## 2 Background
### Operational Costs (OPEX)
#### 2.2.2 Maintenance Costs  
Besides the energy cost, maintenance cost is another aspect of CWP's operating costs. The maintenance cost \(MC_{i}\) for the \(i\)th chiller is determined according to engineering practices [52], and it is influenced by the value of the maximum cooling capacity of the \(i\)th chiller \(CAP_{i}\) shown by (9) and (10).  
\[MC_{i}=CAP_{i}*MC_{unit} \tag{9}\]  
\[MC_{unit}=\begin{cases}\frac{6.4\text{TVUSS}}{Kw}\quad for\ \text{CAP}_{i}<528\ \text{ kW}\\ \frac{4.6\text{USUS}}{Kw}\quad for\ 528\ \text{kW}<=\text{CAP}_{i}<1055\ \text{ kW}\\ \frac{2.5\text{VUSS}}{Kw}\quad for\ \text{CAP}_{i}>=1055\ \text{ kW}\end{cases} \tag{10}\]  
The equation of maintenance cost (\(MC\)) of the whole chiller plant is provided by (11), with a notable calibration factor (\(\mu\)), but its variation is not explicitly explained by [52; 98].  
\[MC=\mu\sum_{i=1}^{n}MC_{i} \tag{11}\]  
Here, the \(\mu\) is set at 0.8 for two-chiller systems and 0.7 for three-chiller systems or those with more than three chillers, provided the multiple chillers are symmetrical. However, this factor is not defined for the remaining design options [52; 98].  
We investigated the maintenance cost calculation for CWPs, focusing on the often-unexplained \(\mu\). Our analysis established a crucial link between \(\mu\) and economies of scale. The primary objective is to attain economies of scale [104] by increasing the number of chillers and reducing costs. Economies of scale, a fundamental principle in business and manufacturing, signifies that larger-scale operations benefit from cost efficiencies, leading to decreased per-unit costs. As the number of chillers increases, maintenance costs decrease due to shared labor and technician expertise, aligning with averaging costs over multiple chillers. Achieving economies of scale allows companies to lower the average cost of their products, resulting in more significant cost savings and higher production levels. The size of the chiller plant or HVAC system matters, with larger industries experiencing more substantial cost savings. However, careful consideration is essential, as increasing the number of chillers may lead to diseconomies of scale beyond a certain point. Hence, the fixed calibration factor (0.7 for three or more chiller systems) provides a balance, ensuring optimal cost-effectiveness. The calibration factor is set at 0.8 for two-chiller systems, encapsulating the nuanced relationship between maintenance costs and the scale of CWP operations.  
Hence, the primary cost in OPEX can be considered as the combined energy and maintenance costs, as shown in (12).  
\[\text{OPEX}=\text{Energy cost}+\text{Maintenance cost} \tag{12}\]In our investigation, we derived TCO by integrating CAPEX and OPEX, as shown in (13). CAPEX is the one-time cost, and energy and maintenance costs are the recurring costs.  
\[\text{TCO}=\text{CAPEX}+\sum_{t=1}^{N}\text{OPEX}_{t} \tag{13}\]  
Here, \(\text{OPEX}_{t}\) represents the operational costs incurred in year \(t\). \(N\) is the total number of years in the system's life cycle. The sum of two key components of TCO, CAPEX and cumulative OPEX over the entire lifespan of the chiller system, has been highlighted in (13). CAPEX, as the initial investment, can be directly calculated using (1) and (2). However, since OPEX represents the ongoing costs and is the predominant factor in TCO [7; 105], the subsequent sections will analyze the factors affecting operational expenses and their predictions. By accurately forecasting future operational costs, we can ultimately optimize TCO [106; 107; 108]. All the equations discussed in this section provide the foundation for calculating key components such as capital expenditure, energy consumption, energy costs, and maintenance costs, which are subsequently used to train AI models for predicting future values, as presented in the Sections 4 and 5.