💻 computer science

Nonlinear Virtual Inertia Control of WTGs for Enhancing Primary Frequency Response and Suppressing Drive-Train Torsional Oscillations

This paper proposes a novel nonlinear virtual inertia controller based on objective holographic feedbacks theory that effectively enhances primary frequency response and suppresses drive-train torsional oscillations in wind turbine generators, outperforming existing methods in simulation scenarios.

Original authors: Bi Liu, Qi Huang, Junbo Zhao, Federico Milano, Yingchen Zhang

Published 2026-03-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bi Liu, Qi Huang, Junbo Zhao, Federico Milano, Yingchen Zhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: The Power Grid as a Heavy Flywheel

Imagine the electrical power grid as a giant, heavy spinning wheel (a flywheel) that keeps the lights on. In the old days, this wheel was powered by massive coal or gas turbines. These heavy machines had a lot of inertia.

What is Inertia? Think of inertia like the momentum of a moving truck. If the truck hits a bump (a sudden drop in power), its heavy weight keeps it moving forward for a while, giving the driver time to react. In the power grid, this "heavy weight" helps stabilize the frequency (the speed of the electricity) when something goes wrong.

The Problem: Today, we are replacing those heavy coal trucks with Wind Turbines. Wind turbines are great, but they are like lightweight electric bikes. They don't have that heavy "momentum." When the grid has a sudden problem (like a power plant tripping offline), the grid speed drops too fast, and the lights could flicker or go out.

To fix this, engineers invented Virtual Inertia Controllers (VICs). These are software programs that tell the wind turbines to act as if they are heavy. They tell the turbine to dump some of its stored energy into the grid to slow down the frequency drop.

The Catch: The "Twisting" Problem

Here is the twist (pun intended). While these controllers help the grid, they can hurt the wind turbine itself.

Imagine a wind turbine has a long, flexible metal shaft connecting the spinning blades to the generator. If you suddenly yank on that shaft (by demanding a sudden burst of power), it doesn't just stretch; it twists and vibrates.

The Analogy: Imagine riding a bicycle. If you are pedaling smoothly and someone suddenly yanks the handlebars hard to the left, your bike wobbles, and your arms get twisted. If you do this too often, your bike frame might crack, or you might crash.
The Reality: Old virtual inertia controllers were like that sudden, jerky yank. They caused low-frequency torsional oscillations (twisting vibrations) in the wind turbine's drive train. This wears out the machine, shortens its life, and can even cause it to break.

Also, after the turbine helps the grid, it needs to "catch its breath" and spin back up to its normal speed. Old controllers were clumsy at this, sometimes causing the grid to wobble a second time (a "secondary frequency dip") or taking too long to recover.

The Solution: The "Smart, Smooth" Controller

This paper introduces a new, Nonlinear Virtual Inertia Controller. Think of this as upgrading from a jerky, manual yank to a sophisticated, AI-driven suspension system.

Here is how it works, broken down into three key features:

1. The "Holographic" Brain (The Math Part)

The authors used a complex math theory called Objective Holographic Feedbacks Theory (OHFT).

Analogy: Imagine a driver who doesn't just look at the road ahead, but also looks at the rearview mirror, checks the fuel gauge, and feels the vibration of the engine all at once. They process all this data instantly to make a perfect steering decision.
Result: This new controller calculates the exact amount of power to release so that it stabilizes the grid frequency without ever making the turbine shaft twist violently. It turns a chaotic, unpredictable system into a smooth, controllable one.

2. The "Smart Throttle" (Adapting to Conditions)

Old controllers were like a cruise control set to one speed. If the wind was weak, they still demanded the same power, which could stall the turbine.

Analogy: This new controller is like a smart driver.
- If the wind is strong: The turbine has plenty of energy stored in its spinning blades. The controller says, "Go ahead, give a big push to the grid!"
- If the wind is weak: The turbine is barely spinning. The controller says, "Hold back! Don't give too much, or you'll stop spinning completely."
Result: It prevents the turbine from stalling and avoids the "secondary dip" where the grid crashes again because the turbine ran out of energy.

3. The "Smooth Landing" (Recovery)

After the emergency is over, the turbine needs to speed back up to its normal speed.

Analogy: Imagine a runner who sprints to catch a bus. When the bus stops, a clumsy runner might trip and fall while trying to slow down. A smart runner slows down gradually and smoothly.
Result: This controller ensures the wind turbine speeds back up smoothly and quickly, returning to its optimal spinning speed without causing any more vibrations or grid instability.

The Teamwork Aspect (Multiple Turbines)

The paper also shows how to use this with a whole farm of wind turbines.

Analogy: Imagine a relay race team. If one runner is tired (low wind) and another is fresh (high wind), you don't ask the tired runner to carry the whole load. You ask the fresh runner to do more.
Result: The new controller automatically figures out which turbines have the most energy and asks them to help the most, while protecting the weaker ones. This makes the whole grid much more stable.

Summary of Benefits

In simple terms, this paper proposes a new software upgrade for wind turbines that:

Stops the shaking: It prevents the wind turbine from twisting and breaking.
Saves the grid: It helps the electricity frequency stay stable much better than before.
Is adaptable: It knows when to push hard and when to hold back based on the wind speed.
Is a team player: It coordinates many turbines to work together perfectly.

The authors tested this in simulations and found it works significantly better than the current methods, keeping both the wind turbines and the power grid healthier and more stable.

