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.