# Extended Simplified Electro-Mechanical Model of a Variable-Speed Wind Turbine for Grid Integration Studies: Emulation and Validation on a Microgrid Lab

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## Abstract

**:**

^{®}software, require significant computational efforts that could make grid studies impractical when its scale tends to increase. To contribute to facing this issue, this paper proposes an extended simplified model for a variable-speed wind turbine that considers the dynamic behavior of its mechanical system and includes an approximate representation of the power electronic converter. This approach broadens the scope of studies related to grid frequency control and power quality (fast-frequency response, primary frequency control, and voltage control, among others), considerably reducing the computational burden. Several validations of the proposed simplified model are presented, including comparisons with a doubly fed induction generator-based wind turbine model (phasor type) from the MATLAB/Simulink

^{®}library, and laboratory experiments under controlled conditions. The results show a good fit of the proposed simplified model to the MATLAB/Simulink

^{®}model, with minimal delays about 3% of the wind turbine inertia constant. Moreover, with the proposal, the computational time is reduced by up to 80% compared to a detailed model. This time reduction is achieved without penalizing the numerical accuracy and the estimation quality of the real behavior of the variable-speed wind turbine.

## 1. Introduction

^{®}environment, whose models are highly robust. However, studies that involve many WTs and their interactions with the electric power system lead to complex problems with many different components characterized by very diverse time scale dynamics. Particularly, the detailed modeling of the power electronic converter (PEC) of each WT in a larger system leads to a multiscale problem that requires so high a computational effort that it is almost intractable with conventional modeling approaches. Therefore, studying efficient methods that manage to reduce the computational burden without compromising the accuracy of the dynamic model of the VSWT and PEC is necessary.

^{®}for WT failure analysis. Among other relevant studies, ref. [14] presents a robust mathematical model of VSWT linked to the rotor in an experimental and simulation way for a WECS in different wind speed conditions.

^{®}library, with separate and joint validations of VSWT and PEC. In Section 3.2, the test-bench for emulating the time-domain behavior of some variables of interest provided by the proposal in an actual microgrid laboratory is presented. In this section, a critical discussion of the results is offered. Section 4 summarizes the conclusions of the paper.

## 2. Modelling of Variable-Speed Wind Turbine

_{t}and T

_{em}are the mechanical and the electromagnetic torque, respectively. P

_{g}is the total output active power, $\omega $

_{t}and $\omega $

_{g}are the angular speed of the turbine and the electric generator, and v and β denote the wind speed and the blade pitch angle. At this point, it is important to mention that the short-term operation of the blocks: wind rotor, pitch angle controller, mechanical system, and active power controller (by MPPT) were successfully validated by simulation in [8]. This modular design incorporates two new and essential components: an approximate representation of the power electronic converter and the generator, and a pair of closed-loop controllers that regulate the active and reactive power injected into the grid.

## 3. Results and Discussion

#### 3.1. Validation of the Model

^{®}.

#### 3.1.1. Validation of the Simplified Electro-Mechanical VSWT-Model

_{c}, similar to the procedure reported in [8]. This adaptation is referred to as Figure 2* in the illustrations below. The simplified model is compared with a Wind Turbine Doubly-Fed Induction Generator block (Phasor Type) from MATLAB/Simulink

^{®}[25], considering a robust model that includes mechanical, electrical, and electromagnetic effects in detail. To have a comparative frame of reference, both models have been subjected to the same operating conditions and parameters. In this sense, the reference model has been connected, with its power losses disabled, to a bus with zero short-circuit impedance, following the diagram shown in Figure 5.

#### 3.1.2. Validation of the Simplified Representation of the PEC

_{d}and i

_{q}setpoints are reached.

^{®}and in the laboratory. Section 3.2 briefly describes the Microgrid Laboratory and provides further information on the actual PEC prototype used in this study.

#### 3.1.3. Validation of the Extended Simplified VSWT Model in Simulation

_{g}dynamics at the output of the proposed model is obtained from the voltage and current measured at the PCC (Figure 12), which is very similar to that achieved with the reference model. In this case, the computational effort in both models has been compared and the results show that the proposed model reduces the computation time by 80% with respect to the detailed model (Figure 5). This computational benefit is achieved despite the fact that the proposed model uses the “continuous” mode for its numerical solver in MATLAB, while the reference model uses the “phasor” approximation to reduce its computational load. Table 1 provides further details about the computational times achieved by running the two models for the simulated case study for a time horizon of 140 s.

#### 3.2. Comparison of the Expected and Emulated Model Results in the Laboratory

## 4. Conclusions

^{®}and with laboratory experiments under controlled conditions. The main novelty of this paper is the development of a simplified electromechanical model of a variable speed wind turbine considering an electronic power controller that optimizes the computational effort, with the aim of having a computer tool that allows the performance of dynamic analyses that would be intractable when simulating frequency events in large-scale power systems with complete models.

