## 1 Introduction  
Traditional distribution network planning and operation methods cannot manage the large-scale access of distributed generations (DGs) and flexible loads. Distribution networks are evolving to become more flexible, reliable, efficient and intelligent [1]. However, current distribution networks lack sufficient measurement devices and rely heavily on pseudo measurements, which leads to poor state estimation accuracy and frequency. This low-frequency state estimation cannot meet the requirements of real-time control in intelligent distribution networks. As a monitoring device, a phasor measurement unit (PMU) can measure the voltage phasor and current phasor synchronously [2]. With the ability to provide phase angle data, along with a high sampling frequency and high data accuracy, the PMU is being widely applied in state estimation [2], faulted line identification [3], voltage monitoring [4] and other fields in smart grid. If each bus of a power system installs a PMU, this system can be fully observable and can have a good state estimation capacity. However, PMUs are very expensive, which makes it difficult to install a large number of PMUs in a distribution network [5]. Exciting prospects are offered by the fact that the application of the distribution-level-phasor measurement unit (D-PMU) in distribution networks significantly reduces the costs of PMU placement [6]. This makes it possible to establish a wide-area measurement system in the distribution network. Nevertheless, due to a large number of distribution network nodes and changeable topology, the placement of D-PMU to ensure the observability of the network is still a huge investment. Therefore, the optimization of the placement of D-PMUs to support various functions of intelligent distribution networks, with limited investment, has become a research hotspot. The current optimal D-PMU placement (OPP) methods for a distribution network focus on improving the observability of the power system and economic efficiency. Ref. [5] proposes an OPP method in the distribution network based on a meta heuristic algorithm and the effect of state estimation is verified. In Ref. [6], an OPP model for maximizing network observability is proposed, and the influence of distributed generation is considered. As the cost is related to the number of branches of the installed bus, an OPP method considering D-PMU installation costs and communication infrastructure is given in Ref. [7]. The solution is installed at multiple stages. Each stage depends on the cost of the utility setup rather than on the number of D-PMUs. In Ref. [8], considering all possible line connections of buses, a new D-PMU placement method for network observability is proposed. Ref. [9] uses the weak-load bus closeness criteria to determine the primary position at the beginning of D-PMU installation. The above methods all operate on the premise that one D-PMU can indirectly observe multiple buses, but this mode of indirect observation reduces the reliability of the observation system. In addition, only satisfying observables may not meet state estimation needs. Therefore, some studies have considered network measurement redundancy (NMR) and have made full use of the existing advanced measurement infrastructure (AMI) and supervisory control and data acquisition (SCADA) measurements, which can improve observation reliability and reduce costs. Ref. [10] proposes a network compression method that combines existing measurements and reduces D-PMU candidate positions. Ref. [11] proposes an OPP model based on conventional measurements and D-PMU channel limitations to optimize the number and NMR. In Ref. [12], an OPP method based on a robust estimator is proposed, which can further increase the accuracy of system state estimation. In Ref. [13], considering existing measurements, a new OPP method is developed to enhance system observability. Two main methods are usually used to solve the OPP model: a numerical algorithm [14; 15] and a heuristic algorithm [16; 17].