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The high penetration of wind power systems in the electrical network has introduced new issues in the stability and transient operation of the grid. By means of providing advanced functionalities to the existing power converters of such power plants it is possible to enhance their performance and also to support the grid operation, as the new grid codes demand. The connection of FACTS based on power converters, such as STATCOMs, are also contributing to the integration of renewable energies improving their behavior under contingencies. However, in both cases it is needed to have a grid voltage synchronization system, able to work under unbalanced and distorted conditions. This paper presents the discrete representation and performance of three PLL's structures, designed to work in that kind of situations. Their synchronization capability will be tested in different scenarios and their performance constraints will be established according to the Grid Code Requirements (GCRs).