^{®}, representing approximately 3% of the WT inertia constant. In general, the transient and steady-state response have accurate approximations.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- A.
- DFIG-WT parameters

Parameter | Symbol | Value and Units |
---|---|---|

Base power | ${P}_{\mathrm{base}}$ | 1.5 MW |

Max./Min. power of the generator | ${P}_{\mathrm{g},\mathrm{max}}{/P}_{\mathrm{g},\mathrm{min}}$ | 1/0.04 pu |

Max./Min. torque of the generator | ${T}_{\mathrm{em},\mathrm{max}}{/T}_{\mathrm{em},\mathrm{min}}$ | 0.826/0.057 pu |

Wind speed at ${P}_{\mathrm{g}}=0.73\text{}\mathrm{pu}$ | ${v}_{\mathrm{nom}}$ | 12 m/s |

Number of pole pairs | $\mathrm{p}$ | 2 |

Nominal frequency | ${f}_{\mathrm{nom}}$ | 60 Hz |

Base speed of the turbine | ${\omega}_{\mathrm{t},\text{}\mathrm{base}}$ | 1.644 rad/s |

Base speed of the generator | ${\omega}_{\mathrm{g},\text{}\mathrm{base}}$ | 157.08 rad/s |

Air density | $\rho $ | 1.225 kg/m^{3} |

Radius of the rotor | $R$ | 38.5 m |

Power constant | ${K}_{\mathrm{p}}$ | $1{.901\times 10}^{-3}{\text{}(\mathrm{m}/\mathrm{s})}^{3}$ |

Speed constant | ${K}_{\lambda}$ | 63.29 m/s |

Min./Max. blade pitch angle | ${\mathsf{\beta}}_{\mathrm{min}}{/\mathsf{\beta}}_{\mathrm{max}}$ | 0°/45° |

Maximum blade pitch angle rate | $\left(\frac{\mathrm{d}\mathsf{\beta}}{\mathrm{dt}}\right)\mathrm{max}$ | 2°/s |

Turbine-generator inertia constant | ${H}_{\mathrm{eq}}$ | 5.29 s |

DFIG-PEC time constant | ${\mathsf{\tau}}_{\mathrm{C}}$ | 20 ms |

Blade pitch servo time constant | ${\mathsf{\tau}}_{P}$ | 0 s |

Pitch controller gains | ${K}_{\mathrm{P}\text{}\mathrm{pc}}{/K}_{\mathrm{I}\text{}\mathrm{pc}}$ | 500/0 |

Speed controller gains | ${K}_{\mathrm{P}\text{}\mathrm{sc}}{/K}_{\mathrm{I}\text{}\mathrm{sc}}$ | 0.3/8 |

