Numerical observability analysis of distribution systems

Observability analysis is a very important tool in state estimation. For a given set of measurements and their geographical location in the system, it determines whether the state of the whole system can be estimated. In this paper a numerical observability analysis, applicable to distribution systems is discussed and applied to the IEEE 34 bus test feeder. The method is based on the inverse function theory and the Jacobian matrix of the system. By calculating the dependent columns of the Jacobian matrix it is possible to determine the unobservable branches in the system. This also gives an indication of how many linearly independent pseudo-measurements are required to make the distribution system observable. Because the R=X ratio is not negligible in the distribution lines, a transformation has been used to simplify the observability analysis.