# Simplified Super Twisting Sliding Mode Approaches of the Double-Powered Induction Generator-Based Multi-Rotor Wind Turbine System

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## Abstract

**:**

_{S}). The IFOC strategy is characterized by its simplicity, ease of use, and fast dynamic speed. However, there are drawbacks to this method. Among its disadvantages is the presence of ripples in the level of torque, active power, and current. In addition, the total harmonic distortion (THD) value of the electric current is higher compared to the direct torque control method. In order to overcome these shortcomings and in terms of improving the effectiveness and performance of this method, a new algorithm is proposed for the super twisting algorithm (STA). In this work, a new STA method called simplified STA (SSTA) algorithm is proposed and applied to the traditional IFOC strategy in order to reduce the ripples of torque, current, and active power. On the other hand, the inverter of the DPIG is controlled by using a five-level fuzzy simplified space vector modulation (FSSVM) technique to obtain a signal at the inverter output of a fixed frequency. The results obtained from this proposed IFOC-SSTA method with FSSVM strategy are compared with the classical IFOC method which uses the classical controller based on a proportional-integral (PI) controller. The proposed method is achieved using the Matlab/Simulink software, where a generator with a large capacity of 1.5 megawatts is used. The generator is placed in a multi-rotor electric power generation system. On the other hand, the two methods are compared in terms of ripple ratio, dynamic response, durability, and total harmonic distortion (THD) value of the electric current. Through the results obtained from this work, the proposed method based on SSTA provided better results in terms of ripple ratio, response dynamic, and even THD value compared to the classical method, and this shows the robustness of the proposed method in improving the performance and efficiency of the generator in the multi-rotor wind system.

## 1. Introduction

- A new super twisting algorithm is proposed and confirmed.
- A new space vector modulation (SVM) scheme is proposed based on the fuzzy logic controller to control the five-level inverter of the DPIG.
- A new IFOC strategy scheme is proposed to control the DPIG-based multi-rotor wind turbine system.
- A new SSTA algorithm is designed to improve the dynamic characteristics of DPIG-based multi-rotor wind turbine systems.

## 2. Multi-Rotor Wind Turbine System

_{t}is the output torque of the dual-rotor wind turbine, T

_{LT}and T

_{ST}are the output torque of the large and small wind turbines, P

_{t}is the output mechanical power of the dual-rotor wind turbine, P

_{LT}and P

_{ST}are the output mechanical power of the large and small wind turbine torque.

_{p}), the mechanical speed of the small and large turbines (w

_{ST}and w

_{LT}), the blade radius of the small and large turbines (R

_{ST}, R

_{LT}), and the tip speed ration of the small and large turbines (λ

_{ST}and λ

_{LT}).

_{ST}and V

_{LT}), The speed of the large and small turbine (w

_{ST}and w

_{LT}), and the blade radius of the small and large turbines (R

_{ST}, R

_{LT}).

_{LT}) and a constant value (C

_{T}= 0.9), as well as the separation distance (x) between the large and small turbine. In this case, this distance between the center of the large and small turbine is 15 m [15].

_{s}), direct and quadrature stator current (I

_{ds}and I

_{qs}), direct and quadrature stator (Ψ

_{qs}and Ψ

_{ds}), and electrical pulsation of the stator (w

_{s}). The direct and quadrature stator flux are represented in Equation (14). These two fluxes are related to both the inductance of the stator (L

_{s}), direct and quadrature rotor current (I

_{dr}and I

_{qr}), and direct and quadrature rotor current (I

_{ds}and I

_{qs}).

_{e}) is related to rotor current, the number of pole pairs (p), and stator flux and its expression can be given by Equation (15) [19].

_{r}is the load torque, Ω is the mechanical rotor speed, J is the inertia, f is the viscous friction coefficient.

## 3. Simplified STA Controller

_{i}and K

_{p}are positive values.

## 4. Proposed Five-Level Fuzzy SVM Strategy

_{1}, K

_{2}, and K

_{3}) are used to improve the response and adjust the response of fuzzy logic. The characteristics of the FLA method used to improve the performance and effectiveness of the proposed five-level SVM technique are shown in the bottom of the Figure 6. The type of fuzzy controller used in this work is the Mamdani controller.

## 5. Traditional IFOC Strategy

_{qr}* and V

_{dr}*).

## 6. Proposed Indirect FOC Strategy

_{qr}* and V

_{dr}* from active and reactive power references for the inverter DPIG control. Controlling the latter very well leads to obtaining a high quality of stator current and active power. On the other hand, the reactive power reference is set to zero. As for the reference value of the active power, it is obtained using the maximum power point tracking (MPPT) technique. The system studied using the proposed indirect FOC method is represented in Figure 12, where almost the same structure as the classical indirect FOC method is preserved.

## 7. Results

_{s}= 0.012 Ω, L

_{r}= 0.0136 H, L

_{m}= 0.0135 H, p = 2, J = 1000 kg·m

^{2}, P

_{sn}= 1.5 MW, R

_{r}= 0.021 Ω, L

_{s}= 0.0137 H, and f

_{r}= 0.0024 N·m/s [35].

_{1}= 13.2 m, R

_{2}= 25.5 m, r

_{1}= 1 m, r

_{2}= 0.5 m, r

_{g}= 0.75 m, J

_{1}= 500 kg·m

^{2}, J

_{2}= 1000 kg·m

^{2}, G

_{1}= r

_{1}/r

_{g}, and G

_{2}= r

_{2}/r

_{g}.