1. Problem Statement

With the increasing penetration of wind turbine generators (WTGs) in power systems, the overall system inertia is decreasing, making the grid more vulnerable to frequency instability. While Virtual Inertia Control (VIC) has been developed to emulate inertia from WTGs, existing methods suffer from several critical limitations:

Drive-Train Torsional Oscillations: Conventional VICs often induce low-frequency torsional oscillations in the WTG drive-train due to sudden changes in electromagnetic torque, potentially reducing the service life of the turbine.
Secondary Frequency Dips: The transition from frequency support mode back to normal Maximum Power Point (MPP) tracking can cause a sharp reduction in power output, leading to a secondary frequency dip.
Lack of Adaptability: Existing controllers often fail to account for varying wind speeds and operating rotor speeds. This can lead to excessive rotor speed reduction at low wind speeds (risking stall or loss of control) or insufficient kinetic energy release at high wind speeds.
Coordination Issues: There is a lack of effective strategies for coordinating frequency support power distribution among multiple WTGs.

2. Methodology

The authors propose a Nonlinear Virtual Inertia Control strategy based on Objective Holographic Feedbacks Theory (OHFT). The methodology involves three main stages:

A. Theoretical Foundation (OHFT)

The paper utilizes OHFT to transform the original nonlinear control problem into a completely controllable Brunovsky system.

The system is modeled with state variables including turbine speed ( $\omega_t$ ), generator speed ( $\omega_g$ ), shaft torsional angle ( $\theta_{sh}$ ), and grid frequency deviation ( $\Delta\omega$ ).
By defining specific output variables and applying Lie derivatives, the nonlinear system is linearized into a form where linear quadratic optimal control (LQOC) can be applied to ensure stability and performance.

B. Control Strategy Design (Single WTG)

The proposed VIC modifies the reference electromagnetic power ( $P_{ref}$ ) using three distinct components:

Nonlinear State Feedback: Derived from the OHFT-based Brunovsky system, this component generates a control signal ( $u$ ) to suppress torsional oscillations and regulate frequency. It is converted to the VIC interface output ( $u'$ ).
Rotor Speed Dependent Function ( $f(\omega_g)$ ): This function scales the control output based on the current rotor speed.
- High Speed: Increases power increment to release more kinetic energy.
- Low Speed: Reduces power increment to prevent the rotor speed from dropping below the minimum operational limit, thereby avoiding secondary frequency dips caused by power cutoff.
Time-Varying Function ( $g(t)$ ): This function manages the transition between frequency support and rotor speed recovery.
- It ensures a smooth switch between modes, preventing instantaneous power jumps that cause torsional oscillations.
- It facilitates a fast and smooth recovery of the rotor speed back to the original MPP point.

C. Extension to Multiple WTGs

The control is extended to a fleet of WTGs by:

Constructing a multi-input Brunovsky system for $N$ turbines.
Calculating a Participating Factor ( $pf_i$ ) for each turbine based on its initial active power output ( $P_{e0,i}$ ). This ensures that turbines with higher initial generation (and thus more available kinetic energy) contribute proportionally more to the frequency support.

3. Key Contributions

Novel Nonlinear Formulation: The derivation of a VIC based on OHFT that transforms the nonlinear control into a controllable linear system, allowing for precise satisfaction of multiple control objectives simultaneously.
Suppression of Torsional Oscillations: The method effectively damps low-frequency drive-train oscillations, addressing a major drawback of conventional VICs.
Adaptive Power Regulation: The introduction of time-varying and rotor-speed-dependent functions allows the controller to automatically adjust power support based on wind speed and operating points, preventing secondary frequency dips and ensuring safe operation at low wind speeds.
Coordinated Multi-Turbine Control: A solution for distributing frequency support power among multiple WTGs, optimizing the collective response to enhance the system frequency nadir.

4. Simulation Results

The proposed method was validated using a test system in MATLAB/Simulink, comparing it against a Conventional VIC and a Modified VIC-I (with time-varying coefficients).

Frequency Response: The proposed VIC achieved a significantly higher frequency nadir (minimum frequency point) compared to existing methods, particularly under high wind speed conditions.
Torsional Oscillations: While conventional and modified VICs exhibited clear low-frequency torsional oscillations (approx. 1.45 Hz), the proposed method effectively suppressed these oscillations.
Rotor Speed Recovery: The proposed VIC enabled the fastest and smoothest recovery of rotor speed to the pre-disturbance MPP point. It avoided the "secondary frequency dip" seen in other methods, which occurred when other controllers abruptly cut power to recover speed.
Wind Speed Robustness:
- High Wind Speed: Maximized kinetic energy release for superior frequency support.
- Low Wind Speed: Limited power release to prevent rotor speed from dropping below the safety threshold (0.71 pu), maintaining stability where other methods failed.
Multiple WTGs: In a scenario with three WTGs (60% penetration), the coordinated control successfully distributed the load based on available kinetic energy, resulting in the best overall system frequency performance.

5. Significance

This paper addresses a critical gap in renewable energy integration: the trade-off between providing fast frequency support and maintaining the mechanical integrity of wind turbines.

System Security: By improving the frequency nadir and preventing secondary dips, the method enhances the stability of power systems with high renewable penetration.
Asset Protection: By suppressing drive-train torsional oscillations, the method reduces mechanical stress, potentially extending the operational lifespan of WTGs and reducing maintenance costs.
Operational Flexibility: The adaptive nature of the controller ensures that wind farms can provide frequency support safely across a wide range of wind conditions, making virtual inertia a more viable and reliable solution for future smart grids.