The algorithm for phase difference determination of low frequency sinusoidal signals

Pouzdano merenje fazne razlike između električnih signala neophodno je u mnogim mernim sistemima kao što su: merenje aktivne i reaktivne električne snage i energije, faktora snage, harmonika u električnom naponu i struji, određivanje kompleksnog odnosa izlaznog i ulaznog signala mernih pretvarača (delitelji napona i strujni šantovi). O značaju merenja faznog ugla najbolje govori činjenica da su mogućnosti merenja i etaloniranja koje se kraće označavaju CMCs (engl. Calibration and Measurement Capabilities) faznog ugla, nacionalnih metroloških instituta pojedinih država, objavljene na internet stranici Međunarodnog biroa za tegove i mere (fr. Bureau International des Poids et Measures - BIPM) http://kcdb.bipm.org, pošto ih je prethodno odobrila regionalna metrološka organizacija EURAMET (engl. European Association of National Metrology Institutes). Danas se fazna razlika između dva kontinualna sinusna signala najčešće određuje koristeći uzorke signala koji se obrađuju nekim od algoritama za određivanje fazne razlike. U NMI (engl. National Metrological Institutes) se za uzorkovanje signala uobičajeno koriste DSV (engl. digital sampling voltmeters) koji obavljaju vremensku i amplitudnu diskretizaciju signala. Uz rezultate merenja obavezno se daje i procena merne nesigurnosti, u skladu sa međunarodnim dokumentima. Predmet istraživanja disertacije je algoritam za određivanje fazne razlike iz uzoraka dva sinusna signala. Na osnovu poznatih algoritama UQDE (engl. unbiased quadrature delay estimator) i QDE (engl. quadrature delay estimator) razvijen je i testiran novi algoritam MSAL (engl. modified simple algorithm) za određivanje fazne razlike iz uzoraka dva sinusna signala. U novom algoritmu, korišćenjem dva postojeća signala uvode se dva nova signala fazno pomerena u odnosu na postojeće signale. Testira se hipoteza da je izborom faznog kašnjenja moguće dobiti vrednost fazne razlike između dva sinusna signala koristeći po jedan uzorak svakog signala (algoritam nazvan SAL), a...The reliable measurement of phase difference between two signals is essential in many measurement systems such as: measurement of active and reactive electric power and energy, power factor, voltage and current harmonics, the determination of the complex ratios between the output and input signals of transducers (voltage dividers and current shunts). The importance of phase angle mesurements is the best illustrated by fact that calibration and measurement capabilities (CMCs) of the national metrological institutes of individual countries are published at website of International Bureau of Weights and Measures (Bureau International des Poids et Measures - BIPM), http://kcdb.bipm.org, as previously approved by the regional metrological organization EURAMET (European Association of National Metrology Institutes). Nowadays, the phase difference between two continuous sinusoidal signals is usually determined by means of discrete samples of signals processed by some of the algorithms for the phase difference estimation. DSV (digital sampling voltmeters) are usually used for the time and amplitude discretization of signals in NMI (National Metrological Institutes). The results of measurements must be accompanied with the estimates of uncertainties according to the international recommendations. The subject of the dissertation research is algorithm for phase difference determination using samples of two sinusoidal signals. On the basis of known algorithms UQDE (unbiased quadrature delay estimator) and QDE (quadrature delay estimator) the new algorithm MSAL (modified simple algorithm) for phase difference determination from the samples of two sinusoidal signals is developed and tested. Two new signals phase shifted to the existing signals are introduced in new algorithm. The hypothesis that it is possible to get the phase difference between two sinusoidal signals..