## 1 Introduction
The purpose of OPP is to find out the most representative location and place a PMU on it. Around the theme of improving the level of observability, the main goals of OPP include minimizing the number of PMUs required, maximizing measurement redundancy and handing contingency constraint. The main goal is to minimize the number of PMUs required. In Reference [13], an OPP method for complete observability of a system under normal operating conditions is proposed. Tabu search algorithm is used to determine the minimum number of PMUs required to make the system observable. A new PMU layout formula is developed to ensure the full observability of the network in Reference [14]. It takes the network observability under all possible arrangements of line connections at complex buses into account. Another goal is to maximize measurement redundancy. Measurement redundancy represents the number of times the bus is observed directly or indirectly. The solution with the largest network measurement redundancy is chosen as the best choice in Reference [15]. Network measurement redundancy is the sum of the measurement redundancy of all buses. In Reference [16], a multi-objective probability model is proposed for the problem of OPP. The proposed model simultaneously optimizes two objective functions: minimizing the number of PMUs and maximizing the expected value of network measurement redundancy. Various accidents may occur in the network. Therefore, it is important to analyze the observability in these conditions which include line outage and PMU failure. In Reference [17], a new OPP method which considers emergency constraints is provided. The proposed method is based on n-k redundancy criterion using robust optimization. This security standard ensures network observability in any accidental state, including up to k loss of PMUs. In Reference [18], the OPP problem is performed in order to achieve a fully observable network under normal and emergency conditions considering network expansion. To this end, the strain index is introduced through the modeling process of n-1 contingency states. Unlike the transmission grid, the measurement data of the distribution network is insufficient, which renders most distribution networks unobservable [19]. Existing real-time measurements of the distribution network are mainly provided by the SCADA system [20], and the remote terminal unit (RTU) is the main measurement device. On the one hand, the sampling period of SCADA is much longer than that of PMU [21]. On the other hand, the SCADA system cannot provide the phase angle data directly. The lack of a sufficient number of measurements is usually solved by introducing pseudo-measurements, which are mainly represented by historical measurements or forecast measurements on generators production and power consumption [22; 23]. The main purpose of improving network measurement redundancy is to improve the accuracy of state estimation. The distribution network state estimation technology is expected to be able to monitor the operating status of the system accurately and provide reliable data for other advanced management software of the active distribution network, such as transient stability [24], voltage security visualization [25], fault location identification [26], dynamic control strategies [27] and so on. Therefore, taking state estimation accuracy instead of network measurement redundancy into the OPP problem can be more helpful to improve the observability and controllability of the distribution network. Distribution system state estimation methods proposed are mainly based on weighted least squares (WLSs) algorithms [28; 29; 30], and considerable effort has been devoted to reducing computational requirements. The main differences between proposals are basically the choice of state variables, the simplification of accelerated estimation and the technique of combining heterogeneous measurements. The two main kinds of state variables are bus voltages and branch currents.