⚡ electrical engineering

Ensemble Forecasting of Power Quality Parameters

This paper demonstrates that ensemble forecasting methods significantly outperform individual models and seasonal naive benchmarks in predicting power quality parameters within transmission systems, offering a robust and scalable solution for proactive asset management based on an analysis of over 700 weekly time series from Germany and Estonia.

Original authors: Max Domagk, Peter Feistel, Jan Meyer, Marco Lindner, Jako Kilter

Published 2026-03-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Max Domagk, Peter Feistel, Jan Meyer, Marco Lindner, Jako Kilter

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 the electrical grid as a massive, high-speed highway system. For a long time, this highway was mostly used by steady, predictable cars (traditional power plants). But recently, the highway has been flooded with a chaotic mix of electric scooters, self-driving trucks, and wind-powered gliders (solar panels, wind turbines, and batteries).

This mix creates "traffic jams" and "potholes" in the electricity flow, known as Power Quality (PQ) issues. If these issues get too bad, they can damage expensive equipment or cause blackouts.

The people in charge of the highway (Transmission System Operators) have been collecting massive amounts of data about these potholes. However, until now, they've mostly just used this data to check if they broke the rules after the fact.

This paper asks a simple but powerful question: "Can we look at this data to predict where the potholes will be next year, so we can fix them before they happen?"

Here is the breakdown of their solution, using some everyday analogies:

1. The Problem: One Weather Forecaster Isn't Enough

The researchers tried to predict the future of these electrical "potholes" using different mathematical models. Think of each model as a different weather forecaster:

The "Naive" Forecaster: "It rained yesterday, so it will rain today." (Simple, but often wrong).
The "Complex" Forecaster: Uses supercomputers and satellite data but sometimes gets confused by the noise.
The "Decomposition" Forecaster: Breaks the weather down into "seasons," "trends," and "random storms" to understand the pattern better.

When they tested these individual forecasters on 700 different locations over a year, they found a problem: No single forecaster was perfect. Sometimes the "Simple" guy was right; other times the "Complex" guy won. It was a game of Russian Roulette to pick the right one.

2. The Solution: The "Council of Experts" (Ensemble Forecasting)

Instead of betting on just one forecaster, the researchers decided to create a Council of Experts.

They took all 8 different forecasting models and asked them to all make a prediction. Then, they didn't just pick the winner; they averaged their answers.

The Analogy: Imagine you are trying to guess the weight of a giant pumpkin.
- Person A guesses 200 lbs.
- Person B guesses 300 lbs.
- Person C guesses 250 lbs.
- If you pick one person, you might be way off. But if you take the average (250 lbs), you are likely much closer to the truth.

This is called Ensemble Forecasting. By combining the "wisdom of the crowd," the errors of one model cancel out the errors of another.

3. The Experiment: A Massive Taste Test

The researchers ran a massive experiment using real data from Germany and Estonia.

They had 716 different time series (like 716 different weather stations).
They tested 247 different combinations of these expert councils (some councils had 2 experts, some had all 8).
They used four ways to combine the votes: Simple Average, Median (the middle vote), and weighted votes (giving more say to the experts who were usually right).

4. The Results: The Team Always Wins

The results were clear and exciting:

The Team Beat the Star: The best single "forecaster" (a model called STL-ARIMA) was good, but the best team (a specific mix of 4 models) was even better.
Consistency is King: The team didn't just win by a little bit; they were more reliable. Sometimes a single model would have a "bad day" and make a huge mistake. The team, however, smoothed out those bad days. It's like a sports team where if one player misses a shot, the others cover for them.
Simplicity Works: You didn't need a super-complex way to combine the votes. Just taking the average or the middle value of the experts' predictions worked better than trying to be fancy.

5. Why This Matters

Why should you care?

Proactive Maintenance: Instead of waiting for a transformer to blow up because the power quality got too bad, grid operators can now see a "storm" coming months in advance.
Saving Money: They can fix the problem before it causes expensive damage.
Green Energy: As we add more wind and solar (which are a bit "jittery"), this method helps keep the grid stable without needing to build more physical infrastructure.

The Bottom Line

The paper concludes that when predicting the future of complex systems like the power grid, don't put all your eggs in one basket.

By gathering a diverse group of different prediction models and letting them vote together, you get a forecast that is smarter, more accurate, and much harder to fool than any single expert could ever be. It's the difference between asking one person for directions and asking a whole room of locals, then taking the route most of them agree on.

1. Problem Statement

The increasing integration of inverter-based technologies (wind, solar, BESS, HVDC, FACTS) has heightened the importance of Power Quality (PQ) monitoring in transmission systems. While Transmission System Operators (TSOs) collect vast amounts of PQ data, its utility is currently limited to retrospective compliance assessment.

There is a critical gap in medium- to long-term forecasting (horizons of several months to one year) of PQ parameters. Accurate forecasting in this timeframe is essential for:

Early detection of adverse trends and threshold exceedances.
Proactive asset management and maintenance planning.
Informed investment decisions.

