###### Abstract
Both proposed approaches in [21] involve the legacy SE and the PMU-based linear estimation, which increase the computational burden. The incorporation of linear and nonlinear models for state estimation has been investigated in [22]. The system is divided into multiple linear and nonlinear areas, which define the distributed architecture of the study. The procedure is expected to be completed based on sequential flow, where the efficiency achieved from PMU measurement-based LSE in the linear regions is compromised. PMU-based topology derivation and extended LSE implementation were studied in [23], where the test system used the breaker status as a digital input to the PMU. Digital inputs in the PMUs require additional communication network upgrades from relays or remote terminal units (RTUs) to PMUs in the substation; furthermore, the proposed approach is centralized. A phasor data-based state estimator with phase bias correction has been proposed in [24]. This work identifies PMU-available high-voltage substations for building phasor state estimators. Identifying the island topology is critical; although, using SMRS in this study limits the efficiency of the overall procedure. A two-level LSE has been proposed in [25; 26; 27]; the proposal investigates the power system at the substation level and network level. The shortcomings of this approach are that the only redundancy for the substation level is the network level, where the computational overhead is high in larger networks. Furthermore, the study was limited to the ring bus arrangement type (RBA) substations only. The effectiveness of the overall approach can be different based on the type of substation arrangement. A physics-based hierarchical TNTP (H-TNTP) approach based solely on node voltages and branch currents measurements utilizing artificial intelligence algorithms was proposed in [28]. H-TNTP can be used to derive the substation area network-level topologies using current and voltage measurements, which is ideal for a distributed LSE architecture. An efficient H-TNTP can be established by incorporating the synchrophasor network (H-TNTP-PMU), which updates the transmission network topology at every PMU frame. The synchrophasor network typically delivers voltage and current phasor measurements at 30 Hz [29]. Thus, incorporating H-TNTP-PMU will enable LSE execution at every PMUmeasurement. This paper proposes a multilevel distributed LSE (D-LSE) architecture with substation-level and area-level estimation utilizing H-TNTP-PMU. The network level based on the SOTA LSE enhanced with the H-TNTP-PMU has been integrated as the redundancy level for the area level. The proposed approach overcomes the limitations identified in the SOTA LSE and the alternative approaches proposed by other researchers. The D-LSE incorporates the efficient and reliable H-TNTP-PMU as the topology processor, which enables the completion of the overall procedure at the PMU rate. The multilevel redundancy improves the reliability of the D-LSE. Incorporating all typical substation arrangements in the substation level ensures the applicability of the proposed D-LSE. The overview of the proposed D-LSE is shown in Figure 1.  
The main contributions of this paper are the following:  
* A multilevel distributed linear state estimation has been developed based on hierarchical transmission network topology processing. With the developed D-LSE, substation bus voltage phasors can be estimated at the substation level and/or area level. This caters to fast and efficient linear state estimation for large power systems. * The traditional linear state estimation has been enhanced with H-TNTP-PMU to provide a network-level model that is updated with the same measurements used for LSE. This improves the accuracy of the traditional LSE. * The D-LSE and enhancement to the traditional LSE have been illustrated on two benchmark test power systems.