Quantized memory proportional–integral control of active power sharing and frequency regulation in island microgrid under abnormal cyber attacks

This paper proposes a quantized memory proportional–integral (QMPI) control scheme to study the active power-sharing and frequency regulation (PSFR) issues of island Micro-Grids (MGs) under abnormal asynchronous stochastic cyber attacks (AASCAs). First, AASCAs are considered, which reflected the randomness and asynchrony of the attacks employed by hackers. Second, a novel relaxed condition that depends on the time delay (TD) is constructed, thereby reducing the usual constraint condition. Then, using the reciprocal convex matrix inequality (RCMI), some appropriate integral inequalities are used to process the integral terms to obtain a tighter upper bound. Next, based on Lyapunov–Krasovskii functional (LKF) method, a new QMPI controller under AASCAs is designed to ensure active PSFR in MGs. Finally, two kinds of experiments and simulations are carried out on the improved IEEE 34 bus test system to verify the performance of the control algorithm proposed in this paper.