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System instability does not occur often in practice and thus the historical data for training a machine learning method has to address the imbalanced and multi-modal probabilistic distribution in the probabilistic transient stability assessment (PTSA). This letter proposes a transient stability index (TSI) density-based weighting scheme and feature-TSI similarity regularization to address that, yielding debiased uncertainty quantification for PTSA in the presence of uncertain wind generations and loads. Numerical results on the IEEE 39-bus and Illinois 200-bus power systems demonstrate the significantly improved performance of the proposed method over other state-of-the-art machine learning approaches in PTSA. 

This paper proposes a deep sigma point processes (DSPP)-assisted chance-constrained power system transient stability preventive control method to deal with uncertain renewable energy and loads-induced stability risk. The traditional transient stability-constrained preventive control is reformulated as a chance-constrained optimization problem. To deal with the computational bottleneck of the time-domain simulation-based probabilistic transient stability assessment, the DSPP is developed. DSPP is a parametric Bayesian approach that allows us to predict system transient stability with high computational efficiency while accurately quantifying the confidence intervals of the predictions that can be used to inform system instability risk. To this end, with a given preset confidence probability, we embed DSPP into the primal dual interior point method to help solve the chance-constrained preventive control problem, where the corresponding Jacobian and Hessian matrices are derived. Comparison results with other existing methods show that the proposed method can significantly speed up preventive control while maintaining high accuracy and convergence. 

This letter proposes a data-driven inertia estimator for inverter-based resources (IBRs) with grid-forming control. It is able to track both constant and time-varying inertia. By utilizing the Thevenin equivalent, the virtual frequency inside IBRs is first estimated with only its terminal voltage and current phasor measurements. The virtual frequency and the measurements are then used together to derive the state-space swing equation model. Then, an enhanced adaptive Unscented Kalman filter (EAUKF) is developed to estimate IBR inertia. Numerical results on the modified IEEE 39-bus power system demonstrate that the proposed inertia estimator remarkably outperforms the existing state-of-art methods both in tracking speed and accuracy. 

The increasing uncertainties caused by the high-penetration of stochastic renewable generation resources and flexible loads pose challenges to the power system voltage stability. To address this issue, this paper proposes a probabilistic transferable deep kernel emulator (DKE) to extract the hidden relationship between uncertain sources, i.e., wind generations and loads, and load margin for probabilistic load margin assessment (PLMA). This emulator extends the Gaussian process kernel to the deep neural network (DNN) structure and thus gains the advantages of DNN in dealing with high-dimension uncertain inputs and the uncertainty quantification capability of the Gaussian process. A transfer learning framework is also developed to reduce the invariant representation space distance between the old topology and new one. It allows the DKE to be quickly fine tuned with only a few samples under the new topology. Numerical results carried out on the modified IEEE 39-bus and 118-bus power systems demonstrate the strong robustness of the proposed transferable DKE to uncertain wind and load power as well as topology changes while maintaining high accuracy. 

The increasing uncertainties caused by the high-penetration of stochastic renewable generation resources poses a significant threat to the power system voltage stability. To address this issue, this paper proposes a probabilistic deep kernel learning enabled surrogate model to extract the hidden relationship between uncertain sources, i.e., wind power and loads, and load margin for probabilistic load margin assessment (PLMA). Unlike other deep learning approaches, a kernel SHAP provides the sensitivity analysis as well as interpretability of the inputs to outputs influences. This allows identifying the critical factors that affect load margin so that corrective control can be initiated for stability enhancement. Numerical results carried out on the IEEE 118-bus power system demonstrate the accuracy and efficiency of the proposed data-driven PLMA scheme.