Modeling and Estimation of the State of Charge of Electric Water Heater Tanks for Demand Response: A Kalman filter-Based Approach
Bibliographic record
Abstract
This paper examines the use of two nonlinear Kalman filters to estimate the thermal profile of the state of charge of an electric water heater (EWH), aiming at leveraging load flexibility for demand response in smart grids. The study begins by establishing an infinite-dimensional model that characterizes the energy profile within the tank, employing a nonlinear parabolic partial differential equation. This model is then discretized using the Crank-Nicolson method to obtain a finite-dimensional lumped system. Two observers, namely the extended Kalman filter and the pseudo-linear Kalman filter, are used in order to accurately estimate the temperature distribution within the tank and the state of charge of the water heater. The application of these advanced filtering algorithms to a discretized PDE model provides a robust performance for state estimation in thermal systems. The effectiveness of the proposed model and estimation methods is assessed by using experimental data obtained from a water heater test bench. The results confirm the validity of the PDE-based model, with the pseudo-linear Kalman filter demonstrating a particularly notable performance, achieving less than $2.5 \%$ mean absolute percentage error in state of charge estimation across diverse scenarios. This study highlights the potential of advanced estimation techniques to reliably represent the state of charge inside an EWH.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 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".