocols.
o Necessary features of everything else
ƒ Rules and pricing incentives compatible with the above.
• Ancillary Services
• Resource Adequacy
•
Big “R” regulation: Frame every problem in its own terms—inadequate demand response,
insufficient infrastructure investment, or market power—and design ad hoc regulatory fixes that
accumulate to undermine market incentives. The slippery slope.
34
William W. Hogan is the Raymond Plank Professor of Global Energy Policy, John F. Kennedy School of Government, Harvard
University and a Director of LECG, LLC. This paper draws on work for the Harvard Electricity Policy Group and the Harvard-Japan
Project on Energy and the Environment. The author is or has been a consultant on electric market reform and transmission issues for
Allegheny Electric Global Market, American Electric Power, American National Power, Australian Gas Light Company, Avista
Energy, Barclays, Brazil Power Exchange Administrator (ASMAE), British National Grid Company, California Independent Energy
Producers Association, California Independent System Operator, Calpine Corporation, Canadian Imperial Bank of Commerce,
Centerpoint Energy, Central Maine Power Company, Chubu Electric Power Company, Citigroup, Comision Reguladora De Energia
(CRE, Mexico), Commonwealth Edison Company, Conectiv, Constellation Power Source, Coral Power, Credit First Suisse Boston,
Detroit Edison Company, Deutsche Bank, Duquesne Light Company, Dynegy, Edison Electric Institute, Edison Mission Energy,
Electricity Corporation of New Zealand, Electric Power Supply Association, El Paso Electric, GPU Inc. (and the Supporting
Companies of PJM), Exelon, GPU PowerNet Pty Ltd., GWF Energy, Independent Energy Producers Assn, ISO New England, Luz del
Sur, Maine Public Advocate, Maine Public Utilities Commission, Merrill Lynch, Midwest ISO, Mirant Corporation, JP Morgan,
Morgan Stanley Capital Group, National Independent Energy Producers, New England Power Company, New York Independent
System Operator, New York Power Pool, New York Utilities Collaborative, Niagara Mohawk Corporation, NRG Energy, Inc.,
Ontario IMO, Pepco, Pinpoint Power, PJM Office of Interconnection, PPL Corporation, Public Service Electric & Gas Company,
PSEG Companies, Reliant Energy, Rhode Island Public Utilities Commission, San Diego Gas & Electric Corporation, Sempra
Energy, SPP, Texas Genco, Texas Utilities Co, Tokyo Electric Power Company, Toronto Dominion Bank, TransÉnergie, Transpower
of New Zealand, Westbrook Power, Western Power Trading Forum, Williams Energy Group, and Wisconsin Electric Power
Company. The views presented here are not necessarily attributable to any of those mentioned, and any remaining errors are solely
the responsibility of the author. (Related papers can be found on the web at www.whogan.com ).
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