- B.
- MPPT-curve parameters

## Appendix B

Utility Grid Parameters | Symbol | Value and Units |
---|---|---|

Three-phase source | ${V}_{ab\left(rms\right)}$ | 480 V |

f | 60 Hz | |

Three-phase load | ${P}_{LA}={P}_{LB}={P}_{LC}$ | 1 kW |

Detailed model parameters | Symbol | Value and Units |

Modulation SVPWM | ${f}_{carrier}$ | 20 kHz |

PI controller | ${K}_{P},{K}_{I}$ | 50, 2500 |

RL filter series | ${R}_{f}$ | 0.1 Ω |

${L}_{f}$ | 12.7 mH | |

DC voltage | ${U}_{d}$ | 800 V |

Simplified model parameters | Symbol | Value and Units |

Active power PI controller | ${K}_{P},{K}_{I}$ | 5, 50 |

Reactive power PI controller | ${K}_{P},{K}_{I}$ | −5, −50 |

Time constant (delay function) | ${\tau}_{C}$ | 0.02 s |

## References

- Worku, M.Y. Recent Advances in Energy Storage Systems for Renewable Source Grid Integration: A Comprehensive Review. Sustainability
**2022**, 14, 5985. [Google Scholar] [CrossRef] - Tchakoua, P.; Wamkeue, R.; Ouhrouche, M.; Slaoui-Hasnaoui, F.; Tameghe, T.A.; Ekemb, G. Wind Turbine Condition Monitoring: State-of-the-Art Review, New Trends, and Future Challenges. Energies
**2014**, 7, 2595–2630. [Google Scholar] [CrossRef] - Herbert-Acero, J.F.; Probst, O.; Réthoré, P.E.; Larsen, G.C.; Castillo-Villar, K.K. A Review of Methodological Approaches for the Design and Optimization of Wind Farms. Energies
**2014**, 7, 6930–7016. [Google Scholar] [CrossRef] - Jaen-Cuellar, A.Y.; Elvira-Ortiz, D.A.; Osornio-Rios, R.A.; Antonino-Daviu, J.A. Advances in Fault Condition Monitoring for Solar Photovoltaic and Wind Turbine Energy Generation: A Review. Energies
**2022**, 15, 5404. [Google Scholar] [CrossRef] - Aljafari, B.; Stephenraj, J.P.; Vairavasundaram, I.; Rassiah, R.S. Steady State Modeling and Performance Analysis of a Wind Turbine-Based Doubly Fed Induction Generator System with Rotor Control. Energies
**2022**, 15, 3327. [Google Scholar] [CrossRef] - Haces-Fernandez, F.; Cruz-Mendoza, M.; Li, H. Onshore Wind Farm Development: Technologies and Layouts. Energies
**2022**, 15, 2381. [Google Scholar] [CrossRef] - Ochoa, D.; Martinez, S. A simplified electro-mechanical model of a DFIG-based wind turbine for primary frequency control studies. IEEE Lat. Am. Trans.
**2016**, 14, 3614–3620. [Google Scholar] [CrossRef] - Ochoa, D.; Martinez, S. Fast-Frequency Response Provided by DFIG-Wind Turbines and its Impact on the Grid. IEEE Trans. Power Syst.
**2017**, 32, 4002–4011. [Google Scholar] [CrossRef] - Kayikçi, M.; Milanović, J.V. Dynamic contribution of DFIG-based wind plants to system frequency disturbances. IEEE Trans. Power Syst.
**2009**, 24, 859–867. [Google Scholar] [CrossRef] - Ihedrane, Y.; Bekkali, C.E.; Bossoufi, B.; Bouderbala, M. Control of Power of a DFIG Generator with MPPT Technique for Wind Turbines Variable Speed. In Modeling, Identification and Control Methods in Renewable Energy Systems. Green Energy and Technology; Derbel, N., Zhu, Q., Eds.; Springer: Singapore, 2018; pp. 105–129. [Google Scholar]
- Jenkal, H.; Lamnadi, M.; Mensou, S.; Bossoufi, B.; Boulezhar, A. A robust control for a variable wind speed conversion system energy based on a DFIG using Backstepping. Wind Eng.
**2022**, 19, 0309524X221122512. [Google Scholar] [CrossRef] - Gianto, R. Constant voltage model of DFIG-based variable speed wind turbine for load flow analysis. Energies
**2021**, 14, 8549. [Google Scholar] [CrossRef] - Seshadri Sravan Kumar, V.; Thukaram, D. Accurate modeling of doubly fed induction generator based wind farms in load flow analysis. Electr. Power Syst. Res.
**2018**, 155, 363–371. [Google Scholar] - Prasad, R.M.; Mulla, M.A. Mathematical Modeling and Position-Sensorless Algorithm for Stator-Side Field-Oriented Control of Rotor-Tied DFIG in Rotor Flux Reference Frame. IEEE Trans. Energy Convers.
**2020**, 35, 631–639. [Google Scholar] [CrossRef] - Behabtu, H.A.; Coosemans, T.; Berecibar, M.; Fante, K.A.; Kebede, A.A.; van Mierlo, J.; Messagie, M. Performance evaluation of grid-connected wind turbine generators. Energies
**2021**, 14, 6807. [Google Scholar] [CrossRef] - Ochoa, D.; Martinez, S. Frequency dependent strategy for mitigating wind power fluctuations of a doubly-fed induction generator wind turbine based on virtual inertia control and blade pitch angle regulation. Renew. Energy
**2018**, 128, 108–124. [Google Scholar] [CrossRef] - Ochoa, D.; Martinez, S. Proposals for Enhancing Frequency Control in Weak and Isolated Power Systems: Application to the Wind-Diesel Power System of San Cristobal Island-Ecuador. Energies
**2018**, 11, 910. [Google Scholar] [CrossRef] - Ochoa, D. Modelo simplificado de una interfaz de conexión a la red basada en un convertidor electrónico de potencia para estudios de red en régimen dinámico. Ingenius
**2021**, 26, 87–98. [Google Scholar] [CrossRef] - Siami, M.; Khaburi, D.A.; Rivera, M.; Rodríguez, J. A Computationally Efficient Lookup Table Based FCS-MPC for PMSM Drives Fed by Matrix Converters. IEEE Trans. Ind. Electron.
**2017**, 64, 7645–7654. [Google Scholar] [CrossRef] - Siami, M.; Khaburi, D.A.; Rodriguez, J. Simplified Finite Control Set-Model Predictive Control for Matrix Converter-Fed PMSM Drives. IEEE Trans. Power Electron.
**2018**, 33, 2438–2446. [Google Scholar] [CrossRef] - Lei, J.; Feng, S.; Wheeler, P.; Zhou, B.; Zhao, J. Steady-State Error Suppression and Simplified Implementation of Direct Source Current Control for Matrix Converter with Model Predictive Control. IEEE Trans. Power Electron.
**2020**, 35, 3183–3194. [Google Scholar] [CrossRef] - Bhesaniya, M.M.; Shukla, A. Computationally efficient method for simulating current source modular multilevel converter. In Proceedings of the 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, Germany, 5–9 September 2016. [Google Scholar]
- Schmidlin Junior, C.R.; Araujo Lima, F.K. Wind Turbine and PMSG Dynamic Modelling in PSIM. IEEE Lat. Am. Trans.
**2016**, 14, 4115–4120. [Google Scholar] [CrossRef] - Reyes, V.; Rodriguez, J.J.; Carranza, O.; Ortega, R. Review of mathematical models of both the power coefficient and the torque coefficient in wind turbines. In Proceedings of the IEEE 24th International Symposium on Industrial Electronics (ISIE), Buzios, Brazil, 3–5 June 2015. [Google Scholar]
- MathWorks—Makers of MATLAB and Simulink—MATLAB & Simulink, (n.d.). Available online: https://www.mathworks.com/ (accessed on 14 October 2022).
- Espinoza, J.L.; Gonzalez, L.G.; Sempertegui, R. Micro grid laboratory as a tool for research on non-conventional energy sources in Ecuador. In Proceedings of the 2017 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, Mexico, 8–10 November 2017. [Google Scholar]
- Rey, J.M.; Vera, G.A.; Acevedo-Rueda, P.; Solano, J.; Mantilla, M.A.; Llanos, J.; Saez, D. A Review of Microgrids in Latin America: Laboratories and Test Systems. IEEE Lat. Am. Trans.
**2022**, 20, 1000–1011. [Google Scholar] [CrossRef]

