## 4 Case Study and Discussion
### Tests on Total Cooling Capacity and Number/Size of Chillers  
A total of 16 sets of simulation trials for the total cooling capacity were conducted between 5100 kW and 6600 kW, with a 100 kW searching interval, for instance, 5100 kW, 5200 kW,..., 6500 kW, and 6600 kW. By taking the total cooling capacity of the chiller plant as 6000 kW for example, the operating COP increases with the chiller number increasing within a certain (i.e., 3 chillers) range, while the COP decreases when the chiller number further increases, as shown in Figure 6. By using the method as mentioned in Section 3.4, the operation cost of a chiller plant is estimated accordingly. Meanwhile, the rated cooling capacities of variable-speed and constant-speed chillers are optimized. The typical electricity price in Hong Kong is 1 HKD/kWh (note: 1 USD = 7.75 HKD). The operation cost of a chiller plant with different chiller combinations is presented in Table 5. Generally, the chiller plant operation cost of two variable-speed chillers is lower than that of one variable-speed chiller. Among all the selected combinations, the design option consisting of two variable-speed chillers (900 kW cooling capacity) and four constant-speed chillers (1050 kW cooling capacity) gets the minimum operation cost. The capital cost mainly includes the space cost and the equipment cost. The chiller plant lifespan is assumed to be 10 years in this case study. The space costs for variable-speed and constant-speed chillers are assumed to be 20,000 HKD and 15,000 HKD, respectively. The equipment costs of constant-speed and variable-speed chillers (rated cooling capacities of these two types of chillers are the same here: 900 kW) are 0.9 MHKD and 1.2 MHKD, respectively, by referring to manufacture data. The equipment costs (EC) of chillers with other capacities can be calculated according to Equation (19) [44; 45]. \[EC=EC_{0}\cdot\left(C/C_{0}\right)^{\alpha} \tag{19}\]  
where, \(EC_{0}\) is the reference equipment cost of a specific chiller capacity \(C_{0}\). \(EC\) is the equipment cost of chiller capacity \(C\). \(\alpha\) is a coefficient and its value is determined as 0.15 according to [46]. The annualized capital cost is calculated as the sum of space cost and equipment cost divided by the lifespan (10 years), and the results are shown in Table 5.  
The availability risk cost means a virtual \"penalty expense\" (i.e., so called \"service sacrifice\") when cooling demands cannot be satisfied due to insufficient cooling supply (e.g., equipment failures), which can be calculated according to the unmet demand and the assumed penalty ratios. Table 6 shows the total costs and the availability risk costs for different design options when there are three levels of penalty ratios (i.e., 1 HKD/kW, 10 HKD/kW, and 100 HKD/kW). The availability risk cost rapidly decreases with the increasing of the chiller number when the number is small. The total cost decreases when the chiller number increases. Since the availability risk cost is high with a small chiller number, while the capital cost is high with a big chiller number, there is a comprised configuration of chiller numbers/sizes with the lowest total cost. In this paper, the penalty ratio is set to be 10 HKD/kW. In all these options, the combination with one variable-speed chiller (1000 kW