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In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to minimize the required computational effort, making it applicable to the real-time environment. One main advantage of the proposed method is model independence, i.e., it is independent of the network model and the dynamic model of generators. Among various applications of the estimated matrix, detecting and locating unexpected network topology change is illustrated in details. Simulation studies have shown that the proposed measurement-based method can provide an accurate and efficient estimation of the dynamic system state matrix under the occurrence of unexpected topology change. Besides, various implementation conditions are tested to show that the proposed method can provide accurate approximation despite measurement noise, missing PMUs, and the implementation of higher-order generator models with control devices.Index Terms-Dynamic system state matrix, Ornstein-Uhlenbeck process, phasor measurement units, topology change.

Considering the increasing penetration of renewable energy sources and electrical vehicles in utility distribution feeders, it is imperative to study the impacts of the resulting increasing uncertainty on the delivery capability of a distribution network. In this paper, probabilistic available delivery capability (ADC) is formulated for a general distribution network integrating various RES and load variations. To reduce the computational efforts by using conventional Monte Carlo simulations, we develop and employ a computationally efficient method to assess the probabilistic ADC, which combines the up-to-date sparse polynomial chaos expansion (PCE) and the continuation method. Particularly, the proposed method is able to handle a large number of correlated random inputs with different marginal distributions. Numerical examples in the IEEE 13 and IEEE 123 node test feeders are presented, showing that the proposed method can achieve accuracy and efficiency simultaneously. Numerical results also demonstrate that the randomness brought about by the RES and loads indeed leads to a reduction in the delivery capability of a distribution network.

The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this paper, a novel data-driven sparse polynomial chaos expansion (DDSPCE) method is proposed for estimating the probabilistic characteristics (e.g., mean, variance, probability distribution) of probabilistic TTC (PTTC). Specifically, the proposed method, requiring no pre-assumed probabilistic distributions of random inputs, exploits data sets directly in estimating the PTTC. Besides, a sparse scheme is integrated to improve the computational efficiency. Numerical studies on the modified IEEE 118-bus system demonstrate that the proposed DDSPCE method can achieve accurate estimation for the probabilistic characteristics of PTTC with a high efficiency. Moreover, numerical results reveal the great significance of incorporating discrete random inputs in PTTC and ATC assessment, which nevertheless was not given sufficient attention.Index Terms-Available transfer capability (ATC), discrete random variables, polynomial chaos expansion (PCE), total transfer capability (TTC).