The Mathematics of Power Outages
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The power grid in the United States suffers from unpredictable blackouts that affect millions of individuals, but what results in a total blackout rather than a simple power outage is not yet known. Through a Mathematica simulation of the power system, we analyze the power grid in the United States in an attempt to discover what factors influence the incidence of blackouts. By utilizing the sandpile theory and the Barabási-Albert model, we aim to uncover what signs can be identified in a simple power station failure that ultimately lead to a blackout. We find that as the failure threshold for a power station varies, there is a phase transition in blackout size, and in addition to this, we also find that the interconnectedness of the network has an unexpected opposing influence on the size and time elapsed between blackouts.
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