IEEE Power & Energy Magazine - May/June 2018 - 23
To study the whole group of household demand distributions,
we will first compute the differences in electricity consumption
patterns between pairs of households.
figure 5. The 2-D illustration for multiple events on 30 September 2012 recorded in the Great Britain networks. Black,
blue, cyan, and purple dots represent the normal data, generation dip, loss of load, and islanding event, respectively.
Generation Dip Event
49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4
Q Load Event
We illustrate the postdisturbance voltage trajectory during
an east-West interconnector 500-mW export trip test event
in the irish network to further demonstrate pca as a powerful dimension reduction tool for visualization.
traditionally, the system operator will monitor the voltage traces from various locations. However, it is difficult
to manage hundreds of pmus through this traditional
approach. in addition, the interaction among multiple voltage variables embedded in multiple locations is unknown.
By applying pca on the pmu data collected from 20
locations across the network, we found that three principal components are enough to monitor voltages across the
entire network. the three selected principal components are
capable of explaining 98% of the data variance during the
Case 2: Visualizing Postdisturbance
Voltage Data from Multiple Locations
in the Irish Networks
once an islanding event is detected in the system, the system operator will try to find out where it is located. We can
accomplish this task by a simple contribution plot to visualize the contribution of individual frequency variables to
the predefined pca statistics. if the contribution of a particular frequency variable toward the Q statistic is large, an
islanding site can be identified. figure 6 illustrates variable 5
(representing pmu installed in the orkney island, where the
islanding occurred), which dominates the contribution to Q
statistic during the 9 min when it happened from 15:03:30 to
15:12:30. Both systems synchronized at 15:12:30.
limit. the normal data from 30 september 2012 fall in this
category. in figure 5, we have also plotted loss of load, generation dip, and islanding events from two locations. How
should we interpret the patterns in this figure? frequency is
the universal parameter of the synchronous power grid, and
it possesses simple and elegant characteristics. that is, the
frequency data points from two locations are approximately
aligned with the y . x line. the first principal component
t 1, which captures 99% of the total variance of the frequency
data, is thus following this direction. in other words, we can
use only one principal component to represent all frequency
variables recorded across the grid.
in figure 5, we also notice that the generation dip and
loss of load events are in line with the first principal component direction, but outside the red box, with the loss of load
sitting at the higher end and the generation dip sitting at the
lower end. When the loss of load and generation dip events
occurred in the system, the frequency variables may significantly deviate from the nominal value (50 Hz in this case)
but not against each other significantly. However, for the
islanding event, it is more likely that the islanded frequency
deviates significantly from the rest of the system frequency
and, thus, is not in line with the principal component direction. that is to say, the islanding data has its projection to the
orthogonal direction to t 1 (represented by the Q axis) and is
outside the red box. in comparison to the traditional timeseries graph, the relative relationship of multiple events in
comparison to normal operation conditions are much more
straightforward, as illustrated in figure 5.
figure 6. A contribution plot to the Q statistic for case 1.
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