A Methodology for Impedance-based Stability Margin Analysis for Interconnected Offshore Wind Clusters

Technical Summary: A Methodology for Impedance-based Stability Margin Analysis for Interconnected Offshore Wind Clusters

Problem Statement
With the evolution of offshore grid architectures, Transmission System Operators (TSOs) are increasingly adopting configurations where multiple Offshore Wind Power Plants (OWPPs) connect directly to a common HVDC converter station switchgear. While this topology offers efficiency, it introduces complex interactions between converter control systems. A critical challenge is assessing how the integration of a new OWPP (or Power Park Module, PPM) affects the small-signal stability margins of existing OWPPs at the Point of Connection (PoC).

Traditional impedance-based stability analysis, widely used for grid-connected converters, relies on the Nyquist stability criterion (NSC) to determine stability by checking for encirclements of the critical point $(-1, 0)$. However, existing methods often have limitations:

1. They primarily provide a binary stability assessment (stable/unstable) rather than quantifying stability margins (phase and gain margins).
2. They often rely on "forbidden regions" based on fixed phase margins, which assume that new loads do not alter the stability margins of existing systems. This is a conservative assumption that fails to account for new resonance frequencies introduced by additional converters.
3. They do not explicitly define the maximum allowable impedance for a new connection to ensure that the existing system maintains its required stability margins.

Methodology
The paper proposes a generalized impedance-based methodology to evaluate stability margins and derive impedance specifications for new PPMs. The approach utilizes a minor-loop gain formulation within a frequency-domain framework.

1. System Partitioning: The system is modeled as a negative feedback loop where the network impedance ($Z_{net}$) acts as the source and the converter impedance ($Z_{OWPP}$) acts as the load. The minor-loop gain is defined as $L(s) = Z_{net}(s) / Z_{OWPP}(s)$.
2. Impedance Modeling: The authors employ harmonic linearization to decouple positive- and negative-sequence components. They utilize a "reverse impedance-based approach," where the grid impedance is extracted via wide-area network frequency scans in an Electromagnetic Transient (EMT) model, treating the selected OWPP as the reference point.
3. Analytical Formulation:
   • The paper derives a relationship between the loop gain of the existing system ($L_{old}$) and the system after adding a new parallel PPM ($L_{new}$).
   • $L_{new}(j\omega) = L_{old}(j\omega) \cdot \frac{1}{1 + \rho(j\omega)}$, where $\rho(j\omega)$ is the ratio of the old network impedance to the new PPM impedance.
   • This formulation allows the calculation of the new phase margin ($PM_{new}$) based on the pre-connection loop gain and the impedance ratio.
4. Impedance Specification: An inequality is derived to constrain the impedance of the new PPM ($Z_{OWPP,new}$) to ensure the existing system maintains a minimum phase margin ($PM_{min}$). The derived constraint is:
   $$|Z_{OWPP,new}(j\omega_{gc})| \leq \frac{|Z_{net,old}(j\omega_{gc})|}{2 \sin\left(\frac{PM_{old}(j\omega_{gc}) - PM_{min}}{2}\right)}$$
   This ensures the new PPM is "weak enough" at critical frequencies to prevent the degradation of the existing system's stability margins.
5. Enhanced Nyquist Regions: To complement the standard NSC, the authors introduce graphical stability regions on the Nyquist plot:
   • Critical Area: Phase margins below the minimum requirement (e.g., $PM < 15^\circ$).
   • Caution Area: Phase margins between the minimum and a warning threshold (e.g., $15^\circ \leq PM < 30^\circ$).
   • Gain Margin Circle: A circle representing the minimum gain margin requirement.

Key Contributions

• Quantitative Margin Analysis: The paper moves beyond binary stability checks to explicitly quantify how integrating a new PPM alters the phase and gain margins of existing connections.
• Impedance Design Criterion: It provides a specific analytical condition (Equation 23) to determine the maximum allowable impedance for a new connection, ensuring the existing system remains compliant with TSO margin requirements.
• Graphical Stability Assessment: The introduction of "Critical" and "Caution" areas on the Nyquist plot offers a visual tool for assessing margin compliance and headroom, addressing the lack of robustness metrics in traditional encirclement-based methods.
• Validation with Real-World Models: The methodology is validated using vendor-supplied EMT models from an actual offshore wind project (involving 475 MW and 500 MW OWPPs) and frequency-domain models in DIgSILENT PowerFactory.

Results
The study was conducted on two case configurations: one with a common transformer and one with separate transformers for the two OWPPs.

• Stability Improvement: In both cases, the integration of a second OWPP (OWPP2) actually improved the stability margins of the existing OWPP (OWPP1). This was attributed to the parallel connection reducing the effective network impedance, which pulled the Nyquist locus away from the critical point.
• Validation of Constraints: When the impedance of the new OWPP was kept below the calculated limit ($|Z_{OWPP2}| < Z_{limit}$), the Nyquist locus did not intersect the unit circle within the critical area, and minimum margin requirements were met.
• Violation Demonstration: When the impedance of the new OWPP was artificially increased to exceed the limit at specific crossover frequencies, the Nyquist locus entered the critical area, violating the minimum phase margin requirement.
• Model Sensitivity: Comparisons between a Thevenin-equivalent grid model and a detailed frequency-domain model showed that while the Thevenin model is sufficient for some internal resonance studies, the frequency-dependent model provides more accurate resonance frequencies and stability assessments for interconnected clusters.

Significance
The paper claims that this methodology provides a practical tool for TSOs and developers to plan and assess the integration of new PPMs in offshore clusters. By providing a direct criterion for impedance specification, the method enables:

1. Compliance Verification: Ensuring that new connections do not violate the stability margin requirements (e.g., phase margins at resonance frequencies) specified by system operators like TenneT.
2. Efficient Planning: Allowing for the assessment of stability margins using impedance data obtained from frequency scans or frequency-domain models, without requiring exhaustive time-domain simulations for every potential configuration.
3. Grid Code Integration: The approach can be readily integrated into routine grid-code compliance studies to evaluate the impact of additional PPM integration, moving away from overly conservative "forbidden region" designs toward dynamic, margin-based specifications.

The authors emphasize that the method is particularly valuable for scenarios involving multiple strings or PPMs where the addition of new converters creates complex resonance interactions that fixed-design criteria fail to capture.