Delay-dependent Stability Analysis of Microgrid with Constant and Time-varying Communication Delays

This article describes the procedure to develop a cyber physical model of a microgrid considering the influence of constant and time-varying communication delays. The microgrid central controller transmits information through an open communication network that imposes certain constraints. One of the major constraints is communication delays, which affect the dynamic performance of the system. These delays may be constant or time varying. The impact of these time delays on the stability is addressed by finding an index called the time-delay margin. This article proposes an analytical method to determine the delay margin of a distributed generation based microgrid with constant and time-varying delays. In the case of constant time delays, the transcendental characteristic equation of the proposed microgrid model is transformed into a polynomial. The real roots of the polynomial coincide exactly with the imaginary roots of the characteristic equation, which decides the delay-dependent stability of the system. For the case of time-varying delays, a sufficient condition that verifies the asymptotic stability of the system is presented in this article. The delay margin values are theoretically calculated for different sets of microgrid central controller gains, and their accuracy is validated by simulation studies.