Abstract
Convex hull pricing is a well-documented method for coping with the non-existence of uniform clearing prices in electricity markets with non-convex costs and constraints. We revisit primal and dual methods for computing convex hull prices, and discuss the positioning of existing approximation methods in this taxonomy. We propose a dual decomposition algorithm known as the Level Method and we adapt the basic algorithm to the specificities of convex hull pricing. We benchmark its performance against a column generation algorithm that has recently been proposed in the literature. We provide empirical evidence about the favorable performance of our algorithm on large test instances based on PJM and Central Europe.
Highlights
Non-convexities are at the heart of power system operations [2], in terms of both the network model as well as in the market orders: (i) they are present in the alternating current (AC) power flow equations which characterize the physics of the grid and (ii) in the mixed integer programming (MIP) constraints that describe the market offers
We demonstrate that the Level Method is able to converge within few iterations to a certain target gap, while exhibiting a stable behaviour, on large instances which, in terms of price space dimension, are comparable to the size of the EU day-ahead auction
It is likely that the choice of the best algorithm for solving Convex hull pricing (CHP) will depend on the specific use-case: the dimension of the network, the time horizon, the complexity of the unit commitment / market orders, the run time that is afforded to the algorithm, etc
Summary
T HE classical analysis of an economic dispatch problem, together with its dual, provides a fundamental argument for uniform pricing in electricity markets [1] — an optimal dispatch can be supported by a set of competitive equilibrium prices. As the argument assumes convexity of the dispatch problem, a fundamental challenge for market efficiency is non-convexity, as the latter implies that it is not guaranteed that a competitive market equilibrium exists. Non-convexities are at the heart of power system operations [2], in terms of both the network model as well as in the market orders: (i) they are present in the alternating current (AC) power flow equations which characterize the physics of the grid and (ii) in the mixed integer programming (MIP) constraints that describe the market offers. The inexistence of equilibrium prices in electricity auctions has triggered a long-lasting debate on the choice of an appropriate pricing scheme in the presence of non-convexities
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