A simple method for shifting local dq impedance models to a global reference frame for stability analysis

Impedance-based stability analysis in the dq-domain is a widely applied method for power electronic dominated systems. An inconvenient property with this method is that impedance models are normally referred to their own local reference frame, and need to be recalculated when referring to a global reference frame in a given network. This letter presents a simple method for translating impedance sub-models within a complex network, from their own reference frames to any given point in the network. What distinguishes this method is that by using a simple rotational matrix, it only needs impedance models in their own local reference frames, to be translated to a global reference in the network. By way of this method, standard circuit analysis rules for series and parallel connection are applicable, as proven in the letter. The method is defined and validated for impedances in the dq and modified sequence domains, and it is shown that the dependency on reference frame is marginal in the latter. An additional finding from the application of this method is that components or subsystems with a certain symmetry property called Mirror Frequency Decoupling are invariant to the choice of reference frame. The method is illustrated and validated by comparing analytical calculations with a frequency sweep in MATLAB Simulink. Keywords—dq-domain, Impedance Modeling, Power Electronic Systems, Modified Sequence Domain, Stability Analysis.