# Small Wind Turbine Emulator Based on Lambda-Cp Curves Obtained under Real Operating Conditions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Wind Turbine and Mechanical System Modeling

^{3}), $A$ is the area swept by the turbine blades given in m

^{2}, and ${V}_{wind}$ is the wind speed given in $\mathrm{m}/\mathrm{s}$. The power coefficient ${C}_{p}$ is the ratio of the power captured by the wind turbine (${P}_{T}$) on the low-speed shaft (${P}_{LSS}$) to the power available in the wind, being expressed as follows:

_{T}is the linear speed at the tip of the turbine blades, ${\omega}_{T}$ is the angular speed of the rotor of the turbine in rad/s, and ${r}_{T}$ is the length of the blade in m. The aerodynamic characteristic of a wind turbine can be modified by varying the pitch angle ($\beta $) of the blades. Such a technique, denoted as pitch control, is usually applied in large wind turbines, but is uncommon in small wind turbines.

## 3. Experimental Method for the Estimation of the $\mathit{\lambda}$-${\mathit{C}}_{\mathit{p}}$ Characteristic Curve of a Small Wind Turbine

_{p}is usually calculated using the electrical generated power (${P}_{e}$) [23]:

^{2}. The value of $\mathit{J}$ has been provided by the manufacturer and is the moment of inertia to be emulated. The turbine starts its operation for ${V}_{wind}$ > 3 m/s, develops the rated power for ${V}_{wind}$ = 12 m/s, and includes an automatic brake system if ${V}_{wind}$ > 14 m/s. The wind turbine is directly coupled to the shaft of the electrical generator, so N = 1. The electrical generator used in the Bornay Wind Plus 25.3+ is a permanent magnet synchronous generator (PMSG) and has the rated values shown in Table 1.

_{ij}of matrix

**N**, where i = 1‥m and j = 1‥n, expressed as follows:

**B**row vector that contains the $\lambda $-${C}_{p}$ points that describe the characteristic curve of the turbines is calculated as follows:

## 4. Proposed Small Wind Turbine Emulator

_{wind}). Wind and turbine speeds are replaced in Equation (6) to obtain the corresponding $\lambda $ value. At this point, a lookup table with the $\lambda $-${C}_{p}$ curve has to be accessed to obtain the actual ${C}_{p}$ value. The $\lambda $-${C}_{p}$ curve is stored in the memory of the DSC as a table. From these results and by applying Equation (5), the power captured by the turbine (P

_{T}) is computed. The incoming aerodynamic torque (${T}_{T}$) is obtained by dividing the captured power by the directly coupled turbine speed (${\omega}_{T}={\omega}_{G}$). By calculating the torque difference and using the value of the moment of inertia

**J**to be emulated, the system acceleration (“a” in Figure 15) can then be found from Equation (2). Finally, considering the gearbox ratio, the turbine speed reference signal to feed the speed control input of the VFD drive is obtained by integrating the resulting acceleration.

^{2}), as was explained previously. This means that the same controller has a different response when the value of $J$ is changed; that is, the load sees a different turbine.

## 5. Conclusions

^{2}parametric continuity.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Variation of the $\mathit{\lambda}$

**-**${\mathit{C}}_{\mathit{p}}$ curve depending on the pitch angle of the blades ($\mathit{\beta}$).

**Figure 3.**Block diagram of the data acquisition (

**left**) and flowchart of the proposed method (

**right**).

**Figure 5.**Description of the data classification in V

_{wind}and λ ranges before the averaging and weighting process.

**Figure 7.**Resulting interpolation from the obtained control points with cubic spline interpolation method.

**Figure 10.**Final $\lambda $-${C}_{p}$ curve obtained from three Bornay Wind Plus 25.3+ small wind generators.

**Figure 17.**Graphic user interface (GUI) of the wind turbine emulator system. Visualization of the real-time operating point during emulation.

Voltage | Rated Power (kW) | Peak Power (kW) | Rated Speed (rpm) | Pole Pairs |
---|---|---|---|---|

3–220 V_{L-L} | 5 kW | 7 kW | 375 | 8 |

Voltage Class | Constant Torque Control Mode | Variable Torque Control Mode | ||
---|---|---|---|---|

Max Power (kW) | Rated Current (A) | Max Power (kW) | Rated Current (A) | |

3–400 V_{L-L} | 11 | 24 | 15 | 31 |

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**MDPI and ACS Style**

Martínez-Márquez, C.I.; Twizere-Bakunda, J.D.; Lundback-Mompó, D.; Orts-Grau, S.; Gimeno-Sales, F.J.; Seguí-Chilet, S.
Small Wind Turbine Emulator Based on Lambda-Cp Curves Obtained under Real Operating Conditions. *Energies* **2019**, *12*, 2456.
https://doi.org/10.3390/en12132456

**AMA Style**

Martínez-Márquez CI, Twizere-Bakunda JD, Lundback-Mompó D, Orts-Grau S, Gimeno-Sales FJ, Seguí-Chilet S.
Small Wind Turbine Emulator Based on Lambda-Cp Curves Obtained under Real Operating Conditions. *Energies*. 2019; 12(13):2456.
https://doi.org/10.3390/en12132456

**Chicago/Turabian Style**

Martínez-Márquez, Camilo I., Jackson D. Twizere-Bakunda, David Lundback-Mompó, Salvador Orts-Grau, Francisco J. Gimeno-Sales, and Salvador Seguí-Chilet.
2019. "Small Wind Turbine Emulator Based on Lambda-Cp Curves Obtained under Real Operating Conditions" *Energies* 12, no. 13: 2456.
https://doi.org/10.3390/en12132456