The primary objective of the benchmark model is to serve as a reference for studying interactions between converters and the grid. It provides a foundation for evaluating small-signal stability analysis methods and instability mitigation techniques. The model includes aggregated grid following (GFL) converters, interconnected via a medium-voltage (MV) cable network.

The model is inspired by a real-life AC cable-connected offshore wind power plant (PP). The GFL converter model is a part of benchmark system, introduced by CIGRE WG C4.49 and published in the CIGRE 928 technical brochure.

The model is developed in the dq-reference frame to simplify modelling and avoid coupling in the control system. The converter is based on a standard insulated-gate bipolar transistor (IGBT)-based two-level voltage source converter (VSC), rated at 12 MW, as typically seen in modern offshore wind turbines (WTs). To simplify the analysis, the mechanical system and its controllers are not included.

Converter control is designed as GFL unit, employing vector control in the dq-reference frame and a synchronous reference frame (SRF) phase-locked loop (PLL) for grid synchronization. The dq currents regulate the DC link voltage and either the voltage or reactive power at the converter terminals. Active damping control, using capacitor current feedback, is also incorporated to enhance stability.

The converter system is linked to the grid through a 0.69/66 kV transformer, where the low-voltage reactance corresponds to the grid-side reactance of the LCL output filter.

## Subsystems of grid-following converter

The converter control system has been tuned to mimic the behavior of a generic converter model and has not yet been customized for the specific grid under study. As a result, various instabilities may arise in both the base case and during disturbance scenarios.

**Anti-aliasing Filter and Sampling:** the anti-aliasing filter is implemented using a second-order Butterworth filter, with the cutoff frequency set at half of the sampling frequency and the sampling delay is approximated using a third-order Padé approximation.

**Park Transformation:** the GFL control is implemented in a synchronous reference frame (SRF), with the phase determined by a phase-locked loop (PLL) that tracks the system frequency.

**Power Calculation:** instantaneous active and reactive power are calculated from voltage and current measurements taken at the output of the LCL filter.

**DC Voltage Control:** the DC voltage regulation is managed through a proportional-integral (PI) controller.

**AC Voltage Control:** the AC voltage regulation is implemented using a simple droop control method.

**Reactive Power Control:** the reactive power regulation is handled by a proportional-integral (PI) controller.

**Phase-Locked Loop (PLL):** the grid synchronization system uses a PLL, where the voltage’s q-component is filtered by a first-order low-pass filter and regulated by a PI controller, which provides the system’s angular frequency, which is then integrated to determine the phase for the Park transformation.

**Current Control:** the converter reactor current regulation is achieved using PI controllers with decoupling in the SRF, and active damping is incorporated to attenuate the capacitor current in the LCL filter, and an output voltage feed-forward component is added to the voltage reference.

**Pulse Width Modulation (PWM):** the modulation block computes the switching functions and provides the pulse patterns to the converter gate drivers and the PWM delay is also included.

## Grid following converter parameters

## References

[1] Ł. Kocewiak, R. Blasco-Gimenez, C. Buchhagen, J. B. Kwon, M. Larsson, Y. Sun, X. Wang, “Practical Aspects of Small-signal Stability Analysis and Instability Mitigation,” in *Proc. The 21 ^{st} Wind & Solar Integration Workshop*, 12-14 October 2022, The Hauge, The Netherlands.

[2] Ł. Kocewiak, R. Blasco‐Giménez, C. Buchhagen, J. B. Kwon, M. Larsson, A. Schwanka Trevisan, Y. Sun, X. Wang, “Instability Mitigation Methods in Modern Converter-based Power Systems,” in

*Proc. The 20*, Energynautics GmbH, 29-30 September 2021.

^{th}International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms[3] Ł. Kocewiak, R. Blasco‐Giménez, C. Buchhagen, J. B. Kwon, Y. Sun, A. Schwanka Trevisan, M. Larsson, X. Wang, “Overview, Status and Outline of Stability Analysis in Converter‐based Power Systems,” in

*Proc. The 19*, Energynautics GmbH, 11-12 November 2020.

^{th}International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms