# Virtual Inertia Adaptive Control of a Doubly Fed Induction Generator (DFIG) Wind Power System with Hydrogen Energy Storage

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## Abstract

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## 1. Introduction

## 2. The DFIG System with Hydrogen Energy Storage

_{s}is the stator power. P

_{r}is the slip power of rotor. P

_{Sr}is the power that is transferred from the rotor to the electrical grid. P

_{b}is the electrolytic hydrogen power. There are two power unbalance statuses that are considered during the system design. The first status is load changes, such as increased load. In order to maintain the power balance of the electrical grid, the DFIG should be able to deliver energy to the electrical grid through both stator and rotor sides under the DFIG is running the super-synchronization operation state conditions. To reduce the loss of wind energy, some of the energy is transported to the HESS system by the converter to start the hydrogen electrolysis, (P

_{r}is the sum of P

_{Sr}and P

_{b}). If wind power is low, then the fuel cell of the HESS will deliver electrical power to the system (P

_{r}and P

_{b}will flow into the electrical grid through the grid-side converter). If the wind power is abundant, the active power will flow from the stator and the rotor to the grid (P

_{Sr}includes P

_{r}and P

_{b}). If the wind power is deficient, then the HESS provides the power to the rotor winding by discharging the fuel cell. In essence, the HESS acts as an energy buffer to balance the power between wind turbines and the grid.

## 3. System Virtual Inertia Definition and Hydrogen Storage Configuration

_{ks}is the kinetic energy of the rotor at rated speed. J is the rotational inertia of the generator. Ω

_{r}is the rated speed of the generator. ${S}_{N}$ is the rated capacity of the generator. The capability of the rapid power response and the reasonable control strategy of the storage device can make the frequency of the wind farm similar to the inertia response from synchronous generators. The average inertia of the wind energy storage system is a constant within a small period time $\Delta t$, such as the change rate of system frequency is unchanged the symbol [27].

_{2}and O

_{2}in the battery pack, respectively. The ohmic polarization’s overvoltage is also called the ohmic droop, which is the voltage drop due to the electrical reactance that is generated by the electrons through the bipolar plate and electrode material. The electrical reactance that is generated by the proton through the proton exchange membrane can be found by

_{m}and z

_{c}are the equivalent membrane impedance and the impedance of protons through the proton membrane, respectively.

_{max}and E

_{min}is equal to the energy stored in a storage tank full of gas. Hence, the capacity of hydrogen storage tank can be seen

^{3}the volume in standard conditions, as shown in the Equation (15) [32]. The operation time of the system and the corresponding control strategy are considered to calculate the volume at the actual case. The capacity of the oxygen storage tank is a half of the hydrogen storage tanks, based on the chemical formula for hydrogen and oxygen combustion. In addition, the capacity of storage tanks can be increased to improve the system reliability. Hence, the charging-discharging time of the hydrogen storage system is longer than the response time of the traditional generators.

## 4. Adaptive Control of the Virtual Inertia of the Auxiliary System of the HESS

#### 4.1. Virtual Inertial Control Model Containing the Hydrogen Storage System

_{L}is the interaction power between the load and electrical grid. P

_{G}is the power of the traditional synchronous unit, which feeds into the electrical grid. P

_{T}is the interaction power to the electrical grid. P

_{p}is the frequency modulation power of the traditional generator. P

_{S}is the power that the wind power system feeds into the electrical grid. P

_{f}is the output power in DC part of the middle of HESS. H is the virtually inertial constant of the system. D is the system damping. f

_{grid}and V

_{grid}, respectively, are the frequency and voltage of the electrical grid. When the active power of the system is balanced, then the output power of HESS is equal to zero, and the balance equation can be expressed as

_{p}and the differential coefficient k

_{d}are positive, then the virtual inertia of the system will increase, which is helpful in dampening the frequency discontinuity of the power system. However, the increasing of the virtual inertia has less impact on maintaining the frequency of the electrical grid at a certain constant, such as 50 Hz. For example, when the frequency of the electrical grid once restores, the continual increasing virtual inertia will prolong the recovery time of the frequency fluctuation [33]. Thus, the effect of the increasing virtual inertia of the energy storage system is related to the frequency of the electrical grid at the specific fluctuating stage.

