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Nonlinear Stability Boundary Assessment of Multi-Converter Systems Based On Reverse Time Trajectory

Sujay Ghosh, Mohammad Kazem Bakhshizadeh, Guangya Yang, Łukasz Kocewiak

TL;DR

This work addresses nonlinear stability of a wind power plant (WPP) connected to an AC grid via an HVac link by developing a unified, high-fidelity model that includes reduced-order Type-4 WTs, a STATCOM, and a detailed collector network. It introduces a hybrid RoA estimation workflow that first builds a linear energy-based initial RoA and then refines it with reverse-time trajectory to yield a time-limited RoA, $A_{TL}(t,x)$, for the multi-converter system. The methodology is validated against PSCAD EMT simulations, including a bolted fault to estimate the critical clearing time (CCT) and to demonstrate boundary crossing and stability when the fault is cleared within the RoA. The approach provides a scalable, geometry-aware view of stability boundaries in high-dimensional WPP dynamics, offering a practical tool for large-scale renewable integration and control design. The results show that the TL RoA can capture complex boundary features and islands, enabling more informed decisions beyond linear stability analyses. $A_{TL}(t,x)$ and the RoA concepts are validated against a benchmark model, reinforcing the method’s robustness for diverse WPP topologies and fault scenarios.

Abstract

As the integration of wind power accelerates, wind power plants (WPPs) are expected to play a crucial role in ensuring stability in future power grids. This paper examines the nonlinear stability boundary of a multi-converter system in a wind power plant (WPP) connected to an AC power grid via a long HVAC cable. Traditionally, for nonlinear analysis of WPPs, a simplification is adopted wherein the WPP is treated as an aggregation of individual wind turbines (WTs), with a simplified portrayal of the collector network. However, in the presence of different technologies, such as STATCOM, that are placed away from the WTs, the model aggregation will not hold. This paper presents a unified methodology to model and investigate the high-dimensional stability boundary of a WPP with a STATCOM. The stability region of the system, i.e. the region of attraction (RoA), is determined by the reverse time (backwards) trajectory technique. Furthermore, the estimated stability boundary is verified using time-domain simulation studies in PSCAD.

Nonlinear Stability Boundary Assessment of Multi-Converter Systems Based On Reverse Time Trajectory

TL;DR

This work addresses nonlinear stability of a wind power plant (WPP) connected to an AC grid via an HVac link by developing a unified, high-fidelity model that includes reduced-order Type-4 WTs, a STATCOM, and a detailed collector network. It introduces a hybrid RoA estimation workflow that first builds a linear energy-based initial RoA and then refines it with reverse-time trajectory to yield a time-limited RoA, , for the multi-converter system. The methodology is validated against PSCAD EMT simulations, including a bolted fault to estimate the critical clearing time (CCT) and to demonstrate boundary crossing and stability when the fault is cleared within the RoA. The approach provides a scalable, geometry-aware view of stability boundaries in high-dimensional WPP dynamics, offering a practical tool for large-scale renewable integration and control design. The results show that the TL RoA can capture complex boundary features and islands, enabling more informed decisions beyond linear stability analyses. and the RoA concepts are validated against a benchmark model, reinforcing the method’s robustness for diverse WPP topologies and fault scenarios.

Abstract

As the integration of wind power accelerates, wind power plants (WPPs) are expected to play a crucial role in ensuring stability in future power grids. This paper examines the nonlinear stability boundary of a multi-converter system in a wind power plant (WPP) connected to an AC power grid via a long HVAC cable. Traditionally, for nonlinear analysis of WPPs, a simplification is adopted wherein the WPP is treated as an aggregation of individual wind turbines (WTs), with a simplified portrayal of the collector network. However, in the presence of different technologies, such as STATCOM, that are placed away from the WTs, the model aggregation will not hold. This paper presents a unified methodology to model and investigate the high-dimensional stability boundary of a WPP with a STATCOM. The stability region of the system, i.e. the region of attraction (RoA), is determined by the reverse time (backwards) trajectory technique. Furthermore, the estimated stability boundary is verified using time-domain simulation studies in PSCAD.
Paper Structure (14 sections, 21 equations, 9 figures, 2 tables)

This paper contains 14 sections, 21 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Modelling
  3. Modelling of reduced-order type-4 WTs
  4. Modelling of STATCOM
  5. Modelling of collector network
  6. Nonlinear Stability Assessment
  7. Steady state load-flow
  8. Estimation of the RoA
  9. Initial conditions
  10. Reverse time trajectory
  11. Time domain verification
  12. Estimation of Critical clearing time
  13. Discussion
  14. Conclusion

Figures (9)

  • Figure 1: WPP with aggregated WTs and a STATCOM, connected to an AC power grid.
  • Figure 2: Wind turbine model: (a) Reduced order model (ROM) of the Type-4 wind turbine considering the actions/assumptions. (b) System representation of ROM in the DQ domain.
  • Figure 3: Re-visualisation of wind power plant for multi-port frequency scan.
  • Figure 4: Projections of initial RoA estimate of the linearised model (1) and (5).
  • Figure 5: Estimated 4D TLRoA for the multi-converter system in the WPP: aggregated WTs and STATCOM.
  • ...and 4 more figures