Learning Active Constraints to Efficiently Solve Linear Bilevel Problems

Bilevel programming can be used to formulate many engineering and economics problems. However, common reformulations of bilevel problems to mixed-integer linear programs (through the use of Karush-Kuhn-Tucker conditions) make solving such problems hard, which impedes their implementation in real-life. In this paper, we significantly improve solution speed and tractability by introducing decision trees to learn the active constraints of the lower-level problem, while avoiding to introduce binaries and big-M constants. The application of machine learning reduces the online solving time, and becomes particularly beneficial when the same problem has to be solved multiple times. We apply our approach to power systems problems, and especially to the strategic bidding of generators in electricity markets, where generators solve the same problem many times for varying load demand or renewable production. Three methods are developed and applied to the problem of a strategic generator, with a DCOPF in the lower-level. We show that for networks of varying sizes, the computational burden is significantly reduced, while we also manage to find solutions for strategic bidding problems that were previously intractable.Comment: 11 pages, 5 figure

Virtual Linking Bids for Market Clearing with Non-Merchant Storage

In the context of energy market clearing, non-merchant assets are assets that do not submit bids but whose operational constraints are included. Integrating energy storage systems as non-merchant assets can maximize social welfare. However, the disconnection between market intervals poses challenges for market properties, that are not well-considered yet. We contribute to the literature on market-clearing with non-merchant storage by proposing a market-clearing procedure that preserves desirable market properties, even under uncertainty. This approach is based on a novel representation of the storage system in which the energy available is discretized to reflect the different prices at which the storage system was charged. These prices are included as virtual bids in the market clearing, establishing a link between different market intervals. We show that market clearing with virtual linking bids outperforms traditional methods in terms of cost recovery for the market participants and discuss the impacts on social welfare

Design of a Continuous Local Flexibility Market with Network Constraints

To the best of our knowledge, this paper proposes for the first time a design of a continuous local flexibility market that explicitly considers network constraints. Continuous markets are expected to be the most appropriate design option during the early stages of local flexibility markets, where insufficient liquidity can hinder market development. At the same time, increasingly loaded distribution systems require to explicitly consider network constraints in local flexibility market clearing in order to help resolve rather than aggravate local network problems, such as line congestion and voltage issues. This paper defines the essential design considerations, introduces the local flexibility market clearing algorithm, and -- aiming to establish a starting point for future research -- discusses design options and research challenges that emerge during this procedure which require further investigation.Comment: Conferenc

Network-Aware Flexibility Requests for Distribution-Level Flexibility Markets

Local flexibility markets will become a central tool to procure flexibility for distribution system operators (DSOs), who need to ensure a safe grid operation against increased costs and public opposition towards new network investments. Despite extended recent literature on local flexibility markets, little attention has been paid on how to determine the amount of flexibility required at each location, considering the constraints that the network introduces (e.g. line and voltage limits). Addressing an open question for several DSOs, this paper introduces a method to design network-aware flexibility requests from a DSO perspective. In that, we also consider uncertainty, which could be the result of fluctuating renewable production or demand. We compare our approach against a stochastic market clearing mechanism, which serves as a benchmark; and we derive analytical conditions for the performance of our method to determine flexibility requests. We demonstrate our methods on a real German distribution grid.Comment: 10 pages, 7 figure