Comparative analysis of single-machine equivalent methods for heterogeneous PMSG-based wind farm with the VSC-HVDC system

Abstract

This paper presents a comparative study of four single-machine equivalent methods used to simplify the analysis of small-signal stability (SSS) in grid-connected wind farms composed of multiple wind turbine generators (WTGs), particularly focusing on heterogeneous permanent magnet synchronous generator (PMSG)-based wind farms with a VSC-HVDC system. The four methods compared are (1) the dynamic aggregation method, (2) the average power or average control parameter method, (3) the weighted average method, and (4) the covering theorem method. The comparative analysis highlights the connections and differences among those four methods that help to gain a better understanding of their strengths and limitations as follows: (1) When the dynamic characteristics of individual PMSGs are different, the dynamic aggregation method may result in errors in assessing system SSS. (2) The average power and weighted average methods are accurate in assessing the system's SSS when a linear relationship exists between the system's oscillation modes and the PMSG output or control parameters. However, both methods may give erroneous SSS assessments when this linearity does not hold. (3) The weighted average method can accurately assess SSS when wind speeds differ across PMSGs, while the average wind speed method produces errors. (4) The covering theorem method is found to be conservative in SSS assessment. Finally, the methods are validated through simulations on two PMSG-based wind farm topologies connected to the grid with a VSC-HVDC system.