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Kaci, A., Kamwa, I., Dessaint, L.-A., Guillon, S..  2014.  Phase angles as predictors of network dynamic security limits and further implications. PES General Meeting | Conference Exposition, 2014 IEEE. :1-6.

In the United States, the number of Phasor Measurement Units (PMU) will increase from 166 networked devices in 2010 to 1043 in 2014. According to the Department of Energy, they are being installed in order to “evaluate and visualize reliability margin (which describes how close the system is to the edge of its stability boundary).” However, there is still a lot of debate in academia and industry around the usefulness of phase angles as unambiguous predictors of dynamic stability. In this paper, using 4-year of actual data from Hydro-Québec EMS, it is shown that phase angles enable satisfactory predictions of power transfer and dynamic security margins across critical interface using random forest models, with both explanation level and R-squares accuracy exceeding 99%. A generalized linear model (GLM) is next implemented to predict phase angles from day-ahead to hour-ahead time frames, using historical phase angles values and load forecast. Combining GLM based angles forecast with random forest mapping of phase angles to power transfers result in a new data-driven approach for dynamic security monitoring.

Kaci, A., Kamwa, I., Dessaint, L.A., Guillon, S..  2014.  Synchrophasor Data Baselining and Mining for Online Monitoring of Dynamic Security Limits. Power Systems, IEEE Transactions on. 29:2681-2695.

When the system is in normal state, actual SCADA measurements of power transfers across critical interfaces are continuously compared with limits determined offline and stored in look-up tables or nomograms in order to assess whether the network is secure or insecure and inform the dispatcher to take preventive action in the latter case. However, synchrophasors could change this paradigm by enabling new features, the phase-angle differences, which are well-known measures of system stress, with the added potential to increase system visibility. The paper develops a systematic approach to baseline the phase-angles versus actual transfer limits across system interfaces and enable synchrophasor-based situational awareness (SBSA). Statistical methods are first used to determine seasonal exceedance levels of angle shifts that can allow real-time scoring and detection of atypical conditions. Next, key buses suitable for SBSA are identified using correlation and partitioning around medoid (PAM) clustering. It is shown that angle shifts of this subset of 15% of the network backbone buses can be effectively used as features in ensemble decision tree-based forecasting of seasonal security margins across critical interfaces.