Frequency-domain modeling of time-periodic switched electrical networks: A review

Power networks are, in nature, nonlinear time-variant systems. Starting with synchronous machines, which function as generators, passing by transmission and distribution networks whose topologies are altered due to different switching actions in the network, and ending with uncontrolled loads, which depend to a large extent on customer behavior and their dynamics. Despite the aforementioned nature, power system analysis mainly relies on taking snap shots of the system to estimate its behavior under different conditions, e.g., normal operation load flow, short circuit analysis, etc. Nevertheless, the time-varying characteristic of modern power systems, e.g., time-periodic switching of power electronic converters, impacts the overall network behavior; such impact can be interpreted as overvoltages, waveform distortion, resonance conditions, and even instability. Here the need to account for time-varying nature in modeling of modern power networks.Frequency-domain (FD) provides a convenient domain to solve a set of differential equations that describes the system as algebraic equations for the aforementioned studies, though limited to linear systems. In performing power system studies, periodic nature of rotating machines is accounted for by Park's transformation, which is able to mask the time-periodic nature of the machine in a manner that does not compromise the simplicity of the solution. Yet, the introduction of converters sidestepped FD for network analyses to the favor of time-domain (TD) analysis tools, albeit their relative complexity and large computational times.However, since the inception of the need to analyze time-periodic (TP) systems in general, numerous techniques evolved with varying degrees of success to provide a practical tool for network studies. This paper provides a brief of those efforts. The paper discusses Floquet theory, Harmonic Domain Dynamic Transfer Functions, and Equivalent Signal theory as tools for analysis of TP power systems, putting special attention to switched networks. Also, the paper compares those tools from the points of view of: (i) computational effort for model preparation, (ii) possible applications to modern power networks, and (iii) suitability for integration with present network analysis tools. Keywords: Frequency-domain models, Time-domain models, Equivalent signal theory, Floquet theory, Time-periodic systems, Harmonic Domain Dynamic Transfer Function