Bad data processing when using the coupled measurement model and Takahashi's sparse inverse method

The paper revisits the computation of residual covariance matrix diagonal entries, which are used for calculating the normalized residuals that are in turn used for bad data identification. It is shown that these entries may be inadvertently computed incorrectly if one uses the commonly accepted implementation of the sparse inverse method due to the numerical cancellations that occur in the formation of the so-called gain matrix. This situation occurs when the coupled measurement model is used. Indeed, the coupled model is required if there are current measurements that do not lend themselves to decoupling. Numerical example will be given for a test power system to show the impact of these cancellations on bad data analysis that uses post-processing of residuals and the largest normalized residual test. The errors may lead to sequential removal of good data eventually leading to a biased estimation. They may also lead to unacceptable covariance values, e.g., less than zero, which will then destroy the validity of bad data analysis. While it appears like a minor oversight in the application of efficient sparse inverse implementation, due to its adverse impact on state estimation and therefore overall power system operation, it will have to be corrected. The paper will first illustrate the issue and then a simple modification in the implementation of the sparse inverse method will be shown in order to avoid this error.