# Enhanced Inertial Response Capability of a Variable Wind Energy Conversion System

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Inertia and Primary Frequency Responses of Traditional Generators

_{sys}and f

_{nom}represent the system frequency and nominal frequency, respectively. H

_{sys}and K represent the system inertia constant and equivalent droop setting of traditional synchronous generators, respectively. ΔP

_{inertial}and ΔP

_{primary}represent output powers of the inertia response and primary frequency response, respectively.

## 3. Modeling of a DFIG

_{m}) can be expressed as:

_{w}, and c

_{p}mean the air density, swept area, wind speed, and power coefficient, respectively. ω

_{r}and R are the rotor angular velocity and blade length, respectively.

_{P,}

_{max}and λ

_{opt}are the maximum value of c

_{P}and optimal tip-speed ratio, respectively.

## 4. Proposed Adaptive Inertial Response Emulated Scheme of a DFIG

_{ref}), which consists of the reference for the MPPT operation (top control loop, which is a cube function of the rotor speed) and the output of inertial response emulated control loop (bottom control loop, which is calculated by control coefficient and df/dt). Hence, the benefit of boosting the inertial response capability of the DFIG critically depends on the control coefficient.

_{MPPT}is the output of MPPT operation. ΔP

_{inertial}is the output of the inertial response emulated control loop. AG is the control coefficient.

_{1}is the inertia time constant control factor and is able to regulate the benefit of improving the inertial response capability of the DFIG. k

_{2}is the order of the power function of the frequency deviation to achieve various increasing rate of the control coefficient.

_{2}= 1, k

_{2}= 2, and k

_{2}= 3. It is clearly indicated that the emulated inertial time and control coefficient decrease with an increasing of the k

_{2}due to the fact that the frequency deviation is smaller than one. In addition, the increasing rate of the emulated inertial time and control coefficient in the case of k

_{2}= 1 is more than in the other cases. Thus, the incremental power for the proposed scheme is generated from the DFIG to improve the inertia response capability.

_{2}= 1) and conventional inertial response emulated control schemes. The control gain of the conventional scheme is irrespective of the disturbance sizes (various frequency deviations). This is the reason that the benefit of improving inertial response capability is limited. The emulated inertia constant and control coefficient of the proposed inertial response emulated control scheme is a function of the frequency deviation (see (10)), which increases with the frequency deviation. In addition, the difference of them between both inertial response emulated control schemes becomes large so as to inject more power to the power grid to compensate for the power imbalance. As a result, the proposed inertial response emulated scheme is adaptive to various disturbances (various frequency deviations).

## 5. Model System

_{4}is tripped out from the power grid at 40 s.

_{2}= 1) is compared to that of MPPT operation and the inertial response emulated control scheme with unchanged control coefficient (conventional scheme), as in [13]. Figure 7, Figure 8 and Figure 9 display the comparison results for all cases.

