In competitive electricity markets, the optimal bid or offer problem of a strategic agent is commonly formulated as a bi-level program and solved as a mathematical program with equilibrium constraints (MPEC). If the lower-level (LL) part of the problem can be well approximated as a convex problem, this approach leads to a global optimum. However, electricity markets are governed by non-convex (partially known) constraints and reward functions of the participating agents. In this paper, an alternative data-driven paradigm, labeled as a mathematical program with neural network constraint (MPNNC), is developed. The method uses a neural network to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., it replaces the lower-level problem with a surrogate model. In the presented case studies, the proposed model is used to find the optimal load shedding strategy of a strategic load-serving entity. First, the MPNNC performance is compared to the MPEC approach, both in convex and non-convex environments, showing that the proposed MPNNC achieves similar performance to an ideal MPEC that has perfect knowledge of the simulated market environment. Then, aggregated supply curves from the Belgian spot exchange are used to assess the potential gains of using the developed model in real-life applications.

This paper presents new risk-based constraints for the participation of an energy community in day-ahead and real-time energy markets. Forming communities offers indeed an effective way to manage the risk of the overall portfolio by pooling individual resources and associated uncertainties. However, the diversity of flexible resources and the related userspecific comfort constraints make it difficult to properly represent flexibility requirements and to monetize constraint violations. To address these issues, we propose a new risk-aware probabilistic enforcement of flexibility constraints using the conditional-valueat- risk (CVaR). Next, an extended version of the model is introduced to mitigate the distributional ambiguity faced by the community manager when new sites with limited information are embedded in the portfolio. This is achieved by defining the worstcase CVaR based-constraint (WCVaR-BC) that differentiates the CVaR value among different sub-clusters of clients. Both reformulations are linear, thus allowing to tackle large-scale stochastic problems. The proposed risk-based constraints are then trained and evaluated on real data collected from several industrial sites. Our findings indicate that using the WCVaRBC leads to systematically higher out-of-sample reliability, while decreasing the exposure to extreme outcomes.

This paper formulates an energy community's centralized optimal bidding and scheduling problem 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. First, it is emphasized in a stylized analysis that risk-based energy constraints are highly beneficial (compared to chance-constraints) in coordinating distributed assets with unknown costs of constraint violation, as they limit both violation magnitude and probability. 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. 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. To bypass the non-trivial task of capturing the underlying time and asset-dependent uncertain processes, real-life measurement data is directly leveraged for both imbalance market uncertainty and load forecast errors. For this purpose, a shape-based clustering method is implemented to capture the input scenarios' temporal characteristics.