⚡ electrical engineering

Distributed Air-Gap Flux and Rotor-Current Fusion for Operating-Regime Identification in a 10-MW Kaplan Hydrogenerator

This paper demonstrates that fusing distributed air-gap magnetic flux descriptors with rotor-current features significantly enhances the accuracy of supervised operating-regime identification in a 10-MW Kaplan hydrogenerator, achieving 99.5% test accuracy with an SVC-RBF model compared to the limited performance of using either data source alone.

Original authors: Eduardo Jr Piedad, Rafel Roig, Xavier Escaler, Eduardo Prieto-Araujo, Oriol Gomis-Bellmunt

Published 2026-06-29

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CC BY 4.0

Original authors: Eduardo Jr Piedad, Rafel Roig, Xavier Escaler, Eduardo Prieto-Araujo, Oriol Gomis-Bellmunt

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a massive 10-megawatt hydroelectric generator as a giant, spinning heart. Just like a human heart, it needs to be monitored to ensure it's beating correctly under different conditions. In this case, the "condition" is how wide the water gates (called guide vanes) are open to let water in. The researchers wanted to figure out exactly how wide those gates are open just by listening to the machine's "heartbeat" and "muscle tension."

Here is how they did it, broken down into simple concepts:

1. The Two Types of "Sensors"

The researchers used two different ways to listen to the generator, kind of like using two different medical tests:

The "Muscle Tension" Test (Rotor Current): They measured the electricity flowing through the spinning part of the generator. Think of this like checking a runner's pulse. If the runner is sprinting (high load), the pulse is high. If they are jogging (low load), the pulse is lower. This measurement told them how hard the generator was working.
The "Heartbeat Map" Test (Air-Gap Flux): They placed ten tiny magnetic sensors (Hall probes) around the inside of the generator's stationary shell. These sensors mapped the invisible magnetic field swirling inside the machine. Think of this like an MRI scan that looks for irregularities in the shape of the heart or turbulence in the blood flow. It doesn't just tell you how hard the heart is working, but how evenly it is working.

2. The Problem: One Test Isn't Enough

The researchers tried to guess the gate opening (the "operating regime") using just one of these tests at a time.

Using only the Magnetic Map: It was like trying to guess a runner's speed just by looking at the shape of their shoes. The magnetic field has a lot of "static noise" caused by the machine's physical shape and manufacturing quirks. It was very hard to tell the difference between a slow jog and a fast run. The computer got it right less than 27% of the time.
Using only the Muscle Tension: This was much better. Since the electricity flow goes up and down with the load, the computer could guess the gate opening about 85% of the time. However, it still got confused when the load was very similar (like distinguishing between a slow jog and a moderate jog).

3. The Solution: Fusing the Data

The breakthrough happened when they combined the two tests. They fed both the "muscle tension" (current) and the "heartbeat map" (magnetic flux) into a smart computer program (machine learning).

Think of it like a doctor who checks both your pulse and your ECG (electrocardiogram) at the same time. The pulse tells them how fast you are going, and the ECG tells them if your heart rhythm is steady or wobbling. Together, they give a perfect picture of your health.

When the researchers combined these two data streams:

The computer became a "super-sensor."
It could distinguish between all seven different gate settings with 99.5% accuracy.
It stopped getting confused by similar-looking loads because the magnetic sensors picked up tiny, unique "wobbles" in the magnetic field that happened at specific settings, which the current sensors missed.

4. What They Learned

The study revealed that:

Current is the best indicator of how much work the generator is doing.
Magnetic Flux is the best indicator of how the machine is shaped and if there are any weird distortions or imbalances in the magnetic field.
Together, they create a complete fingerprint of the machine's state.

The Bottom Line

By fusing the data from the spinning rotor's electricity with the magnetic field measurements from the stationary wall, the researchers created a highly accurate system to identify exactly how a hydro-generator is running. They proved that you don't need complex, expensive deep-learning models to do this; a simpler, well-structured combination of physical sensors and standard machine learning works incredibly well. This method allows for a "smart" way to monitor these massive machines, ensuring they are running smoothly and safely.

