Ensuring stable synchronization of nonlinear oscillators with inertia

Considers the problem of synchronizing the oscillations of nonlinear oscillators with inertia to ensure the conditions for the parallel operation of a large number of electrical energy sources connected to a local power grid via matching voltage-source inverters. The objective is to increase the equivalent inertia or, equivalently, the dynamic stability of a grid with a high penetration of inverter-based generation. Currently, this problem is addressed either without considering inertia or within a family of algorithms broadly referred to as «virtual synchronous machines» (VSM), which allow the inverter control system to emulate the behavior of an equivalent synchronous generator. However, real synchronous machines possess a high overload capacity, which permits voltage synchronization with a certain degree of error and, consequently, the emergence of inrush currents. This study investigates an alternative control strategy based on a virtual nonlinear oscillator, which utilizes the inherent capacity of oscillatory systems for precise self-synchronization. This significantly simplifies the pull-in process without causing inrush currents. Nevertheless, the known classical implementation of dispatchable virtual oscillator (dVOC) algorithms for the parallel operation of inverters unable to increase the time constant of the power grid. This paper proposes a modification of the dVOC algorithm that ensures the stable synchronous or anti-synchronous operation of oscillators on a directed ring topology by augmenting the mathematical model of the virtual oscillator with the General Motors inertial kinematic model. Through computer simulation, the effectiveness of the proposed algorithm for synchronizing a large number of nonlinear oscillators is demonstrated, along with the feasibility of controlling the inertial properties of such an oscillator system, using a local power grid as a case study.

Authors: V. S. Lavrinovsky, N. A. Dobroskok, R. M. Migranov, A. D. Stotskaya, P. D. Shuvalova

Direction: Electrical Engineering

Keywords: virtual oscillator control, virtual inertia, Kuramoto model, car following model, inertial dVOC, VOC synchronization

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