Properties of Convex Hull Pricing. Education Session 2 December 11, 2017

Transcription

1 Properties of Convex Hull Pricing Price Formation Education Session 2 December 11, 2017 Catherine Tyler

2 Overview of Convex Hull Pricing Theoretical pricing model aiming to include start, no load, and minimum energy costs in prices. Computationally infeasible, never implemented Not an established economic concept Solves a multiperiod joint unit commitment and dispatch problem Solution is physically infeasible, resulting in prices that are inconsistent with dispatch

3 What is a convex hull? Convex set Nonconvex set

4 What is a convex hull? Convex set Nonconvex set with a convex hull

5 Mechanics Same cost minimizing unit commitment and dispatch from the actual supply curve Solves a separate solution for pricing using the convex hull supply curve, infeasible solution Convex hull supply violates physical resource constraints like minimum output and ramp rate. Prices consistently include commitment costs. Infeasible outcomes determine prices by violating physical constraints that create nonconvexities

6 Prices Inconsistent with Dispatch Dispatch and prices from two different solutions Prices do not equal the marginal cost of generation or the marginal value of load. Lost allocative efficiency Required lost opportunity cost payments to correct marginal cost dispatch incentives Uplift payments to both generation and load to reduce incentive to follow prices Lower total uplift should result, but magnitude of change is unclear

7 Price Signals Market participants cannot rely on convex hull prices to signal optimal behavior. Congestion patterns would differ from the efficient solution. Creates FTR revenue shortfalls Negative prices become positive Signaling less load where more is needed Signaling more generation where less is needed

8 Correcting Price Signals Lost opportunity costs rely on after the fact settlements to correct price incentives. Commitment costs also part of LOC calculation LOC required for offline resources Mechanism required to ensure tight dispatch following to get correct results in practice More PJM command and control for many resources and load Strong deviation penalties, no LMP if over dispatch, or uplift disqualification may be necessary

9 Correcting Price Signals Resources and load may follow prices instead of dispatch if uncertainty about after the fact true up payments. Prices less transparent More difficult to understand and verify pricing, because inconsistent with dispatch and multiperiod pricing Participant specific LOC payments not public and not known until settlements

10 Multiperiod Solution Uses same time horizon as commitment problem Commitment costs in convex hull pricing are allocated unevenly, based on the economics of the solution. For example, prices for a peak period could include total accrued start and no load costs for resources started several hours earlier. Computationally difficult to solve No concept of rolling period implementation Need to look forward and look back

11 Practical Considerations Theory assumes away practical considerations. Computationally difficult Participants respond differently to prices, dispatch signals, and uplift payments Multiperiod implementation Changes to convex hull model to address practical considerations raise costs and move results away from theory

12 References Gribick, Hogan, and Pope (2007), Market-Clearing Electricity Prices and Energy Uplift. Hogan (2016). Electricity Market Design: Optimization and Market Equilibrium, Workshop on Optimization and Equilibrium in Energy Economics, Institute for Pure and Applied Mathematics (IPAM), UCLA. Shiro, Zheng, Zhao, and Litvinov (2016), Convex Hull Pricing in Electricity Markets: Formulation, Analysis, and Implementation Challenges, IEEE Transactions on Power Systems, Vol. 31, No

13 Monitoring Analytics, LLC 2621 Van Buren Avenue Suite 160 Eagleville, PA (610)