## 1 Introduction
In Reference [35], considering the radiation of the distribution network, an OPP method which decomposes the network into two sub-networks is proposed. This method decomposes the whole network into two sub-networks: the primary sub-network and secondary sub-network. The OPP process of each sub-network is performed separately, so the number of PMU candidate locations is greatly reduced. Although the proposed OPP method saves calculation time, the number of PMUs required for the full observability increases due to the segmentation operation. Numerical algorithms [36; 37] and heuristic algorithms [38; 39; 40; 41; 42] are the main optimization techniques for solving the OPP model. The numerical algorithm is mainly applicable to solve the problem whose model is simple and linear. Reference [36] proposes an iterative weighted least squares algorithm to solve the OPP model for the full observability, which has actual placement variables. The proposed algorithm is implemented by using the available routines in the existing state estimator to avoid the use of other mathematical optimization technologies. Reference [37] proposes a mathematical OPP framework which considers cost and benefits at the same time. The enforcement in reliability is calculated by using the PMU measurement infrastructure and converted to a monetary value as the development benefit. The benefit is reduced by the cost value to get the optimal solution. The heuristic algorithm is applicable to solve the nonlinear, high-dimensional and multi-objective model. In Reference [38], a greedy algorithm is applied to the optimization. The proposed greedy algorithm has good performance with low computational complexity and robustness to solve the uncertainty of PMU placement budget. This performance makes the greedy algorithm attractive in typical scenarios of phased PMU placement because the performance is robust to changes in the PMU budget. Reference [39] develops an effective exponential binary particle swarm optimization algorithm to obtain multiple solutions to OPP. An exponential inertia weighting factor is introduced by the proposed algorithm to improve the group's searchability. In order to combine the previous positions of the particles, two innovative equations are presented to update the particle position. In addition, two useful filtering techniques are applied to converge reliably. Reference [40] proposes a biogeography-based optimization algorithm to solve the OPP problem. This proposed algorithm is suitable to solve the multi-objective optimal PMU placement problem for the full observability. In Reference [41], a backtracking search algorithm is applied to the OPP problem. Selection operation, variation operation and crossover operation of backtracking search algorithm are different from those of other algorithms. The backtracking search algorithm can create more effective individuals in each generation. It controls the magnitude of the search direction in a balanced way that is required for global and local searches. Reference [42] proposes a practical multi-stage simulated annealing algorithm for the optimization of PMU placement. The proposed OPP method can also solve the problem of PMU channel limits. In order to control uphill and downhill motion, the multi-stage simulated annealing algorithm applies multiple stages in the optimization process, which can encourage to converge to the OPP more quickly than classical simulated annealing. In this paper, a new OPP method for a distribution network is proposed, which considers cost and state estimation accuracy. The main contributions are:  
(1) Based on pre-configuration and existing measurements, a network compression method is proposed, which can reduce the candidate locations of the PMUs and improve the network measurement redundancy. Additionally, a hybrid state estimator is applied, which can make full use of supervisory control and data acquisition (SCADA) and PMU measurements to improve state estimation accuracy.