# Understanding Inertial Response of Variable-Speed Wind Turbines by Defined Internal Potential Vector

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. General Concept of the Defined Inner Potential

**E**) as seen in Figure 1.

**E**) maintain original movement state (

**E’**) due to the intrinsic rotating inertia (

**J**) of rotor as shown in Figure 1b. The power angle immediately and dynamically increases to provide the synchronized power for grid support and its own re-synchronization. In this process, the inertia, i.e., the kinetic energy stored in the rotor of SGs, is spontaneously used for the dynamic energy support of the grid frequency. This paper summarizes and compares the main existing inertia controls of the wind turbine.

## 3. Representative Control and Simplified Model of Type-3 and Type-4 Wind Turbines

#### 3.1. WT’s General Controls

#### 3.2. WT’s Simplified Models

_{m}) of DFIG. The electromotive force will produce stator current (

**I**

_{s}) interacting with grid voltage (

**U**

_{g}).

## 4. Defined Inner Potential of the Wind Turbine

#### 4.1. Defined Inner Potential of Type-4 WTs

**E**is the inner potential vector. θ

_{e}and E are the phase and magnitude of the defined inner potential under the reference frame rotating at ω

_{0}. E

_{d}, E

_{q}, U

_{gd}, U

_{gq}, I

_{d}and I

_{q}are the dq-axis components of defined inner potential, grid voltage and current, respectively. X

_{f}is the impedance of filter.

_{PLL}) and the phase (θ

_{PC}) decided by a series of power controls as Figure 4:

_{PC}is the phase angle between the defined inner potential and PLL’s phasor which is decided by power control.

_{g}is the phase of grid voltage.

#### 4.2. Defined Inner Potential of Type-3 WTs

_{s}is the equivalent impedance between the defined inner potential and grid. I

_{sd}and I

_{sq}are the dq-axis current components of WT’s stator.

_{PLL}) and the phase (θ

_{PC}) decided by a series of power controls as in Figure 4:

#### 4.3. Inertial Response Analysis of WTs

_{PC}) and PLL (Δθ

_{PLL}). In typical type-3 WTs, the PLL usually has enough bandwidth to follow the grid’s electromechanical dynamics and to isolate the electromechanical dynamics from WTs. Due to rapid PLL’s decoupling, the electromechanical disturbance from the grid and the WT’s electromechanical motion are completely separated, which is the main reason for the inertia of type-3 WTs being hidden.

_{PC}) of the inner potential and roughly forms a control close loop in power angle as seen in Figure 5b. Usually the DC voltage control has a control bandwidth of about 10-Hz, which can follow the electromechanical dynamic of the grid and keep the output power constant when any electromechanical disturbance occurs in grid. Thus the electromechanical dynamic of type-4 WTs is separated from the grid not only by rapid PLL but also by the equivalent power control loop in the DC voltage. These are the main reasons for the inertia of type-4 WTs being hidden.

## 5. Main Inertial Response Release Methods

#### 5.1. Attaching Supplementary Signal into Power Control

^{TM}feature provides an inertial response capability for WTs by introducing a washout filter to temporarily increase the output power [25] as shown in Figure 6b. A washout filter is also used in [26] to make WTs only act in a transient way using the stored kinetic energy. Reference [27] proposes another different control scheme to create inertial response, that is, the additional torque setpoint is based on the absolutely deviation of the frequency from the nominal value, i.e., ΔT = K

_{f}(f

_{g}− f

_{gref}) as Figure 6c. ENERCON IE is implemented by using the frequency deviation relative to the trigger level that responds to a drop in grid frequency by temporarily increasing active power beyond the available power from the wind [28] as seen in Figure 6d. Similarly, [29] develops a control scheme to improve the frequency response capability of type-4 WTs by a combination of the abovementioned two kinds of terms associated with frequency differential and its absolute deviation.

_{PC}.

#### 5.2. Optimizing the Dynamic Response of Synchronization Control

_{PC}) is decided by the speed controller with electromechanical dynamic. The power angle is equal to the sum of θ

_{PC}and PLL’s phase error (Δθ

_{PLL}). Once the bandwidth of PLL is reduced and its dynamic is slow down, the power angle will obviously enlarge (from $\delta $ to ${\delta}^{\prime}$) with the electromechanical disturbance in grid as in Figure 7a. As a result, the spontaneous and natural inertial response of type-3 WTs is enabled. The inertia constant of the defined inner potential is related to PLL’s bandwidth [36,37].

_{PC}is regulated to ${\theta}_{PC}^{\prime}$ to maintain the power angle and output power constant as Figure 7b, viz. δ = δ′. Thus the electromechanical rotating inertia of type-4 WTs is still hidden when the PLL dynamics slow down.

