Calibrating CVTs of a Substation From Local PMU Data: An SVD Approach

We show that if all the line and bus CVTs within a substation are monitored by PMUs, then it is possible to perform CVT calibration locally. This requires 1) discovery of a set of three phase CVTs which can be used as the reference and 2) calculation of ratio correction factors. We show that the best set of three phase CVTs among the redundant sets can be discovered by minimizing the overall measured unbalance among all the three phase CVT combinations. All the CVTs measure the same bus voltage time series. Hence, the corresponding phase measurement matrix will be a small modification of a rank-1 matrix; each column is a scaled replica of the true voltage vector modified by white noise. A microscopic evaluation of the substation PMU data shows that rank-1 approximation by SVD retains 99.99% information. The magnitude correction factors can be obtained by projecting CVT measurement vectors on the first left singular vector. Phase angle correction factors correspond to angles of elements of the first right singular vector. Results with both simulated and field PMU data of 400 kV substations substantiate the claims made.