Si here we ignore the energy used to transfer data

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Unformatted text preview: . , n. We let di ≥ 0 denote the demand at node k + i, for i = 1, . . . , n − k . We will consider these loads as given. In this simple model we will neglect all power losses on lines or at nodes. Therefore, power must balance at each node: the total power flowing into the node must equal the sum of the power flowing out of the node. This power balance constraint can be expressed as Ap = −g d , where A ∈ Rn×m is the node-incidence matrix of the graph, defined by Aij = +1 edge j enters node i, −1 edge j leaves node i, 0 otherwise. In the basic power flow optimization problem, we choose the generator powers g and the line flow powers p to minimize the total power generation cost, subject to the constraints listed above. The (given) problem data are the incidence matrix A, line capacities P max , demands d, maximum generator powers Gmax , and generator costs c. In this problem we will add a basic (and widely used) reliability constraint, commonly called an ‘N − 1 constraint’. (N is not a paramet...
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