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Unformatted text preview: i = 1, . . . , k .
(a) Minimum total cost of generation. Formulate the problem of choosing generator and edge input
and output powers, so as to minimize the total cost of generation, as a convex optimization
problem. (All other quantities described above are known.) Be sure to explain any additional
variables or terms you introduce, and to justify any transformations you make.
Hint : You may ﬁnd the matrices A+ = (A)+ and A− = (−A)+ helpful in expressing the power
(b) Marginal cost of power at load nodes. The (marginal) cost of power at node i, for i = k +
1, . . . , n, is the partial derivative of the minimum total power generation cost, with respect to
varying the load power li . (We will simply assume these partial derivatives exist.) Explain
how to ﬁnd the marginal cost of power at node i, from your formulation in part (a).
(c) Optimal sizing of lines. Now suppose that you can optimize over generator powers, edge input
and output powers (as above), and the power line radii Rj , j = 1, . . . , m. T...
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