#### 5.3. Virtual Synchronous Control

#### 5.4. Comparisons Between the Inertial Response of Different Control Methods

## 6. Key Challenges and Future Research

#### 6.1. Assessing Mechanical Loading and Stress of WTs

#### 6.2. Frequency Secondary Decline

#### 6.3. Unified Description of WT’s Inertial Response Characteristics and its Effect on Grid Frequency Dynamic

#### 6.4. Operating Under Grid Faults

#### 6.5. Inertial Responses from Multi-WTs

#### 6.6. Grid Codes

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Simplified control block diagram of WTs. (

**a**) Type-4 WTs; (

**b**) Type-3 WTs (X

_{s}is equivalent impedance between inner potential and grid voltage).

**Figure 5.**Phase dynamic of defined inner potential of type-3 and type-4 WTs. (

**a**) Type-3 WTs; (

**b**) Type-4 WTs.

**Figure 6.**Several inertia controls of WTs based on supplementary signals. (K

_{f}is the gain, T

_{LPF}and T

_{HPF}are the time constants of filters, f

_{g}and f

_{gref}are the measured and nominal grid frequency). (

**a**) Overall control block of WT’s inertia control based on supplementary signal; (

**b**) df/dt method; (

**c**) Δf method. (

**d**) Enercon IE (f

_{under}is the set value of under-frequency event. f

_{min}is the minimum grid frequency, P

_{inmax}is the maximum power increase of WTs); (

**e**) Frequency deviation trigger (ΔP

_{int}is the increased power); (

**f**) PLL’s error.

**Figure 7.**Phasor diagram with reducing the control bandwidth of PLL. (

**a**) Type-3 WTs; (

**b**) Type-4 WTs.

**Figure 9.**Enable inertial response of type-3 and type-4 WTs based on virtual synchronous control. (

**a**) type-3 WT; (

**b**) type-4 WT.

**Figure 11.**Simulation results of the WT’s inertial response, the grid frequency and the rotating speed of the WT’s rotor. (

**a**) The dynamic response of the wind turbine’s defined inner potential with different inertia control methods; (

**b**) The inertial response of the wind turbine with different inertia control methods; (

**c**) The grid frequency with different inertia control methods; (

**d**) The rotating speed of the WT’s rotor with different inertia control methods.

df/dt | Δf | |
---|---|---|

Added to speed reference | GE [25] | Enercon [28], Senvion (RePower) [35] |

Added to torque reference (output of speed controller) | / | Senvion (RePower) [35] |

Control Methods | Response Delay | Response Characteristics | Implemented Complexity | Additional Sensed Variables | Main Technical Barriers and Potential Risks |
---|---|---|---|---|---|

df/dt method | Inevitable | Close-loop feedback control | Medium | Grid frequency | omplicated parameters setting |

Easy to cause the power fluctuations | |||||

Δf method | Inevitable | Close-loop feedback control | Simple | Grid frequency | Excessive inertial response of the wind turbine |

Conflict with primary frequency regulation of power system | |||||

Enercon IE | Inevitable | Close-loop feedback control | Very simple | Grid frequency | Conflict with primary frequency regulation of power system |

Frequency deviation trigger | Inevitable | Open-loop feedback control | Very simple | Grid frequency | Excessive power support with large-scale integration of wind turbines |

Conflict with primary frequency regulation of power system | |||||

Optimizing PLL | No | Open-loop natural response | No modification | No | Easy to cause the power fluctuations |

Influence the response of the other control loops | |||||

Excessive inertial response of the wind turbine | |||||

Virtual synchronous control | No | Open-loop natural response | Complexity | No | Altering the control structure of the wind turbine |

Fault tolerance | |||||

Excessive inertial response of the wind turbine |

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**MDPI and ACS Style**

Shang, L.; Hu, J.; Yuan, X.; Chi, Y. Understanding Inertial Response of Variable-Speed Wind Turbines by Defined Internal Potential Vector. *Energies* **2017**, *10*, 22.
https://doi.org/10.3390/en10010022

**AMA Style**

Shang L, Hu J, Yuan X, Chi Y. Understanding Inertial Response of Variable-Speed Wind Turbines by Defined Internal Potential Vector. *Energies*. 2017; 10(1):22.
https://doi.org/10.3390/en10010022

**Chicago/Turabian Style**

Shang, Lei, Jiabing Hu, Xiaoming Yuan, and Yongning Chi. 2017. "Understanding Inertial Response of Variable-Speed Wind Turbines by Defined Internal Potential Vector" *Energies* 10, no. 1: 22.
https://doi.org/10.3390/en10010022