الفهرس 
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Abstract
The appearance of computer simulation techniques has opened up opportunities for numerical studies in many fields of human activity. The field of computer simulation of electric power systems is the main tool in many areas of scientific research. This significantly increases the requirements of adequacy of the numerical methods and computer models. It is widely known that, switching transients and surges in electrical systems are mathematically formalized by the ordinary differential equations. The most difficulty while solving these equations is to obtain stable solutions. In one’s turn stability is closely linked with the concept of stiffness of differential equations. Stiffness is difficult and important concept in numerical solution of ordinary differential equations. It depends on the differential equation itself, the initial conditions (initial step, tolerance), and the numerical method. In particular, for problems of unloaded transformers switching-off at very low values of input capacitances, stiffness of differential equations is very high (it is difficult to obtain stable solutions). So there is a necessity of a special studying of stability to get the ways for obtaining the stable solutions. For this purpose we have chosen two of the most severe switching-off cases. The two cases are switching-off capacitor banks and unloaded transformers. In this research the effective methods of numerical modeling and computer simulation of switching processes in electrical networks are investigated. Also the dielectric properties of vacuum and SF6 as arc quenching medium were considered. Velocities of these mediums’ dielectric strength restoration were analyzed and corresponded formulas were obtained and presented. Finally the results of computer simulation the recovery voltages conditioned by capacitive and small inductive currents switching-offs by high voltage vacuum and auto-compression (SF6) circuit-breakers are analyzed.