Identification of optimal locations for the voltage phasor measurement devices in the electric distribution system

V magistrskem delu smo s pomočjo simulacije v programskih orodjih Matlab in C++ predstavili vpliv postavitve naprav za merjenje kazalcev napetosti na preciznost trifaznega statičnega ocenjevalnika stanja, ki uporablja metodo uteženih najmanjših kvadratov odstopanj v razdelilnem elektroenergetskem omrežju. Pred začetkom simulacije smo zagotovili zadostno število psevdomeritev pametnih števcev v obliki injekcij delovnih in jalovih moči, da je zagotovljena spoznavnost modeliranega električnega omrežja. V programskem okolju Matlab smo nato simulirali realne meritve, torej meritve z dodanim belim Gaussovim šumom, ki ga imajo vse realne merilne naprave, ki dejansko povzročajo varianco rezultatov ocenjevalnika stanja. Pokazali smo, da z razredi točnosti meritev, ki so definirani v vseh tipih meritev, vplivamo na varianco oziroma preciznost ocenjevalnika stanja. Grafično in tabelarično smo prikazali odvisnost variance ocenjevalnika stanja kota Φ in magnitude napetosti |U| od dodajanja števila naprav za merjenje kazalcev napetosti U v 13-zbiralčnem radialnem razdelilnem izvodu. Ugotovili smo, da se z dodajanjem naprav za merjenje kazalcev napetosti PMU varianca statičnega trifaznega ocenjevalnika stanja znatno zmanjšuje le pri kotu Φ, pri magnitudi |U| pa je razlika med dodano 1 napravo in 13 PMU napravami zanemarljiva. S simulacijo smo grafično in računsko v tabelah prikazali, da odvisnost med številom naprav za merjenje kazalcev napetosti in varianco ocenjevalnika stanja predstavlja eksponentna funkcija. Pokazali smo, da je za sprejemljivo varianco ocenjevalnika stanja potrebna 100 % pokritost radialnega distribucijskega omrežja zaradi izrazite nelinearnosti med ocenjenimi koti Φ napetostnih kazalcev in nadaljnimi izračuni pretoki delovne in jalove moči v realnem času. Nadalje smo pokazali, da težko govorimo o optimizaciji postavitev PMU naprav, saj je način izbora postavitev meritev hevristične narave, ker zaradi zahtevnosti simulacij ne moremo zajeti vseh kombinacij postavitev.This Masters Thesis investigates the influence of the voltage phasor measurement unit placement in the power distribution system on the precision of distribution of state estimation results. Using simulations in software tools Matlab and C ++ the influence of such placement of the phasor measurement units on the precision of a three-phase distribution state estimator is demonstrated. Sufficient number of pseudo measurements from smart meters were provided in the form of real and reactive power injections, in order to ensure the electric grid observabilty. In the Matlab software tool we mathematically modeled realistic measurements with added white Gaussian noise, contained by all measuring devices and which in fact causes the variance of state estimation results. It has been shown that the accuracy classes of measurements, which are predefined in all types of measurements in the simulation, influence the variance of the state estimator. By using numerical calculations and graphical visualization it has been shown that the results highlight the relationship between the variance of the state estimator, angle Φ, voltage magnitude |U| and the placement of a number of PMU measurement devices in to the 13-bus radial feeder. It has been shown that by adding the PMU measuring devices, the variance of the static three-phase distribution state estimator is being significantlly decreased only for the angle Φ. Whereas, for the voltage magnitude |U|, the difference between 1 and 13 added PMU measurement devices is insignificant. Further on, by using a computer simulation it has been demonstrated that the relation between the added number of PMU measurement devices and the variance of the static three-phase distribution state estimator is represented by an exponential function. The thesis concludes that for an acceptable variance of the static three-phase distribution state estimator 100% coverage of radial distribution network is needed, due to explicit non-linear relation between the estimated angles Φ of the voltage phasors and further power flow calculations in real-time. Consequently, it is difficult to address the optimization of the PMU measurement devices placement due to heuristic nature of the method, as all combinations of the measurements placement is too complex to be simluated