## 2 Background
### Operational Costs (OPEX)
#### 2.2.1 Energy Cost and Electricity Cost  
In multiple research studies, calculating electricity expenses is a common aspect of operating costs, primarily because energy costs are the most critical part of the TCO for an HVAC system. For instance, previous studies by [PERSON] et al. [97], [PERSON] et al. [103], [PERSON] et al. [98], and [PERSON] et al. [52] calculated OPEX, focusing mainly on electricity costs. While the equations may vary, they all share the same fundamental components, which include power rating (energy consumption) (kW), annual operational hours (hours), and electricity rate (USD/kWh). Considering peak, shoulder, and off-peak hours in electricity cost calculations is crucial for informed financial decisions, optimized energy consumption, and enhanced cost efficiency. [PERSON] et al. [103] have focused on the varying electricity prices during peak, shoulder, and off-peak hours, and [PERSON] et al. [97] only considered the electricity price during peak and off-peak hours.  
After a thorough examination of various cost estimation methods used in prior research [26], we have integrated a compact version of energy cost calculation and is as follows:  
\[\text{Energy Cost}=\sum_{t=1}^{t=8760}c_{t}\times p_{t,k} \tag{3}\]  
where \(c_{t}\) denotes the energy consumption (kWh) of the plant at the \(t\)th hour of a year, and \(p_{t,k}\) represents the electricity price during peak hours (\(p_{\text{P}}\)), shoulder hours (\(p_{\text{c}}\)), and off-peak hours (\(p_{\text{P}}\)), where '\(k\)' can take any value of \(p_{\text{P}}\), \(p_{\text{c}}\), and \(p_{\text{b}}\).  
The annual energy consumption \(c_{t}\) (kWh) of the plant (\(n\) chillers) is calculated by (4), where \(E_{i,j}\) (kW-h) is the energy consumption of the \(i\)th chiller in the \(j\)th hour.  
\[c_{t}=\sum_{j=1}^{8760}\sum_{i=1}^{n}E_{i,j} \tag{4}\]  
\[E_{i,j}=\frac{C_{i,j}}{\text{COP}_{i,j}} \tag{5}\]  
where \(C_{i,j}\) (kW) represents the cooling capacity supplied by the \(i\)th chiller during the \(j\)th hour, and \(\text{COP}_{i,j}\) represents the Coefficient of Performance (COP) of the \(i\)th chiller during the \(j\)th hour.  
\[C_{i,j}=C_{i}\cdot\text{PLR}_{ij} \tag{6}\]  
\[\text{COP}_{i,j}=f\left(\text{PLR}_{i,j}\right) \tag{7}\]  
Here, (6) and (7) show the calculation of \(C_{i,j}\) and \(\text{COP}_{i,j}\). Where based on the PLR-COP curve [52], the energy consumption of \(i\)th chiller during the \(j\)th hour is predicted. The function, denoted as\(f\left(\cdot\right)\), calculates the chiller's COP from part load ration (PLR), and this function can be created using data from existing chillers. Here, \(C_{i}\) is the maximum cooling capacity of the \(i\)th chiller, and \(\text{PLR}_{i,j}\) is the partial load ratio of the \(i\)th chiller in the \(j\)th hour. \(\text{PLR}_{i,j}\) can be calculated from (8).  
\[\text{PLR}_{i,j}=\frac{CL_{j}}{C_{\text{sum},j}} \tag{8}\]Here, \(CL_{j}\) is the cooling load of all conditioning zones in the \(j\)th hour, and \(C_{\text{sum},j}\) is the sum of the cooling capacity of each operating chiller in the \(j\)th hour.  
The equations are employed for computing energy cost, employing physics-based equations without relying on data-driven approaches. However, these calculated values serve as the historical data utilized to train the prediction models, and their accuracy directly impacts the precision of future energy cost predictions, as discussed in the Sections 4 and 5. The TCO estimation is significantly influenced by operating costs, with a major component being energy costs, primarily associated with electricity usage in chiller systems [91].