Stability and Non-Linear Behaviour of Phase-Locked Loops used in Single-Phase Voltage Source Converters
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A robust phase synchronization system is essential for operating a voltage source con- verter connected to the electrical grid. The most widespread synchronization technique for single-phase systems is the synchronous reference frame (SRF)-phase-locked loop (PLL). Stability of the SRF-PLL applied to power converter systems has been the subject of nu- merous studies, though its behaviour has always been assumed linear. In this thesis relevant literature on the non-linear properties of the phase-locked loop is reviewed and applied to the SRF-PLL. The SRF-PLL is shown to be globally stable using a previously derived Lyapunov function. In addition, a non-linear effect called cycle slips, where the phase-locked loop is leaping between multiple 2π-periodic equilibria, is iden- tified in the literature. The results, obtained by numerical simulation, demonstrate how cycle slips can occur when the voltage source converter is connected to a weak grid, and lead to instability in the power output of the converter. Connecting non-linear theory developed for general phase-locked loop applications to phe- nomena observed in power converter systems has not been done before. This thesis does not deliver any control solutions to the problems presented, but should be an important step toward fully understanding the phase-locked loop used in power converters and its limitations.