Characterization of Subsynchronous Oscillation with Wind Farms Using Describing Function and Generalized Nyquist Criterion

Abstract

Eigen-analysis is widely used in the studies of power system oscillation and small-signal stability. However, it may give inaccurate analyses on subsynchronous oscillation (SSO) when nonlinearity is not negligible. In this paper, a nonlinear analytical approach based on the describing function and generalized Nyquist criterion is proposed to analyze the characteristics of SSO with wind farms. The paper first presents describing function-based model reduction considering key nonlinear elements involved in SSO, and then uses a generalized Nyquist criterion for accurate estimation of SSO amplitude and frequency. The results are verified by time-domain simulations on a detailed model with different scenarios considering variations of the system condition and controller parameters.

Analysis of sub‐synchronous resonance between DC‐side dynamics of large‐scale PV plants and nearby synchronous generators shaft

“…where V sD and V sQ denote the dq-components of the grid voltage in the reference frame and 𝜃 denotes the phase difference between the reference frame and the PV plant frame. In addition, the current transformation from the PV frame to the reference frame is described as (20), where i D and i Q denote the dq-components of the PV output current in the reference frame.…”

“…As shown in Figure 7, the input variables of the PV plant state equations are V sd and V sq , which are obtained by transformation of V sD and V sQ using (19). After solving the nonlinear equations of the PV plant (1 -21) and calculating i d and i q , i D and i Q are obtained using (20), which are the output variables of the PV plant and play the role of input variables for the grid model [49]. For modal analysis and controller design, these equations will be linearised by the Linear Analysis Toolbox of Simulink © .…”

“…Unlike PV plants, which exclude any rotating parts, wind plants are more prone to be affected by the SSR. In the SSOs literature, wind plants are mainly studied from the following points of view: effects of series compensated transmission lines on mechanical components and converters of wind plants [13–16], effects of voltage source converters (VSCs) and high‐voltage direct current (HVDC) systems on wind plants [17, 18], and effects of wind plant controllers on increasing SSOs in power systems and interactions with other components [19–22]. …”

“…• effects of voltage source converters (VSCs) and high-voltage direct current (HVDC) systems on wind plants [17,18], and • effects of wind plant controllers on increasing SSOs in power systems and interactions with other components [19][20][21][22].…”

Circuits and Systems Issues in Power Electronics Penetrated Power Grid

“…5. Furthermore, Xu et al [38] presented a describing function-based model that took in account key nonlinear elements involved in sub-synchronous oscillation (SSO), which is caused by the controller's saturating nonlinearity. The generalized Nyquist criterion was used to estimate the SSO amplitude and frequency and to derive the current phase diagrams under different limit values of the saturating nonlinearity.…”