Deregulated Power,
Pollution, and Game
Theory
Frank Deviney
11/16/05
My Questions
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How does deregulation affect the distribution
of pollutant emissions?
Can game theory help answer this question?
Pollution – Cap and Trade
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SO2 allowances are allocated or auctioned
After-market exists for trading allowances
~9 million allowances per year
An allowance permits emission of a fixed amount of
SO2
Local power plants
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Possum Point
Mt Storm
Bremo Bluff
Fear – hot spots
0.001 lbs SO2/mmBtu
0.10 lbs SO2/mmBtu
1.45 lbs SO2/mmBtu
550+ MW
1600 MW
250 MW
Power Grid Situation
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Problems under environment of deregulation
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Energy (Generation) pricing
Congestion management and pricing
Others
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Capacity expansion
Reserve capacity
Environmental/other constraints
- 2004
- 2005
Generation
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Old Paradigm – minimize costs subject to
“Keep the Lights On” constraint. A regulated
monopolies environment.
New Paradigm – Competition leads to
efficiency. Maximize benefits for all.
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Game theory has been used to:
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Justify the switch
Establish bidding procedures for participants
Generation I
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Ferrero, Rivera, and Shahidehpour, 1998
Objective: maximize each participant’s benefit
Assumptions (PoolCo model)
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Coordinator schedules (dispatches) generation
beginning with lowest bid price until demand is met
Generators receive the “spot price”, the max bid of all
dispatched generators
Assumption: spot price equal throughout the grid
“sealed bids” – submit bids at same time
Knows own cost but not others’ costs
Knows others’ bid history, but not their benefit
Gen costs are 2nd order fn of power output
Generation I, cont.
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Aspects of the Game
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Formulated as non-cooperative, two-player
Correlated costs allowed (used in the example)
Strategy is to bid with respect to initial marginal cost (as if
not in the market)
Probability distribution of the game derived from available
information, they use fuel prices in the example.
Demonstrate analytical solution for Nash equilibria  so
presumably participant could use game theory to establish
bidding positions
Generation II
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Park, Kim, Kim, Jung, and Park 2001
Assumptions (PoolCo model)
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Total generation bids  demand
Individual generation bid < demand
Demand is constant
Transmission losses and congestion ignored
Complete information available to all (apparently holds in
some countries)
Again the 2nd order cost function
Generation allocation
 < last-dispatched unit, all generation offered
 = last-dispatched unit, split with others with equal bids
Generation II, cont.
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Aspects of the Game
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Formulated as non-cooperative, two-player
Strategy = (bid price, bid generation) in
continuous space
Suggest a hybrid approach combining analytical
and graphical methods
Inelastic demand  Bidding price cap
A question
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I have tended to think of the allowances as
being a constraint on production. Generator’s
goal is to maximize production or profit
subject to the emission allowance constraint.
Companies tend to re-distribute their
allowances in-house rather than through the
market.
How does the existence of such global
constraints affect the assumptions inherent in
a non-cooperative game?
How does PJM do it?
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As complicated as the game theory models
may be, the actual market is more
complicated
Market Timelines
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Day-ahead
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Until noon – PJM receives bids and offers for energy for
next day
Noon until 4 p.m. Market is closed. PJM computes nextday LMPs.
4 p.m. PJM posts initial day-ahead LMPs.
4-6 p.m. Market re-opens for re-bidding.
6 p.m. – Day-ahead LMPs locked in.
Remainder of day – PJM continually updates the dispatch
list
Real-time ?
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5-minute intervals?
What is congestion?
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When the economic dispatch solution cannot
be implemented due to transmission line
constraints.
Congestion
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Silva, Wollenberg, and Zheng, 2001
Assumptions
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Constant marginal cost for generation
Constant demand
An “economic dispatch” solution exists
Competitors will not provide cost information, but
can estimate others’ costs
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Marginal cost domains are bounded
The pdf is otherwise continuous
Congestion, cont.
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Mechanism Design
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A mechanism is a game. Proposed game is that:
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Generators submit bids to agent
Agent allocates production and reward
Goal is to get generators to provide true cost bids
Claim is that the proposed payment scheme achieves
this
What does PJM do?
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LMPs
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Implicit congestion – payments/receipts based on
bus LMP
explicit congestion – transactions pay differential
between source and sink LMPs
FTRs – Financial Transmission Rights
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Monthly, annual auctions
Serve as a hedge against day-ahead uncertainty
as to when and where congestion will occur.