Incorporating System Frequency Dynamics Into Real-Time Locational Marginal Pricing of Electricity
Bibliographic record
Abstract
This paper presents a method to generalize locational marginal prices (LMPs) to embed the impact of system frequency dynamics into real-time electricity markets. The proposed frequency dynamics-aware LMPs can help to mitigate costs associated with setting aside ever more reserve capacity to offset larger, faster, and more frequent transient excursions arising from greater renewable integration. We formulate a dynamics-aware economic dispatch (ED) by augmenting a traditional static ED with constraints pertinent to system frequency dynamics, including those from inertial response, primary frequency control, and the automatic generation control. We show that, similar to their traditional static counterparts, dynamics-aware LMPs are composed of Lagrange multipliers associated with the power balance and transmission line power flow constraints. Furthermore, through analysis, we detail dynamic and steady-state behaviours of dynamics-aware LMPs. Finally, numerical simulations involving standard test systems validate our findings, confirm added revenue opportunities for generators contributing to frequency support, and demonstrate computational scalability.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".