This paper discusses the analytical analysis of synchrophasor estimation employed in electrical systems. Short-time Fourier transform with a phase-locked loop and Taylor-Fourier series are analysed for signals relating to different states which may occur in real power systems. As a consequence of transients in power system signal waveforms changes may occur. This leads to inconvenient errors in any estimation algorithm. This paper presents the character of these errors and their consequences individually for any signal deviation.
Słowa kluczowe: dynamic phasor, Taylor - Fourier series, phase-locked-loop, dynamic filtering
W artykule przedstawiona została analiza problemu wyznaczania fazorów w systemie elektroenergetycznym. Algorytymy bazuja˛ce na szybkiej transformacie Fouriera z pe˛ tla˛ synchronizacji fazy oraz z rozwinie˛ciem w szereg Taylora-Fouriera zostały przetesotwane na sygnałach odpowiadaja˛cych rzeczywistym przebiegom w systemie elektroenergetycznym. Zmiany sygnałów napie˛ciowych i pra˛dowych skutkuja˛ błe˛dami estymacji parametrów. W artykule przedstawiono charakter błedów estymacji fazorów oraz ich wpływ dla ró˙znych typów analizowanych sygnałów.
Keywords: fazory dynamiczne, szeregi Taylora - Fouriera, p˛ etla synchronizacji fazy, filtracja dynamiczna
An accurate estimation of electrical signal parameters is a fundamental issue as far as the appropriate operation and control of a power system is concerned. The imbalance between power supply and the load leads to dynamic changes in the system state, so that the voltage and current values, waveshapes and system frequency may differ from nominal. Efficient control of an electrical network requires more and more accurate information on signal parameters. This includes accurate measurement of the signal phase, amplitude, frequency, higher harmonics, rate of change of frequency and the amplitude change rate. These parameters can be represented concisely as a complex valued function referred to as a phasor. As a result, in standard C137.118.1- 2011 , estimation algorithms have been organized and divided into P (protection) and M (measurement) classes depending on their purpose. M class algorithms are designed for measurement devices with high accuracy requirements and slow response times. P class algorithms are designed for protection purposes with a strict response time and overshoot limits, but higher estimation errors are acceptable. The phasor estimation issue has been approached in various ways and methods. The most popular concept of a phasor estimation is based on Fourier transform algorithms, in particular short time Fourier transform (STFT). This includes the process of the optimal filter design to ensure appropriate noise damping, good dynamical properties and more effective higher harmonic damping , . It has been observed that even a proper filter design can be insufficient for processing of abnormal signals. More advanced methods of filter design employ dynamic filtering to enhance phasor estimation for off nominal frequencies , . The most accurate estimation method involves polynomial approximation , , . Least square method (LSM) is used to evaluate polynomial coefficients of the correspondi [...]
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