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Unformatted text preview: hese must lie
min
max
min > 0), and we must respect a total volume
between given limits, Rj ∈ [Rj , Rj ] (Rj
constraint on the lines,
m j =1 2
Lj Rj ≤ V max . Formulate the problem of choosing generator and edge input and output powers, as well as
power line radii, so as to minimize the total cost of generation, as a convex optimization
problem. (Again, explain anything that is not obvious.)
(d) Numerical example. Using the data given in ptrans_loss_data.m, ﬁnd the minimum total
generation cost and the marginal cost of power at nodes k + 1, . . . , n, for the case described
in parts (a) and (b) (i.e., using the ﬁxed given radii Rj ), and also for the case described in
part (c), where you are allowed to change the transmission line radii, keeping the same total
volume as the original lines. For the generator costs, use the quadratic functions
2
φ i ( g i ) = a i g i + bi g i , i = 1, . . . , k, where a, b ∈ Rk . (These are given in the data ﬁle.)
+
Remark : In the mﬁle, we give you a load vector l ∈ Rn−k . For consistency, the ith entry of
this vector corresponds to the load at node k + i.
16.8 Utility/power tradeoﬀ in a wireless network. In this problem w...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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