Bhatta Kshitij, Nazerian Amirhossein, Sorrentino Francesco
Department of Mechanical and Aerospace Engineering, Univeristy of Virginia, Charlottesvile, VA 22903, USA.
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, USA.
IEEE Access. 2022;10:72658-72670. doi: 10.1109/access.2022.3188392. Epub 2022 Jul 4.
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.
我们研究多层网络情况下的摇摆方程，其中发电机和电动机的建模方式不同；具体而言，每个发电机的模型由二阶动力学给出，每个电动机的模型由一阶动力学给出。我们还去除了二阶动力学中常用的等阻尼系数假设。在这些一般条件下，我们能够将线性摇摆方程分解为描述小扰动传播的独立模式。在此过程中，我们识别出影响多层网络结构和动力学的对称性，并基于“商网络”推导了一个基本模型。然后，我们比较全网络和商网络的动力学，并获得误差动力学的模态分解。我们还提供了一种量化稳态误差和最大超调误差的方法。给出了两个案例研究来说明我们方法的应用。
