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Research Papers: Design Automation

Sensitivity of Wind Farm Output to Wind Conditions, Land Configuration, and Installed Capacity, Under Different Wake Models

[+] Author and Article Information
Weiyang Tong

Multidisciplinary Design
and Optimization Laboratory,
Department of Mechanical
and Aerospace Engineering,
Syracuse University,
Syracuse, NY 13244
e-mail: wtong@syr.edu

Souma Chowdhury

Mem. ASME
Department of Aerospace Engineering,
Center for Advanced Vehicular Systems,
Mississippi State University,
Starkville, MS 39759
e-mail: chowdhury@bagley.msstate.edu

Ali Mehmani

Multidisciplinary Design
and Optimization Laboratory,
Department of Mechanical
and Aerospace Engineering,
Syracuse University,
Syracuse, NY 13244
e-mail: amehmani@syr.edu

Achille Messac

Professor
Fellow ASME
Department of Aerospace Engineering,
Mississippi State University,
Mississippi State, MS 39762
e-mail: messac@ae.msstate.edu

Jie Zhang

Mem. ASME
Transmission and Grid Integration Group,
National Renewable Energy Laboratory,
Golden, CO 80401
e-mail: jie.zhang@nrel.gov

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 11, 2014; final manuscript received February 12, 2015; published online April 15, 2015. Assoc. Editor: Harrison M. Kim.

J. Mech. Des 137(6), 061403 (Jun 01, 2015) (11 pages) Paper No: MD-14-1339; doi: 10.1115/1.4029892 History: Received June 11, 2014; Revised February 12, 2015; Online April 15, 2015

In conventional wind farm design and optimization, analytical wake models are generally used to estimate the wake-induced power losses. Different wake models often yield significantly dissimilar estimates of wake velocity deficit and wake width. In this context, the wake behavior, as well as the subsequent wind farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these key factors, particularly under the application of different wake models, is paramount to reliable quantification of wind farm power generation. Such an understanding is however not readily evident in the current state of the art in wind farm design. To fill this important gap, this paper develops a comprehensive sensitivity analysis (SA) of wind farm performance with respect to the key natural and design factors. Specifically, the sensitivities of the estimated wind farm power generation and maximum farm output potential are investigated with respect to the following key factors: (i) incoming wind speed, (ii) ambient turbulence, (iii) land area per MW installed, (iv) land aspect ratio, and (v) nameplate capacity. The extended Fourier amplitude sensitivity test (e-FAST), which helpfully provides a measure of both first-order and total-order sensitivity indices, is used for this purpose. The impact of using four different analytical wake models (i.e., Jensen, Frandsen, Larsen, and Ishihara models) on the wind farm SA is also explored. By applying this new SA framework, it was observed that, when the incoming wind speed is below the turbine rated speed, the impact of incoming wind speed on the wind farm power generation is dominant, irrespective of the choice of wake models. Interestingly, for array-like wind farms, the relative importance of each input parameter was found to vary significantly with the choice of wake models, i.e., appreciable differences in the sensitivity indices (of up to 70%) were observed across the different wake models. In contrast, for optimized wind farm layouts, the choice of wake models was observed to have marginal impact on the sensitivity indices.

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Figures

Grahic Jump Location
Fig. 1

General inputs and outputs of an analytical wake model

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Fig. 2

An arraylike farm layout with 16 GE 1.5 MW xle turbines

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Fig. 3

Power curve of GE 1.5 MW xle turbine [33]

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Fig. 4

Single wake test. (a) Wake diameter behind a GE 1.5 MW xle turbine and (b) wake speed behind a GE 1.5 MW xle turbine.

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Fig. 5

Variation of the CF with the LAT. Incoming wind speed of (a) 4 m · s−1 (slightly above the turbine cut-in speed), (b) 8 m · s−1 (in between the turbine cut-in and rated speeds), (c) 11.5 m · s−1 (at the turbine rated speed), and (d) 12 m · s−1 (slightly above the turbine rated speed).

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Fig. 6

Variation of the CF with the incoming wind speed. LAT of (a) 15 ha, (b) 20 ha, and (c) 25 ha.

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Fig. 7

SA of the power output of a wind farm with a 4 × 4 array layout (case 1). (a) Jensen model, (b) Frandsen model, (c) Larsen model, and (d) Ishihara model. U: Incoming wind speed; Ia: ambient turbulence; AMW: land area per MW installed; ar: land aspect ratio.

Grahic Jump Location
Fig. 8

SA of the power output of a wind farm with a 4 × 4 array layout (case 2). (a) Jensen model, (b) Frandsen model, (c) Larsen model, and (d) Ishihara model. U: Incoming wind speed; Ia: ambient turbulence; AMW: land area per MW installed; ar: land aspect ratio.

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Fig. 9

SA of the power output of a wind farm with a 4 × 4 array layout (case 3). (a) Jensen model, (b) Frandsen model, (c) Larsen model, and (d) Ishihara model. U: Incoming wind speed; Ia: ambient turbulence; AMW: land area per MW installed; ar: land aspect ratio.

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Fig. 10

SA on the maximized wind farm CF with optimized layouts (case 1). (a) Jensen model, (b) Frandsen model, (c) Larsen model, and (d) Ishihara model. U: Incoming wind speed; Ia: ambient turbulence; AMW: land area per MW installed; ar: land aspect ratio; PNC: nameplate capacity.

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Fig. 11

SA on the maximized wind farm CF with optimized layouts (case 2). (a) Jensen model, (b) Frandsen model, (c) Larsen model, and (d) Ishihara model. U: Incoming wind speed; Ia: ambient turbulence; AMW: land area per MW installed; ar: land aspect ratio; PNC: nameplate capacity.

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Fig. 12

Illustration of optimized layouts using different wake models. (a) Jensen model (CF = 54.34%), (b) Frandsen model (CF = 54.00%), (c) Larsen model (CF = 54.15%), and (d) Ishihara model (CF = 54.69%).

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