Power system stability is widely assessed based on tools that rely on the representation of voltages and currents through quasi-static phasor calculus, implying that the network itself and the synchronous machine stators are modeled by algebraic equations. Accordingly, the associated fast transients are neglected, assuming those decay rapidly. However, with the increasing penetration of converter interfaced generation in power systems, the reliance on quasi-static phasor calculus is to be questioned. In this paper, the validity of quasi-static phasor calculus models is verified, and dynamic phasor calculus is considered as the alternative. A methodology to systematically compare quasi-static and dynamic phasor calculus is developed. It includes frequency response, modal, and sensitivity analyses. The methodology is applied to an IEEE test network considering penetrations of converter interfaced generation of up to 100%. The models are implemented in MATLAB. The H-infinity norm is proposed as an indicator to identify differences in the applicability of the models. The results show that the quasi-static phasor calculus is suitable for stability analysis only if low bandwidths of converter controls are given. Dynamic phasor calculus instead is suitable and applicable to generic stability studies of integrated power electric and electronic systems with high penetration of renewables.
Analysis and Application of Quasi-Static and Dynamic Phasor Calculus for Stability Assessment of Integrated Power Electric and Electronic Systems
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