Impedance models

In Dr. Jian Sun's 2009 IEEE trans. Power Electronics letter, impedance model (Laplace) application in detecting resonances in circuits is demonstrated. The beauty of this approach is the conversion of a circuit analysis problem into a feedback control stability analysis problem. From that point, Nyquist stability criterion can be applied.

Another advantage of this approach is component level analysis. Unlike eigenvalue based analysis that a whole dynamic system state matrix has to be formulated, impedance models are built component by component. Therefore, sensitivity analysis can be carried at component level which leads to more insights.

Our letter Nyquist-Stability-Criterion-Based SSR Explanation for Type-3 Wind Generators
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6197223&tag=1  (IEEE trans. Energy Conversion, Sep. 2012) adopted impedance modeling approach for Type 3 wind with series compensated network resonance analysis. Two impedance models are formulated: one for the RLC circuit, the other for the DFIG circuit.

For the machine circuit, standard textbooks have well-developed circuit model for induction machine The only difference for DFIG circuit from induction machines is the control circuits of the two converters. With assumptions, the control circuits in vector control can be integrated into scalar impedance model. Another trick of modeling is to integrate mechanical system movement (the rotating speed) into the impedance model.

Intuition wise, we can just write slip(s) = 1-j(wm)/s. Theoretically, this can be derived based on dq-based machine modeling and its conversion to phase domain.

With the developed impedance model, analysis results are super clear which shed insights into key impacting factors of resonance.