#### 5.1. Case1: Wind Speed of 9.0 m/s, Disturbance of 70 MW

#### 5.2. Case 2: Wind Speed of 9.0 m/s, Disturbance of 110 MW

#### 5.3. Case 3: Random Wind Condition, Disturbance of 110 MW

## 6. Conclusions

- (1)
- The proposed inertia constant is coupled with the system frequency deviation. Thus, the proposed inertia control scheme can provide various inertial response capability during disturbance according to the frequency deviation.
- (2)
- Under different disturbances, the DFIG implemented with proposed scheme can generate more power to support the system to improve the inertial response capability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bevrani, H. Robust Power System Frequency Control, 2nd ed.; Springer: New York, NY, USA, 2014. [Google Scholar]
- Landing, D.; Castorani, V.; Germanic, M. Interactive energetic, environmental and economic analysis of renewable hybrid energy system. Int. J. Interact. Des. Manuf.
**2019**, 13, 885–899. [Google Scholar] [CrossRef] - Ackermann, T. Wind Power in Power Systems, 2nd ed.; John Wiley & Sons, Ltd.: Chichester, UK, 2012. [Google Scholar]
- Chen, Z.; Guerrero, J.M.; Blaabjerg, F. A review of the state of the art of power electronics for wind turbines. IEEE Trans. Power Electron.
**2009**, 24, 1859–1875. [Google Scholar] [CrossRef] - Gevorgian, V.; Zhang, Y.; Ela, E. Investigating the impacts of wind generation participation in interconnection frequency response. IEEE Trans. Sustain. Energy
**2015**, 6, 1004–1012. [Google Scholar] [CrossRef] - Yang, D.; Jin, Z.; Zheng, T.; Jin, E.; Zhang, X.; Hua, L. Frequency control scheme with dynamic droop characteristics of a DFIG for mitigating the frequency fluctuations. Int. Trans. Electr. Energy Syst.
**2021**, 31, e13044. [Google Scholar] [CrossRef] - Yang, D.; Kim, J.; Kang, Y.C.; Muljadi, M.; Zhang, N.; Hong, J.; Song, S.-H.; Zheng, T. Temporary frequency support of a DFIG for high wind power penetration. IEEE Trans. Power Syst.
**2018**, 33, 3428–4337. [Google Scholar] [CrossRef] - Abouzeid, S.I.; Guo, Y.; Zhang, H.C.; Ma, X. Improvements in primary frequency regulation of the grid connected variable speed wind turbine. IET Renew. Power Gener.
**2019**, 13, 491–499. [Google Scholar] [CrossRef] - Concordia, C.; Fink, L.H.; Poullikkas, G. Load shedding on an isolated system. IEEE Trans. Power Syst.
**1995**, 10, 1467–1472. [Google Scholar] [CrossRef] - Keung, P.-K.; Li, P.; Banakar, H.; Ooi, B.T. Kinetic energy of wind-turbine generators for system frequency support. IEEE Trans. Power Syst.
**2019**, 24, 279–287. [Google Scholar] [CrossRef] - EirGrid. A Proposal for Rate of Change of Frequency Remuneration Mechanism Recommendations; EirGrid: Dublin, Ireland, 2016. [Google Scholar]
- ENTSO-E. Requirements for grid connection applicable to all generators. In European Network of Transmission System Operators for Electricity; ENTSO-E: Brussels, Belgium, 2013. [Google Scholar]
- Wang, S.; Tomsovic, K. A Novel Active Power Control Framework for Wind Turbine Generators to Improve Frequency Response. IEEE Trans. Power Syst.
**2018**, 33, 6579–6589. [Google Scholar] [CrossRef] - Yang, D.; Jin, Z.; Zheng, T.; Jin, E. An adaptive droop control strategy with smooth rotor speed recovery capability for type III wind turbine generators. Int. J. Electr. Power Energy Syst.
**2022**, 135, 107532. [Google Scholar] [CrossRef] - Hu, Y.-L.; Wu, Y.-K. Approximation to Frequency Control Capability of a DFIG-Based Wind Farm Using a Simple Linear Gain Droop Control. IEEE Trans. Ind. Appl.
**2018**, 55, 2300–2309. [Google Scholar] [CrossRef] - Yang, D.; Gao, H.-C.; Zhang, L.; Zheng, T.; Hua, L.; Zhang, X. Short-term frequency support of a doubly-fed induction generator based on an adaptive power reference function. Int. J. Electr. Power Energy Syst.
**2020**, 119, 105955. [Google Scholar] [CrossRef] - Kheshti, M.; Ding, L.; Nayeripour, M.; Wang, X.; Terzija, V. Active power support of wind turbines for grid frequency events using a reliable power reference scheme. Renew. Energy
**2019**, 139, 1241–1254. [Google Scholar] [CrossRef] - Morren, J.; Pierik, J.; De Haan, S.W. Inertial response of variable speed wind turbines. Electr. Power Syst. Res.
**2006**, 76, 980–987. [Google Scholar] [CrossRef] - Lee, H.; Kim, J.; Hur, D.; Kang, Y.C. Inertial control of a DFIG-based wind power plant using the maximum rate of change of frequency and the frequency deviation. J. Electr. Eng. Technol.
**2015**, 10, 496–503. [Google Scholar] [CrossRef][Green Version] - Lorenzo, Z.; Andreas, J.R.; Janus, M.-S.; Ioannis, M.; Anca, D.H.; Poul, S. Virtual inertia for variable speed wind turbines. Wind Energy
**2013**, 16, 1225–1239. [Google Scholar] - Hwang, M.; Muljadi, E.; Park, J.-W.; Sørensen, P.E.; Kang, Y.C. Dynamic Droop–Based Inertial Control of a Doubly-Fed Induction Generator. IEEE Trans. Sustain. Energy
**2016**, 7, 924–933. [Google Scholar] [CrossRef] - Eto, J.H. Use of Frequency Response Metrics to Assess the Planning and Operating Requirements for Reliable Integration of Variable Renewable Generation; Tech. Rep.; Ernest Orlando Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 2010.
- Kim, J.; Muljadi, E.; Gevorgian, V.; Mohanpurkar, M.; Luo, Y.; Hovsapian, R.; Koritarov, V. Capability-coordinated frequency control scheme of a virtual power plant with renewable energy sources. IET Gener. Transm. Distrib.
**2019**, 13, 3642–3648. [Google Scholar] [CrossRef] - Fernandez, L.M.; Garcia, C.A.; Jurado, F. Comparative study on the performance of control systems for doubly fed induction generator wind turbines operating with power regulation. Energy
**2008**, 33, 1438–1452. [Google Scholar] [CrossRef] - Shen, B.; Mwinyiwiwa, B.; Zhang, Y.; Ooi, B.-T. Sensorless maximum power point tracking of wind by DFIG using rotor position phase lock loop (PLL). IEEE Trans. Power Electron.
**2009**, 24, 942–951. [Google Scholar] [CrossRef] - Byerly, R.T.; Aanstad, O.; Berry, D.H.; Dunlop, R.D.; Ewart, D.N.; Fox, B.M.; Johnson, L.H.; Tschappat, D.W. Dynamic models for steam and hydro turbines in power system studies. IEEE Trans. Power Appar. Syst.
**1973**, 92, 1904–1915. [Google Scholar]

