Structure of measurement Jacobian matrices for power systems

Abstract

In steady-state modelling of power systems, the measurement equations together with the system states may be ordered so that the measurement Jacobian matrix H displays a particular block-sparsity structure, which will become more apparent as system size increases. The resulting partitioned form for H may be regarded as a simply specified decomposition of the measurement equations. The decomposition may then be exploited using a theorem which enables the rank of H to be determined from a set of rank tests on reduced-order matrices. This result has implications for the testing of numerical observability on power systems, particularly when the new rank tests are distributed within a multiprocessor computer system. A novel feature of this approach to the determination of numerical observability is that a degree of localisation of unobservable states becomes possible. The fundamental structure of the decomposition described for H is suitable for exploitation in other areas of steady-state power systems analysis such as state estimation.