# Fast Control-Oriented Dynamic Linear Model of Wind Farm Flow and Operation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Dynamic Flow Predictor

#### 2.1.1. Turbine Operation Model

#### 2.1.2. Flow Model

#### 2.1.3. Kalman Filter and System Update

#### Time Update

#### Data Update

#### Matrix Update

#### 2.2. Simulation Environment: SimWindFarm

#### 2.2.1. Modeling Approach

#### 2.2.2. Validity as Test Environment

#### 2.2.3. Simulation Conditions

## 3. Results and Discussion

#### 3.1. Two-Turbine Case Study

#### 3.1.1. Simulation Set-Up

#### Wind Farm Layout

#### Wind Farm Operation

#### 3.1.2. Results

#### Benefits of Kalman Filtering

#### Computational Efficiency

#### Effect of Wind Direction

#### 3.2. Large-Scale Wind Farm Case Study

#### 3.2.1. Benefit of Kalman Filter

#### 3.2.2. Sensitivity of Wake Model

#### 3.2.3. Wind Speed Prediction

#### 3.2.4. Available Power Prediction

#### 3.2.5. Computation Time

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFD | Computational fluid dynamics |

DFP | Dynamic Flow Predictor |

DTU | Technical University of Denmark |

RMS | Root-mean-square |

SWF | SimWindFarm |

## References

- Global Wind Energy Council (GWEC). Global Wind Report 2017. Available online: http://gwec.net/ (accessed on 19 November 2018).
- Fernandez-Gamiz, U.; Zulueta, E.; Boyano, A.; Ansoategui, I.; Uriarte, I. Five megawatt wind turbine power output improvements by passive flow control devices. Energies
**2017**, 10, 742. [Google Scholar] [CrossRef] - Hansen, M.O.; Sørensen, J.N.; Voutsinas, S.; Sørensen, N.; Madsen, H.A. State of the art in wind turbine aerodynamics and aeroelasticity. Prog. Aerosp. Sci.
**2006**, 42, 285–330. [Google Scholar] [CrossRef] - Pao, L.Y.; Johnson, K.E. A tutorial on the dynamics and control of wind turbines and wind farms. In Proceedings of the 2009 American Control Conference, St. Louis, MO, USA, 10–12 June 2009; pp. 2076–2089. [Google Scholar] [CrossRef]
- Kazda, J.; Zendehbad, M.; Jafari, S.; Chokani, N.; Abhari, R.S. Mitigating adverse wake effects in a wind farm using non-optimum operational conditions. J. Wind Eng. Ind. Aerodyn.
**2016**, 154, 76–83. [Google Scholar] [CrossRef] - Annoni, J.; Gebraad, P.M.; Scholbrock, A.K.; Fleming, P.A.; Wingerden, J.W.V. Analysis of axial-induction-based wind plant control using an engineering and a high-order wind plant model. Wind Energy
**2016**, 19, 1135–1150. [Google Scholar] [CrossRef] - Hansen, A.D.; Sørensen, P.; Iov, F.; Blaabjerg, F. Centralised power control of wind farm with doubly fed induction generators. Renew. Energy
**2006**, 31, 935–951. [Google Scholar] [CrossRef] - Van Wingerden, J.W.; Pao, L.; Aho, J.; Fleming, P. Active power control of waked wind farms. IFAC-PapersOnLine
**2017**, 50, 4484–4491. [Google Scholar] [CrossRef] - Kazda, J.; Merz, K.; Tande, J.O.; Cutululis, N.A. Mitigating turbine mechanical loads using engineering model predictive wind farm controller. J. Phys. Conf. Ser.
**2018**, 1104, 012036. [Google Scholar] [CrossRef] - Soleimanzadeh, M.; Wisniewski, R.; Kanev, S. An optimization framework for load and power distribution in wind farms. J. Wind Eng. Ind. Aerodyn.
**2012**, 107–108, 256–262. [Google Scholar] [CrossRef] - Horvat, T.; Spudic, V.; Baotic, M. Quasi-stationary optimal control for wind farm with closely spaced turbines. In Proceedings of the 35th International Convention MIPRO, Opatija, Croatia, 21–25 May 2012; pp. 829–834. [Google Scholar]
- Gebraad, P.M.O.; Teeuwisse, F.W.; van Wingerden, J.W.; Fleming, P.A.; Ruben, S.D.; Marden, J.R.; Pao, L.Y. Wind plant power optimization through yaw control using a parametric model for wake effects—A CFD simulation study. Wind Energy
**2016**, 19, 95–114. [Google Scholar] [CrossRef] - Kazda, J.; Göçmen, T.; Giebel, G.; Cutululis, N. Possible improvements for present wind farm models used in optimal wind farm controllers. In Proceedings of the 15th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Power Plants, Vienna, Austria, 15–17 November 2016. [Google Scholar]
- Crespo, A.; Hernández, J. Turbulence characteristics in wind-turbine wakes. J. Wind Eng. Ind. Aerodyn.
