Facilitating Market Participation of Flexible Energy Resources via Mathematical Programming

Accelerating the transition to renewable-dominated electric power systems poses many challenges for practitioners. The intermittent nature of renewable energy resources amplifies the need for flexible, including consumer-owned, resources. This evolution may introduce many changes to the conventionally used electricity market modeling paradigm to capture a larger number of possibly irrational players' behaviour in the presence of parametric and structural uncertainty. This dissertation tackles a number of mathematical programming challenges arising with the changing electricity markets, offering methodological advances to better understand and exploit flexible energy resources. In particular, the developed models seek to (i) capture parametric uncertainty and ambiguity of an energy community aggregating various distributed energy resources via risk-based probabilistic constraints, (ii) reduce model uncertainty via internalizing a machine-learning surrogate model into an optimization framework, (iii) represent and exhaustively study a strategic energy storage system in an oligopolistic setting via the formulation of a multi-leader game. In each application presented in this dissertation, a dedicated model set-up is developed, depending on whether strategic behaviour, parametric, or structural uncertainty is considered. The employed models involve both convex and non-convex optimization methods, complemented by data-driven solution techniques. For objective (i) an energy community's centralized optimal bidding and scheduling problem is formulated as a time-series scenario-driven stochastic optimization model, building on real-life measurement data. In the presented model, a surrogate battery storage system with uncertain state-of-charge (SoC) bounds approximates the portfolio's aggregated flexibility. The presented research extends state-of-the-art models by implementing a worst-case conditional value at risk (WCVaR) based constraint for the storage SoC bounds, hedging the flexibility schedule against distributional ambiguity. Then, an extensive numerical comparison is conducted to analyze the trade-off between out-of-sample violations and expected objective values, revealing that the proposed WCVaR based constraint shields significantly better against extreme out-of-sample outcomes than the conditional value at risk based equivalent. In addressing objective (ii) a mathematical program with neural network constraints (MPNNC) is developed to capture the dynamics of the electricity market, which are governed by nonconvex (partially known) constraints and reward functions of the participants, in the strategic bidding problem of a demand agent. The developed method offers a more realistic alternative to the commonly employed bi-level programming strategies, and holds potential for incorporating various objectives and constraints in the strategic agent's problem (which may be an advantage over reinforcement learning methods). The MPNNC closely approximates the outcomes of a theoretical benchmark, assuming a perfect representation of the market clearing problem in the lower level. In a real-life case study, the aggregated supply curves from the Belgian spot exchange are used to assess the potential gains of using the developed model in concrete applications. Lastly, to tackle objective (iii), an equilibrium problem with equilibrium constraints (EPEC) is implemented to capture the underlying multi-leader common follower game in an oligopolistic electricity market. The decision problem of each agent is modeled as a bi-level optimization problem, consisting of the strategic agent's decision problem in the upper-level and the market clearing problem in the lower-level. Real-life applicability or policy-oriented studies based on state-of-the-art EPECs are challenged by the potential multiplicity of equilibria and the difficulty of exhaustively exploring this range of equilbria. To improve explainability of the EPEC's results, the range of equilibria is explored by using a novel simultaneous solution method. The proposed solution technique relies on applying Scholtes' regularization before concatenating the strategic actor's decision problems' optimality conditions. The attained solutions are stationary points with high confidence. Our analysis reveals that these model outcomes may span a broad range, impacting the derived economic metrics significantly, but the average outcomes (when a larger set is triggered) show consistency with the underlying strategic opportunity. The presented methodological advances may contribute to future electricity markets by (i) allowing to hedge against distributional ambiguity, related to the market participation of various DERs, in a computationally tractable way, (ii) capturing dynamics (which are difficult to capture within a convex optimization problem) in the joint exploitation of mathematical optimization and machine learning models, (iii) exhaustively studying the system-wide implications of the simultaneous strategic actions of multiple market actors.

Jaar van publicatie:2022

Toegankelijkheid:Open