Hung D. Nguyen

Parikshit Pareek, Hung D. Nguyen

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration as well as load uncertainties, while requiring much less number of samples and elapsed time.

Parikshit Pareek, Chuan Wang, Hung D. Nguyen

In this work, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on the Gaussian Process (GP) learning to understand the power system behavior under uncertainty for better operational decisions. The technique can provide "semi-explicit" power flow solutions by implementing the learning and testing steps which map control variables to inputs. The proposed NP-PLF leverages upon GP upper confidence bound (GP-UCB) sampling algorithm. The salient features of this NP-PLF method are: i) applicable for power flow problem having power injection uncertainty with an unknown class of distribution; ii) providing probabilistic learning bound (PLB) which further provides control over the error and convergence; iii) capable of handling intermittent distributed generation as well as load uncertainties, and iv) applicable to both balanced and unbalanced power flow with different type and size of power systems. The simulation results performed on the IEEE 30-bus and IEEE 118-bus system show that the proposed method can learn the voltage function over the power injection subspace using a small number of training samples. Further, the testing with different input uncertainty distributions indicates that complete statistical information can be obtained for the probabilistic load flow problem with average percentage relative error of order $10^{-3}$\% on 50000 test points.

Chao Zhai, Hung D. Nguyen

This paper introduces a novel framework to construct the region of attraction (ROA) of a power system centered around a stable equilibrium by using stable state trajectories of system dynamics. Most existing works on estimating ROA rely on analytical Lyapunov functions, which are subject to two limitations: the analytic Lyapunov functions may not be always readily available, and the resulting ROA may be overly conservative. This work overcomes these two limitations by leveraging the converse Lyapunov theorem in control theory to eliminate the need of an analytic Lyapunov function and learning the unknown Lyapunov function with the Gaussian Process (GP) approach. In addition, a Gaussian Process Upper Confidence Bound (GP-UCB) based sampling algorithm is designed to reconcile the trade-off between the exploitation for enlarging the ROA and the exploration for reducing the uncertainty of sampling region. Within the constructed ROA, it is guaranteed in probability that the system state will converge to the stable equilibrium with a confidence level. Numerical simulations are also conducted to validate the assessment approach for the ROA of the single machine infinite bus system and the New England $39$-bus system. Numerical results demonstrate that our approach can significantly enlarge the estimated ROA compared to that of the analytic Lyapunov counterpart.

Hung D. Nguyen, Konstantin Turitsyn

High levels of penetration of distributed generation and aggressive reactive power compensation may result in the reversal of power flows in future distribution grids. The voltage stability of these operating conditions may be very different from the more traditional power consumption regime. This paper focused on demonstration of multistability phenomenon in radial distribution systems with reversed power flow, where multiple stable equilibria co-exist at the given set of parameters. The system may experience transitions between different equilibria after being subjected to disturbances such as short-term losses of distributed generation or transient faults. Convergence to an undesirable equilibrium places the system in an emergency or \textit{in extremis} state. Traditional emergency control schemes are not capable of restoring the system if it gets entrapped in one of the low voltage equilibria. Moreover, undervoltage load shedding may have a reverse action on the system and can induce voltage collapse. We propose a novel pulse emergency control strategy that restores the system to the normal state without any interruption of power delivery. The results are validated with dynamic simulations of IEEE $13$-bus feeder performed with SystemModeler software. The dynamic models can be also used for characterization of the solution branches via a novel approach so-called the admittance homotopy power flow method.

Hung D. Nguyen, Konstantin Turitsyn

Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical "robust stability" criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of Robust Stability Assessment (RSA) that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies.