The paper presents a simple, systematic and novel graphical method which uses computer graphics for prediction of limit cycles in two dimensional multivariable nonlinear system having rectangular hysteresis and backlash type nonlinearities. It also explores the avoidance of such self-sustained oscillations by determining the stability boundary of the system. The stability boundary is obtained using simple Routh Hurwitz criterion and the incremental input describing function, developed from harmonic balance concept. This may be useful in interconnected power system which utilizes governor control. If the avoidance of limit cycle or a safer operating zone is not possible, the quenching of such oscillations may be done by using the signal stabilization technique which is also described. The synchronization boundary is laid down in the forcing signal amplitudes plane using digital simulation. Results of digital simulations illustrate accuracy of the method for 2×2 systems.

This paper proposes two nonlinear exact and simple state space models of a Zsource converter (ZSC) connected to an ac grid. A generic model of a ZSC accompanied with proper controllers are proposed and a dynamic model of the whole system is derived; as a result, based on a simple one, an equivalent block diagram of the current-controlled ZSC system is proposed. The ac small signal stability method is applied and the impact of controller parameters on network’s stability is discussed. Besides, overall system dynamic performance has been assessed in the event of perturbations. Time-domain simulations have been implemented in PSCAD/EMTDC to validate the accuracy of the models and effectiveness of the proposed controllers. The results of the exact model are compared with the response of the equations which are applied in MATLAB.