Price-Based Commitment Decisions in the Electricity Market

1 Introduction.- 2 The Unit Commitment Problem.- 2.1 Unit Commitment in a Regulated Industry.- 2.2 Present Unit Commitment Solution Methods.- 2.3 Interruptible Service Contracts.- 3 Unit Commitment in a Deregulated Environment.- 3.1 Possible Formats for the Electricity Market.- 3.1.1 The Poolco Marketplace.- 3.1.2 The Market of Bilateral Contracts.- 3.2 Unit Commitment for an Individual Supplier.- 3.2.1 Bilateral Market.- 3.2.2 Poolco Market.- 3.3 Multiple Generation.- 3.4 Secondary Market for Reliability.- 3.5 Other Issues.- 4 Survey of the Dynamic Programming Formulation.- 4.1 Finite Horizon Problems.- 4.2 Infinite Horizon Problems with a Discount Factor.- 4.3 Stochastic Shortest Path Problems.- 4.4 Average Cost per Stage Problems.- 5 Unit Commitment for an Individual Power Producer.- 5.1 Unit Commitment without Generation Limits.- 5.2 Unit Commitment with Generation Limits.- 5.2.1 Truncated Normal Distributions.- 5.2.2 Truncated Lognormal Distributions.- 5.2.3 Expected Profit of Generation.- 6 Price Process of Electricity.- 6.1 Price Process Models.- 6.1.1 Long Term Model Behavior.- 6.1.2 Price Models using Logarithms.- 6.1.3 Unit Root Tests.- 6.1.4 Application of Unit Root Test to PJM Electricity Data.- 6.2 Correlation of Price with Load.- 6.2.1 Expanded Price Process Models.- 6.2.2 Test for Mean Reversion.- 6.2.3 Price Prediction Algorithms.- 6.3 Correlation of Load with Date.- 6.4 Correlation of Load with Temperature.- 6.4.1 Overview of Linear Regression Analysis.- 6.4.2 Application of Regression to Temperature/Load Data.- 6.4.3 Conclusions of Regression Analysis for Load vs. Temperature.- 6.5 Effects of Variance of Load Estimation.- 7 Computational Complexity of Unit Commitment.- 7.1 Dynamic Programming Algorithm.- 7.2 Heuristic Simplifications.- 7.3 Ordinal Optimization.- 7.3.1 Overview of Ordinal Optimization.- 7.3.2 Application to Unit Commitment.- 7.4 Example.- 7.4.1 Solution by Dynamic Programming.- 7.4.2 Solution by Ordinal Optimization.- 8 Forward Contracts and Futures.- 8.1 Forward Contracts.- 8.2 Producer Profits with Forward Contracts.- 8.3 Forward Contract Strategies.- 8.3.1 One Hour Forward Contracts.- 8.3.2 Multi-Hour Forward Contract.- 8.3.3 Example.- 8.4 Temporal Forward Contract Problem.- 9 Reserve Markets for Power System Reliability.- 9.1 General Form of a Reserve Market.- 9.1.1 Payment for Power Delivered.- 9.1.2 Payment for Reserve Allocated.- 9.1.3 Price Process for Reserve Price.- 9.2 Individual Power Producer Strategies for Selling Reserve.- 9.2.1 Payment for Power Delivered.- 9.2.2 Payment for Reserve Allocated.- 9.3 Provision of Reserve for Transactions.- 9.4 Effect of Reserve Market on Unit Commitment.- 9.5 Example.- 10 Unit Commitment in Congested Transmission Systems.- 10.1 Probabilistic Model of Congestion.- 10.1.1 Modifications to Price Model.- 10.1.2 Congestion Model with Limits.- 10.2 Producer Strategy under Congestion.- 10.3 Example.- 10.4 Solution of Unit Commitment under Congestion and Reserve.- 11 Conclusions.- A Calculation of Parameters for Price Processes.- A.1 Exponential of a Normally Distributed Variable.- A.2 Nonlinear Least Squares Regression.- A.3 Recursive Least Squares Algorithm.- B Results of Regression of Load vs. Temperature.- B.1 Regression on Same Day High Temperature.- B.2 Regression using Previous Day’s High Temperature.- C Derivation of Formulas for Truncated Random Variables.- C.1 Truncated Normal Distributions.- C.2 Truncated Lognormal Distributions.- D Software for Unit Commitment.- D.1 Dynamic Programming Software.- D.2 Ordinal Optimization Software.- D.3 Reserve and Congestion DP Software.- D.4 Source Code for uci2. c.- D.5 Source Code for ucool. c.- D.6 Source Code for uci2rs. c.- D.7 Source Code for uci2con. c.- D.8 Source Code for ucerr.h.- D.9 Source Code for ucerroo. h.- E Stochastic Unit Commitment in a Regulated Industry.- E.1 Unit Commitment with a Finite Horizon.- E.2 Solution of Optimal Power Flow.- E.2.1 Uncongested, Lossless Optimal Power Flow wi...