A Gray-Box Method for Stability and Controller Parameter Estimation in HVDC-Connected Wind Farms Based on Nonparametric Impedance

Abstract

Estimation of critical control parameters is a desirable tool feature for stability analysis and impedance shaping of high voltage dc (HVDC)-connected wind farms. Accurate estimation of such parameters would be enabled by access to detailed models, which is not always the case in real wind farms. Industrial secrecy is one of the main factors hindering the access to such models. This paper proposes a Grey-box method that, with basic assumptions about the control structure of the wind energy conversion system (WECS), can estimate the parameters of its controllers. The method is based on the measurements of frequency domain equivalent impedance combined with nonparametric impedance identification used in the solution of an inverse problem. The method makes possible to specify which part of the equivalent WECS impedance has a major impact on the stability of the system and according to this, re-shape the impedance to enforce stability. Once the critical controller bandwidth is identified with this method, an instability mitigation technique is proposed based on reshaping the impedance by re-tuning the critical controllers of the interconnected converters. In order to avoid interaction between the HVDC rectifier and the WECS inverter, the controllers of both converters need to be re-tuned in such a way that the q-axis impedance magnitude of the HVDC system is kept lower than the q-axis impedance magnitude of the wind farm at the frequency of the phase-lockedloop bandwidth. The results show that the method ensures the stability of the system by re-tuning only the critical controller parameters.

Effect of Reactive Power Characteristic of Offshore Wind Power Plant on Low-Frequency Stability

“…It can be seen that the system is unstable with P ref = 10. The low-frequency stabilization method based on PLL controller parameters re-tuning has actually been investigated in [18], [25], [26]. However, phase tracking performance may be weakened, if the PLL bandwidth is decreased.…”

“…In addition, when G f f v is 1.0435e-3 or 1.3043e- Both the impedance-based stability analysis and the simulation results indicate that the system can be unstable if too large or too small G f f v is adopted. On the other hand, as derived in Section III.C, the system can be stabilized only if amount of the negative reactive power injection Q ref is larger than Q ref min which is calculated based on (26).…”

“…In [18], the stability margin under weak grid condition is improved by optimizing current controller parameters. In [25], [26], the stability margin under weak grid condition is improved by decreasing PLL bandwidth. However, system dynamic performances will be degraded, if a lower PLL bandwidth is adopted.…”

An Adaptive Frequency Phase-Locked Loop Based on a Third Order Generalized Integrator

“…The structure of the AC/DC controller is shown in Figure 18 Table 3. According to [33], the ac voltage control-loop bandwidth is around five times lower than the inner-loop current controller and that satisfies the standard bandwidth ratio design criterion. Therefore, the system is expected to operate stably.…”

Impedance Circuit Model of Grid-Forming Inverter: Visualizing Control Algorithms as Circuit Elements

“…In practice, the system identification can be greatly facilitated by the prior knowledge of the model. These considerations lead to the idea of a gray-box model, where the structure of the state-space model is considered known, whereas the parameters are identified from the impedance either measured or disclosed by manufacturers [19]. However, such a graybox model still needs to be converted to either state-space or impedance (transfer function) format in stability analysis, which means that the model is only gray in the set-up phase, but becomes white or black in the analysis phase.…”