Bi-level optimization of a low-carbon industrial park with an air source heat pump array considering the cold island effect: A real case from China

Air source heat pump arrays (ASHP-A) have emerged as an economical and low-carbon heating supply approach for central heating by low-carbon industrial park (LCIP) operators in northern China. At low wind speeds, it causes a progressive decrease in the inhaling air temperature of the ASHP-A, leading to the formation of the cold island effect (CIE). Furthermore, this phenomenon will cause a decrease in the coefficient of performance (COP) within ASHP-A. In this condition, CIE should be considered carefully. In this context, this paper investigates a bi-level optimization of an LCIP with an ASHP-A considering the CIE. This study focused on the analysis of the validity of the following thesis: 1) The proposed bi-level optimization approach can optimize the objectives of two distinct decision-makers concurrently. 2) Furthermore, the novelty of this research compared to existing works lies in the introduction of a specific physical CIE model, which can minimize the impact of CIE on ASHP-A efficiency by optimizing each ASHP within ASHP-A. 3) Compared to previous studies, innovatively incorporating the thermal inertia of FBs enables the optimization of energy usage schedules through radiator operation, which not only effectively reduces costs for FB customers but also further mitigates the CIE effect, thereby enhancing the overall efficiency. A real ALCIP in Tianjin, China is carried out as the testing case. Numerical results show the effectiveness of the bi-level optimization method that balances both the profit of the LCIP operator and the costs of FB customers. Compared with extreme scenarios, the LCIP operator 's profit decreases by 3.542 %, while the costs of FB customers are reduced by 6.108 %, achieving the optimal overall equilibrium. Utilizing the flexibility of the FB heating load results in cost reductions ranging from 4.952 % to 8.623 % for FB customers. Moreover, it is demonstrated that operation with the proposed ASHP-A model effectively avoids the CIE and reduces the consumption of the LCIP operator by 6.987 %.