Existing challenges include data heterogeneity, strong seasonality, and the difficulty of selecting a single "best" model that performs robustly across diverse PQ parameters and measurement sites.

2. Methodology

A. Data Collection and Preprocessing

Dataset: The study analyzed 716 weekly time series (3 years each) from 27 measurement sites across German and Estonian transmission systems (voltage levels: 110 kV to 380 kV).
Parameters: Monitored parameters included long-term flicker severity ( $U_{plT}$ ), voltage unbalance ( $U_{NB}$ ), total harmonic distortion ( $U_{THD}$ ), and individual harmonic voltages ( $U_{03}$ to $U_{15}$ ).
Preprocessing:
- Raw 10-minute data was aggregated to weekly values using the 95th percentile.
- Missing data (up to 20% of weeks) was imputed using the most recent available 95th percentile.
- Values were normalized against national grid code planning levels (e.g., VDE-AR-N 4120/4130 in Germany) to calculate "utilization."

B. Forecasting Models

The study evaluated 8 individual forecasting models suitable for interpretable, medium-to-long-term prediction:

Baselines: Seasonal Naive (SNaive), Drift.
Statistical Methods: Holt-Winters (HW), SARIMA, Exponential Smoothing (ES).
Modern Frameworks: Prophet (additive regression with trend/seasonality).
Decomposition-Based: STL (Seasonal-Trend decomposition using Loess) combined with Drift, ES, Holt, or ARIMA.

C. Ensemble Framework

The core methodology involved constructing an ensemble forecasting system:

Configuration: All possible combinations of the 8 models were generated, resulting in 247 unique ensemble configurations (ranging from 2 to 8 models).
Combination Strategies: Four aggregation methods were tested for each configuration:
1. Mean: Equal-weight averaging.
2. Median: Pointwise median (robust to outliers).
3. sMAPE-weighted: Weights assigned based on inverse mean sMAPE performance.
4. Rank-weighted: Weights assigned based on inverse mean rank performance.
Evaluation: A 105-week training set and a 52-week test set were used. Performance was measured using Mean Absolute Error (MAE), symmetric Mean Absolute Percentage Error (sMAPE), and a Benchmark Ratio (BR) relative to the SNaive baseline.

3. Key Results

A. Individual Model Performance

Decomposition Dominance: Models utilizing STL decomposition (specifically STL-ARIMA and STL-ES) outperformed all other individual models.
Benchmark Comparison: Only STL-ARIMA, STL-ES, and SARIMA successfully outperformed the Seasonal Naive (SNaive) baseline (Benchmark Ratio < 1).
Limitations: Complex models like Prophet and Holt-Winters failed to surpass the simple SNaive baseline in this specific context, highlighting that complexity does not guarantee better long-term accuracy for PQ data.

B. Ensemble Performance

Superior Accuracy: Ensemble methods consistently outperformed the best individual model. The top ensemble (D28 Median) achieved an sMAPE of 17.68%, compared to the best individual model (STL-ARIMA) at 18.22%.
Improvement Metrics:
- 2.6% improvement over the best single model.
- 15.3% improvement over the SNaive baseline.
Robustness: The best ensemble did not appear in the top 100 rankings of individual models, proving that combination reduces model-selection risk.
Composition vs. Aggregation: The study found that the diversity and composition of the model pool were more critical to success than the specific aggregation method. The most successful ensembles typically included the top 5 individual models. While the Median method was most frequent in the top 100, simple Mean and Median combinations yielded results comparable to complex weighted schemes.
Stability: Ensembles significantly reduced performance variance and prevented extreme forecast failures seen in single-model selections. In 62% of cases, the best ensemble outperformed the best individual model.

4. Key Contributions

Systematic Evaluation: Provided the first large-scale, systematic evaluation of ensemble forecasting for PQ parameters in transmission systems, analyzing over 700 time series.
Validation of Ensembles: Demonstrated that ensemble forecasting is a robust, scalable approach for medium-to-long-term PQ prediction, effectively mitigating the uncertainty of selecting a single optimal model.
Methodological Insight: Showed that for PQ data, decomposition-based models (STL) are superior to "black box" or complex trend models, and that simple aggregation (Median/Mean) of diverse models is often sufficient for high accuracy.
Practical Framework: Established a reproducible framework for TSOs to move from reactive compliance monitoring to proactive asset management.

5. Significance and Conclusion

The paper confirms that ensemble forecasting is the preferred strategy for long-term Power Quality prediction in transmission networks. It offers a computationally efficient and reliable solution that enhances trend detection and supports infrastructure planning.

The findings suggest that TSOs should not rely on a single "best" model but rather deploy a diverse portfolio of decomposition-based models aggregated via simple statistical methods (like the median). This approach ensures stability against model uncertainty and seasonal variations. Future work is proposed to extend this to distribution systems and develop probabilistic forecasts with asymmetric error metrics to prioritize accuracy near critical PQ limits.