The purpose of this work is studying the stability of the power grid, consisting of an arbitrary number of synchronous generators supplying a common passive linear load, to disconnection and connection of generators.

Methods. In this paper, numerical modeling of the power grid operation and the second Lyapunov method are used.

Results. Conditions for safe disconnection and connection of generators have been revealed, under which a synchronous mode is established in the disturbed power grid.

Conclusion. The power grid consisting of an arbitrary number of synchronous generators supplying a common passive linear load is considered. Using the approach based on the second Lyapunov method, conditions on parameters are found that ensure safe disconnection of generators, including, if any, a generator involving in the “inhomogeneous” load supply path, that differs from the others in current and transmitted power. The obtained estimates are confirmed numerically for power grids of various sizes. The evolution of the area corresponding to the safe connection of a generator to the power grid of five generators is also numerically traced.