optimal electricity supply bidding by markov decision process
DESCRIPTION
Optimal Electricity Supply Bidding by Markov Decision Process. Presentation Review By: Feng Gao, Esteban Gil, & Kory Hedman IE 513 Analysis of Stochastic Systems Professor Sarah Ryan March 28, 2005. Authors: Haili Song, Chen-Ching Liu, Jacques Lawarree, & Robert Dahlgren. Outline. - PowerPoint PPT PresentationTRANSCRIPT
Optimal Electricity Supply Optimal Electricity Supply Bidding by Markov Decision Bidding by Markov Decision
ProcessProcessAuthors: Haili Song, Chen-Ching Liu, Jacques Lawarree, & Robert DahlgrenAuthors: Haili Song, Chen-Ching Liu, Jacques Lawarree, & Robert Dahlgren
Presentation Review By:
Feng Gao, Esteban Gil, & Kory Hedman
IE 513 Analysis of Stochastic Systems
Professor Sarah Ryan
March 28, 2005
OutlineOutline
Summary of the previous presentationSummary of the previous presentation Model ValidationModel Validation Implementation and case studyImplementation and case study Description of ExamplesDescription of Examples SummarySummary
Summary of previous presentationSummary of previous presentation IntroductionIntroduction
Electric Market is now CompetitiveElectric Market is now Competitive GenCos Bid on DemandGenCos Bid on Demand
PurposePurpose MDP Used to Determine Optimal Bidding StrategyMDP Used to Determine Optimal Bidding Strategy
Problem FormulationProblem Formulation Transition Probability Determined by Current State, Subsequent State, Transition Probability Determined by Current State, Subsequent State,
& Decision Made& Decision Made 7 Variables to Define a State7 Variables to Define a State Aggregation Used to Limit Dimensionality ProblemsAggregation Used to Limit Dimensionality Problems
Model OverviewModel Overview 7 Day Planning Horizon7 Day Planning Horizon Objective is to Maximize Summation of Expected RewardObjective is to Maximize Summation of Expected Reward Value IterationValue Iteration
Value Iteration DiscussionValue Iteration Discussion V (i, T+1): Total V (i, T+1): Total
Expected Reward in Expected Reward in T+1 Remaining Stages T+1 Remaining Stages from State Ifrom State I
At the last stage T = 0At the last stage T = 0 Value Iteration Value Iteration
(Backward Induction)(Backward Induction) Ignore discount factorIgnore discount factor The immediate reward The immediate reward
is dependent on the is dependent on the initial state, following initial state, following state and decision astate and decision a
Model Overview ClarificationModel Overview Clarification
Sum of all Scenarios S Sum of all Scenarios S that result in a given spot that result in a given spot price, cleared quantity, price, cleared quantity, and production limit. and production limit.
Prob to Move from State i Prob to Move from State i to j given decision a = to j given decision a = [Prob (that the spot price, [Prob (that the spot price, production level are production level are correct and load forecast correct and load forecast = demand)*prob(of having = demand)*prob(of having the proper load forecast)]the proper load forecast)]
Resulting Spot Price can Resulting Spot Price can be dependent on Decision be dependent on Decision a if the bidder has market a if the bidder has market powerpower
Model ValidationModel Validation
For model validation:For model validation: Accumulate actual data and observations from the Accumulate actual data and observations from the
market over a period of time (e.g. 1 year)market over a period of time (e.g. 1 year) Market data set provides the actual scenariosMarket data set provides the actual scenarios Relationship between estimated by the BIDS Relationship between estimated by the BIDS
representation r(i,j,a) and actual rewards w(i,j,a) representation r(i,j,a) and actual rewards w(i,j,a) can be analyzed by linear regression.can be analyzed by linear regression.
