The following pages depict the evolution of a simulated
failure of the Eastern Interconnect, one of three large-scale
transmission grids in the United States, with tens of thousands buses
(nodes) and lines (arcs). The cascade is started by disabling
several major lines in a simulated "contingency".
We evaluate a cascade
according to three criteria:
the yield, which is the percentage of
total demand still satisfied after the grid becomes stable
the time taken until the grid
becomes stable. We measure time in
'rounds'. A 'round' should be long enough for control actions,
such as load shedding, to be applied. Typically, around would be on the
order of several minutes
the number of lines that become
outaged during the cascade.
We study two cases of the
cascade. In one case the cascade is uncontrolled, that is to say,
no action is taken and the cascade is allowed to run its course. In the
second case the cascade is governed by an affine, adaptive
load-shedding control. The control is constrained
in two ways:
demand can only be shed in
rounds 1 - 10 of the cascade, using time-dependent affine scaling rules
(see references below).
if, at the end of the 20th
some lines are still overloaded, then an 'emergency' load shedding is
carried out so as to remove all overloads.
material is found in this report (a short version, here).
work was funded by DOE grant DE-SC000267.
The uncontrolled cascade becomes stable in the 25th round with a yield
of approximately 60% and 5559 outaged lines. The control
we consider in these pages is approximately optimal subject to the
above constraints. It sheds load in rounds 1 and 4 only; it achieves stability at
the 4th round with a yield of approximately
75% and 11 outaged lines.
The images shown display the 737 most significant buses, and the lines
connecting them. The lines are rendered using the following color
green: line is
shades of red
and yellow: line is progressively more overloaded
line is outaged
blue: line was
disabled in the initial contingency