A Setting-Free Differential Protection for Power Transformers Based on Second Central Moment

This paper describes a differential algorithm for the protection of a three-phase transformer to differentiate transient phenomena, such as inrush currents and external faults from solid and turn-to-turn faults. This algorithm is based on the behavior of the second central moment (SCM) to identify the kind of event. Instantaneous differential currents are used as input signals to the algorithm once they are filtered and normalized. The algorithm compares the magnitude of the SCM with an established threshold based on the binomial distribution to achieve a successful identification of the event. If the magnitude of the SCM is above the limit, the algorithm identifies the event as a fault condition. Otherwise, the event is determined as a transient event or a steady-state condition. The threshold is setting-free if the transformer parameters are changed or if the harmonic content of the differential current varies. Also, the threshold does not have to be recalculated if the power system is modified. The D index was introduced to improve the fault-detection time when the current transformers experience saturation. This index uses the magnitude of the SCM as a basis and is compared with an established limit to detect the fault current. Both indices run in parallel, and if any of them does cross its respective threshold, a fault condition is determined. The algorithm is tested in a real-time digital simulator and is implemented in MATLAB. The algorithm was compared against the conventional differential protection with harmonic restraint to evaluate the performance of both indices in critical conditions. The results validate the performance of the algorithm and indicate that it can be the basis of a new algorithm to protect power transformers.