Optimal electricity pricing in a microgrid network
Bibliographic record
Abstract
The evolution of microgrid and its demand-response characteristics not only will change the paradigms of the century-old electric grid but also will shape the electricity market. In this new scenario, once always energy consumers, now may act as sellers due to the excess energy generation from the newly deployed distributed generators (DGs). In this paper, we propose a novel mathematical model and its solution methodology to minimize the overall electricity price. The model is nonlinear and nonconvex due to the nonlinear and nonconvex characteristics of the marginal costs. To solve the minimum electricity price model (MEPM) problem efficiently and optimally, we decompose the problem into two subproblems: overall marginal cost problem (OMCP), and minimum cost allocation problems. A solution of OMCP determines the boundary of the overall marginal costs, and the allocation problem maps the optimal amount of energy from sellers to buyers for minimum price. The MEPM solution uses a divide-and-conquer method that divides the overall marginal cost boundary (solution OMCP) into two and determines the allocations for minimum cost, interactively. We compare MEPM with a first come first serve pricing scheme.
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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 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".