Realizing complete observability in the three-phase distribution system remains a challenge that hinders the implementation of classic state estimation algorithms. In this paper, a new method, called the pruned physics-aware neural network (P2N2), is developed to improve the voltage estimation accuracy in the distribution system. The method relies on the physical grid topology, which is used to design the connections between different hidden layers of a neural network model. To verify the proposed method, a numerical simulation based on one- year smart meter data of load consumptions for three-phase power flow is developed to generate the measurement and voltage state data. The IEEE 123-node system is selected as the test network to benchmark the proposed algorithm against the classic weighted least squares (WLS). Numerical results show that P2N2 outperforms WLS in terms of data redundancy and estimation accuracy.

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