Study on electromechanical wave continuum model for power systems in mechanics

It is observed from PMU measurements that disturbances of frequency and voltage angle propagate much more slowly in real power systems than electromagnetic wave. By modeling an electric power system as a continuum, the nonlinear partial differential equation in the form of a wave equation has been proposed which exhibits traveling wave behavior of these disturbances. In this paper, the nonlinear electromechanical wave equation is proposed by modeling power system in mechanics. According to the relation of wave motion to forced transverse vibration of coupled particles in classical mechanics, the wave equation of multi-mass damping disks is derived from its torsional vibration. Electromechanical dynamic of the power system is shown to be mathematically similar to the vibration of multi-mass disks. The analytical solution to the linearized wave equation about an equilibrium reveals some potentially important properties of wave propagation. The disturbance propagation with both the discrete model and analogous continuum model are investigated. Simulation results on a 64 generators ring system prove the correctness of the proposed continuum model for power system.