Robust Data-Driven Transmission-Line Parameter Estimation for Reliable and Sustainable Smart Grid Operation

Accurate transmission-line parameters are essential for reliable, efficient, and sustainable smart grid operation, especially under increasing renewable-energy integration and data-driven grid management. However, line aging, temperature variations, and measurement outliers may cause significant deviations between actual and nominal grid models, thereby degrading the state estimation, power-flow analysis, and operational security assessment. To address these challenges, this paper proposes a robust transmission-line parameter estimation method based on a variable-projection framework. The proposed framework decomposes the original high-dimensional, strongly coupled, and non-convex joint estimation problem into two subproblems associated with line-parameter identification and operating-state calibration. An iteratively reweighted least-squares algorithm based on the Huber M-estimator is introduced to dynamically adjust measurement weights and suppress the influence of outliers. The preconditioned conjugate-gradient method is further employed to avoid the explicit inversion of large-scale normal matrices. Simulations on the IEEE 118-bus system demonstrate that the proposed method achieves a higher parameter-estimation accuracy and stronger robustness than conventional weighted least-squares and joint state-parameter estimation methods. In the base case, the proposed method reduces the RMSRE of line reactance to 0.0794%, compared with 0.1558% for WLS and 0.1126% for JSE. Under the representative 5% gross-error case, the proposed method maintains lower RMSREs of 0.9772%, 0.0875%, and 5.8536% for $R_l$, $X_l$, and $B_{sh}$, respectively. Further sensitivity tests under contamination ratios from 1% to 20%, outlier magnitude factors from 1.5 to 5.0, and different outlier-location patterns confirm that the proposed method maintains a more stable estimation accuracy than WLS, conventional JSE, and Huber-JSE without VPM under diverse bad-data conditions. In downstream operational evaluations, it reduces the branch active-power flow RMSE from 1.6842 MW to 0.7215 MW, voltage-magnitude RMSE from 0.00482 p.u. to 0.00216 p.u., and active-power-loss error from 2.4368% to 0.9327% compared with WLS. These quantitative results indicate that the proposed approach can improve the grid model accuracy under imperfect measurements, thereby supporting reliable and sustainable smart-grid operation.