**1996**, 61, 71–85. [Google Scholar] [CrossRef] - Riverso, S.; Mancini, S.; Sarzo, F.; Ferrari-Trecate, G. Model predictive controllers for reduction of mechanical fatigue in wind farms. IEEE Trans. Control Syst. Technol.
**2017**, 25, 535–549. [Google Scholar] [CrossRef] - Mikkelsen, T.; Angelou, N.; Hansen, K.; Sjoholm, M.; Harris, M.; Slinger, C.; Hadley, P.; Scullion, R.; Ellis, G.; Vives, G. A Spinner-integrated wind lidar for enhanced wind turbine control. Wind Energy
**2013**, 16, 625–643. [Google Scholar] [CrossRef] [Green Version] - Schlipf, D.; Schlipf, D.J.; Kühn, M. Nonlinear model predictive control of wind turbines using LIDAR. Wind Energy
**2013**, 16, 1107–1129. [Google Scholar] [CrossRef] - Boersma, S.; Gebraad, P.; Vali, M.; Doekemeijer, B.; van Wingerden, J. A control-oriented dynamic wind farm flow model: “WFSim”. J. Phys. Conf. Ser.
**2016**, 753, 032005. [Google Scholar] [CrossRef] [Green Version] - Soleimanzadeh, M.; Wisniewski, R.; Brand, A. State-space representation of the wind flow model in wind farms. Wind Energy
**2014**, 17, 627–639. [Google Scholar] [CrossRef] - Knudsen, T.; Bak, T.; Soltani, M. Prediction models for wind speed at turbine locations in a wind farm. Wind Energy
**2011**, 14, 877–894. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Hu, J. A robust combination approach for short-term wind speed forecasting and analysis—Combination of the ARIMA (Autoregressive Integrated Moving Average), ELM (Extreme Learning Machine), SVM (Support Vector Machine) and LSSVM (Least Square SVM) Forecasts Using a GPR (Gaussian Process Regression) Model. Energy
**2015**, 93, 41–56. [Google Scholar] [CrossRef] - Jung, J.; Broadwater, R.P. Current status and future advances for wind speed and power forecasting. Renew. Sustain. Energy Rev.
**2014**, 31, 762–777. [Google Scholar] [CrossRef] - Shapiro, C.R.; Meyers, J.; Meneveau, C.; Gayme, D.F. Wind farms providing secondary frequency regulation: evaluating the performance of model-based receding horizon control. Wind Energy Sci.
**2018**, 3, 11–24. [Google Scholar] [CrossRef] [Green Version] - Gebraad, P.M.O.; van Wingerden, J.W. A Control-oriented dynamic model for wakes in wind plants. J. Phys. Conf. Ser.
**2014**, 524, 012186. [Google Scholar] [CrossRef] - Gogmen, T.; Giebel, G.; Poulsen, N.K.; Sørensen, P.E. Possible power of down-regulated offshore wind power plants: The PossPOW algorithm. Wind Energy
**2018**. [Google Scholar] [CrossRef] - Boersma, S.; Doekemeijer, B.; Vali, M.; Meyers, J.; Wingerden, J.w.V. A Control-oriented dynamic wind farm model: WFSim. Wind Energy Sci.
**2018**, 3, 75. [Google Scholar] [CrossRef] - Gebraad, P.M.O.; Fleming, P.A.; Van Wingerden, J.W. Wind turbine wake estimation and control using FLORIDyn, a control-oriented dynamic wind plant model. In Proceedings of the American Control Conference, Chicago, IL, USA, 1–3 July 2015; pp. 1702–1708. [Google Scholar] [CrossRef]
- Bay, C.J.; Annoni, J.; Taylor, T.; Pao, L.; Johnson, K. Active power control for wind farms using distributed model predictive control and nearest neighbor communication. In Proceedings of the Annual American Control Conference, Milwaukee, WI, USA, 27–29 June 2018; pp. 682–687. [Google Scholar] [CrossRef]
- Göçmen, T.; Giebel, G.; Sørensen, P.E.; Poulsen, N.K. Possible Power Estimation of Down-Regulated Offshore Wind Power Plants. Ph.D. Thesis, Technical University of Denmark (DTU), Kongens Lyngby, Denmark, 2016. [Google Scholar]
- Øye, S. Tjæreborg Wind Turbine (Esbjerg): First Dynamic Inflow Measurement; Technical Report; DTU Wind Energy: Roskilde, Denmark, 1991. [Google Scholar]
- Machefaux, E.; Larsen, G.C.; Troldborg, N.; Gaunaa, M.; Rettenmeier, A. Empirical modeling of single-wake advection and expansion using full-scale pulsed lidar-based measurements. Wind Energy
**2015**, 18, 2085–2103. [Google Scholar] [CrossRef] - Frandsen, S.; Barthelmie, R.; Pryor, S.; Rathmann, O.; Larsen, S.; Hojstrup, J. Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy
**2006**, 9, 39–53. [Google Scholar] [CrossRef] - Kalman, R.E.; Bucy, R.S. New results in linear filtering and prediction theory. J. Basic Eng.
**1961**, 83, 95. [Google Scholar] [CrossRef] - Grunnet, J.; Soltani, M.; Knudsen, T. Aeolus toolbox for dynamics wind farm model, simulation and control. In Proceedings of the European Wind Energy Conference & Exhibition (EWEC 2010), Warszawa, Poland, 20–23 April 2010; pp. 3119–3129. [Google Scholar]
- Grunnet, J.; Soltani, M.; Knudsen, T. SimWindFarm Official Website. 2016. Available online: http://www.ict-aeolus.eu/SimWindFarm/ (accessed on 19 November 2018).
- Jonkman, J.; Butterfield, S.; Musial, W.; Scott, G. Definition of a 5-MW Reference Wind Turbine for Offshore System Development; Technical Report No. NREL/TP-500-38060; National Renewable Energy Laboratory: Golden, CO, USA, 2009. [Google Scholar]
- Kazda, J.; Göçmen, T.; Giebel, G.; Courtney, M.; Cutululis, N. Framework of multi-objective wind farm controller applicable to real wind farms. In Proceedings of the WindEurope Summit 2016, Hamburg, Germany, 27–29 September 2016. [Google Scholar]
- Energinet.dk. Technical Regulation for Wind Power Plants with a Power Output Above 11 kW. Available online: http://osp.energinet.dk/ (accessed on 19 November 2018).
- Jensen, N.O. A Note on Wind Generator Interaction; Risø National Laboratory: Roskilde, Denmark, 1983. [Google Scholar]