**Figure 4.**Comparison of inertia constant and control coefficient for the proposed inertial response emulated scheme (k

_{2}= 1, k

_{2}= 2, k

_{2}= 3).

**Figure 5.**Comparison of inertia constant and control coefficient for the proposed (k

_{2}= 1) and conventional inertial response emulated scheme.

**Figure 7.**Results for Case 1: (

**a**) system frequency; (

**b**) output power; (

**c**) rotor speed; (

**d**) auxiliary active power; (

**e**) rate of change of frequency.

**Figure 8.**Results for Case 2: (

**a**) system frequency; (

**b**) output power; (

**c**) rotor speed; (

**d**) auxiliary active power; (

**e**) rate of change of frequency.

**Figure 9.**Results for Case 3: (

**a**) wind speed; (

**b**) system frequency; (

**c**) output power; (

**d**) rotor speed; (

**e**) rate of change of frequency.

Title | Schemes | Case 1 | Case 2 | Case 3 |
---|---|---|---|---|

Frequency nadir (Hz) | Proposed | 59.415 | 59.080 | 59.074 |

Conventional | 59.364 | 58.967 | 58.955 | |

MPPT | 59.347 | 58.939 | 58.925 | |

Maximum ROCOF (Hz/s) | Proposed | −0.338 | −0.532 | −0.533 |

Conventional | −0.377 | −0.605 | −0.607 | |

MPPT | −0.402 | −0.645 | −0.646 |

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**MDPI and ACS Style**

Wang, J.; Xu, Y.; Wu, X.; Huang, J.; Zhang, X.; Yuan, H.
Enhanced Inertial Response Capability of a Variable Wind Energy Conversion System. *Energies* **2021**, *14*, 8132.
https://doi.org/10.3390/en14238132

**AMA Style**

Wang J, Xu Y, Wu X, Huang J, Zhang X, Yuan H.
Enhanced Inertial Response Capability of a Variable Wind Energy Conversion System. *Energies*. 2021; 14(23):8132.
https://doi.org/10.3390/en14238132

**Chicago/Turabian Style**

Wang, Jun, Yien Xu, Xiaoxin Wu, Jiejie Huang, Xinsong Zhang, and Hongliang Yuan.
2021. "Enhanced Inertial Response Capability of a Variable Wind Energy Conversion System" *Energies* 14, no. 23: 8132.
https://doi.org/10.3390/en14238132