Graph Neural Networks for Electric and Hydraulic Data Fusion to Enhance Short-term Forecasting of Pumped-storage Hydroelectricity

TL;DR

This work tackles the challenge of short-term state forecasting in pumped-storage hydropower plants by fusing electric and hydraulic sensor data with a data-driven spectral-temporal graph neural network (STGNN). The method learns a unified PSH-wide graph ${\mathcal{G}}_{\phi}$ from time-windowed sensor data and applies graph- and time-spectral filtering to forecast electrical currents for horizon $h$ (e.g., $h=1$) from a window of length $w$ (e.g., $w=24$). Compared with strong baselines including LSTM and Spacetimeformer, the STGNN with attention-based graph learning yields improved forecasting accuracy, interpretable attention patterns that reflect plant topology, and robust generalization without relying on predefined network diagrams. The approach demonstrates that cross-domain data fusion across hydraulic and electrical subsystems enhances PSH reliability and sensor fault detection, offering a scalable, calibration-free tool for real-world grid operations, with potential extensions to physics-informed losses.

Abstract

Pumped-storage hydropower plants (PSH) actively participate in grid power-frequency control and therefore often operate under dynamic conditions, which results in rapidly varying system states. Predicting these dynamically changing states is essential for comprehending the underlying sensor and machine conditions. This understanding aids in detecting anomalies and faults, ensuring the reliable operation of the connected power grid, and in identifying faulty and miscalibrated sensors. PSH are complex, highly interconnected systems encompassing electrical and hydraulic subsystems, each characterized by their respective underlying networks that can individually be represented as graphs. To take advantage of this relational inductive bias, graph neural networks (GNNs) have been separately applied to state forecasting tasks in the individual subsystems, but without considering their interdependencies. In PSH, however, these subsystems depend on the same control input, making their operations highly interdependent and interconnected. Consequently, hydraulic and electrical sensor data should be fused across PSH subsystems to improve state forecasting accuracy. This approach has not been explored in GNN literature yet because many available PSH graphs are limited to their respective subsystem boundaries, which makes the method unsuitable to be applied directly. In this work, we introduce the application of spectral-temporal graph neural networks, which leverage self-attention mechanisms to concurrently capture and learn meaningful subsystem interdependencies and the dynamic patterns observed in electric and hydraulic sensors. Our method effectively fuses data from the PSH's subsystems by operating on a unified, system-wide graph, learned directly from the data, This approach leads to demonstrably improved state forecasting performance and enhanced generalizability.

Figures (8)

• Figure 1: An overview of the two processing steps of our spectral-temporal graph neural network to fuse data from the electrical and hydraulic subsystems of a PSH. Utilizing attention-based graph learning, our method dynamically constructs a graph based on an input window $\bar{\mathbf{X}}^{t-w:t}$. Subsequently, by operating on this graph, the graph- and time-spectral filtering module efficiently extracts information from the hydraulic and electrical sensor data to forecast the subset of electrical sensors $\widetilde{\mathbf{X}}_{\text{elec}}^{t:t+h}$.
• Figure 2: Segment of the dataset, displaying all 21 normalized phasor current sensors (the forecasting target of our case study), indicating the dynamic nature of the sensor measurements. We show the same day of the week ($i$ and $i+7$) for two consecutive weeks.
• Figure 3: Comparison of normalized phasor current forecasts with (EL+HYD) and without the hydraulic information (EL) for our proposed STGNN model. We show the forecast for single node $N_i$ ($i = 1$) across a randomly selected day including ground truth. In the upper Figure, we display the dynamic range of the forecast. In the lower Figure, we display the normalized MSE of both approaches with respect to the ground truth. Removing hydraulic information results in heightened discrepancies and more pronounced outliers in the predictions. First, we select the data based on the above criteria. Then, we normalize the selected data using min-max scaling.
• Figure 4: The averaged learned attention across the test set of the attention-based graph learning module over all 58 signals from the electrical and hydraulic subsystems. We show three random seeds. The learned attention is stable for different random initializations.
• Figure 5: The heatmap represents the averaged learned attention by the attention-based graph learning module across the test set as for the model processing only electrial information (EL). Counterintuitively, the model focuses on the PSH output (SP) when forecasting the phasor currents of the electromagnetic generators, which represent the PSH input.