When an optimal power flow problem is formualted using Semi-definite programming method, the equivalent OPF problem contains one constraint
X or W = vv^H
where v is a vector of bus voltages and H is the complex conjugate transpose operator (v = [v1 v2 .... vn]^T where (1,2,...n) are buses indexes)
In various publications, authors say that this particular constraint is a rank-1 constraint and it is a non-convex?
I want to know how is this constraint a rank-1 constraint (What is actual meaning of rank-1 constraint)? Further, how is this constraint non-convex?
I guess ,because you can check the rank of a matrix by computing it's determinant. If determinant is non zero then the matrix holds full rank. In this case the determinant involves the product of vectors in the corresponding matrix. So it is non convex.
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