In complex optimization of instantaneous steady-state modes of complex electric power system, the improved methods of successive intervals (IMSI) for determining the study-state mode of the system for various values of the vector of the independent variables on each elementary step of the generalized reduced-gradient method (GRGM) has found extensive application. The IMSI ia a definite reasonable combination of the method of successive linear approximation of the dependent variables as implicit functions of a certain independent parameter characterizing the process of natural or artificial deformation of the corresponding equations and the Newton-Rafson methods. A generalization of the IMSI (GIMSI) is presented using approximations of these implicit functions by polynomials of second and higher order, the method of constraining the limiting allowable deformation step on the basis of the condition of fairly rapid convergence, etc. Such a generalization allows the efficiency of the IMSI to be increased and its field of utilization to be expanded. A series of other fairly effective modern methods for determining steady-state modes, which are obtained in another way but actually contain an application of the Newton-Rafson technique, may be derived from the GIMSI as particular cases. Various applications of the GIMSI are considered for complex optimization, the investigation of modes that are limiting in terms of a periodic stability, the sensitivity of the solution of the equations for steady-state modes, etc. A definite systematization of methods that may be treated within the framework of the GIMSI for natural and artificial deformation of the equations is presented.