Modelling of power electronics controllers for harmonic analysis in power systems
The research work presented in this thesis is concerned with the modelling of this new generation of power electronics controllers with a view to conduct comprehensive power systems harmonic analyses. An issue of paramount importance in this research is the representation of the self-commutated valves used by the controllers addressed in this work. Such a representation is based on switching functions that enable the realization of flexible and comprehensive harmonic models. Modularity is another key issue of great importance in this research, and the model of the voltage source converter is used as the basic building block with which to assemble harmonic models of actual power systems controllers. In this research the complex Fourier series in the form of operational matrices was used to derive the harmonic models. Also, a novel methodology is presented in this thesis for conducting transient analysis of electric networks containing non-linearities and power electronic components. The methodology is termed the extended harmonic domain. This method is based on the use of time-dependent Fourier series, operational matrices, state-space representation and averaging methods. With this method, state-space equations for linear circuit, non-linear circuits, and power electronics controllers models are obtained. The state variables are the harmonic coefficients of x(t) instead of x(t) itself. The solution of the state-space equations gives the dynamic response of the harmonic coefficients of x(t). Moreover, a new harmonic power flow methodology, based on the instantaneous power flow balance concept, the harmonic domain, and Newton-Raphson method, is developed and explained in the thesis. This method is based on the instantaneous power balance as opposed to the active and reactive power balance, followed by traditional harmonic power flow methods. The power system and the power electronics controllers are modelled entirely in the harmonic domain.