## 1 Introduction  
District cooling systems (DCSs), which generate cold water in a central plant that is distributed to end uses to fulfill its cooling demands, have become a widely used solution for large-area buildings in many countries [1; 2]. Generally, there are two types of DCSs that differ according to the type of water that is produced at the central plant; the two types are as follows: (1) a centralized chilled water system; and, (2) a centralized cooling water system. In the first type, the central chiller is designed to have large cooling capacity to promote a high coefficient of performance (COP); additionally, the removal of terminal chillers makes it possible to more efficiently utilize the building space [3]. It also provides an ideal platform for interrelated thermal technologies implementing tri-generation [2] or thermal storage [4]. The second system, also referred to as the water-loop heat pump system, produces cooling water via a cooling tower or natural sources, such as seawater and transports it to end-use chillers [5]. This system is designed to utilize the distributed chillers to achieve variable cooling loads in end uses. Another advantage of this system is that it can incorporate vast varieties of cooling sources and recover the rejected heat inside of a building [6; 7; 8]. Because systems with variable cooling loads are the focus of this study, the second system with centralized cooling water was selected for further research. However, it should be noted that DCSs do possess limitations. For instance, the water transportation system consumes a large amount of energy, as an America-based study showed that the pumping system in a typical DCS consumed 30% of the total energy of the system [9]. The reason for this can be explained by the design and control strategy of conventional central circulation pump (CCCP) systems. The central circulating pumps are designed for the most remote consumer; thus, the flow rate and pump head are quite excessive for the other consumers. Therefore, the remaining consumers must employ valves to control water flow, which responds slow and causes additional losses in local pressure. The use of throttling valves alters the resistance characteristics of the network, resulting in the low efficiency of pump operation. In addition, the precision of water flow control is reduced when the end-use cooling demand varies according to each consumer, which leads to an imbalance in cold supply. Under the assumption that a large flow of water would offset the cold supply imbalance, most of the pumps currently in use generate large flows, which again increases transport energy consumption [10]. However, these problems can be solved by employing distributed variable-frequency pumps (DVFPs). When the cooling load varies, the chiller adjusts the heat that is released to condensing water side and the DVFP adjusts the pump speed to control the cooling water flow, maintain the supply, and return water temperature difference (\(\Delta\)T) at a preset value. Each DVFP is designed to provide the pressure drop in corresponding end-use building and main pipes. Thus, the main circulating pumps, which are also referred to as primary pumps (PPs), are removed and the transportation energy is reduced. By replacing the valves with pumps, the pump head is reduced and the resistance characteristics of the main pipes become relatively stable, thereby increasing pump efficiency. Additionally, variable-frequency pumps are able to rapidly and precisely adjust water flow, while maintaining a level of high-efficiency operation, preventing extra flow, and satisfying the specific cooling demand of each end-user. Variable frequency pumps (VFPs) have been studied for many years and are implemented in a wide variety of applications in fields related to air-conditioning, district heating, and municipal water distribution. Some studies have focused on control strategies for VFPs. [PERSON] and [PERSON] optimized pump speed and sequence control in a complex air-conditioning system to save energy [11].