We study the autocovariance structure of a general Markov switching second-order stationary VARMA model.Then we give stable finite order VARMA(p*, q*) representations for those M-state Markov switching VARMA(p, q) processes where the observables are uncorrelated with the regime variables. This allows us to obtain sharper bounds for p* and q* with respect to the ones existing in literature. Our results provide new insights into stochastic properties and facilitate statistical inference about the orders of MS-VARMA models and the underlying number of hidden states.

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.