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Market Suitability and Performance Tradeoffs Offered by Commercial Wind Turbines across Differing Wind Regimes^{ †}

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## Abstract

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## 1. Introduction

#### 1.1. A Temporally- and Spatially-Varying Energy Resource

#### 1.2. Role of Turbine Selection in Wind Farm Design

- The installed capacity of the wind farm,
- The land configuration and the placement of turbines in the wind farm (i.e., macro- and micro-siting), and
- The types of wind turbines to be installed.

- Actual energy production capacity of a turbine (when operating as a group) based on the local wind resource, and
- Leveled cost of the wind farm attributable to the turbines.

#### 1.3. Geographical Variation of Wind Patterns

#### 1.4. Exploring “Turbine-Wind Regime” Compatibilities

**Step 1**The geographical variation/distribution of wind regimes (in terms of AWS) in the target market is characterized; the U.S. onshore market is used as the case study.**Step 2**The types of commercial turbines that provide the minimum COE values are determined for different wind regimes, where the minimum COE value is given by optimized arrangement of a group of such turbines.**Step 3**The likely demand/market-suitability of the currently available (commercial) turbine feature combinations (namely, rated power, rotor diameter and hub height) is determined for the entire target market, based on the expected installation rate, geographical distribution of wind regimes (Step 1) and estimated economic potential of the best-suited turbines for different wind regimes (Step 2).**Step 4**The tradeoffs between the cost and capacity factor offered by the best performing turbines (for different wind regimes) are also determined to explore how these tradeoffs are related to the turbine-feature combinations.

## 2. Determining Optimal Wind Turbines (under Group Operation) for Different Wind Regimes

#### 2.1. Characterizing Wind Regimes

#### 2.1.1. Extracting Wind Map Information

#### 2.1.2. Distribution of Wind Regimes in the Target Market

#### 2.2. Approach to Determine Optimal Turbine Choices

#### 2.3. Turbine Characterization Model

#### 2.4. Wind Turbine Cost Model

#### 2.5. Optimization of Farm Layout and Turbine Type Selection

## 3. Pool of Optimal Turbine Choices for Differing Wind Regimes

## 4. Market Suitability of Turbines

#### 4.1. Development of a Market Suitability Metric for Wind Turbines

- How often different feature combinations were selected during the $13\mathrm{n}$ wind farm optimizations, across the different wind regimes (from Section 3);
- What level of performance (in terms of COE) was offered by the best performing turbines (from each rated-power class); and
- The probability of occurrence of each of the n sample average wind speeds (for which wind farm optimization was performed) over the U.S. onshore market; determined in Section 2.1.

#### 4.2. Suitability of Wind Turbine Features for the U.S. Onshore Market

## 5. Performance Tradeoffs Offered by Current Commercial Turbines

#### 5.1. Turbine Best Tradeoffs for Different Wind Classes

- $C{F}_{A}>C{F}_{B}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}Cos{t}_{A}\le Cos{t}_{B}$, or
- $C{F}_{A}\ge C{F}_{B}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}Cos{t}_{A}<Cos{t}_{B}$.

#### 5.2. Comparing the Features of the Best Tradeoff Turbines to those of all Turbines Considered

## 6. Conclusion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Wind Map of the U.S.: annual average wind speed at 80 m, published by National Renewable Energy Laboratory (NREL) [21].

**Figure 3.**Capturing the long-term variability AWS over the contiguous United State of America; $\mu =5.6$ m/s and $\sigma =1.3$ m/s).

**Figure 4.**Rayleigh distributions capturing the wind speed variations over time for given average wind speeds (AWS).

**Figure 5.**Rated powers of turbines that provide the lowest values of the minimized cost of energy (COE) for different AWS.

**Figure 6.**The minimized COE given by the best performing turbines (of each rated-power class) for each sample AWS.

**Figure 7.**The capacity factor given by the best performing turbines (of each rated-power class) for each sample AWS.

**Figure 8.**The cost/hr per kW installed given by the best performing turbines (of each rated-power class) for each sample AWS.

**Figure 9.**Implementation of a multiplicative regression model to represent the minimum COE (for each class) as a function of AWS.

**Figure 10.**Variation of the minimized COE (given by the best performing turbines) with AWS: polynomial regression fits.

**Figure 11.**Features of the best performing turbines (of each rated-power class) for different AWS. (

**a**) Turbine rotor diameter; (

**b**) turbine hub height.

**Figure 12.**Performance-based expected market suitability (PEMS) of commercially available turbine feature combinations for the U.S. onshore wind market. (

**a**) Rated power and rotor diameter combinations; (

**b**) rated power and hub height combinations; (

**c**) rotor diameter and hub height combinations.

**Figure 13.**Best tradeoffs between wind farm capacity factor and average annual cost ($/kW installed) for different wind classes.

