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{\bfseries \large Abstract}
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There are significant concerns regarding the stability of weak power grids due to feeders of high impedance. This thesis investigates the stability domain of Squirrel Cage Induction Generator - Wind Turbines  (SCIG-WTs) with series compensation and weak interconnections to the power grid. Detailed time-domain and state-space modeling have revealed new bifurcations and oscillatory modes for a SCIG-WT connected radially or non-radially to a weak grid through a series compensated line. The stability domain analyses are carried out by computing bifurcations in the system by analyzing eigenvalues of the linearized system. 

A Static Var Compensator (SVC) with an improved voltage regulator design has been proposed to improve the stability domain of the radial system with respect to series compensation. The analyses demonstrate for the first time how the degree of compensation at which the Hopf bifurcation occurs depends on the X/R ratio of the line, operating slip of the induction generator, and voltage regulator parameters as well as the time delays in measurements. A damping controller design is proposed which greatly improves the dynamic stability of the WT-SCIG and eliminates destructive Hopf bifurcations in weak grids for a wide range of series compensation. This allows for a much larger percentage series compensation than what is usually possible while avoiding instabilities and thereby maximizing power transfer capability.

In addition to analyzing the stability of SCIG-WTs with radial and non-radial interconnections, the stability domains of induction motor loads fed through series compensated feeders have been analyzed. The presence of subcritical Hopf bifurcations resulting in motor stalling and reversal in the rotation of the induction motor has been shown for the first time. The influence of Automatic Voltage Regulator (AVR) parameters on the stability domain of the system with respect to series compensation has been studied. The influence of AVR gain and time constant along with the time constant of the voltage measurement transducer has been analyzed for the first time. The applications of this would help system planners to implement an appropriate level of series compensation so that safe, secure and reliable operation of the system can be achieved.