1. Deregulated Power, Pollution, and Game Theory
Frank Deviney
11/16/05

2. My Questions
How does deregulation affect the distribution of pollutant emissions?
Can game theory help answer this question?

3. Pollution – Cap and Trade
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
Possum Point lbs SO2/mmBtu MW
Mt Storm lbs SO2/mmBtu MW
Bremo Bluff 1.45 lbs SO2/mmBtu 250 MW
Fear – hot spots

4. Power Grid Situation Problems under environment of deregulation
Energy (Generation) pricing
Congestion management and pricing
Others
Capacity expansion
Reserve capacity
Environmental/other constraints

5. - 2004
- 2005

8. Generation
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.
Game theory has been used to:
Justify the switch
Establish bidding procedures for participants

9. Generation I Ferrero, Rivera, and Shahidehpour, 1998
Objective: maximize each participant’s benefit
Assumptions (PoolCo model)
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

10. Generation I, cont. Aspects of the Game
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

11. Generation II Park, Kim, Kim, Jung, and Park 2001
Assumptions (PoolCo model)
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

12. Generation II, cont. Aspects of the Game
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

13. A question
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?

14. How does PJM do it?
As complicated as the game theory models may be, the actual market is more complicated

17. Market Timelines Day-ahead Real-time ?
Until noon – PJM receives bids and offers for energy for next day
Noon until 4 p.m. Market is closed. PJM computes next-day 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 ?
5-minute intervals?

21. What is congestion?
When the economic dispatch solution cannot be implemented due to transmission line constraints.

24. Congestion Silva, Wollenberg, and Zheng, 2001 Assumptions
Constant marginal cost for generation
Constant demand
An “economic dispatch” solution exists
Competitors will not provide cost information, but can estimate others’ costs
Marginal cost domains are bounded
The pdf is otherwise continuous

25. Congestion, cont. Mechanism Design
A mechanism is a game. Proposed game is that:
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

26. What does PJM do? LMPs FTRs – Financial Transmission Rights
Implicit congestion – payments/receipts based on bus LMP
explicit congestion – transactions pay differential between source and sink LMPs
FTRs – Financial Transmission Rights
Monthly, annual auctions
Serve as a hedge against day-ahead uncertainty as to when and where congestion will occur.