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Deregulated Power, Pollution, and Game Theory

Deregulated Power, Pollution, and Game Theory. Frank Deviney 11/16/05. My Questions. How does deregulation affect the distribution of pollutant emissions? Can game theory help answer this question?. Pollution – Cap and Trade. SO 2 allowances are allocated or auctioned

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Deregulated Power, Pollution, and Game Theory

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  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 0.001 lbs SO2/mmBtu 550+ MW • Mt Storm 0.10 lbs SO2/mmBtu 1600 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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?

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

  13. Market Timelines • Day-ahead • 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?

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

  15. 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

  16. 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

  17. What does PJM do? • LMPs • 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.

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