This preview shows page 1. Sign up to view the full content.
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 nodeincidence 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...
View
Full
Document
 Fall '13
 F.Borrelli
 The Aeneid

Click to edit the document details