bv_cvxbook_extra_exercises

# n with variables rn 172 radiation treatment planning

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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 j j 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: 2 pin = pout + α(Lj /Rj )(pout )2 , j j j j = 1, . . . , m, where Lj &gt; 0 is the length of transmission line j , Rj &gt; 0 is the radius of the conductors on line j , and α &gt; 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 2 conductor radius: pin ≤ σRj , j = 1, . . . , m, where σ &gt; 0 is a constant. j Generators are attached to nodes i = 1, . . . , k , and loads are a...
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