In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

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.