Dual Grid-Forming Converter Control Strategy Based on Complex Frequency Duality

Core Concepts

This letter proposes a novel grid-forming (GFM) converter control strategy based on complex frequency duality, which utilizes instantaneous bandwidth for power balance and reactive power for frequency regulation, eliminating the need for frequency measurements.

Abstract

Bibliographic Information:

Milano, F. (2024). Dual Grid-Forming Converter. Submitted to IEEE PES Letters.

Research Objective:

This research letter proposes a novel control strategy for grid-forming converters that leverages the concept of complex frequency duality, aiming to achieve power balance and frequency regulation without relying on frequency measurements.

Methodology:

The authors develop a dual GFM control model inspired by the symmetrical structure of active and reactive power equations in lossy synchronous machine models. This model utilizes the instantaneous bandwidth (voltage magnitude time derivative) for maintaining power balance and the reactive power for regulating frequency deviations. The performance of the proposed control strategy is evaluated through simulations on the WSCC 9-bus system and a 1479-bus dynamic model of the all-island Irish transmission system.

Key Findings:

The simulation results demonstrate that the proposed dual-GFM control strategy effectively maintains power balance and restores normal operating conditions following significant disturbances like load outages and three-phase faults. Notably, this is achieved without relying on frequency measurements, unlike conventional GFM converters and synchronous machines.

Main Conclusions:

The study concludes that the proposed dual-GFM control strategy offers a robust and stable approach for controlling grid-forming converters. Its ability to maintain power balance without frequency measurements makes it particularly suitable for applications in distribution and low voltage networks, and potentially even in DC systems.

Significance:

This research introduces a novel concept of complex frequency duality in GFM converter control, potentially paving the way for developing new control strategies that are not reliant on frequency measurements. This has significant implications for the stability and reliability of future power grids with high penetration of converter-interfaced renewable energy sources.

Limitations and Future Research:

The study primarily focuses on simulation-based analysis. Further research involving hardware-in-the-loop experiments and practical implementation considerations is necessary to validate the feasibility and robustness of the proposed control strategy in real-world grid environments. Additionally, exploring the application of this concept in DC grids is a promising avenue for future research.

Stats

The armature resistance (ra) in synchronous machines is typically small compared to transient reactance (x′d) and often neglected.
The proposed dual-GFM control uses a virtual parameter K, representing the negative inverse of armature resistance (K = -1/ra).
The study uses a WSCC 9-bus system and a 1479-bus dynamic model of the all-island Irish transmission system for simulations.
The dual-GFM parameters used in the WSCC 9-bus system are: K = 0.1 pu, ˜M = 30 s, ˜D = 20, ˜Tm = 2 s, ˜R = 0.05, Kq = 10, Tq = 5 s, ˜Kr = 40, and ˜Tr = 1 s.
For the Irish transmission system model, the parameters are: K = 1 pu, ˜M = 15 s, and ˜D = 0.5, with other parameters remaining the same as the WSCC 9-bus system.

Quotes

"This letter proposes an alternative approach, which, while taking inspiration from the synchronous machine model, constitutes a new type of duality."
"This work, on the other hand, considers the dual parts of (1) and (2), that is, the terms that depend on the armature resistance and suppose that the reactance x′d is zero or negligible. This can be done because a converter is not a machine with physical coils and its parameters can be tuned as desired."
"In particular, this letter shows how to set up a GFM control that utilizes the instantaneous bandwidth (voltage magnitude time derivative) rather than the instantaneous frequency (voltage phase angle time derivative) as slack variable to maintain the power balance of the grid."

Key Insights Distilled From

Dual Grid-Forming Converter

by Federico Mil... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2408.13185.pdf

Deeper Inquiries

How does the computational complexity of the proposed dual-GFM control compare to that of conventional GFM control strategies, and what are the implications for real-time implementation?

The computational complexity of the dual-GFM control, in comparison to conventional GFM strategies, is an interesting point of discussion. Here's a breakdown:

Conventional GFM: These controls often rely on computationally intensive operations like coordinate transformations (e.g., Park transformation) and complex variable calculations for power decoupling and grid synchronization.
Dual-GFM: This novel approach utilizes simpler mathematical operations. The core control laws, as seen in equations (7), (8), (15), and (19), primarily involve additions, multiplications, and trigonometric functions. The absence of coordinate transformations further reduces the computational burden.
Implications for Real-Time Implementation:

Reduced Computational Resources: The dual-GFM's relative simplicity suggests it could be implemented on less powerful and potentially more cost-effective hardware. This is advantageous for large-scale deployments of grid-forming converters.
Faster Execution Times: Simpler calculations translate to faster execution times, which is crucial for real-time control systems. This allows for quicker responses to grid disturbances, potentially enhancing stability.
Algorithm Optimization: While the paper doesn't delve into specific implementation details, the dual-GFM's structure might lend itself well to optimization techniques for digital signal processors (DSPs) or field-programmable gate arrays (FPGAs), further improving real-time performance.
However, a definitive comparison requires further investigation:

Practical Implementation: A detailed analysis of the control algorithms' implementation on specific hardware platforms is needed to quantify the computational difference accurately.
Control Loop Dynamics: The choice of control parameters (e.g., time constants, gains) in both conventional and dual-GFM will influence the actual computational load.
In conclusion, the dual-GFM control, in principle, appears to have a lower computational complexity than conventional GFM methods. This has positive implications for real-time implementation, potentially enabling faster response times and the use of less expensive hardware. However, a thorough comparative analysis considering practical implementation aspects is necessary for a definitive conclusion.

