Energy and Reserve Dispatch with Renewable Generation Using Data-Driven Distributionally Robust Optimization
Bibliographic record
Abstract
With the increasing penetration of renewable generation such as wind power in modern power systems, there are many new challenges arising in power system operation with respect to reliability and economy. In this work, we study a two-stage data-driven distributionally robust (DR) energy and reserve dispatch problem with uncertain wind power. Different from the general moment-based ambiguity set, we design a new distance-based ambiguity set to describe the uncertain probability distribution of wind power, which can be constructed in a data-driven manner from historical data. Base on this new ambiguity set, the second-stage worst-case expectation of the problem is reformulated to a combination of conditional value-at-risk (CVaR) and an expected cost with respect to a reference distribution. Thus, the proposed two-stage DR model becomes a two-stage stochastic optimization problem which can be readily solved. Case studies are carried out to verify the effectiveness of the proposed method based on the IEEE 6-bus test system and modified IEEE 118-bus test system. Simulation results show the value of data in controlling the conservatism of the problem, and the DR problem converges to the stochastic problem with fixed distribution as the data size goes to infinity.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".