The major task of this work is to develop the simulation model which can be useful for the extreme behavior analysis of the global distributed high-voltage grids. This problem is connected with the fact that under high power load the network throughput is strongly depend on the matched work of the network elements and can significantly differ from the precalculated values. In this work in addition to the conventional algebraic and statistical models for the extreme cases investigations as well as for the network design and optimization problems it is suggested the simulation model which is based on the solution of the correspondent boundary-value problem on the graphs for the partial differential equations. Thus, the proposed model has the set of the essential distinctions from the existing: – it takes into account the time dynamics the all network processes and well enough simulates work of the global distributed high-voltage grids with given topology, – it can compute possible effects from the impact of the arbitrary external factors as well as investigate a possibility of the extreme case origination in the power grids, – it can be used for the network testing in the different operating modes before putting them into operation as well as on the system design phase, – it also can be used in the searching of the optimal energy-saving operating modes for the power grids with given topology.