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-/super-synchronous 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. 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 the use of look-up tables for the IBR equivalent impedances, i.e. no need to 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 of an aggregated model of a power plant 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 power system 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 consideration of operating point dependencies and the coupling over frequency effect. This is especially of interest for frequencies below the 2nd harmonic order. The methodology for consideration of the coupling over frequency effect in the frequency sweep for multi-connection assessment is explained and derived theoretically.

While 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, including the consideration of contingency cases.

An example of a 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 and operating point dependency.