Smart Grids: Security and Privacy Issues by Kianoosh G. Boroojeni M. Hadi Amini & S. S. Iyengar

Author:Kianoosh G. Boroojeni, M. Hadi Amini & S. S. Iyengar
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.31)

If the parameter μ is small, it means that the columns subspace of the matrix U is not aligned with the standard basis. The orthogonal matrix U is used to measure the sparse vector. Thus, it is essential that U not to be a sparse matrix. In [52], it was shown that if

(3.32)

then the optimal point of

(3.33)

is equal to s with probability at least (1 −δ), where c is a constant number. It means that an N-dimensional sparse vector can be recovered from a small random non-adaptive linear measurements and the sufficient number of measurements is linearly dependent on the number of non-zero elements of the sparse vector (or if it is not exactly sparse, the number of dominant elements [55]). As it has been mentioned, in order to model the noise vector, we update the DC power flow model to

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