A Fast-Response Method for Determining the Amplitude of a Signal in Microprocessor Automation and Control Systems with Frequency Fluctuations

In microprocessor automation and control systems, the amplitude (effective) values of the fundamental harmonic of the input signals are widely used as information parameters of the controlled quantities. They are most often determined by samples of one or a pair of orthogonal components of the signal, for the formation of which digital Fourier filters and their modifications are mainly used. At the rated frequency in the power system, these filters ensure reliable reception of the signal amplitude without additional error. If the frequency deviates from the rated one, the number of samples per signal period is not an integer and the discretization becomes asynchronous. As a result, a corresponding error appears in the amplitude of the signal, and its change becomes oscillating. With minor frequency fluctuations in the normal mode, the amplitude error is insignificant. However, in abnormal situations, the frequency can have significant variations. At the same time, in critical situations, failure of automation and control systems, as well as incorrect operation of their functional algorithms, cannot be excluded. Known methods for determining the amplitude of a signal with frequency fluctuations provide a solution to the existing problem, but they are characterized by a slow response. The proposed high-response method for determining the amplitude during frequency fluctuations is focused on using as initial information samples of instantaneous values of the cosine orthogonal component of the signal, which are formed using an appropriate digital Fourier filter. Based on these samples, the dynamic cosine and sine of the angle of one sample are calculated, the use of which in calculating the amplitude ensures its independence from frequency. Processing of the received amplitude with an amplifying element with a nonlinear coefficient makes it possible to achieve acceptable performance. The effectiveness of the proposed solution was evaluated by a computational experiment using a digital model implemented in the MATLAB-Simulink dynamic modeling environment. In this case, both sinusoidal input signals and complex ones, close to the real secondary signals of measuring transformers, were used as test actions. As a result of the research, it was found that the proposed method for determining the amplitude during frequency fluctuations has a performance at the level of a quarter of the period and provides effective elimination of frequency error both in load modes and in damage modes.

1. Novash I. V., Romaniuk F. A., Rumiantsev V. Yu., Rumiantsev Yu. V. (2021) Testing of Microprocessor Current Protections: Theory, Modeling, Practice. Minsk, BNTU. 168 (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. 2nd ed. Chichister, John Wiley & Sons, Ltd., 326. https://doi.org/10.1002/9780470749722.

4. Ribeiro P. F., Duque C. A., Silveira P. M. da, Cerqueira, A. S. (eds.) (2014) Power Systems Signal Processing For Smart Grids. John Wiley & Sons, Ltd. 417. https://doi.org/10.1002/9781118639283.

5. Solopov R. V., Kovzhenkin V. S., Vaitelenok L. V. (2018) Error Estimation under Fourier Filter Operation in Protective Relays. Vestnik Irkutskogo Gosudarstvennogo Tehnicheskogo Universiteta = Proceedings of Irkutsk State Technical University, 22 (10), 117–128 (in Russian). https://doi.org/10.21285/1814-3520-2018-10-117-128.

6. Romaniuk F. A., Rumiantsev V. Yu., Rumiantsev Yu. V., Dziaruhina A. A. (2020) Reducing the Impact of the Frequency Change on the Formation of Orthogonal Components of the Relay Protection Input Signals. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 63 (1), 42–54 (in Russian). https://doi.org/10.21122/ 1029-7448-2020-63-1-42-54.

7. Romaniuk F. A., Rumiantsev V. Yu., Rumiantsev Yu. V. (2022) Improving of Functioning Stability of Current Measuring Elements in Microprocessor Protections. Nauka i Tehnika = Science & Technique, 21 (5), 419–425 (in Russian). https://doi.org/10.21122/2227-1031-2022-21-5-419-425.

8. Romaniuk F. A., Loman М. 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 (in Russian). https://doi.org/10.21122/1029-7448-2019-62-1-5-14.

9. Romaniuk F. A., Rumiantsev Yu. V., Rumiantsev V. Yu. (2022) Formation of Orthogonal Components of Input Signals in Digital Measuring Protection Elements with Correction of Dynamic Errors. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 65 (4), 289–300 (in Russian). https://doi.org/10.21122/1029-7448-2022-65-4-289-300.

10. Romaniuk F. A., Rumiantsev V. Yu., Rumiantsev Yu. V., Dziaruhina A. A., Klimkovich P. I. (2023) Principles for Implementation of Digital Power Direction Control in Microprocessor Current Protections. Nauka i Tehnika = Science & Technique, 22 (4), 317–325 (in Russian). https://doi.org/10.21122/2227-1031-2023-22-4-317-325.

11. Romaniuk F. A., Rumiantsev Yu. V., Rumiantsev V. Yu., Novash I. V. (2021) Improvement of Algorithm for Formation of Orthogonal Components of Input Quantities in Microprocessor Protection. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64 (2), 95–108 (in Russian). https://doi.org/10.21122/1029-7448-2021-64-2-95-108.

12. Romaniuk F. A., Rumiantsev V. Yu., Novash I. V., Rumiantsev Yu. V. (2019) Technique of Performance Improvement of the Microprocessor-Based Protection Measuring Element. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 62 (5), 403–412 (in Russian). https://doi.org/10.21122/1029-7448-2019-62-5-403-412.

13. Romanyuk F. A., Rumyantsev V. Yu., Rumyantsev Yu. V. (2023) Digital Measuring Element of Relay Protection Current of an Electric Power System. Patent Republic of Belarus. No 23972 (in Russian).

14. Chernykh I. V. (2011) Simulation of Electrical Devices in MATLAB, SimPowerSystems and Simulink. Moscow, DMK Press; St. Petersburg, Peter. 288 (in Russian).