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.

In this study, a new algorithm for discrimination between internal faults and inrush current conditions in power transformers is presented. First, the proposed algorithm removes the pre-fault conditions of the fault currents. Then, those currents are processed using the discrete wavelet transform to obtain the wavelet matrix. The correlation matrix is computed from wavelet matrix to know the eigenvalues associated with each frequency scale and to reduce the analysed information. This algorithm, which the authors are going to call wavelet correlation modes, is used to identify inrush and internal fault currents in power transformer. To validate the proposed algorithm, simulations are carried out in power systems computer-aided design software, and the obtained signals are analysed in order to evaluate its performance and sensitivity.

This study describes a new differential protection algorithm for power transformers, which is not affected by transient conditions. The proposed algorithm uses the statistical second central moment, statistical variance, to characterise the signal waveform. The goal is to obtain the variance from each differential current after a pre‐processing filter stage and to compare it with a threshold. The event will be identified as an internal fault, or otherwise as an inrush current. The algorithm was implemented in MATLAB, and a broad array of cases was carried out using the electromagnetic transient software PSCAD. All results show the algorithm successfully differentiated inrush from the internal fault conditions in over 2000 cases.

This study describes an extended approach to the differential protection of power transformers to identify turn‐to‐turn faults based on the second central moment (SCM). The proposal uses the differential currents as the input signals to the algorithm. Differential currents are filtered and normalised to allow the proposed algorithm to be independent of the transformer parameters (power, reactance, connection etc.). Then, the SCM magnitude of the differential currents is computed and compared with an established threshold to detect the internal faults. If the SCM magnitude exceeds the limit, an internal fault is detected. Otherwise, the event is determined as a transient event or steady state. The proposed algorithm was implemented in MATLAB and was tested on a three‐phase system using a Real‐Time Digital Simulator. For laboratory experiments, a real 55‐kVA transformer setup was used to validate the effectiveness of the algorithm. The algorithm successfully identified turn‐to‐turn faults from steady state, as well as during transformer energisations, in over 1000 cases.

Reliable discrimination between power swings and short-circuit faults is essential for secure transmission line protection, since misclassification may lead to unnecessary tripping or delayed fault clearing. Conventional power swing blocking techniques, particularly those based on impedance trajectory analysis, often require system-dependent settings and may exhibit reduced reliability under dynamic operating conditions with increasing renewable generation penetration. This paper proposes a setting-independent method for power swing and fault discrimination based on the Second Central Moment (SCM) of normalized instantaneous voltage and current signals. In this context, setting-independent means that the method does not require line-specific protection settings or case-by-case threshold tuning, although nominal voltage, nominal current, system frequency, and sampling frequency are required for signal normalization and sliding-window implementation. The SCM provides a statistical measure of signal dispersion that enables classification into three operating states: steady-state operation, power swing conditions, and fault events. Common SCM decision boundaries are applied without adjustment across the evaluated transmission lines, operating conditions, fault characteristics, power-swing frequencies, and levels of inverter-based resource penetration. The proposed method is validated through time-domain simulations using the Kundur two-area benchmark system and the IEEE 14-bus network under a wide range of disturbance scenarios, including oscillatory conditions, symmetrical and asymmetrical faults, renewable integration, and swing–fault sequences. For benchmarking purposes, the SCM-based algorithm is compared with a commercial Swing Center Voltage (SCV)-based blocking scheme widely implemented in digital relays. The results show that the proposed method achieves reliable swing–fault discrimination with low computational complexity while providing earlier blocking activation under slow oscillatory conditions and inherent fault discrimination capability. These characteristics support its practical application in real-time transmission line protection.