**Figure 14.**Tradeoffs offered by the best performing turbines of different rated powers for Case I: Class 1–2 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 15.**Tradeoffs offered by the best performing turbines of different rated powers for Case II: Class 2–3 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 16.**Tradeoffs offered by the best performing turbines of different rated powers for Case III: Class 3–4 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 17.**Tradeoffs offered by the best performing turbines of different rated powers for Case IV: Class 4–5 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 18.**Tradeoffs offered by the best performing turbines of different rated powers for Case V: Class 5–6 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 19.**Tradeoffs offered by the best performing turbines of different rated powers for Case VI: Class 6–7 winds. (

**a**) Best tradeoffs between the capacity factor and average annual cost ($/kW installed); (

**b**) rotor diameters and hub heights of the best tradeoff turbines.

**Figure 20.**Variation of the average annual cost (in $/kW installed) of wind farms with respect to the hub height and rated power of turbines, assuming a 70 m rotor diameter.

**Figure 21.**Rated powers and rotor diameters of the best tradeoff turbines (circles) and other available commercial turbines (triangles).

**Figure 22.**Rotor diameters and hub heights of the best tradeoff turbines (circles) and other available commercial turbines (triangles); grey lines enclose the $D/H$ ratios of the best tradeoff turbines, and black dashed line encloses $D/H$ ratios of all available turbines.

Property | Value |
---|---|

Nameplate capacity | 25.0 MW |

Radius of the circular farm | 964.0 m |

Average terrain roughness | 0.1 m (grassland) |

Density of air | 1.2 kg/m${}^{3}$ |

Rated-Power Class (MW) | Number of Available Choices | Number Installed in the Farm |
---|---|---|

0.60 | 3 | 42 |

0.80 | 7 | 31 |

0.85 | 13 | 29 |

0.90 | 3 | 28 |

1.25 | 6 | 20 |

1.50 | 16 | 17 |

1.60 | 5 | 16 |

1.80 | 10 | 14 |

2.00 | 36 | 13 |

2.30 | 14 | 11 |

2.60 | 3 | 10 |

2.75 | 4 | 9 |

3.00 | 11 | 8 |

**Table 3.**Details of the polynomial regression curves: representing the variation of minimized COE with AWS (for each turbine class).

Rated-Power Class (MW) | ${c}_{1}$ | ${c}_{2}$ | R${}^{2}$ value | RMS Error |
---|---|---|---|---|

0.60 | 1.190 | −2.222 | 0.9720 | 0.0027 |

0.80 | 0.363 | −1.746 | 0.9691 | 0.0015 |

0.85 | 0.447 | −1.845 | 0.9741 | 0.0015 |

0.90 | 0.725 | −2.028 | 0.9895 | 0.0012 |

1.25 | 0.526 | −1.897 | 0.9797 | 0.0015 |

1.50 | 0.299 | −1.684 | 0.9791 | 0.0011 |

1.60 | 0.414 | −1.789 | 0.9722 | 0.0016 |

1.80 | 0.474 | −1.796 | 0.9837 | 0.0013 |

2.00 | 0.239 | −1.563 | 0.9792 | 0.0010 |

2.30 | 0.293 | −1.676 | 0.9850 | 0.0009 |

2.60 | 0.369 | −1.716 | 0.9753 | 0.0014 |

2.75 | 0.430 | −1.769 | 0.9783 | 0.0015 |

3.00 | 0.184 | −1.433 | 0.9784 | 0.0009 |

© 2016 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**

Chowdhury, S.; Mehmani, A.; Zhang, J.; Messac, A.
Market Suitability and Performance Tradeoffs Offered by Commercial Wind Turbines across Differing Wind Regimes. *Energies* **2016**, *9*, 352.
https://doi.org/10.3390/en9050352

**AMA Style**

Chowdhury S, Mehmani A, Zhang J, Messac A.
Market Suitability and Performance Tradeoffs Offered by Commercial Wind Turbines across Differing Wind Regimes. *Energies*. 2016; 9(5):352.
https://doi.org/10.3390/en9050352

**Chicago/Turabian Style**

Chowdhury, Souma, Ali Mehmani, Jie Zhang, and Achille Messac.
2016. "Market Suitability and Performance Tradeoffs Offered by Commercial Wind Turbines across Differing Wind Regimes" *Energies* 9, no. 5: 352.
https://doi.org/10.3390/en9050352