**Figure 1.**System structure of a dynamic flow predictor (DFP), showing the system update process and Kalman filter time update and data update.

**Figure 3.**Simulated operation of two-turbine array used for comparison with DFP. Shown are (

**a**) total farm power and (

**b**) blade pitch angle.

**Figure 4.**Sampled rotor effective wind speed simulated using SWF and predicted using DFP with and without use of Kalman filter. Shown are wind speeds of (

**a**) turbine No. 1 and (

**b**) turbine No. 2.

**Figure 5.**Root-mean-square (RMS) deviation of rotor effective wind speed estimation at turbines of two-turbine array. RMS deviation is normalized with mean freestream wind speed.

**Figure 6.**Wind farm in two operation scenarios used for demonstration of effect of update limit on model update frequency, model accuracy and computational cost. Shown are (

**a**) total power of wind farm and (

**b**) power coefficient at upstream turbine.

**Figure 7.**Impact of matrix update limit on downstream turbine wind speed prediction accuracy (right) and matrix update frequency (left).

**Figure 8.**Effect of alignment of turbine array with wind direction on accuracy of estimation of rotor effective wind speed. Shown are (

**a**) accuracy for each turbine and (

**b**) ratio of RMS wind speed estimation error at downstream turbine to RMS wind speed estimation error at upstream turbine.

**Figure 10.**Accuracy of DFP in estimation of current rotor effective wind speed at turbines of large-scale wind farm. Accuracy is quantified as normalized RMS error of wind speed estimated using DFP given SWF as reference. Shown are (

**a**) distribution of accuracy across turbines in wind farm with DFP using Kalman filter, and (

**b**) effect of Kalman filter on row-wise accuracy statistics, that is, mean error (bars) and standard deviation of error (errorbars).

**Figure 11.**Effect of wake deficit model on error of DFP in estimation of current rotor effective wind speed at turbines of large-scale wind farm. Shown are the row-wise statistics, that is, mean (bars) and standard deviation (errorbars) of the normalized RMS difference of wind speed between the DFP and SWF.

**Figure 12.**Accuracy of 10-step ahead prediction of rotor effective wind speed at rows of large-scale wind farm. Accuracy is normalized RMS difference between DFP prediction and SWF flow model averaged over turbine rows. Kalman filter in DFP is active.

**Figure 13.**Accuracy of 10-step ahead prediction of turbine available power for each row of large-scale wind farm. Accuracy is normalized RMS difference between DFP prediction and SWF averaged over turbine rows. Kalman filter in DFP is active.

Rated Power | Cut-In/Rated/Cut-Out Wind Speed | Rotor Diameter |
---|---|---|

5 MW | 3 m/s/11.4 m/s/25 m/s | 126 m |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kazda, J.; Cutululis, N.A.
Fast Control-Oriented Dynamic Linear Model of Wind Farm Flow and Operation. *Energies* **2018**, *11*, 3346.
https://doi.org/10.3390/en11123346

**AMA Style**

Kazda J, Cutululis NA.
Fast Control-Oriented Dynamic Linear Model of Wind Farm Flow and Operation. *Energies*. 2018; 11(12):3346.
https://doi.org/10.3390/en11123346

**Chicago/Turabian Style**

Kazda, Jonas, and Nicolaos Antonio Cutululis.
2018. "Fast Control-Oriented Dynamic Linear Model of Wind Farm Flow and Operation" *Energies* 11, no. 12: 3346.
https://doi.org/10.3390/en11123346