###### Abstract  
State estimation (SE) is an important energy management system application for power system operations. Linear state estimation (LSE) is a variant of SE based on linear relationships between state variables and measurements. LSE estimates system state variables, including bus voltage magnitudes and angles in an electric power transmission network, using a network model derived from the topology processor and measurements. Phasor measurement units (PMUs) enable the implementation of LSE by providing synchronized high-speed measurements. However, as the size of the power system increases, the computational overhead of the state-of-the-art (SOTA) LSE grows exponentially, where the practical implementation of LSE is challenged. This paper presents a distributed linear state estimation (D-LSE) at the substation and area levels using a hierarchical transmission network topology processor (H-TNTP). The proposed substation-level and area-level D-LSE can efficiently and accurately estimate system state variables at the PMU rate, thus enhancing the estimation reliability and efficiency of modern power systems. Network-level LSE has been integrated with H-TNTP based on PMU measurements, thus enhancing the SOTA LSE and providing redundancy to substation-level and area-level D-LSE. The implementations of D-LSE and enhanced LSE have been investigated for two benchmark power systems, a modified two-area four-machine power system and the IEEE 68 bus power system, on a real-time digital simulator. The typical results indicate that the proposed multilevel D-LSE is efficient, resilient, and robust for topology changes, bad data, and noisy measurements compared to the SOTA LSE. distributed architecture; linear state estimation; synchrophasor measurements; topology processor +
Footnote †: journal: Medical  
an efficient approach for state estimation is favorable over the traditional state estimation in the modern power system. State-of-the-art (SOTA) linear state estimation (LSE) has improved the estimation capabilities [11], where efficient measurements are used to establish a linear relationship with the state variables. LSE can accurately estimate bus node voltage phasors utilizing measurements such as available the noisy voltage phasor and current phasor measurements. LSE can be implemented solely based on the phasor measurement units (PMUs) [12] and the network model. The network model of the SOTA LSE is derived from the SOTA transmission network topology processing (TNTP) approach, which is based on the asynchronous supervisory control and data acquisition (SCADA) monitoring of relay signals (SMRS), where the reliability can be challenged [13; 14] and only updates the topology from 2 s to 5 s [15]. Furthermore, the SOTA LSE is not scalable for large power systems, because computation time increases rapidly with the size of the network. The power system transmission network is a large, geographically distributed network. Thus, a distributed architecture is favorable to ensure the efficient process of the LSE with PMU measurements. A comprehensive analysis of the state estimation has been conducted in [16], where shortcomings of the literature and existing operational state estimations have been identified, including accuracy and security. In [17], a robust hybrid state estimator was built against the non-Gaussian noise in PMU measurements; the filtration process utilized SCADA-based state estimation, which still limits the efficiency achieved by the PMU-only state estimation. Distributed state estimation architectures for multiarea power systems have been proposed in [8; 18; 19; 20]. The different architectures utilize the least squares estimation techniques and information exchange between the control areas. Although distributed architecture improves computational efficiency, the approaches are based on traditional iterative estimation methods, where the efficiency is compromised. A semidefinite programming formulation based on distributed state estimation utilizing synchrophasor measurements was studied in [21].