Great interest in the field of dynamic systems and nonlinear processes is caused by research in the field of energy networks. A power grid is a complex network of coupled oscillators that demonstrates collective behavior by synchronizing
network elements at the base frequency of a power grid.

The purpose of the work is to study the dynamic stability of the synchronous state of the grid. The behavior of a network with homogeneous characteristics and a ring-shaped topology is investigated. An idealized energy network consisting of ten generators and ten consumers is considered. The influence of the generator output power and the inertia coefficient on the network synchronization is considered.

Method. An efficient network model (Nishikawa T., Motter A.E. Comparative analysis of existing models for powergrid synchronization) is studied, which excludes changes in consumer power from consideration, assuming that the power of all consumers is constant. This model allows us to consider the generators of the power system as coupled oscillators, the dimensionless parameters of which are determined by a large set of real physical parameters.

Results. The results showed that the natural frequency of the oscillator depends on the output power of the generator and does not always coincide with the synchronization frequency of the oscillators. With increasing generator power, the natural frequency is much higher than the synchronization frequency. At a critical value of the output power, oscillator oscillations become unstable, the generator frequency becomes equal to its natural frequency. The value of inertia plays a significant role in the stability of the generators; it is shown in the work that small values of the coefficient of inertia generators can produce energy in large ranges of output power without loss of synchronous state and regardless of the set of initial conditions.

Discussion. From obtained results it became known that the stable functioning of the generators with increase in output power is possible at small values of inertia coefficient. At large values of inertia coefficient, the synchronism of one or several generators is disrupted, leading the output generator to work at its own frequency, the value of which significantly exceeds the frequency of the network standard 50 Hz. The frequency perturbation depends on the location of one or another generator with respect to unstable generator.