energy system operators

Abstract: This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.

Abstract: Traditional energy forecasting solutions rely on task-specific supervision and energy asset representations, limiting transferability and the ability to capture general temporal dynamics across heterogeneous assets. We address this by proposing a distributed Joint Embedding Predictive Architecture (JEPA) for self-supervised learning from heterogeneous energy time-series. The framework predicts latent representations of masked temporal segments while integrating temporal observations and contextual information within a shared embedding space. To prevent representation collapse, training combines a latent-space predictive objective with covariance and temporal variance regularization. The evaluation was conducted on energy consumption and generation datasets under data-degradation scenarios and compared with a Transformer forecasting baseline. The learned representations remained stable (cosine similarity $\approx 0.98$; effective rank 185-235). JEPA achieved performance comparable to a Transformer on building energy data, higher $R^2$ in 3/5 consumer clusters, and outperformed the baseline on 9/10 unseen PVs ($R^2$=0.73-0.88 vs. <0.45), while showing greater robustness to missing data.