**Figure 2.**Schematic representation of the proposed extended simplified electromechanical model of the VSWT.

**Figure 5.**Schematic representation of the reference-test bench designed for the assessment of the proposal (Detailed model).

**Figure 6.**Comparison of the mechanical stage of the simplified VSWT model vs. detailed MATLAB/Simulink model.

**Figure 13.**Schematic representation of CCTI-B Microgrid Laboratory components: 1. Utility grid, 2. Bus operation in grid-connected mode, 3. Bus operation in isolated mode, 4. Energy storage components, 5. Loads and programmable sources, 6. Other loads, 7. Photovoltaic generation, 8. Mini-wind generation, 9. Thermal generation, 10. Hydrokinetic generation.

**Figure 14.**General scheme proposed for emulating the dynamics of some electrical variables of the VSWT model expected and emulated in a Microgrid-Laboratory.

**Figure 15.**Comparison of the dynamics of some electrical variables of the expected model with respect to emulated in laboratory.

Computer and Processor Features | ||
---|---|---|

Processor: Intel(R) Core(TM) i7-4510U CPU @ 2.00 GHz 2.60 GHz. Installed RAM: 8.00 GB (7.89 GB usable). OS Type: 64-bit OS, x64-based processor. | ||

Simulator features | ||

MATLAB R2020a Update 6 (9.8.0.1538580) | ||

Simulated model | Detailed (Figure 5) | Proposed (Figure 3) |

Computer usage | ||

Used RAM (% of total GB) | 87 | 68 |

Used CPU (% of total GHz) | 35 | 34 |

Simulator parameter | ||

Simulation type | Phasor | Continuous |

Solver | ode14x (extrapolation) | ode23tb (stiff/TR-BDF2) |

Step size | 10^{−3} s (Fixed-step) | Max. 10^{−3} s (Variable-step) |

Elapsed simulation time | 84.97 s | 18.46 s |

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**MDPI and ACS Style**

Ochoa, D.; Martinez, S.; Arévalo, P. Extended Simplified Electro-Mechanical Model of a Variable-Speed Wind Turbine for Grid Integration Studies: Emulation and Validation on a Microgrid Lab. *Electronics* **2022**, *11*, 3945.
https://doi.org/10.3390/electronics11233945

**AMA Style**

Ochoa D, Martinez S, Arévalo P. Extended Simplified Electro-Mechanical Model of a Variable-Speed Wind Turbine for Grid Integration Studies: Emulation and Validation on a Microgrid Lab. *Electronics*. 2022; 11(23):3945.
https://doi.org/10.3390/electronics11233945

**Chicago/Turabian Style**

Ochoa, Danny, Sergio Martinez, and Paul Arévalo. 2022. "Extended Simplified Electro-Mechanical Model of a Variable-Speed Wind Turbine for Grid Integration Studies: Emulation and Validation on a Microgrid Lab" *Electronics* 11, no. 23: 3945.
https://doi.org/10.3390/electronics11233945