An Autonomous Demand Response Algorithm based on Online Convex Optimization
Bibliographic record
Abstract
A price-based demand response program is a viable solution for distribution network operators (DNOs) to motivate electricity consumers toward scheduling their load demand during off-peak periods. This paper addresses the problem of load scheduling in a demand response program, while accounting for load demand uncertainty and the distribution network operational constraints. The centralized load control is a non convex optimization problem due to the ac power flow equations. We use convex relaxation techniques to transform the problem into a semidefinite program (SDP), which is solved using online convex optimization techniques to address the load demand uncertainty. To tackle the issue of computational complexity, we use proximal Jacobian alternating direction method of multipliers (PJ-ADMM) to decompose the centralized problem into the customers' load scheduling subproblems. The decentralized algorithm is executed by each customer to schedule its load demand in real-time. Via simulations on the IEEE 37-bus test feeder, we show that the proposed algorithm enables customers to approximate the optimal load profile in the benchmark scenario without load uncertainty, and the approximation is tight. Furthermore, we show a negligible gap of 2.3% between the customers' cost with the proposed algorithm and the cost in the benchmark scenario.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".