The impedance-based stability analysis is emerging as a common method to evaluate the stability of networks containing large shares of inverter-based resources (IBR, incl. HVDC VSC/MMC) in the sub-/supersynchronous and harmonic frequency ranges. The analysis can be applied to evaluate the system stability in the frequency domain regarding the identification of unstable system configurations or remaining stability margins. The method requires the evaluation of frequency-dependent equivalent impedances of the power system. The two major approaches to determine the frequency-dependent equivalent power system impedances are the frequency scan in the time-domain (EMT simulation) and the frequency sweep in the frequency domain by means of frequency-dependent impedance characteristics. The differences between both approaches as well as the respective advantages and challenges have been discussed in a previous publication. The major advantages of the frequency sweep are reduced computational cost and that there is no need to use and exchange highly detailed EMT models.

As part of a prior publication, the frequency sweep method has been implemented to carry out single-connection assessment, for example grid connection assessment of a single IBR or larger plants consisting of multiple IBRs. This is done by evaluating the Nyquist criterion of a SISO system (single input single output), where the stability of the extended network is assessed. This also includes the consideration of the coupling over frequency effect, where voltage perturbations at one frequency can cause currents at a shifted frequency via transfer impedances of IBRs. The effect is inherently considered in the frequency scan but needs to be explicitly modelled for the frequency sweep.

This paper expands on the previous work and presents the application of the frequency sweep for multi-connection assessment with coupling over frequency effects and considerations of operating point dependencies, which are especially of interest for frequencies below the 2nd harmonic order. Whereas the single-connection assessment requires that both the newly connected plant as well as the network including all other plants are stable on their own, the multi-connection assessment evaluates the stability of a MIMO system (multiple input multiple output), which can split the network into a passive or known stable part and the group of newly added IBRs or plants. This is especially relevant for larger power systems for which the stability of the network itself is often unknown, since not every future operating point and switching configuration is tested and known to be stable. Furthermore, long-time network planning uses drastically modified networks, for which the overall stability is unknown. Setting up detailed EMT models for future expansions with all their uncertainties would be a major challenge. Analysis based on a frequency-domain model can simplify the effort required to create suitable power system models. In addition, the consideration of contingency cases can be easily integrated in the analysis.

An example using a larger power system is provided to showcase the application of the frequency sweep for the multi-connection assessment under consideration of the coupling over frequency effect, operating point dependency and contingencies. Lastly, the observability and participation and of IBRs in stability issues identified via the multi-connection assessment is addressed.