#### 4.2. Virtual Inertia Fuzzy and Adaptive PD Controller Design

_{c}, and the corrected parameter Δk

_{pf}and Δk

_{df}are used for finalizing the input and output parameters of the controller to restrain the frequency fluctuations of the electrical grid in Figure 3. A fuzzy adaptive PD controller with dual input and output is built to simulate the response characteristics of the virtual inertia and compensate the virtual inertia of the wind power unit. Here, e and e

_{c}are defined as

_{c}are positive, which the frequency of system is in the deterioration process. If e is positive and the e

_{c}is negative, which shows that the system frequency is in the recovery process. If e and e

_{c}are negative, which expresses that the frequency of system is in the deterioration process. When e is negative and e

_{c}is positive, which shows that the system frequency is in the recovery process. Therefore, the fundamental inference rule of the fuzzy adaptive PD controller can be summarized as: (1) if the system frequency increasingly worsens, then the HESS and the exchange energy should be as large as possible to prevent the further deterioration of the frequency; (2) If the system frequency is gradually recovering, then the HESS and the exchange energy should be as small as possible to promote the recovery speed.

_{c}are [−2, 1] and [−3, 3]. $\Delta {k}_{p}$ and $\Delta {k}_{d}$ of fuzzy controller’s output are set to [−5, 12] and [−1, 3], respectively. The fuzzy subsets of the input and output can be represented as {NB, NM, NS, ZO, PS, PM, PB}. The subordinate function of the input and output, respectively, are the Gaussian functions and trigonometric functions, which consider the stability of the coupled system. The speed regulating characteristic of DFIG is used to select the centroid method as the defuzzification algorithm. Figure 4 reveals the corrected parameters of the fuzzy adaptive PD controller. When the sign of e is the same with that of e

_{c}, (the system frequency is deteriorating), $\Delta {k}_{d}$ and $\Delta {k}_{p}$ all are positive and the values increase with the input.

_{c}, (the system frequency is improving), $\Delta {k}_{d}$ and $\Delta {k}_{p}$ all are negative and the values decrease with the increasing of the input, as shown in Figure 4. In addition, the corrected parameters are directly related to the virtual inertia. Then, if the system frequency is deteriorating, then there will be an automatic increase of the virtual inertia to dampen the change in the system frequency. If the system frequency is improving, then there will be an automatic decrease of the virtual inertia to support the rapid recovery of system frequency.

## 5. Results and Analysis

#### 5.1. Data Analysis at the System Load Discontinuity

#### 5.2. Data Analysis at Different HESS Capacity Configuration

#### 5.3. Data Analysis for the Wind Speed Fluctuations

## 6. Conclusions

- (1)
- The HESS can effectively change the virtual inertia of the wind turbine and provide wind farm with support for the system frequency stability.
- (2)
- When the system load suddenly changes, the proposed adaptive control strategy can efficiently increase the virtual inertia, responding to the change of the system frequency, and supports the stability of the system frequency.
- (3)
- The virtual inertia of the system increases with the HESS capacity, which can improve the frequency modulation. The storage system with the 5% rated power is effective in producing the inertia that is required by a conventional synchronous generator with the same rating.
- (4)
- The proposed adaptive control strategy can assure the good inertia response and restrain the frequency change even if the frequency change reaches the lower limit of the system.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Energy transfers relation of the doubly fed induction generator (DIFG) coupling hydrogen energy storage system (HESS).

