# Mjerenje mrežne frekvencije u stvarnom vremenu korištenjem vremensko-frekvencijskih transformacija : doktorski rad / Petar Mostarac ; [mentor Roman Malarić]

##### By: Mostarac, Petar.

##### Contributor(s): Malarić, Roman [ths].

Material type: TextPublisher: Zagreb : P. Mostarac ; Fakultet elektrotehnike i računarstva, 2013Description: viii, 128 str.: ilustr. ; 30 cm + CD.Summary: SAŽETAK: U doktorskoj disertaciji istražena je primjena vremensko-frekvencijskih transformacija za mjerenje mrežne frekvencije u stvarnom vremenu. Predstavljena je nova metoda za mjerenje dinamičkih promjena mrežne frekvencije. U radu je prikazan postupak definiranja pojedinih dijelova nove metode za mjerenje mrežne frekvencije. Analizirano je i vrijeme potrebno da se metoda izvrši. Provedena je minimizacija broja operacija potrebnih za izračunavanje metode smanjivanjem broja podataka neophodnih za izračunavanje frekvencije te odabirom odgovarajućih parametara metode. Na temelju usporedbi s već postojećim metodama analizirane su prednosti i nedostaci nove metode. Analizirane su mogućnosti upotrebe nove metode za mjerenje spektralnih komponenti promatranog signala. Predstavljena je metoda za određivanje frekvencijskog spektra i efektivne vrijednosti napona mreže primjenom metode za mjerenje dinamičkih promjena frekvencije. Analizirana je mjerna nesigurnost nove metode definiranjem utjecaj svih pojedinih dijelova mjernog lanca na ukupnu mjernu nesigurnost nove metode uz vođenje računa o propagaciji složene mjerne nesigurnosti kroz sustav. Obavljeno je optimiranje mjerenja mrežne frekvencije u stvarnom vremenu pri određivanju parametara kvalitete električne energije. - KLJUČNE RIJEČI: mjerenje, mrežna frekvencija, brza Fourierova transformacija, Chirp-z transformacija, mjerna nesigurnost, frekvencijski spektarSummary: SUMMARY: Measurement of time varying frequency is important in many fields: acoustics, radar signal analysis, seismology, power quality analysis. The speed of frequency measurement and the ability to detect transients is of extreme importance. The number of periods needed to measure frequency can vary from several to several tens of periods. Resolution of frequency range in time–frequency transformations is proportional to the ratio between sampling frequency and number of samples in data sequence. For better resolution it is necessary to increase the length of sequence of data. Usage of time-frequency transform for real time measurement of power line frequency has been explored in the doctoral dissertation. New method for measurement of power line frequencies in real time is presented: Adaptive Chirp Transform (ACT) algorithm for power frequency measurement. It is adjusted for continuous monitoring of power frequency. Signal is first preprocessed with adaptive filter to minimize the error of non-linear model parameters. The resulting parameters are used to narrow the frequency range for CZT method to be effective. Algorithm code has been analyzed and computation complexity has been significantly decreased. Using this algorithm it is possible to measure frequency transients with sufficient accuracy and low execution time. Algorithm is verified through simulations and real-time data. Algorithm presented in this paper can estimate instantaneous frequency. It can perform two tasks. First task is to measure frequency of continuously monitored signal, and the second task is to evaluate that information quickly and as often as possible. Achieving the first task requires the use of Interpolated Descrete Fourier Transform (IpDFT) algorithm, because of it small execution time, and relatively small error. To achieve second task it is necessary to observe very short sequence of data, so that transients in frequency can be detected. As the signal is sampled in real time, the signal frequency can be calculated from small sequence of data. There are two main problems in this method. By reducing the size of data sequence, error of IpDFT algorithm is increased and also, the total time in which the algorithm needs to be evaluated is reduced. It can also be noted that in data sequences shorter than one period of signal best results are obtained with the CZT algorithm. Consequently, to achieve a low relative error, a large number of points in frequency spectrum is needed which increases computation time of CZT. Therefore, it was necessary to develop new method to reduce algorithm complexity. Proposed algorithm is based on adaptive filter and CZT. Preprocessing of data sequence is made by adaptive filter to narrow the frequency range in order to decrease the number of points in the frequency spectrum that needs to be calculated. Within this range, the frequency of data sequence is calculated using the CZT algorithm. All parts of algorithm which are not dependent on the measured signal are calculated offline and located in data base. Data base also include points in the frequency spectrum that are essential for CZT calculation. It is created in the beginning of the algorithm first run as the result of computation complexity analysis of adaptive filter and CZT. Data base reduces the number of operation calculated online to minimum. Proposed algorithm retains low relative error of CZT algorithm for very short sequences of data (below one period). Computation time is minimized so that the complete algorithm calculation is done before the next time sequence. Algorithm is developed for continuous frequency monitoring and is robust for noise in signal. Based on comparison with existing methods, advantages and disadvantages of this method have been analysed. Method for determining frequency spectra and RMS value of power line voltage by applying method for measurement of dynamic frequency changes has been presented. Measurement uncertainty of the new method has been analysed and optimization of power line frequency measurement in real time by determining power quality has been performed. - KEYWORDS: measurement, power frequency, fast Fourier transform, Chirp-z transforms, measurement uncertainty, frequency spectraItem type | Current location | Call number | Status | Notes | Date due | Barcode | Item holds |
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Doktorska disertacija | Središnja knjižnica KF | KF-4640 | Available | 0000000918749 | |||

