Price Formation with Non-Convexities: Theory and Applications for the Electricity Market

Since the restructuring policies that led to the liberalization of the electricity sector and to the existence of a market for power, electricity markets have been organised in a highly centralized fashion, relying on uniform-price auctions. These auctions typically include non-convex bids. The main implication of these non-convexities is that they impede the existence of a uniform “market-clearing” price. Therefore, what the electricity price should be under these settings is an open question, which has attracted the interest of both academics and practitioners over the past thirty years. This dissertation is composed of three main essays that study various aspects of this question. The first part of the dissertation studies some short-term impacts of the market failure we are interested in, namely the non-convexities in the production processes. We look first at the economic properties of various pricing solutions that have been envisioned in the literature, or implemented by some auctioneers. We analyse six different pricing methods and we establish several mathematical properties for enabling their accurate comparison. The findings are illustrated on stylized examples and numerical simulations that are performed on realistic auction datasets. Both theoretical and numerical evidences that are gathered point towards the advantages of the so-called “convex hull pricing” method. The dissertation then goes on with the analysis of some computational challenges. If convex hull pricing is proven to come with several advantages, it is also known for being computationally difficult to calculate. In this chapter, 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 provide empirical evidence about the favorable performance of our algorithm on large test instances. The second part of the dissertation studies some long-term impacts of non- convexities. If the topic of pricing non-convexities in power markets has been primarily focused on indivisibilities in short-term auctions, this second part analyses a source of non-convexities that is not discussed as broadly: the indivisibilities in investment decisions. The absence of equilibrium that we are concerned about is the long-term equilibrium. We derive a capacity expansion model with indivisibilities and we highlight the failure arising from it. We then investigate to what extent a capacity market can mitigate the lumpiness problem. We illustrate the main findings with a numerical experiment conducted on the capacity expansion model used by ENTSO-E to assess the adequacy of the European system.

Recommended citation: Stevens, N. (2024). Price Formation with Non-Convexities: Theory and Applications for the Electricity Market (Doctoral dissertation, UCLouvain).
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