Extraction of frequency-dependent impedances of residential loads in low-voltage grids for harmonic stability assessment

Abstract

The impedance-based stability criterion (IBSC) is increasingly being researched and tested for the analysis and prognosis of harmonic stability or converter-driven stability. Due to the necessary division into two different subsystems for the application of the IBSC (e.g. depicting the grid and loads), frequency-dependent impedances representing the small-signal characteristics are necessary to model these subsystems. Load modeling is particularly necessary for grid-forming systems with active control loops (e.g. voltage-controlled inverters) since interactions between voltage-controlled and current-controlled components can occur. Due to a large number of systems and components as well as the related number of manufacturers in low-voltage grids, the extensive analytical modeling of all components and types is a challenge. A conceivable alternative is the experimental extraction of component impedances based on measurements of the terminal behavior.In this paper, a test bench is presented and used that includes different household appliances representing residential loads. These appliances are individually measured and the frequency-dependent impedances are extracted. From the extracted impedances, requirements are derived for the measurement and modeling. One key contribution of this paper is the analysis of the frequency resolution and the demonstration of advantages resulting from a regression-based calculation. It is shown that a linearly decreasing frequency resolution can be used, which can reduce the measurement time at the expense of accuracy. Furthermore, an approach to a black-box model parameter fitting is shown based on transfer functions with an a priori unknown model order. The results demonstrate that a model order can be found from which all measured household appliances can be modeled. In a final step, the individual impedances are analytically aggregated for larger grids into an equivalent impedance, and a sensitivity analysis is carried out by varying the individual penetration rates.