Optimal Electricity Supply Bidding by Markov Decision Process
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Transcript Optimal Electricity Supply Bidding by Markov Decision Process
Optimal Electricity Supply
Bidding by Markov Decision
Process
Authors: 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
Outline
Summary of the previous presentation
Model Validation
Implementation and case study
Description of Examples
Summary
Summary of previous presentation
Introduction
Electric Market is now Competitive
GenCos Bid on Demand
Purpose
MDP Used to Determine Optimal Bidding Strategy
Problem Formulation
Transition Probability Determined by Current State, Subsequent State,
& Decision Made
7 Variables to Define a State
Aggregation Used to Limit Dimensionality Problems
Model Overview
7 Day Planning Horizon
Objective is to Maximize Summation of Expected Reward
Value Iteration
Value Iteration Discussion
V (i, T+1): Total
Expected Reward in
T+1 Remaining Stages
from State I
At the last stage T = 0
Value Iteration
(Backward Induction)
Ignore discount factor
The immediate reward
is dependent on the
initial state, following
state and decision a
Model Overview Clarification
Sum of all Scenarios S
that result in a given spot
price, cleared quantity,
and production limit.
Prob to Move from State i
to j given decision a =
[Prob (that the spot price,
production level are
correct and load forecast
= demand)*prob(of having
the proper load forecast)]
Resulting Spot Price can
be dependent on Decision
a if the bidder has market
power
Model Validation
For model validation:
Accumulate actual data and observations from the
market over a period of time (e.g. 1 year)
Market data set provides the actual scenarios
Relationship between estimated by the BIDS
representation r(i,j,a) and actual rewards w(i,j,a)
can be analyzed by linear regression.
Case Study
3 suppliers: GenCoA, GenCoB, and GenCoC, all
bidding in the spot market
GenCoA is the decision maker using the Markov
Decision Process technique
GenCoA: 1 generating unit
GenCoB: 2 generating units
GenCoC: 2 generating units
Planning Horizon: 7 days (bid decision for next day
considers the entire week ahead
Case Study
GenCoA makes a decision from a set of pre-specified
decision options
GenCoA does not know exactly how GenCoB and
GenCoC are going to bid
But their individual bidding behavior is modeled by
bid prices, quantities and the associated probabilities
based on GenCoA’s knowledge and information
Transition probabilities and rewards are calculated
using algorithm described in previous presentation
Two Basic Market Situations
EXAMPLE 1:
Decision-maker has a production limit over the
planning horizon
Decision-maker does not have market power
(perfect competition)
Optimal strategy is time dependent due to the
production limit
In some states the optimal decision is not to sell,
but to save the resources for more profitable days
Two Basic Market Situations
EXAMPLE 2:
Decision-maker has market power: it can manipulate
the bid to influence the spot price
Decision-maker has no production limit
Decision-maker makes the bidding decision to
maximize the expected reward over the planning
horizon
Daily maximum strategy is time independent:
decision-maker makes the same decision as long as the
system is in the same state
BIDS value iteration is time dependent: it takes into
account how current biddings affect future spot prices
Comparison of Two Cases
Without market power, bidder is concerned with
saving resources for more expensive periods
With market power, bidder is concerned with
properly influencing the future spot price to
maximize profit
Knowing whether the bidder has market power or
not is crucial since the relationship between spot
prices and decisions would depend on each other
Summary
Model Overview
7 Day Planning Horizon
Objective is to Maximize Summation of Expected Reward
Value Iteration
Model Validation
Comparison of Predicted and Actual Results (by linear
regression)
Implementation and case study
Three GenCos, GenCo A is the Decision Maker
5 Generators among the 3 GenCos
Description of 2 Examples:
Production Limit without Market Power
Market Power without Production Limit
Next Time: Presentation and Discussion of Results and Conclusions
Questions???