The article considers the problem of excessive triggering of a transformer differential protection during external short circuits. The existing restraining algorithms for automatically increasing the protection tripping current during external short circuits are described. It is noted that in the modes with deep saturation of current transformers, none of the restraining algorithms provide reliable performance of the differential protection. It is proposed to apply the phase comparison principle for currents in the protection legs, in addition to restraining, to improve the reliability of the differential protection. A logical scheme of the algorithm and formulas for specifying the conditions of operation of the advanced differential protection has been developed. Testing the proposed restraining algorithm with phase comparison principle on the simulation model in MATLAB Simulink showed that the probability of a false tripping during external short circuits decreases by almost 10 times compared with the known restraining algorithms and is no more than 2% in the most heavy modes. The operation of the algorithm was tested during a short circuit in the protected area, the sensitivity of the differential protection is provided in all modes.

This paper considers the task of calculating the primary time constant of the DC component of the short circuit current in order to determine the time to saturation of the current transformer according to IEC 61869-2:2012. The features of equivalent circuits for calculating time constants for three- and single-phase short circuits are described. It is proposed to use the parameters of the symmetrical AC component of the short-circuit current to calculate the time constant of the DC component instead of equivalenting the circuit's impedance and calculating the resulting resistance and inductive reactance. The method is tested on a simulation model in MATLAB Simulink, full compliance with the calculation of the time constant is obtained through the ratio of reactance and resistance and through the magnitude and phase of the short circuit current. The features of calculating the equivalent time constant of the total short circuit current from branches which have different ratios of resistance and inductive reactance are considered.

The article considers the problem of improving the differential protection reliability in transient modes with current transformers' saturation. It is noted that in recent years in the power systems there have been repeated some incorrect trips of these protections in transient conditions. Tripping was observed not only during external short circuits, but also during motor starts and external load switching. The digital differential protection models for generator and transformer are developed using MATLAB Simulink. Transient modes are simulated, which confirmed the possibility of incorrect protection tripping during external short circuits and during motor starts and generator switching. To increase the protection reliability, it is proposed to apply blocking principle by the aperiodic (DC) component in the differential current in addition to digital restraining. Modeling the advanced protection operation confirmed the complete exclusion of incorrect trips during external short circuits and maintaining sensitivity to internal damage. The problem of measuring the aperiodic (DC) current component in the current transformer secondary circuits is noted. It can be solved by the use of current converters based on Hall sensors.

We develop a simplified model of a current transformer based on its current-voltage characteristic. This model is applicable for studying relay protection operation in transient conditions when no high accuracy or consideration of current transformer magnet core hysteresis is required. The model was developed in MATLAB Simulink using elements of the SimPowerSystems and Simscape libraries. The model uses the transformation ratio and current-voltage characteristic obtained during operational tests of a current transformer. Calculation experiments with non-linear resistance found that a currentvoltage characteristic of voltage and current values can be used to model a current transformer, rather than instantaneous values. The following conditions were simulated: for nominal currents in current transformer windings to check the transformation ratio; for opened secondary winding; with current transformer saturation by increasing secondary loading; increasing the primary current ratio and presence of aperiodic current at the start of the transition process. It was found that the developed current transformer model allows for a correct imitation of all the above conditions. To verify the model, secondary current oscillograms were obtained using real current transformers 10 kV at known primary current, which were compared with nominal oscillograms in the model. The discrepancy between the results of calculational and real experiments was no more than 10% in amplitude values, with high-quality matching obtained for current charts in the model and real current transformers. A significant advantage of the developed model is that its setting requires no information on magnet core cross-section, power line length, steel grade, and the number of current transformer winding turns.

Differential protection is one of the most reliable and simple by the principle of relay protection, which has absolute selectivity and performance [1]. The protection measures the vector sum of the currents (a differential current) on all sides of the protected object. In the case of a short circuit in the protection zone, the current rises and the protection turns off the damaged element. With an external short-circuit, the through-currents on the sides of the protected elements according to the first Kirchhoff law together give a current close to zero and called the unbalance current [2]. This current is mainly due to the error of current transformers (CTs). The error of the relaying CT depends on their load, residual induction, primary current and the presence of an aperiodic component. In the steady-state fault mode, the CT error usually cannot exceed 5% or 10%, depending on the accuracy class. However, when the primary current, secondary load or an aperiodic current is exceeded (especially in combination with the residual induction of the CT), the error may increase to 50-80%. The unbalance current increases in these modes. It can cause an incorrect operation of protection during external faults. To prevent incorrect operation of the protection the restraining is applied [3], [4]. The restraining in differential protection is an automatic increase trip current when the current through the CT is increased. Typically, as a restraint current, analog current protections use a current or several sides (legs) [5].

RELEVANCE. The increase in the share of high nonlinear loads in power systems, causing non-sinusoidal currents and voltages, leads to negative technical consequences and economic losses for the power system and non-distorting consumers. Currently, there are no practical recommendations on choosing the lengths of power lines for supplying high nonlinear loads considering their negative impact on power quality indicators.THE PURPOSE. The study analyzes the conditions for the occurrence of harmonic resonant overvoltages in a power supply scheme of a nonlinear load. METHODS. The main methods used for the study include the compilation of equivalent diagrams of the electrical network elements and calculation of currents and voltages in lumped-element circuits. The Fourier series decomposition is applied to analyze non-sinusoidal currents and voltages. Using simulation models in MATLAB Simulink environment, the conditions for the occurrence of higher harmonic resonances at different lengths of 35, 110, and 220 kV power transmission lines and different power ratings of the power system are determined.RESULTS. Calculated resonant lengths of overhead power lines 35-220 kV, supplying a nonlinear load, at which resonant overvoltages occur in the electrical network on higher harmonics with numbers from 3 to 49, were obtained. The resonant lengths of power transmission lines on particular harmonics were determined taking into account the impact of the power supply system reactance. The obtained combinations of resonant line lengths and system reactances are proposed to be considered in the design of external power supply schemes for nonlinear loads to eliminate harmonic overvoltages. The calculations in this study provided an explanation for the abnormal levels of currents and voltages of the 35^th and 37^th harmonics in the external power supply scheme of an aluminum plant.CONCLUSION. Practical recommendations are given for choosing the lengths of 35-220 kV power transmission lines in power supply systems with high nonlinear loads to eliminate resonant overvoltages. The results of determining the resonant lengths of power transmission lines agree with the data from measuring experiments in an operating power system.