Increasing renewable energy increases uncertainty in energy systems. As a consequence, generator-side control for frequency regulation, impacted by the slow reaction of generators to meet urgent needs, may no longer suffice. With increasing integration of smart appliances which are able to sense, communicate and control, load-side control can help alleviate the aforementioned problem as it reacts fast and helps to localize disturbances. However, almost all existing methods for optimal load-side control require full information control coverage in the system. Framing the problem as an optimization problem and applying saddle-point dynamics, we obtain a control law that rebalances power and asymptotically stabilizes frequency after a disturbance. We generalize previous work to design a controller which only requires partial control coverage over all nodes, yet still achieves secondary frequency control. We verify these results via simulation.

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We propose a novel framework of using a parsimonious statistical model, known as mixture of Gaussian trees, for modeling the possibly multimodal minority class to solve the problem of imbalanced time-series classification. By exploiting the fact that close-by time points are highly correlated due to smoothness of the time-series, our model significantly reduces the number of covariance parameters to be estimated from O(d(2)) to O(Ld), where L is the number of mixture components and d is the dimensionality. Thus, our model is particularly effective for modeling high-dimensional time-series with limited number of instances in the minority positive class. In addition, the computational complexity for learning the model is only of the order O(Ln+d(2)) where n+ is the number of positively labeled samples. We conduct extensive classification experiments based on several well-known time-series data sets (both single- and multimodal) by first randomly generating synthetic instances from our learned mixture model to correct the imbalance. We then compare our results with several state-of-the-art oversampling techniques and the results demonstrate that when our proposed model is used in oversampling, the same support vector machines classifier achieves much better classification accuracy across the range of data sets. In fact, the proposed method achieves the best average performance 30 times out of 36 multimodal data sets according to the F-value metric. Our results are also highly competitive compared with nonoversampling-based classifiers for dealing with imbalanced time-series data sets.