Mixed integer control speeds underground pumped hydro scheduling nearly optimally
Mixed-Integer Nonlinear Differentiable Predictive Control for Underground Pumped Hydro Energy Storage Systems
Machine Learning
Summary
Scheduling underground pumped hydro energy storage is hard because of complex decisions and nonlinear equipment behavior. The authors improved a method called Mixed-Integer Differentiable Predictive Control to handle these complexities more efficiently. They trained a smart control policy using neural networks that can quickly decide both continuous settings and switching modes. Their approach solves the scheduling problem almost as well as traditional methods but runs about 100,000 times faster in practice.
What this means in practice
- •For energy system operators: Perform day-ahead scheduling of underground pumped hydro plants with near-optimal decisions much faster than previous methods.
- •For industrial control engineers: Implement fast predictive control policies for mixed discrete-continuous plants with nonlinear dynamics beyond pumped hydro systems.
Authors
Honghui Zheng, Ján Boldocký, Yury Dvorkin, Ján Drgoňa
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.