The use of tangent vectors for voltage collapse analysis

Nowadays, it has been observed that the load demand increase in many electrical systems has not been matched with the necessary investments to upgrade the power generation and transmission. This has caused such systems to work more stressed leading to voltage stability problems. The understanding of the events leading to the voltage collapse phenomenon has been the aim of many researchers which resulted in the development of a great number of simulation programs. Many tools have been chosen to help determine the weakest system bus with less computational effort as possible in order to enable a quick response regarding the search of preventive measures to improve the system voltage stability level. In this sense, eigenvectors and tangent vectors are very useful sources of information. These two elements combined allow the determination of the critical bus and the generators which most influence the system stability. These analyses will allow the operators to make decisions on what variables to work on in order to avoid the voltage collapse