Here we consider consumption of a metabolite as

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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 m-file, 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 trade-off 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.

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