Complex Frequency
This work provides a new theoretical tool for power system engineers to analyze transient frequency and voltage dynamics, but it is an incremental extension of existing frequency concepts.
The paper introduces the concept of complex frequency for power systems, where the imaginary part represents bus frequency variation and the real part captures voltage magnitude variation, enabling accurate analysis of transient dynamics. The proposed framework is validated through analytical and numerical examples.
The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for constant elements of the network admittance matrix. A variety of analytical and numerical examples show the applications and potentials of the proposed concept.