## 2 Design Schematic and Principles  
A descriptive schematic diagram of the current CCCP system is shown in Figure 1. S1-S12 illustrate the terminal end users with chillers; the primary pumps are responsible for circulating the whole cooling water loop, whereas cooling towers are designed to coordinate with them. The power of primary pumps \(Q_{pp}\) in units W is given as:  
\[Q_{pp}=\frac{2.72G_{total}H_{pp}}{\eta_{1}} \tag{1}\]  
where \(H_{pp}\) is the pump head (unit: mH\({}_{2}\)O), \(G_{total}\) is the total flow rate (unit: m\({}^{3}\)/h), and \(\eta_{1}\) is the efficiency of the pump. The pump head, which is the total pressure drop of the entire water loop, is simply described as  
\[H_{pp}=H_{ct}+H_{sn}+H_{m} \tag{2}\]  
where \(H_{ct}\) is cooling tower pressure loss. \(H_{sn}\) is the pressure loss in most unfavorable end use. \(H_{m}\) is the loss in main pipes. All of the units are in mH\({}_{2}\)O. The losses in auxiliary equipment, such as check valves are also considered in corresponding components. For a CCCP system, because quantity control is only implemented on the primary pumps and cooling tower, the power of cooling towers is the product of the number of operating towers and nominal power. For water pumps, the relationship between the pump head and water flow rate can be written as a polynomial below:\[H_{pp}=\alpha_{0}+\alpha_{1}G_{pp}+\alpha_{2}{G_{pp}}^{2} \tag{3}\]  
where \(\alpha_{0}\), \(\alpha_{1}\), and \(\alpha_{2}\) are obtained through pump operation curve-fitting data. Additionally, the relationship between pressure loss and flow rate in water loops can be written as  
\[\mathrm{H}=H_{0}+\beta{G_{total}}^{2} \tag{4}\]  
where \(H_{0}\) is the static pressure loss and \(\beta\) is calculated from the resistance characteristics of the pipes and auxiliary equipment. The pumps operate at the intersection of the pump curve (3) and loops curve (4). End-use water flow is controlled by throttling valves fixed at each branch. During operation, the pumps operate at a constant speed and valve operation is variable; this alters the parameter \(\beta\) in Equation (4), as well as the loops resistance curve, thereby changing the operating point of the pumps and decreasing pump efficiency as a result. Furthermore, water flow cannot be controlled by valves as precisely as is required by the end user; thus, imbalance of the cold supply between the nearest building and building frequently occurs. The actual water flow distributed at each end use is not related to the cooling load; thus, the \(\Delta\)T and the subsequent COP of the chiller is affected. A common way to offset this \(\Delta\)T imbalance is to increase the circulating water flow, which would also increase energy consumption. However, the DVFP and WS system shown in Figure 2 has made many improvements. The water tank has partitioned the cooling water into two different sides: the source side and transportation side. On the transportation side, DVFPs fixed at each terminal are designed to initiate the pressure drop in the end-use water loop and corresponding main pipes. It is capable of varying the pump speed to control water flow. The flow rate of the \(i\)-th pump \(G_{si}\) in pump curve (3) is  
\[G_{si}=\frac{n}{50}G_{nominal} \tag{5}\]  
where \(n\) is the operating frequency, which can be altered and \(G_{nominal}\) is the nominal flow rate of the pump, which is designed according to the maximum cooling load. \(G_{total}\) is the sum of \(G_{si}\). The resistance curve at the end use remains stable as the speed of the pumps changes, assuring pump efficiency. Note that the PPs are removed for this observation, the total power of DVFPs can be calculated as  
\[\mathrm{Q}=\sum_{i=1}^{n}2.72G_{si}\frac{H_{si}}{\eta_{si}} \tag{6}\]  
Figure 1: Schematic diagram of the current conventional central circulating pump (CCCP) system. where \(H_{\text{s}i}\) is the pump head of the \(i\)-th pump.