Approximation of the frequency response of power systems based on scale invariance

Power networks are complex systems composed of many heterogeneous and interacting components. Smart grids are even more complex systems due to the convergence of electrical and communication networks. In order to deal with this complexity, a mathematical model that is reduced-size, accurate, wide-band and knowledge based is required for dynamic studies. This paper introduces a novel modeling approach based on scale invariance to build an approximation of the frequency response of power systems. This approach combines an asymptotic and a resonant model. Both use the spectral dimension of the network which is a key parameter to describe its scale invariance. The resonant model is identified by using an improved vector fitting method. The improvement consists in a guess of the initial poles used for the identification which is deduced from the scale invariant distribution of the dynamic modes of the network. An application to an IEEE test transmission system is finally shown.