# Impedance Modeling Based Method for Sub/Supsynchronous Oscillation Analysis of D-PMSG Wind Farm
## 1 Introduction
### Related Works  
Plenty of researches have been carried out to study on the mechanism of the SSO of the grid-connected D-PMSG farm. But yet the cause of this new type of SSO is not clear.  
Time-domain simulation, eigenvalue analysis, and impedance-based stability analysis are the mostly used methods in the analysis of SSO. It is intuitive to observe the SSO phenomenon by using time-domain simulation. However, it has difficulties in figuring out the interactions between the wind farm and power system. Eigenvalue analysis has the advantages in the mechanism analysis of SSO but this method needs plenty of information of power system and it is not realistic to apply in the large-scale system. Impedance-based stability analysis is a newly developed method in the analysis of SSO. In this method, D-PMSGs are considered to provide a capacitive impedance for the system which will lead to SSO. This method is not limited by the system scale and can be used in the black-box systems, which have flexible application scenario.  
Progress has been made in the study of impedance-based stability analysis. Existing approaches to analyzing such instability problems focus on small-signal impedance modeling [14]. As mentioned above, since the DC link capacitor between two converters isolates the machine side converter (MSC) and the grid side converter (GSC), the interactions between the GSC and the power grid are mainly concerned. Impedance-based stability analysis separates the inverter-grid system into two independent parts and calculates their impedance respectively. The inverter-grid system will remain stable if the ratio between the grid impedance and the inverter output impedance satisfies the Nyquist stability criterion.  
There are two methods to construct this impedance model: (1) transform the converter model into the \(dq\) reference frame, and use small-signal linearization; (2) use harmonic linearization method and directly model the three-phase positive- and negative-sequence impedance in the phase domain [15; 16]. The first method could easily obtain the impedance model for the \(dq\)-domain control system. However, several limitations were discussed: not suitable for unbalanced grid; the \(dq\) impedance is coupled and it is hard to measure in practical systems. The harmonic linearization method overcomes these disadvantages by modeling three-phase voltage source inverter (VSC) impedance directly in the phase domain. Despite the complex derivation, this method is widely used to investigate the impedance characteristic of grid-connected full converter wind farm. The work in References [17; 18] analyzed the interaction between D-PMSGs and grid by experimentally measuring the impedance, but the mathematical expression was not proposed. Reference [19] built the impedance model of grid-connected VSC and it was further developed in Reference [20] to describe impedance characteristics of LCL-type converter, but the stability analysis was not mentioned in both articles. References [21; 22] modeled the D-PMSG impedance and analyzed the system stability with or without outer-loop control, but the frequency coupling was not considered. The coupling phenomenon introduced by phase locked loop (PLL) was discussed in References [23; 24; 25] and derived the coupled impedance model of grid-connected converter. However, this model was too complicated and the relationship of sub/supsynchronous currents was not analyzed either.