Document Type


Publication Date



Institute of Electrical and Electronic Engineers

Source Publication

IEEE Access

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Original Item ID

DOI: 10.1109/ACCESS.2022.3188392


We study the swing equation in the case of a multilayer network in which generators and motors are modeled differently; namely, the model for each generator is given by second order dynamics and the model for each motor is given by first order dynamics. We also remove the commonly used assumption of equal damping coefficients in the second order dynamics. Under these general conditions, we are able to obtain a decomposition of the linear swing equation into independent modes describing the propagation of small perturbations. In the process, we identify symmetries affecting the structure and dynamics of the multilayer network and derive an essential model based on a ‘quotient network.’ We then compare the dynamics of the full network and that of the quotient network and obtain a modal decomposition of the error dynamics. We also provide a method to quantify the steady-state error and the maximum overshoot error. Two case studies are presented to illustrate application of our method.


Accepted version. IEEE Access, Vol. 10 (July 2022): 72658-72670. DOI. © 2022 Institute of Electrical and Electronic Engineers (IEEE). Used with permission.

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