Analiza širjenja elektromehanskih motenj v elektroenergetskem sistemu s pomočjo modela kontinuuma

MOMIROVSKI, ALEKSANDAR (author), Rudež, Urban (mentor)

Magistrsko delo obsega del področja dinamike in oscilatorne stabilnosti tradicionalnega EES, v katerem so glavni proizvajalci električne energije sinhronski generatorji. Morebitni izpadi generatorjev, mehanski sunki na turbini, nepričakovano delovanje turbinske regulacije ter vklop ali izklop večjih bremen so tipični razlogi zaradi katerih pride do potujočega nihanja generatorjev, ki ga imenujemo širjenje elektromehanske motnje. Poiskati pravo formulo za izračun hitrosti in časa prihoda motnje ter analitično opisati časovno-krajevni potek širjenja motnje v nehomogenem anizotropnem zvezno-diskretnem EES sta bila izziv velikega števila matematikov, fizikov in elektroinženirjev ter predstavljata osnovni cilj te magistrske naloge. V uvodnem poglavju magistrske naloge je pridobljen vpogled v zgoraj opisano problematiko ter je potegnjena povezava med zapleteno matematiko in fizikalnim ozadjem pojava širjenja elektromehanske motnje. Tam so pojasnjeni tudi prednosti in slabosti načinov merjenja časa prihoda motnje, skupaj s kratkim opisom obstoječih PMU naprav ter WAMS/WAMPAC tehnologije. V drugem poglavju je na enostavnem radialnem modelu zgoščenega prenosnega EES izpeljana parcialna diferencialna enačba, ki nam pokaže valovno naravo širjenja motenj, ter je podana matematično-fizikalna analiza le-te. V tretjem poglavju se ukvarjamo z ustvarjanjem hitrostnih zemljevidov in računanjem časa prihoda motnje ter naredimo korak h konkretni aplikaciji v praksi. V četrtem pa se ukvarjamo z reševanjem, interpretacijo in vizualizacijo valovne enačbe. V tej magistrski nalogi so uporabljene originalno ustvarjene filtrske funkcije za razpršitev količine diskretno porazdeljenih elementov in istočasno ohranitev količine le-teh vzdolž prenosne linije. Na podlagi izpeljave valovne PDE, pri kateri je narejena linearizacija zgoščenega radialnega prenosnega sistema, so podani odgovori na neka ključna vprašanja, kot sta npr. ali je širjenje motnje odvisno od delovne točke generatorjev, in, zakaj se čas prihoda motnje iz točke A v točko B razlikuje od časa prihoda motnje iz točke B v točko A, če naredimo na obeh lokacijah identično motnjo. V petem, zaključnem poglavju je podana razprava doseženega dela ter so predlagane ideje o nadaljnjem delu. Za širši spekter razumevanja mag. naloge je ustvarjeno dodatno poglavje, v katerem so prikazani rezultati velikega števila različnih scenarijev, ki so bili simulirani z lastno izpisano programsko kodo, ki je izvirno podana na samem koncu mag. dela.

• Language: Slovenian
• Keywords: čas prihoda motnje, elektromehanska motnja, elektromehanski val, filtrska funkcija, hitrostni zemljevid, nihajna enačba, sinhronski generator, valovna parcialna diferencialna enačba, zvezni model, zgoščeni elektroenergetski sistem.
• Work type: Master's thesis/paper
• Organization: FE - Faculty of Electrical Engineering
• Year: 2019
• PID: 20.500.12556/RUL-106539
• Publication date in RUL: 04.03.2019

Secondary language

• Language: English
• Title: Electromechanical disturbance propagation analysis by means of continuum modelling

Abstract

The master thesis includes part of the dynamics and small-signal stability analysis of the traditional electrical power system, where the electrical energy is mainly generated by synchronous generators. The potential generator trips, mechanical shocks inside the turbine, unexpected operation of the turbine regulator or the switching of big loads are the typical reasons for the travelling swings of the generators across the network – a phenomena, that is called propagation of electromechanical disturbances. To find the right formula for the propagation velocity and the time of arrival of the electromechanical disturbances, as well as to analytically describe the propagation of the disturbances across the non-homogeneous anisotropic non-continuous power system in the space-time domain has been challenge for the physicists, mathematicians and engineers, and it represents the main aim of this master thesis. In the introductory chapter we give insight in the problematics and make a comparisson between the complex mathematics and the physical background of the phenomena. We briefly explain the pros and cons of the excisting phasor measurement units and the wide-area monitoring system as well. In the second chapter, a wave partial differential equation is derived for a simplified radial dense high-voltage power system. A mathematical and physical analysis of the wave equation is given as well. In the third chapter, we create speed maps, calculate the time of arrival of a disturbance and give an idea to a real application of such maps. In the fourth chapter, we analyze and vizualize a few important numerical solutions of the wave equation. In this master thesis, original filter functions are used for creating a continuum density of the discrete elements. At the same time, the filters preserve the quantity of every discrete element across the network path. By using the facts of the derivation of the wave PDE, we may answer very important questions such as: does the operation point influence the propagation, or, why the propagation differs from point A to point B and vice versa, when an identical disturbances are made at that two different locations A and B. Finally, in the fifth conclusional chapter, we discuss the achieved work and give ideas for a further work and upgrades. In the last additional chapter, we give the original program code and the results of various additional simulations for a broader understanding of the problematics.

• Keywords: time of arrival, electromechanical disturbance, electromechanical wave, filter function, speed map, swing equation, wave partial differential equation, synchronous generator, continuum model, dense electrical power system