Nonlinear damping effects in a simplified power grid model based on coupled Kuramoto-like oscillators with inertia

Abstract

In our work, we simulate an uneven balance of produced and consumed energy in an artificially created network that can be considered as a simplified model of the operation of some energy network. The system under consideration has a ring topology consisting of locally connected power generators alternating with power consumers. Each node of the network is represented as a Kuramoto-type phase oscillator with inertia. Oscillatory network equations are transformed in accordance with the efficient network model proposed in [24], and studied numerically. The purpose of the work is to find conditions that prevent the loss of network synchronization. Nonlinear damping of oscillators has been proposed as a possible solution to the problem of stabilizing synchronicity. The maps of regimes constant with constant damping and with time-varying nonlinear damping are compared. In addition, the case of external action on a separate network node in the form of a rectangular pulse is considered. The research results show that nonlinear damping can prevent asynchronous behavior of oscillators and increase the stability of the ensemble to sudden fluctuations in systems. The results obtained can be applied in the field of power systems as a possible tool for increasing the sustainability of power grids. The opposite side of the results is the limitation of the use of nonlinear damping. The adaptive damping has a strong negative effect on the connected power generators, which leads to overheating and failure.