This paper first presents a step-by-step tutorial on modal analysis of a doubly-fed induction generator (DFIG)-based series compensated wind farm. The model of the system includes a wind turbine aerodynamics, a sixth-order order induction generator, a second-order two-mass shaft system, a fourth-order order series compensated transmission line, an eighth-order rotor-side converter (RSC) and grid-side converter (GSC) controllers, and a first-order DC-link model. Then, using modal analysis and time-domain simulations, it is shown that a fixed-series compensated DFIG is highly unstable due to the subsynchronous resonance (SSR) mode. In order to damp the SSR mode, the wind farm is interfaced with the gate-controlled series capacitor (GCSC) -which is a new series flexible AC transmission system (FACTS) device. A SSR damping controller (SSRDC) is designed for the GCSC using residue-based analysis and root locus diagrams, and an effective input control signal (ICS) to the SSRDC is identified in order to simultaneously increase damping of both the SSR and super-synchronous (SupSR) modes. The IEEE first benchmark model on SSR is adapted with an integrated DFIG-based wind farm to perform studies. Matlab/Simulink is used as a tool for designing process, and PSCAD/EMTDC is used for time-domain simulations.Nomenclature R line transmission line resistance (pu) X line transmission line reactance (pu) X T transformer reactance (pu) X S system reactance (pu) X C fixed series capacitor (pu) X tg transformer reactance in grid-side converter (GSC) (pu) i lq , i ld transmission line qd-axis currents (pu) i qg , i dg GSC qd-axis currents (pu) i qs , i ds stator qd-axis currents (pu) i qr , i dr rotor qd-axis currents (pu) v qs , v ds generator's terminal qd-axis voltages (pu) v qc , v dc qd-axis voltages across the fixed series capacitor (pu) v qr , v dr generator's rotor qd-axis voltages (pu) v qg , v dg GSC terminal qd-axis voltages (pu) E Bq , E Bd infinite bus qd-axis voltages (pu) Q s 0.5(v qs i ds −v ds i qs ), stator reactive power (pu) P s 0.5(v qs i qs + v ds i ds ), stator active power (pu) Q r 0.5(v qr i dr −v dr i qr ), rotor reactive power (pu) P r 0.5(v qr i qr + v dr i dr ), rotor active power (pu) Q g 0.5(v qg i dg −v dg i qg ), GSC reactive power (pu) P g 0.5(v qg i qg + v dg i dg ), GSC active power (pu) Q line 0.5(v ql i dl −v dl i ql ), transmission line reactive power (pu) P line 0.5(v ql i ql + v dl i dl ), transmission line active power (pu)T e 0.5X M (i qs i dr −i ds i qr ), electric torque (pu) i 0s , v 0s stator zero sequence components (pu) i 0r , v 0r rotor zero sequence components (pu) T tg mechanical torque between two masses (pu) P w , T w wind power and wind torque (pu) D g , D t damping coefficient of generator and turbine (pu) D tg damping coefficient between two masses (pu) K tg inertia constant of turbine and generator (pu) H t , H g inertia constants of turbine and generator (s) C DC-link capacitor (F) I DC DC-link current (A) v DC DC-link voltage (V) V w wind speed (m/s) R rotor radius of the wind...