#### 7.1. First Test

#### 7.2. Second Test

## 8. Conclusions

- A new fuzzy SVM technology was introduced to control the five-level inverter to give a constant frequency at the inverter output, with this method confirmed by numerical simulation.
- A new simplified STA controller was proposed in this paper.
- A new indirect FOC strategy based on the simplified STA controller and the proposed five-level fuzzy SVM technique was presented and confirmed with numerical simulation.
- The robustness of the proposed indirect FOC strategy was presented.
- The characteristics of the designed indirect FOC strategy was analyzed, showing that the undulations of the reactive power, stator current, torque, and active power were minimized.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 13.**First test results. (

**a**) Active power; (

**b**) Reactive power; (

**c**) Torque; (

**d**) Stator current; (

**e**) THD value of stator current (IFOC-SSTA strategy); (

**f**) THD value of stator current (IFOC strategy).

**Figure 14.**Zoom in the first test results. (

**a**) Active power; (

**b**) Reactive power; (

**c**) Torque; (

**d**) Stator current.

**Figure 15.**Second test results. (

**a**) Active power; (

**b**) Reactive power; (

**c**) Torque; (

**d**) Stator current; (

**e**) THD value of current (IFOC-SSTA strategy); (

**f**) THD value of current (IFOC strategy).

**Figure 16.**Zoom in the second test results. (

**a**) Active power; (

**b**) Reactive power; (

**c**) Torque; (

**d**) Stator current.

Traditional Indirect FOC Technique | Proposed Indirect FOC Technique | |
---|---|---|

Type controller used | PI controller | SSTA controller |

Rise time | High | Low |

Modulation | PWM | Fuzzy SVM |

Degree of complexity | Medium | High |

Ease | Medium | Complicated |

Simplicity of implementation | Medium | Complicated |

Response dynamic | Slow | Quick |

Robustness | Low | High |

THD | High | Low |

Power ripple | High | Low |

Classical IFOC Technique | Proposed IFOC Technique | Ratios | |
---|---|---|---|

Torque ripple (N·m) | Around 60 | Around 5 | 91.66% |

Reactive power ripple (VAR) | Around 8000 | Around 500 | 93.75% |

Active power ripple (W) | Around 10,000 | Around 880 | 91.20% |

Stator current (A) | Around 19 | Around 3 | 84.21% |

Response Time | |||
---|---|---|---|

Torque | Reactive Power | Active Power | |

Classical IFOC strategy | 0.12 s | 0.13 s | 0.12 s |

Proposed IFOC strategy | 2.95 ms | 0.0023 s | 2.95 ms |

Ratios | 97.54% | 98.23% | 97.54% |

Response Time | ||||
---|---|---|---|---|

Torque | Reactive Power | Active Power | ||

Proposed technique: IFOC-SSTA | 2.95 ms | 0.0023 s | 2.95 ms | |

[36] | Direct power control | 18 ms | 17 ms | 18 ms |

Neuro-second order SMC technique | 5 ms | 9 ms | 5 ms |

Traditional IFOC Strategy | Designed IFOC Technique | Ratios | |
---|---|---|---|

Torque ripple (N·m) | Around 172 | Around 11.60 | 93.35% |

Reactive power ripple (VAR) | Around 25,000 | Around 500 | 98% |

Active power ripple (W) | Around 30,000 | Around 5000 | 83.33% |

Stator current (A) | Around 40 | Around 5 | 87.50% |

References | Techniques | THD (%) |
---|---|---|

[37] | Field-oriented control with PI controllers | 0.77 |

Super twisting algorithm (STA) | 0.28 | |

[38] | Fuzzy DTC strategy | 2.40 |

[39] | Fractional-order sliding mode control | 1.31 |

[40] | Integral SMC technique | 9.71 |

Multi-resonant-based sliding mode controller (MRSMC) | 3.14 | |

[41] | Backstepping control | 2.19 |

[6] | Field-oriented control | 3.7 |

[12] | DPC control with PI controllers | 0.46 |

DPC control with terminal synergetic controllers | 0.25 | |

[42] | Direct torque control with second-order continuous SMC technique | 0.78 |

[28] | DPC control with integral-proportional controllers | 0.43 |

[9] | DFOC control with PI controllers | 1.45 |

DFOC control with synergetic- SMC technique | 0.50 | |

[13] | Field-oriented control with neuro-fuzzy controller | 0.78 |

Field-oriented control with type-2 fuzzy logic controllers | 1.14 | |

[43] | Multilevel DTC strategy | 1.57 |

[32] | Vector control | 2.20 |

Adaptive backstepping sliding mode control | 1.15 | |

[44] | Traditional direct vector control | 1.65 |

[45] | DPC with sliding mode controller | 1.66 |

DPC with super twisting sliding mode controller | 0.11 | |

Proposed IFOC strategy | First test | 0.10 |

Second test | 0.11 |

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## Share and Cite

**MDPI and ACS Style**

Benbouhenni, H.; Bizon, N.; Colak, I.; Thounthong, P.; Takorabet, N.
Simplified Super Twisting Sliding Mode Approaches of the Double-Powered Induction Generator-Based Multi-Rotor Wind Turbine System. *Sustainability* **2022**, *14*, 5014.
https://doi.org/10.3390/su14095014

**AMA Style**

Benbouhenni H, Bizon N, Colak I, Thounthong P, Takorabet N.
Simplified Super Twisting Sliding Mode Approaches of the Double-Powered Induction Generator-Based Multi-Rotor Wind Turbine System. *Sustainability*. 2022; 14(9):5014.
https://doi.org/10.3390/su14095014

**Chicago/Turabian Style**

Benbouhenni, Habib, Nicu Bizon, Ilhami Colak, Phatiphat Thounthong, and Noureddine Takorabet.
2022. "Simplified Super Twisting Sliding Mode Approaches of the Double-Powered Induction Generator-Based Multi-Rotor Wind Turbine System" *Sustainability* 14, no. 9: 5014.
https://doi.org/10.3390/su14095014