Classification trees for complex synchrophasor data

Classification and regression trees (CART) has been used for various applications in power systems. In most of these applications, phasor data obtained from phasor measurement units are used for building the decision tree. However, the splits in CART are based on a single attribute or a combination of variables chosen by CART itself rather than the user. But as phasor measurement unit data are complex numbers, both the attributes - real and imaginary - should be considered simultaneously for making critical decisions. For example, changing the reference bus in situations where the split is only on the real or imaginary part of a complex voltage (or current) measurement can cause the performance of the tree to degrade significantly. An algorithm is proposed in this article to allow splits on complex synchrophasor data. The methodology is implemented on two systems: a detailed model of the California Power System, where it is used for developing an adaptive protection scheme, and the IEEE 118-bus system, where it is used to classify dynamic events based on trajectories of voltage measurements obtained from phasor measurement units. MATLAB® (The MathWorks, Natick, Massachusetts, USA) implementation of classification and regression trees (classregtree.m) has been used for performing both analyses.