| Abstract | Ova disertacija bavi se mjerenjem izmjeničnih signala i električne snage u vrhunskoj točnosti. Uvod donosi kratak pregled trenutnog stanja u svijetu na tom polju mjeriteljstva te ističe prednosti i nedostatke postojećih mjernih metoda. Naglasak je na mjerenjima termičkim pretvornicima i elektroničkim množilima, kao već dugo upotrebljavanim i provjerenim metodama, dok se metoda uzorkovanja razvijena u njemačkom PTB-u, koja je najsličnija našem rješenju, samo kratko opisuje na kraju uvoda. Tu metodu moguće je razumijeti i objektivno usporediti s našom tek nakon usvajanja teorijske podloge koja se sustavno razrađuje u cijelom tekstu, stoga su ta razmatranja u uvodu izostavljena i ostavljena za kraj cijele disertacije. Prvo poglavlje započinje raspravom o tehničkim ograničenjima koja uvelike određuju mogućnosti metoda temeljenih na uzorkovanju i obrazlaganjem specifičnosti našeg postupka uzorkovanja u odnosu na najčešće primjenjivana. Potom se detaljno razrađuje teorijska podloga naše metode za mjerenje spektralno čistog sinusoidnog signala pod pretpostavkom savršenog uzorkovanja i nizom računalnih simulacija procjenjuje njene krajnje dosege u pogledu točnosti. Nakon detaljne kritičke provjere rezultata simulacija, teorija se proširuje i na posve realna mjerenja uzimanjem u obzir svih predvidivih nesavršenosti samog uzorkovanja. Točnost predloženih računskih metoda i postupaka opet se prvo procjenjuje računalnim simulacijama, a kao konačan dokaz valjanosti teorijskih postavki daju se rezultati niza mjerenja u Primarnom elektromagnetskom laboratoriju Fakulteta elektrotehnike i računarstva u Zagrebu koji dokazuju da mjerna nesigurnost pri mjerenju amplitude sinusoidnog signala u laboratorijskim uvjetima ne prelazi 5 ppm (uz primijenjeni faktor proširenja mjerne nesigurnosti k = 2). Ostatak prvog poglavlja posvećen je proširenju teorijske podloge ove metode i na signale sastavljene od više valova (harmonika), opet poštujući slijed izlaganja od teorijske podloge, preko računalnih simulacija do stvarnih pokusa. Tu se primjenjuje teorija obrade vremenski diskretnih signala, ponajprije diskretna Fourierova analiza i digitalno filtriranje, ali u kombinaciji s prethodno razvijenom metodom za mjerenje spektralno čistog sinusoidnog signala. I računalne simulacije i pokusi u PEL-u dokazali su izvanrednu točnost ove metode, tj. mjernu nesigurnost samo malo veću nego za čistu sinusoidu, točnije oko 8 ppm (k = 2). Drugo poglavlje posvećeno je mjerenju snage. Na početku se primjena metode izložene u prvom poglavlju proširuje i na mjerenja faze, odnosno fazne razlike dvaju signala, čime ona postaje potpuno cjelovita metoda prikladna za primjenu u mjerenjima snage. To proširenje primjene dovelo je do daljnjeg unaprijeđenja prethodno razvijene računske procedure pa se točnost izračunavanja svih ključnih parametara mjerenog signala gotovo izjednačuje. Nizom pokusa u PEL-u dokazuje se mjerna nesigurnost fazne razlike od približno 10 ppm (k = 2). Na kraju se razmatraju razne mogućnosti za primjenu te metode u mjerenjima snage. Predlažu se u osnovi tri različita mjerna sustava i ističu njihove razlike, odnosno prednosti i nedostatci u međusobnim usporedbama te se uspoređuje naše rješenje mjerenja snage s PTB-ovim. Probnim pokusima, s relativno skromnom (rekli bismo neprimjerenom) opremom, potvrđene su pretpostavke o relativno visokoj razini ostvarivih točnosti primjenom predloženih rješenja jer je već pri prvim mjerenjima postignuta mjerna nesigurnost od petnaestak ppm. |
| Abstract (english) | This dissertation is concerned with high accuracy measurements of AC signals and electrical power. The introduction contains a short survey of the current stage in that field of metrology and also reveals advantages and disadvantages of the existing measurement methods. The main stress is on the measurements applying thermal converters and time division multipliers, as already long used and proven methods, while the sampling method developed in German PTB, although the most similar one to our method, is only briefly described. That method can be objectively evaluated and compared with our method only after adoption of the theoretical basis, which is systematically studied throughout the whole text, so such discussions were left for the end of the whole dissertation. The first chapter begins with the treatise of the technical limits that strongly influence the abilities of sampling methods, followed by explanation of specifics of our manner of sampling in comparison with the most frequently used ones. In continuation, the detailed discussion on theoretical basis of our method for measurement of spectrally clean sinusoid signal, assuming the perfect sampling, is carried out, as well as a number of computer simulations in order to estimate the highest reachable accuracy. After thorough evaluation of the simulation results, the theory is extended to the real measurements, taking into account all predictable imperfections of sampling. Accuracy of suggested calculating procedure is again estimated by computer simulation, and as the final proof of worthiness of theoretical thesis, the results of a series of real measurements in the Primary Electromagnetic Laboratory of the Faculty of Electrical Engineering and Computing in Zagreb are given, which clearly show that the measurement uncertainty for measurements of amplitude of sinusoid signal in laboratory conditions does not exceeds 5 ppm (with the measurement uncertainty extension factor k = 2 applied). The rest of first chapter introduces spectral analysis as further development of the theoretical basis of our method, so that it can be used also in measurements of signals composed of many harmonics, again following the sequence of explanation from theoretical basis, over computer simulations to the real measurements. Here, the theory of discrete time signal processing is applied, first of all the Discrete Time Fourier Transform and digital filtering, but in conjunction with the previously developed method for measurement of spectrally clean sinusoid signal. Computer simulations, as well as experiments in PEL have proven an extraordinary accuracy of this method, that is, only a little higher measurement uncertainty than for the measurement of clean sinusoid, i.e. about 10 ppm (k = 2). Second chapter is devoted to the power measurement. At the beginning, an improvement of the method introduced in the first chapter is described, which enables that method to be applied also in measurement of the phase, i.e. phase difference between two signals. Improved in that way, this method becomes completely finished and suitable for power measurement. Besides enabling it to measure phase difference, the last development resulted with advance in calculation of signal parameters, so all relevant parameters can be calculated with almost equal accuracy. Uncertainty of phase difference is about 8 ppm (k = 2), what is proven with a series of experiments in PEL. Finally, suitability of that method for power measurement is considered. Basically, three different measurement systems are proposed and their similarities, as well as differences noticed. Also, an objective comparison with the PTB’s solution is provided. Trial experiments, using relatively inappropriate equipment, justified our assumptions about relatively high reachable accuracy of proposed measurement systems and method, because already in these first measurements an uncertainty of about fifteen ppm was obtained. |
