Improved stability analysis of delayed frequency regulation systems for a cyber-physical microgrid

In a microgrid, the types of power supply and users are diverse. To use the frequency support potential of the multi-type of power supply units in the microgrid, these units can be connected to form a frequency control system with the help of an open network. However, a signal transmission delay exists in the network, which may affect the control performance and further lead to instability. Considering the effects of the delay type, this paper analyzed the micro-grid system stability during frequency support, and the allowable time delay range is estimated when the frequency control system can work normally. Firstly, based on the frequency support principle in a micro-grid, the mechanism equations of each part involved in the micro-grid frequency support are presented, and the time delay of the control loop is considered so that the state-space model of the frequency support control system is built. Secondly, based on Lyapunov stability theory, a time delay-related discriminant approach is proposed for the control system to maintain stability using increasing range function, integral inequality of auxiliary function, and matrix injection. Finally, the delay tolerance in different scenarios of a specific micro-grid system is estimated by the proposed approach. The result shows that the proposed approach is less conservative than the existing methods. Meanwhile, the relationship between controller gain and delay tolerance is given, which can be used as a reference in the controller design.