## 1 Introduction
The weight associated with measurement is proportional to the accuracy of the measurement. Reference [28] discusses the correlation and importance of the weighted least squares estimation approach and presents the impact of the input data correlation on state estimation results. The implementation details of the constrained weighted least squares state estimation method are proposed in Reference [29], which can implement the equality constraint formula of the WLS method. Reference [30] uses real-time measurements and all available pseudo-measurements, the model is extended to include the slack bus voltage during the estimation process, and the possibility to treat radial and weakly mesh topologies is also present. In order to reduce the number of PMUs required for the full observability, zero injection bus (ZIB) should be considered into the OPP model. If a bus is not connected with any load, and the current injection of the bus and the power measurements of the bus are both zero, this kind of bus can be called a ZIB [6]. The observability of the distribution network can be improved by the presence of ZIB by Kirchhoff laws [31]. The existing methods of taking ZIBs into consideration are mainly divided into three types: linear inequality constraint, nonlinear modification and topology transformation. Reference [17] incorporates ZIBs to the OPP model by adding a linear inequality constraint. The number of added inequality constraints is equal to the number of ZIBs. Although this kind of method can guarantee that the model is nonlinear, this kind of method is difficult to apply when there are other measurements or multiple ZIBs are connected in the system. Topology transformation refers to merging the ZIB with one of the connected buses. Nonlinear modification means that the ZIB is applied to the OPP problem by modifying existing constraints. This method is easy to implement and has good adaptability, but it also makes the model nonlinear. In Reference [32], selection rules for topology transformation are proposed. ZIBs are merged with one of their connected buses. Based on the three rules, the proposed method determines the best bus to merge with the ZIB to get the minimum number of PMUs required for the full observability. However, using topology transformation to deal with ZIBs has two limitations: to identify the locations of PMUs and the importance of selecting the merged bus. Although the number of PMUs required for the full observability is reduced, the optimization effect is affected by the selection of the bus which is merged with ZIB. Due to a large number of buses in the distribution network, only using PMU measurements to realize the network observable fully is not economic. Therefore, conventional measurements should also be applied to the OPP problem. Conventional measurements of the distribution network are mainly provided by the SCADA system. In Reference [33], conventional measurements are modeled, and a recipe is introduced when multiple branches are adjacent to the same bus. The changes in the flow measurements after branch interruption are also considered in the proposed OPP method to obtain a more practical solution for the distribution network. Only power flow measurements are used in this OPP model, and other useful measurements are not utilized. Reference [34] presents a new integration model which considers the impact of current measurement and ZIB on the OPP model. The OPP model considering current measurements and ZIB is based on the logical sum of the observability of the bus, which can take advantage of the maximum capabilities of current measurement and ZIB. In addition, this method can also be applied to other systems with multiple topologies. Compared with the transmission network, the number of buses in the distribution network is large, so it is difficult to solve the model and verify the optimal solution. In order to search the optimal solution efficiently, some OPP methods are proposed to reduce the PMU candidate locations and improve the optimization effect.