Adequacy of the Single-Generator Equivalent Model for Stability Analysis in Wind Farms With VSC-HVDC Systems

Abstract

Due to the complexity of detailed models, the single-generator equivalent model (SEM) of a wind farm is commonly used to facilitate the stability analysis. However, the adequacy of the SEM for stability analysis in direct-drive wind farms with VSC-HVDC systems is still uncertain. Therefore, this paper analyzes the SEM adequacy in two aspects: the oscillation modes analysis and the sub-synchronous oscillation (SSO) stability enhancement by optimizing wind farm parameters. Firstly, various critical oscillation modes are characterized according to the frequency, and a comparison of these modes between the two-generator equivalent model and the SEM is presented. The effect of single-generator aggregation on the critical oscillation modes is discussed. Then, the impact of permanent magnet synchronous generator (PMSG) parameters on the inside-wind-farm/wind-farm-grid SSO modes is explored. It is revealed that with the change of PMSG parameters, the damping effect of the two SSO modes is identical. This implies that the SEM can be used to improve the SSO stability of the multi-machine system by optimizing the PMSG parameters. PSCAD/EMTDC simulations are further performed to verify the theoretical analysis.

Study on the oscillation transmission paths in direct‐drive wind farm transmitted via flexible dc system based on dynamic energy flow

“…Based on the model of mathematical model built in ()–(), the system state space can be shown in () as [7]: $$\begin{equation}\frac{{d\Delta x}}{{dt}} = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{4}{l}@{}} {D_{11}}&\quad {H_{12}}&\quad \ldots &\quad {H_{1n}}\\[5pt] {H_{21}}&\quad {D_{22}}&\quad \ldots &\quad {H_{2n}}\\[5pt] \vdots &\quad \vdots &\quad \ddots &\quad \vdots \\[5pt] {H_{n1}}&\quad {H_{n2}}&\quad \ldots &\quad {D_{nn}} \end{array} } \right]\Delta x,\end{equation}$$where $$\Delta x = [\Delta x_1,\Delta x_2, \ldots ,\Delta x_n]^T$$ is the linearized state variable, and D ii and H ij is the state variable matrix which can obtained from () to ().…”

“…Based on the model of mathematical model built in (1)-(4), the system state space can be shown in (5) as [7]:…”

“…Currently, methods used in the study of the oscillation transmission path mainly include hybrid analysis method [7, 8], energy function method [9, 10] and traveling wave detection method [11, 12]. Hybrid analysis method was used to locate the oscillation source relatively early.…”

“…The methods used to analyze the stability problems in wind farms transmitted via flexible DC transmission system mainly include two categories: the frequency-domain theory based impedance analysis method and the state space based eigenvalue analysis method. References [5,6] and references [7,8] used the eigen-value method and the impedance analysis method separately to study the wind farm transmitted via flexible DC system in depth. Their results show that, the interaction between the wind farm and the control system of the flexible DC station may cause instability problems, and the instability has to do with the oscillation modes inside the wind farm and the flexible DC system.…”

“…Currently, methods used in the study of the oscillation transmission path mainly include hybrid analysis method [7,8], energy function method [9,10] and traveling wave detection…”