While the dual-GFM control shows promise in simulation, could its reliance on voltage magnitude derivatives make it more susceptible to noise and disturbances in real-world grid environments compared to traditional frequency-based controls?

You raise a valid concern. The dual-GFM control's reliance on voltage magnitude derivatives (ϱ) could indeed make it more sensitive to noise and disturbances in real-world grid environments compared to traditional frequency-based controls. Here's a closer look:
Increased Susceptibility to Noise:

Voltage Magnitude Fluctuations: Real-world grids experience voltage fluctuations due to load switching, capacitor bank operations, and other transients. These fluctuations, when passed through a derivative, can be amplified, potentially leading to control instability or erratic behavior in the dual-GFM.
Measurement Noise: Voltage sensors inevitably introduce measurement noise. Differentiating noisy signals can exacerbate the noise, further affecting the accuracy and stability of the ϱ signal.
Mitigation Strategies:

Signal Filtering: Employing low-pass filters on the voltage magnitude measurements before differentiation can help attenuate high-frequency noise. Careful filter design is crucial to avoid introducing unwanted phase lags that could negatively impact control performance.
Robust Control Techniques: Incorporating robust control techniques, such as H-infinity or sliding mode control, can enhance the dual-GFM's resilience to noise and disturbances. These methods explicitly consider uncertainties and disturbances in the design process.
Adaptive Filtering: Adaptive filters that adjust their characteristics based on the noise characteristics of the grid could provide a more sophisticated solution.
Comparison with Frequency-Based Controls:

Frequency Measurement: Traditional frequency-based controls rely on frequency measurements, which are generally less susceptible to high-frequency noise due to the inherent averaging effect of frequency estimation over multiple cycles.
Trade-off: While frequency-based controls might be less sensitive to certain types of noise, they might not respond as quickly to rapid voltage changes, which the dual-GFM is designed to address.
Further Research:

Real-World Testing: Evaluating the dual-GFM's performance in real-world grid environments or using hardware-in-the-loop (HIL) simulations that accurately emulate grid noise and disturbances is essential.
Noise Sensitivity Analysis: A rigorous analysis of the dual-GFM's noise sensitivity and the effectiveness of different mitigation techniques is crucial for practical implementation.
In summary, the dual-GFM control's reliance on voltage magnitude derivatives does introduce potential susceptibility to noise and disturbances. However, appropriate signal filtering, robust control techniques, and real-world testing can mitigate these challenges. The trade-off between noise sensitivity and responsiveness to voltage dynamics needs careful consideration in practical applications.

Could the principles of complex frequency duality explored in this research be extended to other power system control applications beyond grid-forming converters, such as microgrid control or voltage stability enhancement?

Yes, the principles of complex frequency duality explored in the dual-GFM research hold significant potential for application beyond grid-forming converters, extending to areas like microgrid control and voltage stability enhancement:
Microgrid Control:

Enhanced Power Sharing: In microgrids with multiple distributed energy resources (DERs), complex frequency duality could enable novel control strategies for accurate and dynamic power sharing based on both voltage magnitude and frequency deviations.
Islanding Operation: During grid islanding events, where a microgrid disconnects from the main grid, dual-frequency control could provide smoother transitions and improved voltage and frequency stability within the islanded system.
Virtual Inertia Emulation: The concept of virtual inertia, central to the dual-GFM, can be applied to other DERs within a microgrid to enhance overall system inertia and improve stability in the face of disturbances.
Voltage Stability Enhancement:

Reactive Power Control: Complex frequency duality could lead to advanced reactive power control strategies that leverage both voltage magnitude and frequency information to provide faster and more effective voltage regulation.
Voltage Collapse Prevention: By incorporating voltage magnitude derivatives into control laws, it might be possible to develop more sensitive and proactive control actions to mitigate voltage instability and prevent voltage collapse.
Dynamic Voltage Support: Dual-frequency control could enable DERs to provide dynamic voltage support in a manner that complements traditional voltage regulation devices, enhancing overall system stability.
Further Research Directions:

Control Architectures: Exploring different control architectures that exploit complex frequency duality for microgrid and voltage stability applications is crucial.
Stability Analysis: Rigorous stability analysis of systems employing dual-frequency control is essential to ensure robust performance under various operating conditions.
Experimental Validation: Validating the effectiveness of these extended applications through simulations and experimental testing on real or scaled-down power system platforms is necessary.
In conclusion, the principles of complex frequency duality presented in the dual-GFM research offer a promising avenue for innovation in power system control. Extending these principles to microgrid control and voltage stability enhancement could lead to more sophisticated and effective control strategies, ultimately contributing to a more reliable and resilient power grid.