Power network observability: the assessment of the measurement system strength

Two main ideas concerning power network observability analysis are developed, based on the fact that measurement-to-branch incidence matrix M, and node-to-branch incidence matrix A are both totally unimodular matrices. The first idea may be stated as follows: if the product matrix W=MA^t is considered, where W is the measurement-to-node incidence matrix, its Gramian G(W)=det(W^tW) is nonzero for observable networks, and equals zero for unobservable networks. The second idea may be stated as follows: for a given network and measurement system the Gramian of W, G(W)=det(W ^tW) is an invariant (there is one matrix M and n distinct matrices A), therefore there are n distinct matrices W