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As the penetration of complex grid-connected devices, such as power electronic inverters, increases, so too does the complexity of analyzing system stability. A graphical application of the Nyquist stability criterion is presented that indicates how an individual load and source each contribute to the closed-loop system grid eigenvalues. The case study is not limited to particular impedance forms or scenarios like the more common complex torque coefficient method or passivity theory method. From the individual frequency responses of the load and source impedances, the graphical technique indicates how each impedance contributes to the system stability. Examples are provided that successfully indicate the cause of instability for a digitally controlled voltage source inverter (VSI) operating as a microgrid, with a current source inverter as a load. A second example is provided that identifies the potential instability of a VSI running an induction machine. A 42-kW inverter system is used to confirm the findings, showing a close correlation with the theoretical analysis.
Turner et al. (2012) studied this question.