Abstract-The pattern recognition approach to transient stability analysis (TSA) has been presented as a promising tool for online application. This paper applies a recently introduced learning-based nonlinear classifier, the support vector machine (SVM), showing its suitability for TSA. It can be seen as a different approach to cope with the problem of high dimensionality. The high dimensionality of power systems has led to the development and implementation of feature selection techniques to make the application feasible in practice. SVMs' theoretical motivation is conceptually explained and they are tested with a 2684-bus Brazilian system. Aspects of model adequacy, training time, classification accuracy, and dimensionality reduction are discussed and compared to stability classifications provided by multilayer perceptrons.Index Terms-Feature selection, neural networks, support vector machine, transient stability analysis.

Expanding an electrical transmission network requires heavy investments that need to be carefully planned, often at a regional or national level. We study relevant theoretical and practical aspects of transmission expansion planning, set as a bilinear programming problem with mixed 0-1 variables. We show that the problem is NP-hard and that, unlike the so-called Network Design Problem, a transmission network may become more efficient after cutting-off some of its circuits. For this reason, we introduce a new model that, rather than just adding capacity to the existing network, also allows for the network to be re-designed when it is expanded. We then turn into different reformulations of the problem, that replace the bilinear constraints by using a "big-M" approach. We show that computing the minimal values for the "big-M" coefficients involves finding the shortest and longest paths between two buses. We assess our theoretical results by making a thorough computational study on real electrical networks. The comparison of various models and reformulations shows that our new model, allowing for re-design, can lead to sensible cost reductions.

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