arXiv subjects

Eléa Prat

Publications and source records attributed to Eléa Prat.

9 recordsLinked to original sources

arXiv2026

How long is long enough? Finite-horizon approximation of energy storage scheduling problems

Energy storage scheduling problems, where a storage system is operated to maximize its profit in response to a price signal, are naturally formulated as infinite-horizon optimization problems, since storage systems operate continuously, without a foreseen end to their operation. Such problems can be solved to optimality with a rolling-horizon approach, provided that the planning horizon over which the problem is solved is long enough. Such a horizon is termed a forecast horizon. Despite its importance, the planning horizon is usually chosen arbitrarily for such applications. We introduce an easy-to-check condition that confirms whether a planning horizon is a forecast horizon, and which can be used to derive a bound on suboptimality when it is not the case. In practice, this condition enables practitioners to evaluate whether the planning horizon chosen is sufficient, thereby providing, for the first time, a practical means of evaluating and selecting planning horizons for energy storage scheduling problems. We also derive a lower bound on the minimum forecast horizon. Building on the theoretical results, we develop an algorithm to determine the minimum forecast horizon. It enables the identification, a posteriori, of the shortest planning horizon that guarantees optimal rolling-horizon decisions while avoiding unnecessary forecasting effort and computational cost. Numerical experiments illustrate the practical use of the proposed framework and investigate how storage system characteristics and electricity price patterns influence the minimum forecast horizon.

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arXiv2025

Sufficient A Priori Conditions for the Linear Relaxation of the Energy Storage Scheduling Problem

When modeling energy storage systems, an essential question is how to account for the physical infeasibility of simultaneous charge and discharge. The use of complementarity constraints or of binary variables is common, but these formulations do not scale well. Alternatively, assumptions such as perfect efficiencies or positive prices are often used to justify the choice of a linear model. In this paper, we establish new a priori conditions that guarantee the existence of an optimal solution without simultaneous charge and discharge when solving the linear relaxation of the storage scheduling problem. They are based on the characteristics of the storage system, in particular, the duration of charge. They can be valid for negative prices and with inefficiencies, thereby enlarging the set of conditions for which the complementarity constraints can be relaxed. We prove mathematically the validity of these conditions and illustrate them with practical examples. We also introduce a refined mixed-integer linear equivalent, in which the number of binary variables can be drastically reduced.

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arXiv2025

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 consecutive market clearings poses challenges for market properties, and this is not well studied 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 storage systems in which the energy available is discretized to reflect the different prices at which the storage system was charged. These prices are then included as virtual bids, establishing a link between different market clearings. We show that market clearing with such virtual linking bids has the advantage of guaranteeing cost recovery for market participants and can outperform traditional approaches in terms of social welfare.

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arXiv2024

Optimal Operation of a Building with Electricity-Heat Networks and Seasonal Storage

As seasonal thermal energy storage emerges as an efficient solution to reduce CO2 emissions of buildings, challenges appear related to its optimal operation. In a system including short-term electricity storage, long-term heat storage, and where electricity and heat networks are connected through a heat pump, it becomes crucial to operate the system on two time scales. Based on real data from a university building, we simulate the operation of such a system over a year, comparing different strategies based on model predictive control (MPC). The first objective of this paper is to determine the minimum prediction horizon to retrieve the results of the full-horizon operation problem with cost minimization. The second objective is to evaluate a method that combines MPC with setting targets on the heat storage level at the end of the prediction horizon, based on historical data. For a prediction horizon of 6 days, the suboptimality gap with the full-horizon results is 4.31%, compared to 11.42% when using a prediction horizon of 42 days and fixing the final level to be equal to the initial level, which is a common approach.

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arXiv2024

On the Efficiency of Energy Markets with Non-Merchant Storage

Energy market designs with non-merchant storage have been proposed in recent years, with the aim of achieving optimal market integration of storage. In order to handle the time-linking constraints that are introduced in such markets, existing works commonly make simplifying assumptions about the end-of-horizon storage level, e.g., by imposing an exogenous level for the amount of energy to be left for the next time horizon. This work analyzes market properties under such assumptions, as well as in their absence. We find that, although they ensure cost recovery for all market participants, these assumptions generally lead to market inefficiencies. Therefore we consider the design of markets with non-merchant storage without such simplifying assumptions. Using illustrative examples, as well as detailed proofs, we provide conditions under which market prices in subsequent market horizons fail to reflect the value of stored energy. We show that this problem is essential to address in order to preserve market efficiency and cost recovery. Finally, we propose a method for restoring these market properties in a perfect-foresight setting.

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arXiv2023

Network-Aware Flexibility Requests for Distribution-Level Flexibility Markets

This paper proposes a method to design network-aware flexibility requests for local flexibility markets. These markets are becoming increasingly important for distribution system operators (DSOs) to ensure grid safety while minimizing costs and public opposition to new network investments. Despite extended recent literature on local flexibility markets, little attention has been paid to quantifying the flexibility required at each location, considering physical network constraints (e.g. line and voltage limits). The method introduced uses a chance-constrained optimization model and a LinDistFlow approximation to consider both physical network constraints and uncertainty caused by renewable production or demand fluctuations. Unlike other methods, it avoids sharing sensitive grid data with the market operator. 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 show on two case studies that our method outperforms the stochastic market-clearing benchmark in terms of computation time while achieving comparable social welfare and costs for the DSOs. One of the case studies is conducted on an actual German distribution grid, showing that the proposed method can scale well to real-sized networks.

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arXiv2022

Learning Active Constraints to Efficiently Solve Linear Bilevel Problems: Application to the Generator Strategic Bidding Problem

Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations of bilevel problems to mixed-integer linear programs 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, by moving the selection of active constraints to an offline process, and becomes particularly beneficial when the same problem has to be solved multiple times. We apply our approach 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. These methods are heuristic and as so, do not provide guarantees of optimality or solution quality. Yet, 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.

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arXiv2021

Auction-Based vs Continuous Clearing in Local Flexibility Markets with Block Bids

Flexibility markets can be introduced as a tool for the distribution system operator (DSO) to avoid high costs and public opposition against new network investments. Continuous flexibility markets have the advantage of allowing more liquidity, which can be critical in the earlier stages of such markets, and can be operated closer to real-time, thereby enabling a better use of the latest forecasts; but, by design, they also result to a lower social welfare compared to auction-based markets. This paper has two main contributions. First, it introduces a continuous local flexibility market which includes both network constraints and asymmetric block bids. Second, it proposes an algorithm that can accurately determine the upper and lower bound of the social welfare loss compared with an auction-based clearing model.

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arXiv2021

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.

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