Case StudyCase Study 3 suppliers: GenCoA, GenCoB, and GenCoC, all 3 suppliers: GenCoA, GenCoB, and GenCoC, all
bidding in the spot marketbidding in the spot market GenCoA is the decision maker using the Markov GenCoA is the decision maker using the Markov
Decision Process techniqueDecision Process technique GenCoA: 1 generating unitGenCoA: 1 generating unit GenCoB: 2 generating unitsGenCoB: 2 generating units GenCoC: 2 generating unitsGenCoC: 2 generating units Planning Horizon: 7 days (bid decision for next day Planning Horizon: 7 days (bid decision for next day
considers the entire week aheadconsiders the entire week ahead
Case StudyCase Study GenCoA makes a decision from a set of pre-specified GenCoA makes a decision from a set of pre-specified
decision optionsdecision options GenCoA does not know exactly how GenCoB and GenCoA does not know exactly how GenCoB and
GenCoC are going to bidGenCoC are going to bid But their individual bidding behavior is modeled by But their individual bidding behavior is modeled by
bid prices, quantities and the associated probabilities bid prices, quantities and the associated probabilities based on GenCoA’s knowledge and informationbased on GenCoA’s knowledge and information
Transition probabilities and rewards are calculated Transition probabilities and rewards are calculated using algorithm described in previous presentationusing algorithm described in previous presentation
Two Basic Market SituationsTwo Basic Market Situations
EXAMPLE 1:EXAMPLE 1: Decision-maker has a production limit over the Decision-maker has a production limit over the
planning horizonplanning horizon Decision-maker does not have market power Decision-maker does not have market power
(perfect competition)(perfect competition) Optimal strategy is time dependent due to the Optimal strategy is time dependent due to the
production limitproduction limit In some states the optimal decision is not to sell, In some states the optimal decision is not to sell,
but to save the resources for more profitable daysbut to save the resources for more profitable days
Two Basic Market SituationsTwo Basic Market Situations EXAMPLE 2:EXAMPLE 2:
Decision-maker has market power: it can manipulate Decision-maker has market power: it can manipulate the bid to influence the spot pricethe bid to influence the spot price
Decision-maker has no production limitDecision-maker has no production limit Decision-maker makes the bidding decision to Decision-maker makes the bidding decision to
maximize the expected reward over the planning maximize the expected reward over the planning horizonhorizon
Daily maximum strategy is time independent: Daily maximum strategy is time independent: decision-maker makes the same decision as long as the decision-maker makes the same decision as long as the system is in the same statesystem is in the same state
BIDS value iteration is time dependent: it takes into BIDS value iteration is time dependent: it takes into account how current biddings affect future spot pricesaccount how current biddings affect future spot prices
Comparison of Two CasesComparison of Two Cases
Without market power, bidder is concerned with Without market power, bidder is concerned with saving resources for more expensive periodssaving resources for more expensive periods
With market power, bidder is concerned with With market power, bidder is concerned with properly influencing the future spot price to properly influencing the future spot price to maximize profitmaximize profit
Knowing whether the bidder has market power or Knowing whether the bidder has market power or not is crucial since the relationship between spot not is crucial since the relationship between spot prices and decisions would depend on each otherprices and decisions would depend on each other
SummarySummary Model OverviewModel Overview
7 Day Planning Horizon7 Day Planning Horizon Objective is to Maximize Summation of Expected RewardObjective is to Maximize Summation of Expected Reward Value IterationValue Iteration
Model ValidationModel Validation Comparison of Predicted and Actual Results (by linear Comparison of Predicted and Actual Results (by linear
regression)regression) Implementation and case studyImplementation and case study
Three GenCos, GenCo A is the Decision MakerThree GenCos, GenCo A is the Decision Maker 5 Generators among the 3 GenCos5 Generators among the 3 GenCos
Description of 2 Examples:Description of 2 Examples: Production Limit without Market PowerProduction Limit without Market Power Market Power without Production LimitMarket Power without Production Limit
Next Time: Presentation and Discussion of Results and ConclusionsNext Time: Presentation and Discussion of Results and Conclusions
Questions???Questions???