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Unformatted text preview: d as a set of n nodes and
m directed edges (which represent transmission lines), with topology described by the node-edge
incidence matrix A ∈ Rn×m , deﬁned by
Aij = +1 edge j enters node i, −1 edge j leaves node i,
0 otherwise. We let pin ≥ 0 denote the power that ﬂows into the tail of edge j , and pout ≥ 0 the power that
emerges from the head of edge j , for j = 1, . . . , m. Due to transmission losses, the power that ﬂows
into each edge is more than the power that emerges:
pin = pout + α(Lj /Rj )(pout )2 ,
j j = 1, . . . , m, where Lj > 0 is the length of transmission line j , Rj > 0 is the radius of the conductors on line
j , and α > 0 is a constant. (The second term on the righthand side above is the transmission line
power loss.) In addition, each edge has a maximum allowed input power, that also depends on the
conductor radius: pin ≤ σRj , j = 1, . . . , m, where σ > 0 is a constant.
j Generators are attached to nodes i = 1, . . . , k , and loads are a...
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- Fall '13
- The Aeneid