Technical Summary: Distributed Air-Gap Flux and Rotor-Current Fusion for Operating-Regime Identification in a 10-MW Kaplan Hydrogenerator

Problem Statement
Reliable monitoring of hydroelectric generators requires descriptors that capture both electrical loading and electromagnetic field behavior. In Kaplan turbine-generator units, variations in guide vane opening (GVO) alter generator loading and can influence air-gap flux distortion, modulation, and spatial non-uniformity. While rotor-current measurements provide useful loading information, they do not fully describe the spatial distribution of the air-gap magnetic field. Conversely, distributed magnetic sensing offers direct insight into electromagnetic asymmetry and field distortion but has been less explored in combination with rotor-current features for operating-state classification. This work addresses the need for a data-driven framework that fuses these two modalities to accurately identify operating regimes under changing hydraulic and electrical conditions.

Methodology
The study utilizes synchronized measurements from a 10-MW Kaplan hydrogenerator (Porjus U9) operating under seven steady-state GVO settings (14° to 26°). The dataset comprises ten stator-mounted Hall probes measuring air-gap flux density and six rotor-current channels, sampled at 250 Hz.

The proposed framework processes 300-second steady-state records segmented into non-overlapping 1-second windows. Feature extraction is performed in parallel branches:

Spatial Flux Features: A discrete spatial Fourier transform is applied to the mean flux values from the ten probes to derive the fundamental spatial amplitude ( $B_1$ ) and a Spatial Non-Uniformity Index (SNI).
Temporal Flux Features: For each probe, Welch's method estimates the power spectral density to extract the dominant temporal amplitude ( $A_1$ ), a Flux Temporal Distortion Index (FTDI), and a Flux Modulation Index (FMI) for low-frequency components.
Rotor-Current Features: Channel-wise Root Mean Square (RMS) values are computed for the six current channels.

These features are analyzed using Pearson correlation and Principal Component Analysis (PCA) to understand their relationship with GVO. Supervised classification is then performed using Random Forest (RF), Radial-Basis-Function Support Vector Classification (SVC-RBF), and Multilayer Perceptron (MLP) models to distinguish the seven GVO states.

Key Contributions

Spatiotemporal Feature Extraction: The paper introduces a specific set of descriptors that separate spatial magnetic structure (via Fourier analysis of distributed probes) from temporal flux dynamics (via spectral analysis) and electrical loading (via RMS current).
Fusion Framework: It demonstrates a systematic approach to fusing distributed air-gap flux data with rotor-current measurements, moving beyond single-modal analysis.
Interpretability: Through correlation and PCA, the study decouples the physical meaning of the features, showing that current features primarily track the electrical loading axis, while flux features reveal complementary information regarding spatial imbalance and waveform distortion.

Results

Feature Behavior: Correlation analysis confirms that RMS current features have a very strong monotonic relationship with GVO (Pearson $\rho \approx 0.978$ ), serving as the primary loading descriptor. In contrast, spatial features (SNI, $B_1$ ) show weak correlation with GVO, suggesting they reflect persistent structural asymmetries rather than load changes. Temporal distortion (FTDI) shows a moderate positive correlation.
Classification Performance:
- Spatial-only features yielded poor separability, with test accuracies below 27%.
- Current-only features achieved a baseline accuracy of approximately 84–85% but struggled to distinguish neighboring low-load conditions.
- Flux-only features performed better than spatial-only (up to ~88% with MLP) but were less effective than current features alone.
- Fused Features: Combining flux and current information provided the most discriminative representation. The SVC-RBF model achieved a test accuracy of 99.5% and a macro-F1 score of 0.995. Adding all available features did not consistently improve performance beyond the flux-current fusion, indicating redundancy in the full set.

Significance and Claims
The paper claims that distributed air-gap magnetic sensing, when fused with rotor-current measurements, supports accurate and interpretable data-driven monitoring of Kaplan hydrogenerator operating regimes. The results indicate that while rotor current defines the dominant loading direction, flux-based features encode essential spatial and modulation structures that are orthogonal to the loading axis. This combination allows for highly reliable classification of guide vane opening states. The authors position this framework as a compact basis for future condition-monitoring and digital-twin applications for hydrogenerator systems, emphasizing that simpler machine-learning methods with physically interpretable features can outperform complex deep learning models when informative signal features are available.