This letter proposes a new robust data-driven sparse voltage sensitivity estimation approach for large-scale distribution systems with PVs. It has a high statistical efficiency to mitigate the impacts of PV stochasticity and unknown measurement noise under various system operating conditions. A new adaptively-weighted l1 sparsity-promoting regularization is developed, exploiting the temporal characteristic of time-varying sensitivities for better accuracy. The l2 regularization is used to mitigate collinearity impacts. The Huber loss function and a concomitant scale estimate are adopted to mitigate the impacts of unknown and non-Gaussian noise. These techniques are implemented in a fast recursive parallel computing framework. The proposed estimator is tested by quasi-static time series simulations of a large three-phase unbalanced system with PVs and various discrete time-delayed control devices. Results validate the superior robustness and efficiency of the proposed estimator over existing alternatives.
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