Determining the Current Frequency in Digital Relay Protection Devices

In digital relay protection devices, fundamental harmonic signals are used as useful information. To isolate them from complex input currents and voltages of the protected object, non-recursive digital Fourier filters are used. The signals obtained as a result of filtering are the basis for determining the information parameters of the quantities controlled by digital organs. At the nominal frequency in the power system, the information parameters are calculated without additional error. In the event of a frequency deviation from the nominal value due to a number
of reasons, an additional error component appears in the information parameters of the controlled values. When there are minor frequency fluctuations, the specified component is insignificant and can be neglected in practice. In case of significant frequency deviations in the power system, the additional component of error in the information parameters can negatively affect the operation of the functional algorithms of the relay protection. One of the ways to solve this problem is to correct the specified component when the frequency deviates from the nominal one. To implement this, it is necessary to have the results of frequency assessment. The most rational way to correct the frequency component of the error is to use the current frequency. Determining the specified frequency of alternating current consists of measuring the instantaneous frequency at different points in time and averaging these values over a certain interval. The instantaneous frequency is calculated from the instantaneous value of the dynamic cosine of the sampling angle, for the determination of which two functional algorithms have been developed and studied. The first of these is based on the use of three consecutive values of one of a pair of orthogonal signals. The second algorithm is implemented using two adjacent values of each of the mutually orthogonal signals. The results of the conducted studies showed that the developed algorithms for determining the current frequency in digital relay protection devices ensure its receipt with acceptable reliability in the range of 47–51 Hz at a change rate of up to 4 Hz/s. 

1. Fedoseev A. M. (1984) Relay Protection of Electric Power Systems. Moscow, Energoatom-izdat Publ. 520 (in Russian).

2. Schneerson E. M. (2007) Digital Relay Protection. Moscow, Energoatomizdat Publ. 549 (in Russian).

3. Phadke A. G., Thorp J. S. (2009). Computer Relaying for Power Systems. John Wiley & Sons. https://doi.org/10.1002/9780470749722.

4. Ribeiro P. F., Duque C. A., Silveira P. M. da, Cerqueira A. S. (eds.) (2013) Power Systems Signal Processing For Smart Grids. John Wiley & Sons. https://doi.org/10.1002/9781118639283.

5. Ananicheva S. S., Alekseev A. A., Myzin A. L. (2012) Power Quality. Voltage and Frequency Regulation in Power Systems. 3rd ed. Ekaterinburg, Ural Federal University. 93 (in Russian).

6. Aminev A. V., Blokhin A. V. (2018) Measurements in Telecommunication Systems. 2nd ed. Moscow, Finita Publ. 224 (in Russian).

7. Fink L. M. (1984) Signals, Interference, Errors… Notes on Some Surprises, Paradoxes, and Misconceptions in Communication Theory. 2nd ed. Moscow, Radio i Svyaz Publ. 256 (in Russian).

8. Romaniuk F. A., Loman M. S., Kachenya V. S. (2019) Methods of Forming Orthogonal Components of Input Signals for Relay Protection. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 62 (1), 5–14. https://doi.org/10.21122/1029-7448-2019-62-1-5-14 (in Russian).

9. Zaitseva, I. N., & Ugol’kov, V. N. (2024). Some Problems of Discretization and Determination of Basic Parameters of Harmonic Signals. Journal of Radio Electronics, (7) (in Russian). https://doi.org/10.30898/1684-1719.2024.7.2.

10. Rumiantsev Yu. V., Romaniuk F. A., Rumiantsev V. Yu. (2024) A Fast-Response Method for Determining the Amplitude of a Signal in Microprocessor Automation and Control Systems with Frequency Fluctuations. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 67 (1), 5–15. https://doi.org/10.21122/1029-7448-2024-67-1-5-15 (in Russian).

11. Romaniuk F. A., Rumiantsev Yu. V., Rumiantsev V. Yu. (2025) Correction of Amplitude and Phase Errors of the Signal in Microprocessor Automation and Relay Protection Systems when Frequency Changes. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 68 (1), 5–16. https://doi.org/10.21122/1029-7448-2025-68-1-5-16 (in Russian).

12. Dabney J. B. (2001) Simulink 4 Upper Saddle River. New Jersey.

13. Novash I. V., Romanyuk F. A., Rumyantsev V. Yu., Rumyantsev Yu. V. (2021) Testing of Microprocessor-Based Current Protection: Theory, Modeling, Practice. Minsk, Belarusian National Technical University. 168 (in Russian).

14. Gilat A. (2015) MATLAB: an introduction with applications. Wiley.