Doktorska disertacija | Središnja knjižnica | KF-4640 | 1 | CD-ROM | 0000000918756 | ||

Doktorska disertacija | Središnja knjižnica | KF-4640 | 1 | 0000000918763 | |||

Doktorska disertacija | Zavod za osnove elektrotehnike i električka mjerenja ZOEM | 4009 | Available | 0000000924788 |

Bibliografija: str. 103-109. - Sažetak na hrv. i eng. jeziku. - Popis kratica. - Životopis [uključuje i popis objavljenih radova autora]

SAŽETAK: U doktorskoj disertaciji istražena je primjena vremensko-frekvencijskih transformacija za mjerenje mrežne frekvencije u stvarnom vremenu. Predstavljena je nova metoda za mjerenje dinamičkih promjena mrežne frekvencije. U radu je prikazan postupak definiranja pojedinih dijelova nove metode za mjerenje mrežne frekvencije. Analizirano je i vrijeme potrebno da se metoda izvrši. Provedena je minimizacija broja operacija potrebnih za izračunavanje metode smanjivanjem broja podataka neophodnih za izračunavanje frekvencije te odabirom odgovarajućih parametara metode. Na temelju usporedbi s već postojećim metodama analizirane su prednosti i nedostaci nove metode. Analizirane su mogućnosti upotrebe nove metode za mjerenje spektralnih komponenti promatranog signala. Predstavljena je metoda za određivanje frekvencijskog spektra i efektivne vrijednosti napona mreže primjenom metode za mjerenje dinamičkih promjena frekvencije. Analizirana je mjerna nesigurnost nove metode definiranjem utjecaj svih pojedinih dijelova mjernog lanca na ukupnu mjernu nesigurnost nove metode uz vođenje računa o propagaciji složene mjerne nesigurnosti kroz sustav. Obavljeno je optimiranje mjerenja mrežne frekvencije u stvarnom vremenu pri određivanju parametara kvalitete električne energije. - KLJUČNE RIJEČI: mjerenje, mrežna frekvencija, brza Fourierova transformacija, Chirp-z transformacija, mjerna nesigurnost, frekvencijski spektar

SUMMARY: Measurement of time varying frequency is important in many fields: acoustics, radar signal analysis, seismology, power quality analysis. The speed of frequency measurement and the ability to detect transients is of extreme importance. The number of periods needed to measure frequency can vary from several to several tens of periods. Resolution of frequency range in time–frequency transformations is proportional to the ratio between sampling frequency and number of samples in data sequence. For better resolution it is necessary to increase the length of sequence of data. Usage of time-frequency transform for real time measurement of power line frequency has been explored in the doctoral dissertation. New method for measurement of power line frequencies in real time is presented: Adaptive Chirp Transform (ACT) algorithm for power frequency measurement. It is adjusted for continuous monitoring of power frequency. Signal is first preprocessed with adaptive filter to minimize the error of non-linear model parameters. The resulting parameters are used to narrow the frequency range for CZT method to be effective. Algorithm code has been analyzed and computation complexity has been significantly decreased. Using this algorithm it is possible to measure frequency transients with sufficient accuracy and low execution time. Algorithm is verified through simulations and real-time data. Algorithm presented in this paper can estimate instantaneous frequency. It can perform two tasks. First task is to measure frequency of continuously monitored signal, and the second task is to evaluate that information quickly and as often as possible. Achieving the first task requires the use of Interpolated Descrete Fourier Transform (IpDFT) algorithm, because of it small execution time, and relatively small error. To achieve second task it is necessary to observe very short sequence of data, so that transients in frequency can be detected. As the signal is sampled in real time, the signal frequency can be calculated from small sequence of data. There are two main problems in this method. By reducing the size of data sequence, error of IpDFT algorithm is increased and also, the total time in which the algorithm needs to be evaluated is reduced. It can also be noted that in data sequences shorter than one period of signal best results are obtained with the CZT algorithm. Consequently, to achieve a low relative error, a large number of points in frequency spectrum is needed which increases computation time of CZT. Therefore, it was necessary to develop new method to reduce algorithm complexity. Proposed algorithm is based on adaptive filter and CZT. Preprocessing of data sequence is made by adaptive filter to narrow the frequency range in order to decrease the number of points in the frequency spectrum that needs to be calculated. Within this range, the frequency of data sequence is calculated using the CZT algorithm. All parts of algorithm which are not dependent on the measured signal are calculated offline and located in data base. Data base also include points in the frequency spectrum that are essential for CZT calculation. It is created in the beginning of the algorithm first run as the result of computation complexity analysis of adaptive filter and CZT. Data base reduces the number of operation calculated online to minimum. Proposed algorithm retains low relative error of CZT algorithm for very short sequences of data (below one period). Computation time is minimized so that the complete algorithm calculation is done before the next time sequence. Algorithm is developed for continuous frequency monitoring and is robust for noise in signal. Based on comparison with existing methods, advantages and disadvantages of this method have been analysed. Method for determining frequency spectra and RMS value of power line voltage by applying method for measurement of dynamic frequency changes has been presented. Measurement uncertainty of the new method has been analysed and optimization of power line frequency measurement in real time by determining power quality has been performed. - KEYWORDS: measurement, power frequency, fast Fourier transform, Chirp-z transforms, measurement uncertainty, frequency spectra

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