Uncertainties of multiport VNA S-parameter measurements applying the GSOLT calibration method

For the general short-open-load-thru (SOLT) calibration of the n-port vector network analyzer with n + 1 measurement channels, the sensitivity coefficients for the S-parameters of the n-port device under test are developed as functions of the deviations of the scattering parameters for the SOLT calibration standards. Using the concept of general node equation, a generalized formula for the S-parameter deviations with respect to the error terms has been deduced. In addition, expressions representing the deviations of error terms with respect to the non-ideal calibration standards are given by a series of matrix operations. Finally, after calculation of sensitivity coefficients, they can be used for establishing the type-B uncertainty budget for S-parameter measurements

The importance of measurement of transmission losses and associated measurement uncertainty on the cross-border energy exchange

U početnoj fazi istraživanja napravljen je pregled znanstvene literature vezano za procjenu mjerne nesigurnosti. Utvrđeno je da je najzastupljenija metoda sukladno međunarodno prihvaćenom dokumentu „Guide to the expression of uncertainty in measurement“, tzv. GUM metoda. Ova metoda sadrži određene nedostatke te je izdana dopuna istog dokumenta koja preporuča uporabu Monte Carlo metode. Nadalje, u disertaciji je prikazan trenutno zastupljeni način za utvrđivanje razmijenjene energije kod prekogranične razmjene električne energije uključujući metode izračuna gubitaka prijenosa. Utvrđeno je da niti jedna metoda ne uključuje mjernu nesigurnost odnosno sistematske pogreške obračunskog mjerenja. Naime, uslijed velikih količina prenesene energije mali postotci sistematskih pogrešaka mogu rezultirati značajnom krivo raspodijeljenom energijom između operatora prijenosnih sustava odnosno potencijalnom financijskom štetom za sudionike razmjene. U okviru disertacije proveden je postupak izračuna mjerne nesigurnosti otpora prijenosnog voda i gubitaka s pomoću GUM i Monte Carlo metode. Za potrebe potonje metode proveden je postupak procjene razdiobe izlazne veličine. Također je razvijen je način utvrđivanja mjerne nesigurnosti razmijenjene energije i gubitaka prijenosa što uključuje metodu za ispravak razmijenjene energije i gubitaka za iznos sistematskih pogrešaka čime je smanjena ukupna mjerna nesigurnost te metodu za raspodjelu razmijenjene energije i pripadajućih gubitaka. Praktični rezultati pokazuju da je mjerna nesigurnost smanjena nakon ispravka sistematskih pogrešaka čime je potvrđena hipoteza disertacije. Može se zaključiti da ova metoda predstavlja pravedniji način za utvrđivanje razmijenjene energije i gubitaka prijenosa kod prekogranične razmjene energije.In the initial phase of the research process, a review of scientific literature was performed regarding the measurement uncertainty calculation methods. It is found that the most commonly used method is according to the internationally accepted document "Guide to the expression of uncertainty in measurement", i.e. GUM method. However, this method contains certain deficiencies and has been followed by the Supplement 1 which recommends using the Monte Carlo method. Furthermore, the dissertation presents the current method for determining the exchanged energy on the cross-border energy exchange as well as methods for calculation of the transmission losses. It is found that the actual methods do not involve measurement uncertainty nor systematic errors in the calculation procedure. Namely, due to large amounts of exchanged energy small percentages of systemic errors can result in significant erroneously associated energy to the transmission system operators, i.e. potential financial damage for energy exchange participants. A method for calculating the measurement uncertainty of transmission line resistance and transmission line losses using the GUM and the Monte Carlo method is developed. For the purpose of the latter method, the procedure for estimating the distribution of the output value is performed. A method for determining the measurement uncertainty of the exchange of energy and the transmission losses, including the method for correcting the exchanged energy and transmission losses for the amount of systematic errors is developed, thus reducing the total measurement uncertainty. A method for allocating the exchanged energy and the transmission losses between transmission system operators is developed as well. Practical results show that the measurement uncertainty is reduced after correcting systematic errors, thus confirming the hypothesis of the dissertation. It can be concluded that this method represents a fairer way to determine the exchanged energy and the transmission losses on the cross-border energy exchange