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Faults lead to de-energising of a section of transmission line thus decreasing the reliability of the system. Power swing affects the distance relays leading to false alarms which were the leading cause of unreliability. Faults cause permanent movement of the operating point in RX plot with a transient oscillation. The locus of power swing forms closed loops. Here, impedance angles were used to discriminate the faults from power swing. The investigation was carried out along with three dimensional plots to visualize the locus of impedance in resistance, reactance and time axis. Results signify that faults were differentiated from power swing using differential impedance angle. The test cases include all the unbalanced faults as well as an unstable swing. Power swing formed bi-conical loops above and below the ideal operating impedance, while differential impedance formed hyperboloid with the mean impedance being zero. Simulations were carried out in a 2 bus system and all the voltages and currents were extracted from the center of transmission line. Visual representation of normal operating impedances and power swing using three dimensional plots (R-X-t space) and (dR/dt-dX/dt-t space) were shown in the Appendix.

Grid disturbance is one of the largest areas of concern in the protection of power systems after high penetration of distributive generation. They are responsible for causing mass blackouts. This paper analytically derives the equations for resistances and reactances as a function of time. The derived expressions were validated using real time digital simulator (RTDS) for variation in power factor of system and frequency of the power swing. Results signify that the derived equations were able to provide the locus of instantaneous values of the real time power swing occurring in the system for changes in power factor and swinging frequency. Two dimensional R-X plane and three dimensional R-X-t space plots were also used to study the static and dynamic variations of impedances in time domain. The expressions r(t) and x(t) will be useful in determining the instantaneous short circuit ratios and also for tuning the impedance relays.

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