Bottom-Up Load Forecasting With Markov-Based Error Reduction Method for Aggregated Domestic Electric Water Heaters
Bibliographic record
Abstract
Domestic electric water heaters (DEWHs) can provide operational flexibility for load control due to their energy storage capacity. Load forecasting for aggregated DEWHs is important for providing information of baseline load and controlling electricity demand profile without negative impact to the normal end use. Advanced metering infrastructures nowadays provide more possibilities to further enhance forecasting with bottom-up method. This article proposes a bottom-up forecasting with Markov-based error reduction method to predict power consumption of aggregated DEWHs for multiple forecast horizons. DEWHs are randomly divided into small aggregations, whose power consumption is forecasted by independent forecast engines. In this paper, the engines are K-means and wavelet decomposition-based neural networks. After summing all forecasting of small aggregations up, a new Markov-based error reduction method is proposed to extract features in residuals and mitigate forecasting error accumulation introduced by the summation, providing opportunities to further improve forecasting accuracy for the total DEWH load. Differing from traditional Markov-based error reduction, two new compensation parameters (compensation coefficient, and compensation threshold) are proposed. They are determined by using particle swarm optimization algorithm. Experiments on real and simulated DEWH loads verified the effectiveness of the proposed forecasting method. The proposed method improved the forecast accuracy over selected benchmark algorithms by about 20% to 80%, according to four performance metrics: mean absolute error, mean absolute percentage error, root-mean-square error, normalized form RMSE. The aggregation effects on performance were also analyzed in theory and tested with simulated DEWHs, providing a good indication of the forecast dependence on the aggregation size.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".