Hierarchical optimization of district heating plants by integrating evolutionary and non-linear programming algorithms
Bibliographic record
Abstract
In district heating systems, the capacity and types of energy sources, along with their control mechanisms to meet heating demands, are intricately linked. Effective planning must consider financial constraints and system operations, especially with thermal storage. Control methods can significantly influence sizing decisions by adjusting heat production and storage rates across different equipment. Addressing these issues concurrently is essential to maximize cost savings throughout the system's lifespan. This study addresses critical research gaps, such as the lack of integrated bi-level schemes that combine evolutionary and mathematical optimizers while maintaining original non-linear problem formulations. Specifically, it puts forward a novel tri-level optimization framework aimed at minimizing the lifecycle cost (LCC) of district heating plants, powered by a mix of green (solar thermal and biomass) and conventional (gas) heat sources, along with daily thermal storage. The three levels of this scheme are: i) a particle swarm optimizer (PSO) to explore capacities of heat production and storage devices to minimize LCC; ii) an interior-point optimizer (Ipopt) to minimize annual operating costs with explicit operational constraints; and iii) a simulation layer to enhance computational efficiency. Technical suggestions regarding the initialization and early termination of Ipopt to achieve the global optimal solution with reasonable computation time are described in detail. When applied to the multi-source plant, this methodology showed successful and rapid convergence of PSO towards feasible system designs. The study achieved a minimum LCC of 36.34 million USD, corresponding to a levelized cost of heat of 0.0256 USD/kWh, by maximizing green heat sources and using moderate-volume storage. Biomass fuel (74.8%) and capital costs of biomass (8.1%) and solar (7.9%) systems were the primary LCC contributors. Thermal storage enhanced operational flexibility; without it, the gas boiler capacity increased by 112.1 times, and LCC and carbon emissions rose by 3.4% and 106.97%, respectively. In conclusion, the proposed methodology successfully demonstrated substantial cost savings and environmental benefits through strategic renewable energy use and thermal storage, laying the groundwork for its reapplication to more complex system configurations.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".