[Paper Review] Non-parametric Impedance based Stability and Controller Bandwidth Extraction from Impedance Measurements of HVDC-connected Wind Farms

Mohammad Amin, Marta Molinas|arXiv (Cornell University)|Apr 16, 2017

HVDC Systems and Fault Protection4 citations

TL;DR

This paper proposes a non-parametric method to extract critical controller bandwidths—particularly from PLL and ac voltage controllers—in HVDC-connected offshore wind farms using measured impedance data, enabling stability assessment and mitigation without access to internal control details. The method identifies instability sources via impedance ratio analysis and Nyquist criterion, with results showing that retuning the PLL bandwidth to be 10× lower than the HVDC controller bandwidth ensures stability.

ABSTRACT

Impedance measurements have been widely used with the Nyquist plot to estimate the stability of interconnected power systems. Being a black-box method for equivalent and aggregated impedance estimation, its use for the identification of sub-components bandwidth is not a straightforward task. This paper proposes a simple method that will enable to identify the specific part of the equivalent impedance (e.g. controller's bandwidth) that has major impact on the stability of the system. For doing that, the paper analyses the stability of an interconnected system of wind farms and high voltage dc (HVDC) transmission system. The impedance frequency responses of the wind farms and HVDC system from the ac collection point are measured and it is shown by the method proposed in this paper, which controller has major impact in the observed oscillation. A mitigation technique is proposed based on re-tuning of the critical controller bandwidth of the interconnected converters. The method suggested can reveal the internal controllers' dynamics of the wind farm from the measured impedance combined with an analytical expression of the impedance and a transfer function identity when no information about the controllers is provided by the vendors due to confidentiality and industry secrecy.

Motivation & Objective

• Address the challenge of assessing stability in HVDC-connected offshore wind farms when detailed control models are unavailable due to industry confidentiality.
• Identify which controller (e.g., PLL or ac voltage controller) is primarily responsible for system oscillations in interconnected converters.
• Develop a practical, non-parametric method to infer internal controller dynamics from measured impedance frequency responses.
• Propose a mitigation strategy based on re-tuning critical controller bandwidths to ensure system stability.
• Establish a general design rule for stable interconnection: HVDC rectifier controller bandwidth should be 10× higher than the wind farm’s PLL bandwidth.

Proposed method

• Measure the frequency-domain impedance responses of the wind farm and HVDC system at the AC collection point under stable operating conditions.
• Apply system identification techniques to derive a continuous transfer function for the aggregated wind farm impedance from measured data, treating the system as a black/grey box.
• Use the impedance ratio between the HVDC rectifier and wind farm to apply the Nyquist criterion for stability assessment.
• Leverage transfer function identities and analytical impedance expressions to infer internal controller dynamics without access to vendor-provided control parameters.
• Perform participation factor analysis on eigenvalues to determine which controller states contribute most to instability.
• Propose a mitigation strategy based on re-tuning the PLL bandwidth such that the q-axis impedance magnitude of the HVDC system remains below that of the wind farm below the PLL bandwidth.

Experimental results

Research questions

• RQ1 How can controller bandwidths be extracted from measured impedance data when no internal control information is available?
• RQ2 Which controller in an HVDC-connected wind farm system is primarily responsible for observed low-frequency oscillations?
• RQ3 What is the impact of the ratio between PLL bandwidth and HVDC rectifier controller bandwidth on system stability?
• RQ4 Can a general design rule be established to prevent instability in black-box converter systems?
• RQ5 How can impedance-based stability analysis be applied effectively to real-world HVDC-connected offshore wind farms with limited model access?

Key findings

• The PLL and ac voltage controller were identified as the most contributing states to instability through participation factor analysis.
• The system becomes unstable when the q-axis impedance magnitude of the HVDC rectifier exceeds that of the wind farm below the PLL bandwidth, particularly around 8.5 Hz.
• Retuning the PLL with a 42° phase margin and a 4.72 Hz closed-loop bandwidth successfully stabilized the system, confirmed by Nyquist plots not encircling (-1, j0).
• A general stability rule was observed: if the PLL open-loop phase margin exceeds 40° and the PLL bandwidth is 10× smaller than the ac voltage controller’s crossover frequency, the system remains stable.
• The method successfully identified that the HVDC rectifier’s q-axis impedance behaves as a bandpass filter at the ac voltage controller’s bandwidth, while the wind farm’s q-axis impedance acts as a band-reject filter up to the PLL bandwidth.
• The mitigation technique—re-tuning the PLL bandwidth to be significantly lower than the HVDC controller bandwidth—was validated through both Nyquist analysis and time-domain simulations, ensuring stable operation.