Modeling of wind farms to determine their short circuit contribution in response to faults is a crucial part of system impact studies performed by power utilities. Short circuit calculations are necessary to determine protective relay settings, equipment ratings and to provide data for protection coordination. The plethora of different factors that influence the response of wind farms to short circuits makes short circuit modeling of wind farms an interesting, complex, and challenging task. Low voltage ride through (LVRT) requirements make it necessary for the latest generation of wind generators to be capable of providing reactive power support without disconnecting from the grid during and after voltage sags. If the wind generator must stay connected to the grid, a facility has to be provided to by-pass the high rotor current that occurs during voltage sags and prevent damage of the rotor side power electronic circuits. This is done through crowbar circuits which are of two types, namely active and passive crowbars, based on the power electronic device used in the crowbar triggering circuit. Power electronics-based converters and controls have become an integral part of wind generator systems like the Type 3 doubly fed induction generator based wind generators. The proprietary nature of the design of these power electronics makes it difficult to obtain the necessary information from the manufacturer to model them accurately. Also, the use of power electronic controllers has led to phenomena such as sub-synchronous control interactions (SSCI) in series compensated Type 3 wind farms which are characterized by non-fundamental frequency oscillations. SSCI affects fault current magnitude significantly and is a crucial factor that cannot be ignored while modeling series compensated Type 3 wind farms. These factors have led to disagreement and inconsistencies about which techniques are appropriate for short circuit modeling of wind farms. Fundamental frequency models like voltage behind transient reactance model are incapable of representing the majority of critical wind generator fault characteristics such as sub-synchronous interactions. The Detailed time domain models, though accurate, demand high levels of computation and modeling expertise. Voltage dependent current source modeling based on look up tables are not stand-alone models and provide only a black-box type of solution. The short circuit modeling methodology developed in this research work for representing a series compensated Type 3 wind farm is based on the generalized averaging theory, where the system variables are represented as time varying Fourier coefficients known as dynamic phasors. The modeling technique is also known as dynamic phasor modeling. The Type 3 wind generator has become the most popular type of wind generator, making it an ideal candidate for such a modeling method to be developed. The dynamic phasor model provides a generic model and achieves a middle ground between the conventional electromechanical models and the cumbersome electromagnetic time domain models. The essence of this scheme to model a periodically driven system, such as power converter circuits, is to retain only particular Fourier coefficients based on the behavior of interest of the system under study making it computationally efficient and inclusive of the required frequency components, even if non-fundamental in nature. The capability to model non-fundamental frequency components is critical for representing sub-synchronous interactions. A 450 MW Type 3 wind farm consisting of 150 generator units was modeled using the proposed approach. The method is shown to be highly accurate for representing faults at the point of interconnection of the wind farm to the grid for balanced and unbalanced faults as well as for non-fundamental frequency components present in fault currents during sub-synchronous interactions. Further, the model is shown to be accurate also for different degrees of transmission line compensation and different transformer configurations used in the test system.

The power converter is one of the key components in power system applications such as high voltage direct current (HVDC) systems and the grid connection of intermittent sources such as wind and solar power. However, the increased penetration of converter-based generation introduces challenges, such as sub-synchronous interaction between the converter control system and the grid. These control interactions are characterized by fast-growing, subsynchronous oscillations (SSO). This thesis deals with the analysis of sub-synchronous control interactions (SSCI) between doubly-fed induction generator (DFIG)-based wind farms and series compensated transmission lines. Moreover, the thesis aims to identify a method for mitigating the sub-synchronous oscillations using a static synchronous compensator (STATCOM), with a supplementary damping controller. The study is based on work in PSCAD/EMTDC and uses a system based on the IEEE first benchmark model, acting as a grid, and the scaled power output of a DFIG turbine model, modeling a wind farm. Initial impedance-based analysis in the frequency domain shows that the DFIG wind farm has a negative resistance throughout the sub-synchronous frequency range. A negative resistance may result in negative damping of the system and further introduce the risk of instability. The wind farm resistance and, in turn, system stability is affected by the current control loop of the DFIG-converter. The transmission line compensation factor largely impacts the system stability, while the power output has a minor effect. A time-domain analysis is performed to verify the result of the frequency domain analysis. Further on, a grid-forming STATCOM is added to the system for VAr compensation. Additional stability analysis shows that even though improvingthe stability, the STATCOM alone is not adequate to mitigate the SSCI. The proposed damping strategy is based on modifying the STATCOM voltage reference andcan be divided into three steps: detecting the SSO, estimating the sub-synchronous component, and modifying the extracted signal. The detection algorithm is based on a half-cycle comparator, while the modification is done through a proportional gain. When estimating the sub-synchronous components, two methods are proposed and compared. The first estimation method is based on a conventional power system stabilizer (PSS) method, and the second is afilter-less method.