**Figure 4.**Fuzzy adaptive PD corrected parameters drawing. (

**a**) Drawing of $\text{}\Delta {k}_{p}$; (

**b**) Drawing of $\Delta {k}_{d}$. and $\Delta {k}_{p}$.

**Figure 5.**The frequency’s response curve at the load sudden increase and decrease. (

**a**) The frequency’s response curve of fuzzy adaptive control, conventional generator and without inertia control with load increase; (

**b**) The frequency’s response curve of fuzzy adaptive control and conventional PD control with load increase; (

**c**) The frequency’s response curve of fuzzy adaptive control, conventional generator and without inertia control with load decrease; and (

**d**) The frequency’s response curve of fuzzy adaptive control and conventional PD control with load decrease with load decrease.

**Figure 6.**The inertial response and system output of HESS capacity changes. (

**a**) The frequency’s response curve at the load sudden increase; (

**b**) The frequency’s response curve at the load sudden decrease; and (

**c**) Energy’s response curve.

**Figure 7.**Data analysis for the wind speed fluctuation. (

**a**) The wind speed fluctuation of the wind farm; (

**b**) The connected-grid power of the doubly fed induction generator wind power system with hydrogen energy storage.

**Figure 8.**The change of the system frequency and the HESS output at the power fluctuation. (

**a**) The system frequency responses with and without inertia control; (

**b**) Output power response of HESS; and (

**c**) Output energy response of HESS.

e_{c} | NB | NM | NS | ZO | PS | PM | PB | ||
---|---|---|---|---|---|---|---|---|---|

Δk_{p}/Δk_{b} | |||||||||

e | |||||||||

NB | PB | PB | PB | PM | PS | ZO | NS | ||

NM | PB | PB | PM | PS | ZO | NS | ZO | ||

NS | PB | PM | PS | ZO | NS | ZO | PS | ||

ZO | PM | PS | ZO | ZO | ZO | PS | PM | ||

PS | PS | ZO | ZS | ZO | PS | PM | PB | ||

PM | ZO | NS | ZO | PS | PM | PB | PB | ||

PB | NS | ZO | PS | PM | PB | PB | PB |

Unit capacity (MVA) | 1.5 | Number of pole-pairs | 3 |

Stator voltage (V) | 575 | Rotor voltage (V) | 1975 |

Stator resistance (p.u.) | 0.023 | Rotor resistance (p.u.) | 0.016 |

Stator inductance (p.u.) | 0.18 | Rotor inductance (p.u.) | 0.16 |

Mutual inductance (p.u.) | 2.9 | Frequency (Hz) | 50 |

Capacity (MVA) | 40 | Number of pole-pairs | 1 |

Stator voltage (V) | 575 | Frequency (Hz) | 50 |

Stator resistance (p.u.) | 0.0045 | Inertia time constant (s) | 2 |

d-axis synchronous reactance (p.u.) | 1.65 | q-axis synchronous reactance (p.u.) | 1.59 |

d-axis transient reactance (p.u.) | 0.25 | q-axis transient reactance (p.u.) | 0.46 |

d-axis subtransient reactance (p.u.) | 0.2 | q-axis subtransient reactance (p.u.) | 0.2 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, T.; Wang, J.; Guan, Y.; Liu, Z.; Song, X.; Che, Y.; Cao, W.
Virtual Inertia Adaptive Control of a Doubly Fed Induction Generator (DFIG) Wind Power System with Hydrogen Energy Storage. *Energies* **2018**, *11*, 904.
https://doi.org/10.3390/en11040904

**AMA Style**

Yuan T, Wang J, Guan Y, Liu Z, Song X, Che Y, Cao W.
Virtual Inertia Adaptive Control of a Doubly Fed Induction Generator (DFIG) Wind Power System with Hydrogen Energy Storage. *Energies*. 2018; 11(4):904.
https://doi.org/10.3390/en11040904

**Chicago/Turabian Style**

Yuan, Tiejiang, Jinjun Wang, Yuhang Guan, Zheng Liu, Xinfu Song, Yong Che, and Wenping Cao.
2018. "Virtual Inertia Adaptive Control of a Doubly Fed Induction Generator (DFIG) Wind Power System with Hydrogen Energy Storage" *Energies* 11, no. 4: 904.
https://doi.org/10.3390/en11040904