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Facing stochastic variations of the loads due to an increasing penetration of renewable energy generation, online decision making under uncertainty in modern power systems is capturing power researchers' attention in recent years. To address this issue while achieving a good balance between system security and economic objectives, we propose a surrogate-enhanced scheme under a joint chance-constrained (JCC) optimal power-flow (OPF) framework. Starting from a stochastic-sampling procedure, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo (MC) method, we propose to use a polynomial-chaos-based surrogate that allows us to efficiently evaluate the power-system model at non-Gaussian distributed sampled values with a negligible computing cost. Learning from the MC simulated samples, we further proposed a hybrid adaptive approach to overcome the conservativeness of the JCC-OPF by utilizing correlation of the system states, which is ignored in the traditional Boole's inequality. The simulations conducted on the modified Illinois test system demonstrate the excellent performance of the proposed method. 

The observability analysis of a time-varying nonlinear dynamic model has recently attracted the attention of power engineers due to its vital role in power system dynamic state estimation. Generally speaking, due to the nonlinearity of the power system dynamic model, the traditional derivative-based observability analysis approaches either rely on the linear approximation to simplify the problem or require a complicated derivation procedure that ignores the uncertainties of the dynamic system model and of the observations represented by stochastic noises. Facing this challenge, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only brings a low complexity, but also enables us to quantify the degree of observability by considering the stochastic nature of the dynamic systems. The excellent performances of the proposed method is demonstrated using simulations of a decentralized dynamic state estimation performed on a power system using a synchronous generator model with IEEE-DC1A exciter and a TGOV1 turbine-governor. 

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges, this paper proposes a cost-effective, nonparametric method to quantity the impact of uncertain power injections on the load margins. First, we propose to generate system uncertain inputs via a novel vine copula due to its capability in simulating complex multivariate highly dependent model inputs. Furthermore, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. The simulations conducted on the IEEE 57-bus system, to which correlated renewable generation are attached, reveal the excellent performance of the proposed method. 

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges, this paper proposes a cost-effective, nonparametric method to quantify the impact of uncertain power injections on the load margins. First, we propose to generate system uncertain inputs via a novel vine copula due to its capability in simulating complex multivariate highly dependent model inputs. Furthermore, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. The simulations conducted on the IEEE 57-bus system, to which correlated renewable generation are attached, reveal the excellent performance of the proposed method. 

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator allows us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method. 

Risk assessment of power system failures induced by low-frequency, high-impact rare events is of paramount importance to power system planners and operators. In this paper, we develop a cost-effective multi-surrogate method based on multifidelity model for assessing risks in probabilistic power-flow analysis under rare events. Specifically, multiple polynomial-chaos-expansion-based surrogate models are constructed to reproduce power system responses to the stochastic changes of the load and the random occurrence of component outages. These surrogates then propagate a large number of samples at negligible computation cost and thus efficiently screen out the samples associated with high-risk rare events. The results generated by the surrogates, however, may be biased for the samples located in the low-probability tail regions that are critical to power system risk assessment. To resolve this issue, the original high-fidelity power system model is adopted to fine-tune the estimation results of low-fidelity surrogates by reevaluating only a small portion of the samples. This multifidelity model approach greatly improves the computational efficiency of the traditional Monte Carlo method used in computing the risk-event probabilities under rare events without sacrificing computational accuracy.