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Self-Supervised Graph Neural Networks for Full-Scale Tertiary Voltage Control

Balthazar Donon, Geoffroy Jamgotchian, Hugo Kulesza, Louis Wehenkel

Abstract

A growing portion of operators workload is dedicated to Tertiary Voltage Control (TVC), namely the regulation of voltages by means of adjusting a series of setpoints and connection status. TVC may be framed as a Mixed Integer Non Linear Program, but state-of-the-art optimization methods scale poorly to large systems, making them impractical for real-scale and real-time decision support. Observing that TVC does not require any optimality guarantee, we frame it as an Amortized Optimization problem, addressed by the self-supervised training of a Graph Neural Network (GNN) to minimize voltage violations. As a first step, we consider the specific use case of post-processing the forecasting pipeline used by the French TSO, where the trained GNN would serve as a TVC proxy. After being trained on one year of full-scale HV-EHV French power grid day-ahead forecasts, our model manages to significantly reduce the average number of voltage violations.

Self-Supervised Graph Neural Networks for Full-Scale Tertiary Voltage Control

Abstract

A growing portion of operators workload is dedicated to Tertiary Voltage Control (TVC), namely the regulation of voltages by means of adjusting a series of setpoints and connection status. TVC may be framed as a Mixed Integer Non Linear Program, but state-of-the-art optimization methods scale poorly to large systems, making them impractical for real-scale and real-time decision support. Observing that TVC does not require any optimality guarantee, we frame it as an Amortized Optimization problem, addressed by the self-supervised training of a Graph Neural Network (GNN) to minimize voltage violations. As a first step, we consider the specific use case of post-processing the forecasting pipeline used by the French TSO, where the trained GNN would serve as a TVC proxy. After being trained on one year of full-scale HV-EHV French power grid day-ahead forecasts, our model manages to significantly reduce the average number of voltage violations.

Paper Structure

This paper contains 22 sections, 17 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Background & Motivations
  2. Related Literature
  3. Contributions
  4. Paper Organization
  5. Methodology
  6. Initial Optimization Problem
  7. Context Variable $x$
  8. Decision Variable $y$
  9. Objective Function $f$
  10. Continuous Surrogate Optimization Problem
  11. Line Controllers
  12. Shunt Controllers
  13. SVR Controllers
  14. RTC Controllers
  15. Surrogate Gradient Estimation
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Illustration of the various levers for action. On the left part of each subfigure is displayed a Single Line Diagram (SLD) of small simplistic systems where controllable devices are shown in red. On the right part is displayed the corresponding H2MG representation, where dots () correspond to addresses and all other symbols are hyper-edges defined in Table \ref{['tab:classes']}.
  • Figure 2: Histogram of voltage violation counts per context, over the Test set. The red curve corresponds to initial values, and the blue curve to the outcome of the GNN's decision. (a) and (b) display the same data on different y-axis scales.
  • Figure 4: Distributions of control levers' setpoints and usages. All y-axes are in logarithmic scale, so as to highlight outliers.