## 1 Introduction
The numerical algorithm has a fast calculation speed, but its universality is poor. Therefore, the numerical algorithm is mainly suitable for solving linear models. The heuristic algorithm has a strong global search ability and is mainly suitable for solving nonlinear, high-dimensional and multi-objective models. However, although NMR can improve observation reliability to a certain extent, it cannot fully reflect the impact of various faults on system observations. The influences of line fault, D-PMU fault and other factors require more D-PMUs to ensure distribution network observability under different operating conditions. The \(N\)-1 contingencies resulting from D-PMU and line fault should be considered in the OPP problem. Ref. [18] considers the impact of power network expansion planning and line \(N\)-1 contingencies. Ref. [19] considers the impact of line \(N\)-2 contingencies. Ref. [20] takes observability under D-PMU \(N\)-1 contingencies as the constraint condition. Most of these references take observability under \(N\)-1 contingencies as a constraint and establish a single target and multi-constraint model. However, there are three problems in the implementation of the above method:  
1. Realizing full observability under all contingency conditions is difficult. Many studies take system observability under \(N\)-1 contingencies as the constraint condition, which greatly increases the number of D-PMUs. When considering topology variation, the D-PMU number increase is more serious. It is necessary to find a compromise method in dealing with \(N\)-1 contingencies. 2. Distribution network topology frequently changes, which may render the existing configuration unable to ensure observability after topology changes. Most of the above OPP methods do not consider the current economic reconfiguration and future topology changes. 3. D-PMU placement often faces the problem of insufficient funds in the short term. It is necessary to study how to better determine the placement order of D-PMUs in the placement scheme when short-term funds are insufficient. To solve the above problems, a new OPP method for the distribution network is proposed in this paper. This method can not only improve the effect of D-PMUs on state estimation accuracy and frequency, but it can also improve the reliability of the distribution network measurement system. Firstly, we place D-PMU in advance on some important buses. Then, an OPP model is built based on the full usage of the existing measurement system, and, considering the topology changes, an OPP model is established to ensure complete observability of the main topologies, with the goal of improving economic efficiency, NMR and the average number of observable buses under contingencies (ANOBC). A solution based on non-dominated sorting genetic algorithm-III (NSGA-III) is proposed. A compromise solution that takes the above three objectives into account can be obtained in the Pareto solution set. Finally, in order to improve state estimation effectiveness faster, placement order is calculated based on the spatial electric distance. The proposed method successfully guides the D-PMU placement of the Nansha demonstration project in China. Compared with the existing methods, the main contributions of this method are as follows:  
1. An overall placement process of distribution network D-PMU is presented, which includes initial placement, overall placement and multistage placement. 2. A topology generation method is proposed, which takes both the current and future economic reconfigurations of distribution networks into account. 3. A multi-objective optimal D-PMU placement model considering topology changes and contingencies is proposed. The proposed model takes both zero-injection buses and other measurements into account, which not only minimizes the number of D-PMUs, but it also maximizes the ANOBC and NMR under the topology observability constraint. Compared with other methods, the proposed method can greatly reduce the D-PMU number with a high ANOBC and NMR. 4.