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In this paper, a compact mathematical model having an elegant structure, together with a generic control framework, are proposed for generic power systems dominated by power converters that are interconnected through a passive transmission and distribution (T&D) grid, by adopting the port-Hamiltonian (pH) systems theory and the fundamental circuit theory. The models of generic T&D lines are developed and then the model of a generic T&D grid is established. With the proposed control framework, the controlled converters are proven to be passive and Input-to-State Stable (ISS). The compact mathematical model is scalable and can be applied to power systems with multiple power electronic converters with generic passive controllers, passive local loads, and different types of passive T&D lines connected in a meshed configuration without self-loops, so it is very generic. Moreover, the resulting power system is proven to be ISS as well. The analysis is carried out without assumptions on constant frequency/voltage, constant loads, and/or lossless networks, except the need of passivity for all parts involved, and without using the Clarke/Park transformations or the graph theory. To simplify the presentation, three-phase balanced systems are adopted but the results can be easily adapted for single-phase or unbalanced three-phase systems.
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This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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