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Accurate quantification of uncertainty in solar photovoltaic (PV) generation forecasts is imperative for the efficient and reliable operation of the power grid. In this paper, a data-driven non-parametric probabilistic method based on the Naïve Bayes (NB) classification algorithm and Dempster–Shafer theory (DST) of evidence is proposed for day-ahead probabilistic PV power forecasting. This NB-DST method extends traditional deterministic solar PV forecasting methods by quantifying the uncertainty of their forecasts by estimating the cumulative distribution functions (CDFs) of their forecast errors and forecast variables. The statistical performance of this method is compared with the analog ensemble method and the persistence ensemble method under three different weather conditions using real-world data. The study results reveal that the proposed NB-DST method coupled with an artificial neural network model outperforms the other methods in that its estimated CDFs have lower spread, higher reliability, and sharper probabilistic forecasts with better accuracy. 

The Bayesian approach has been used for the dynamic state estimation (DSE) of a power system. However, due to the complexity of noise resources, it is difficult to quantify measurement and process noise using probability density functions (PDFs). To overcome the difficulty, the authors of this article propose a modified eigen-decomposition-based interval analysis (MEDIA) method, which employs bounds instead of PDFs to quantify the noise, and uses the eigen decomposition method to reduce the negative impact of the overestimation problem. Using the simulation data generated from IEEE 16-machine and IEEE 10-machine systems, it is shown that the proposed MEDIA method can estimate the hard boundaries of dynamic states in real time. Comparison with the forward-backward propagation method and the extended set-membership filter also shows that the proposed MEDIA method performs better by providing narrower boundaries in the DSE. 

The negative impact of measurement time skew on the static state estimation of the power grid has been exacerbated by increasing variation of system operating conditions. To mitigate the time skew problem, this paper proposes a regression model forecasting (RMF) method to forecast the time-skewed measurements, along with a confidence interval estimation (CIE) method to determine the weights associated with the forecasted measurements. The proposed RMF-CIE method is compared against several benchmark methods through Monte-Carlo simulation on the IEEE 16-machine, 68-bus model. It was observed that the proposed RMF-CIE consistently achieved more accurate state estimation on average. In addition, it was found that its estimation accuracy increases with the decrease of the skew time and variation levels. 

To guide the selection of probabilistic solar power forecasting methods for day-ahead power grid operations, the performance of four methods, i.e., Bayesian model averaging (BMA), Analog ensemble (AnEn), ensemble learning method (ELM), and persistence ensemble (PerEn) is compared in this paper. A real-world hourly solar generation dataset from a rooftop solar plant is used to train and validate the methods under clear, partially cloudy, and overcast weather conditions. Comparisons have been made on a one-year testing set using popular performance metrics for probabilistic forecasts. It is found that the ELM method outperforms other methods by offering better reliability, higher resolution, and narrower prediction interval width under all weather conditions with a slight compromise in accuracy. The BMA method performs well under overcast and partially cloudy weather conditions, although it is outperformed by the ELM method under clear conditions. 

This paper reports two extensions to the authors’ recent work on the design of an optimally robust topology detector for a power transmission circuit with uncertain loads. Such a detector was implemented as a linear discriminator for the IEEE 9-bus system to identify, with a sub-millisecond latency, the intact circuit, or any single open-circuited line, using only the phasor measurements at the generators’ terminals. The first extension aims to replace the previously required bounded uncertain load set by a load distribution that permits rarer measurement outliers. This problem is formulated and solved as a support vector classifier. The second extension explores the solvability of a linear discriminator for topology identification for larger power systems under a bounded uncertain load set. A measure of adequacy of the involved measurement network is introduced, under which a sensor placement problem is formulated for the addition of a minimum number of phasor measurement units to meet a prescribed level of topology identifiability. In this case, sensor placement, detector design, and detector performance and robustness are demonstrated on the IEEE 68-bus system. 

Observability and detectability analyses are often used to guide the measurement setup and select the estimation models used in dynamic state estimation (DSE). Yet, marginally observable states of a synchronous machine prevent the direct application of conventional observability and detectability analyses in determining the existence of a DSE observer. To address this issue, the authors propose to identify the marginally observable states and their associate eigenvalues by finding the smallest perturbation matrices that make the system unobservable. The proposed method extends the observability and detectability analyses to marginally observable estimation models, often encountered in the DSE of a synchronous machine. The effectiveness and application of the proposed method are illustrated on the IEEE 10-machine 39-bus system, verified using the unscented Kalman filter and the extended Kalman filter, and compared with conventional methods. The proposed analysis method can be applied to guide the selection of estimation models and measurements to determine the existence of a DSE observer in power-system planning. 

The state estimation (SE) has been widely used in power system control centers to optimally estimate the states of the power grid in real time. Using different objective functions, many SE algorithms have been proposed to filter out measurement noise in different ways. In this paper, three widely-used SE algorithms, i.e., the weighted least squares (WLS), least absolute value (LAV), and projection statistics (PS) based algorithms, are compared in their estimation accuracy and computation time. The comparison was made using the simulation data generated from the IEEE 14-bus system and IEEE 118-bus system through the Monte-Carlo method. It is found that when the measurement noise is reasonably small and follows the independent Gaussian distribution, the WLS algorithm has the best accuracy and shortest computation time. When some measurements at leverage points were compromised by outliers, the PS based algorithm is the most robust among the three methods. The study results can be used to assist control centers in choosing the right SE algorithm based on the features of the measurement noise and setup.