## 6 Simulation Results and Discussion  
The efficiency of the OPP method proposed in this paper is verified by the (Institute of Electrical and Electronics Engineers) IEEE standard bus systems. Figure 1: The flow chart of the proposed optimal phasor measurement unit (PMU) placement (OPP) method in the compressed distribution network considering cost and state estimation accuracy. The topology of IEEE 33 bus system, as shown in Figure 2, is used in this paper to carry out the analysis; 1-33 is the bus number. The SCADA measurements include the voltage amplitudes of buses 1, 2, 3, 6, 18, 23, 33; the current amplitudes of branches 3-4, 6-7, 2-19, 6-26; the injections at buses 5, 6, 13, 21; the power flows of branch 2-19, 23-24, 28-29. In the process of simulation, the power flow calculation results of the IEEE 33 bus system are selected as the truth values, and various measurements are generated by superimposing the corresponding random errors on the truth values. The standard deviations of measurement errors of voltage amplitude and current amplitude provided by the SCADA system are 1%. The standard deviation of the power measurement error is 2%. The standard deviations of measurement errors of voltage amplitude and branch current amplitude provided by PMU are 0.2%, the standard deviation of measurement errors of voltage phase angle provided by PMU is 0.5%, and the standard deviation of measurement errors of branch current phase angle provided by PMU is 0.5%. The standard deviation of the pseudo-measurement error is 20%. Before applying NSGA-II to solve the model, the network is compressed through the pre-configuration and existing measurements. Buses 5, 13, 21 are equivalent to \"lesser ZIBs\" with two neighbors, so buses 5, 13, 21 are merged with buses 4, 12, 22 into new buses 4', 12', 21' respectively. Bus 6 is equivalent to a \"lesser ZIB\" with three neighbors. Buses 1, 18, 21, 25, 33 are leaf buses, which are not placed with PMUs. The connected buses 2, 17, 20, 24, 32 are pre-configured with PMUs and merged with buses 1, 18, 21, 25, 33 into new buses 2', 17', 20', 24', 33' respectively. The compressed network and observable buses are shown in Figure 3.  
The compressed system, as shown in Figure 3, is pre-configured with some PMUs. The buses pre-configured with PMUs are no longer involved in genetic operations, and their values of genes are 1. The specific parameters of applying NSGA-II to solve the model are as follows:  
The number of individuals in the parent population is 60. The number of individuals in the offspring population is 60. The number of iterations is 400. The number of buses in the system is 33. The number of branches is 32. The number of buses in the compressed system is 25. The number of  
Figure 3: Compressed IEEE 33 bus system. Figure 2: IEEE 33 bus system. variables in the placement vector is 25. The number of objectives is 2. The value of the initial front of each individual is 1. The number of intersections in the crossover operation is 2. The value of each subjective weight is 1. The number of rows in the chromosome matrix is 60, and the number of columns in the chromosome matrix is 29. The value of the penalty factor is 1000. The Pareto set obtained by the optimization is shown in Figure 4. As shown in Figure 4, at least 10 PMUs are needed to ensure the observability of the network. The locations of PMUs are: buses 2, 8, 11, 15, 17, 20, 24, 26, 30, 32. Considering the cost and state estimation accuracy comprehensively, the compromise solution is selected by TOPSIS. The compromise solution needs 11 PMUs, and the locations are buses 2, 4, 8, 11, 15, 17, 20, 24, 26, 30, 32. In order to reflect the influence of network compression on OPP, this paper uses the single variable method to compare two cases, the result of the comparison is shown in Table 1. As shown in Table 1, on the one hand, network compression based on pre-configuration and existing measurements can effectively reduce the number of PMUs of the most economical solution and the compromised solution.