Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part I: Theory

Data-driven sparse estimation of distribution factors (DFs) facilitates online power flow sensitivity analysis for secure system operation. However, existing methods are vulnerable to time-varying non-Gaussian PMU measurement noise, bad data, and uncertain renewable energy sources (RESs). Moreover, they lack scalability to large-scale systems. This two-part paper proposes a robust and scalable sparse DF estimation framework considering PMU data quality and RES uncertainty. In this Part I, a novel Adaptive
M
-Lasso estimator with theoretically guaranteed robustness is proposed. It mitigates the impacts of measurement and RES uncertainties to yield accurate dominant DF estimates while promoting sparsity. The key idea is to integrate the robust statistics theory with sparse representation techniques, in particular the Huber loss function, adaptively-weighted
l
₁
regularization, concomitant scale estimate, and pseudo-residuals. Two important robustness properties of this estimator are theoretically proven, i.e., the bounded influence function and the asymptotic consistency of dominant DF estimates given limited samples. The breakdown points of this estimator to measurement and RES uncertainties are derived. Test results validate that the proposed estimator allows accurate estimation without relying on power flow models or massive operating data. It achieves significantly superior robustness over existing methods in multiple scenarios.