Detecting multiple solutions in state estimation in the presence of current magnitude measurements

This paper investigates the observability problem when the network contains current magnitude measurements. Use of these measurements may lead to multiple solutions and therefore to the loss of unique observability for certain measurement configurations. The paper proposes a simple method based on the commonly used measurement residual covariance matrix, in order to detect the possibility of multiple solutions for a given measurement set. The proposed test is simple to implement and uses the already available matrices and data structures of the commonly used weighted least squares state estimation programs. It can be utilized as a planning tool during the initial stages of measurement system design as well as an online observability analysis tool to enhance the capability of the existing observability programs which can not properly process the current magnitude measurements. Numerical examples are provided to demonstrate the performance of the proposed method on sample power systems