Abstract
This paper proposes to extend the fast-decoupled state estimation formulation to bring its well-known efficiency and benefits to the processing of networks with embedded FACTS devices. The proposed method approaches shunt-, series-, and shunt -series -type devices. The controller parameters are included as new active or reactive state variables, while controlled quantity values are included in the metering scheme of the decoupled approach. From the electrical model adopted for each device, the extended formulation is presented, and a modified fast-decoupled method is devised, seeking to ensure accuracy and impart robustness to the iterative solution. Simulation results conducted throughout the IEEE 30 -bus test system with distinct types of FACTS devices are used to validate and evaluate the performance of the proposed decoupled approaches.

Abstract
The need to improve the flexibility and dynamism of the Electric Power Systems (EPS) has driven the development and integration of new devices. Among these, FACTS controllers are particularly notable for their ability to regulate multiple system variables. Incorporating FACTS into the grid requires integrating their electrical models into the analysis and operational tools of the EPS, ensuring precise monitoring and effective system control. This article presents novel steady-state models for FACTS controllers, specifically designed for decoupled state estimation methods. The framework updates the algorithm decoupled and model decoupled state estimators and introduces the modified algorithm decoupled estimator, which offers enhanced robustness and convergence. These improvements are validated through theoretical analysis and simulations. The methodology introduces new state variables and decoupled nonlinear functions to represent FACTS controllers, enabling seamless integration into decoupled estimation frameworks. The study assesses the effectiveness of bad data processing using the Largest Normalized Residual Test (LNR-Test), ensuring robustness under decoupled FACTS modeling. Simulations on the IEEE 30-bus and IEEE 118-bus test systems include shunt, series, series-shunt, and multiple FACTS controllers, as well as single and multiple bad data. Results demonstrate the accuracy and effectiveness of the decoupled estimators with FACTS controllers and confirm the practical applicability of LNR-Test within the proposed approaches.