Doctor of Philosophy / Department of Electrical and Computer Engineering / Anil Pahwa / Shelli K. Starrett / Analysis of power system voltage stability has practical value in increasing wind penetration levels. As wind penetration levels increase in power systems, voltage stability challenges arise due to locating wind resources far away from load centers. This dissertation presents several different voltage stability methods for sizing new wind farms. Power system wind penetration levels depend on the available voltage stability margins (VSMs) of the existing power system and system load characteristics. Three new iterative methods have been developed to maximize wind penetration level in weak power systems based on systems’ VSMs. The first two methods use an iterative approach for increasing the size of each wind farm until reaching the collapse point. Wind farms with less negative impact on system VSMs are sized larger than others. A third wind farm sizing method has been developed using modal analysis in conjunction with the traditional voltage stability method (Q-V method). Wind farms are placed at buses in the power system which have the lowest negative impact on voltage instability modes (strong wind injection buses). By placing the wind farms at the strongest wind injection buses, higher amounts of wind power can be injected into the power system. To further increase wind penetration in weak power systems, two additional techniques are introduced and applied to the western Kansas power system. The first technique uses modes of voltage instability to place voltage support equipment like static var compensators at locations in the power system where they provide the needed reactive power support for increasing levels of wind penetration. The second technique uses the fact that wind patterns at a wind farm site may rarely allow the wind farm to produce its maximum capacity during the peak loading hours. Wind farm maximum sizes can be increased above their maximum voltage stable size limit without driving the power system into becoming voltage unstable. Preventing voltage collapse for the additional increases in wind farm sizes is accomplished by disconnecting some wind turbines inside the wind farm during critical times to reduce its power output to a voltage stable level.