# Multi-Scale Simulation of Wind Farm Performance during a Frontal Passage

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Case Study and Observations

## 2. Methods

#### 2.1. Computational Setup

#### 2.2. Model Validation

#### 2.3. Model Improvements

#### 2.3.1. Turbine Yawing

#### 2.3.2. Turbine Power Calculation

## 3. Results

#### 3.1. Background Flow and Turbine Wake Comparison

#### 3.2. Turbulence Downscaling

#### 3.3. Turbine Power Output Comparison

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABL | Atmospheric boundary layer |

AGL | Above ground level |

ASL | Above sea level |

CFD | Computational fluid dynamics |

CPM | Cell perturbation method |

GAD | Generalized actuator disk |

GFS | Global forecast system |

LES | Large-eddy simulation |

MYJ | Mellor–Yamada–Janjić |

NAM | North American Mesoscale |

NCEP | National Centers for Environmental Prediction |

PBL | Planetary boundary layer |

TKE | Turbulence kinetic energy |

UTC | Coordinated universal time |

WRF | Weather Research and Forecasting |

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**Figure 1.**Terrain height for the innermost domain, d06, shown in meters above sea level (ASL). In addition, the locations of 21 simulated wind turbines, as well as the meteorological tower used for validation in Section 2.2, are included. Note that the lidar used for validation is roughly 4 km south of the region depicted here.

**Figure 2.**Comparison of WRF modeled (

**a**) wind speed; (

**b**) wind direction; and (

**c**) temperature to observations at 80 m AGL (turbine hub height). Mesoscale WRF model results (from d03) are shown as instantaneous values every 10 min for various forcing datasets and nudging options. Observations are displayed as the 10-min mean ± standard deviation, with data points at the middle of the 10-min range. In (b), the wind direction is modified for visualization purposes by subtracting 360${}^{\circ}$ from values above 180${}^{\circ}$ (such that 0${}^{\circ}$ is northerly flow, 90${}^{\circ}$ is easterly flow, −90${}^{\circ}$ is westerly flow, and 180${}^{\circ}$/−180${}^{\circ}$ is southerly flow).

**Figure 3.**Hub-height wind speed comparison between radar observations and time-shifted WRF model results at the times indicated by the dotted lines in the bottom panel. Wind speed observed at the meteorological tower at 80 m AGL, as in Figure 2, and time-shifted modeled wind speeds from domain d06 at the same height, are shown in the bottom panel, with 10-min average values shown at the middle of the 10-min range.

**Figure 4.**Hub-height wind speed perturbation ${W}_{p}$ (Equation 3) comparison between radar observations and time-shifted WRF model results at the times shown in Figure 3 and indicated in the bottom panel. The observed and modeled inflow wind speed ${W}_{in}$ at 80 m AGL are also shown in the bottom panel.

**Figure 5.**Comparison of hub-height velocity between WRF model runs (

**a**,

**c**) with and (

**b**,

**d**) without the cell perturbation method. Results are shown (

**a**,

**b**) before the frontal passage, and (

**c**,

**d**) after the frontal passage. The times shown, 14:43:00 and 16:06:10 UTC (+ 50 min.), correspond to panels in Figure 3 and Figure 4.

**Figure 6.**Power output comparison between observations and time-shifted WRF model results, both with and without the cell perturbation method, for turbines (

**a**) 7 and (

**b**) 17 (see Figure 1); (

**c**) average power output from time-shifted WRF model results with the cell perturbation method, including averages for northern and southern turbine rows.

**Figure 7.**Comparison of WRF-GAD model power curve, created using idealized simulations with flat terrain and a constant forcing velocity, to actual power curve for the turbines in the study area.

**Table 1.**Selected parameters for six-way nested WRF model setup spanning the outermost (d01) to innermost (d06) domains.

Domain | $\mathsf{\Delta}\mathit{x}$ [m] | Nest Ratio | ${\mathit{N}}_{\mathit{x}}\times {\mathit{N}}_{\mathit{y}}$ | $\mathsf{\Delta}\mathit{t}$ [s] | Turb. Closure | Nudging |
---|---|---|---|---|---|---|

d01 | 18,750 | - | $202\times 202$ | 15 | MYJ | Yes |

d02 | 6250 | 3 | $202\times 202$ | 5 | MYJ | Yes |

d03 | 1250 | 5 | $201\times 201$ | 1 | MYJ | Yes |

d04 | 250 | 5 | $201\times 201$ | 0.2 | MYJ | No |

d05 | 50 | 5 | $481\times 481$ | 0.04 | TKE 1.5 | No |

d06 | 10 | 5 | $601\times 601$ | 0.008 | TKE 1.5 | No |

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## Share and Cite

**MDPI and ACS Style**

Arthur, R.S.; Mirocha, J.D.; Marjanovic, N.; Hirth, B.D.; Schroeder, J.L.; Wharton, S.; Chow, F.K. Multi-Scale Simulation of Wind Farm Performance during a Frontal Passage. *Atmosphere* **2020**, *11*, 245.
https://doi.org/10.3390/atmos11030245

**AMA Style**

Arthur RS, Mirocha JD, Marjanovic N, Hirth BD, Schroeder JL, Wharton S, Chow FK. Multi-Scale Simulation of Wind Farm Performance during a Frontal Passage. *Atmosphere*. 2020; 11(3):245.
https://doi.org/10.3390/atmos11030245

**Chicago/Turabian Style**

Arthur, Robert S., Jeffrey D. Mirocha, Nikola Marjanovic, Brian D. Hirth, John L. Schroeder, Sonia Wharton, and Fotini K. Chow. 2020. "Multi-Scale Simulation of Wind Farm Performance during a Frontal Passage" *Atmosphere* 11, no. 3: 245.
https://doi.org/10.3390/atmos11030245