## 1 Introduction  
High penetration of distributed generator and controllable load has changed the fundamental way of the operation in the distribution network from a passive to active network [1; 2; 3]. The distribution network is developing in an intelligent direction [4]. The uncertainty of distributed generator and load brings great challenges to the stable operation of the distribution network, such as bidirectional power flow and increased voltage fluctuation. Furthermore, the distribution network topology changes dynamically to reduce power loss and voltage deviation [5]. As uncertainty increases, real-time measurement devices need to be added to the distribution network. Improving the observability of the distribution network is an important way to realize the intellectualization of the distribution network. Monitoring network state is traditionally done through the supervisory control and data acquisition (SCADA) system whose measurements are usually unsynchronized [6]. Among those newly-developed devices that aim at realizing the online system monitoring, phasor measurement unit (PMU) opens a new avenue for the distribution system. PMU is a real-time measurement device based on global positioning system (GPS), and it can receive the GPS timing signal to realize the synchronous acquisition of bus data. Compared with other measurement devices, PMU can deliver highly synchronized direct phasor measurements because it has high GPS synchronization accuracy. Therefore, the PMU can not only be applied to real-time state estimation of the distribution system and optimize its operating state,but also can quickly deal with problems such as anomaly detection [7], overcurrent protection [8], steady-state model synthesis [9], network topology detection [10], reliability analysis [11] and so on. Reference [7] proposes a layered architecture for monitoring networks based on the PMU measurements and establishes a set of analyses and sensor primitives to detect anomalous behavior in the control perimeter. Reference [8] proposes a scheme to enhance the traditional overcurrent protection scheme by using PMU functions embedded in solid state transformer and feeder protection relay. The proposed solution not only can enable the relay to operate correctly at its original range but also can maintain coordination with each other. In Reference [9], a new method of synthesizing the steady-state model of the unbalanced distribution network is proposed, which uses real-time measurements provided by PMU and can reduce the complexity of the network model caused by the increase of the power supply in the distribution network. In Reference [10], a new method for detecting topology changes in the distribution network is proposed, which is called the time series signature verification method for topology detection. This method analyzes the measurements provided by PMU installed on the distribution feeder. Reference [11] analyzes the reliability of the distribution system in the presence of the adjusted download resources with the PMU measurements from the same distribution feeder, which considers the practical regulation-eligible load types, the practical distribution-level protection devices, the impact of delay and so on. Therefore, PMU is considered as one of the most important measurement devices, and utilization of PMU in the distribution network is of great interest. PMU can acquire the voltage phasor of the bus and the associated branch current phasor at high frequency [12]. When the voltage phasor of a bus can be measured directly or indirectly, the bus is called an observable bus. When all the buses of the distribution network are observable, the network is called an observable network. If PMU is installed on each bus, the network is fully observable. However, the installation cost is high, and it is difficult to achieve the full deployment of PMU in the short term. How to achieve optimal PMU placement (OPP) in a distribution network encounters technical challenges.