I. Introduction
Power system stability has gained much attention and has been acknowledged as an important problem for secure system operation [1]. Many major blackouts occurrence due to power system instability have demonstrated the importance of this phenomenon [1]–[5]. Initially, angle stability has been of primary concern to power utilities. However, in the last two decades power systems have been operating under more stressed conditions than previously due to several factors such as continuing growth in interconnections and integration of emerging new technologies. Limitations to install new generating plants due the environmental pressures and economical reason caused the transmission lines to operate near the loading limits in order to cater for the electricity power consumption in heavy load areas. In addition, the system loading pattern due to deregulation in the electricity market, the growing use of induction machines and large penetration of renewable energy sources in distribution systems have made local coordination control system to appear more complex. All these stressed conditions in a power system exhibit a new type of unstable behavior which is known as voltage instability.