Remark the beam pattern matrix in this problem

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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 balance constraints. (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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