^{1}

^{2}

Recently, there is a growing interest in seismic qualification of ridges, buildings and mechanical equipment worldwide due to increase of accidents caused by earthquake. Severe earthquake can bring serious problems in the wind turbines and eventually lead to an interruption to their electric power supply. To overcome and prevent these undesirable problems, structural design optimization of a small vertical axis wind turbine has performed, in this study, for seismic qualification and lightweight by using a Genetic Algorithm (GA) subject to some design constraints such as the maximum stress limit, maximum deformation limit, and seismic acceleration gain limit. Also, the structural design optimizations were conducted for the four different initial design variable sets to confirm robustness of the optimization algorithm used. As a result, all the optimization results for the 4 different initial designs showed good agreement with each other properly. Thus the structural design optimization of a small vertical-axis wind turbine could be successfully accomplished.

Since the adoption of the UNFCC (United Nations Framework for Convention on Climate Change) in 1992, requiring each country to reduce green-house gases, extensive R & D efforts for new renewable energy have been exerted across the globe [

^{3}, yield strength = 55 MPa, and allowable stress = 38 MPa). The material for the pole and gearbox is steel (young’s modulus = 200 GPa, Poisson’s ratio = 0.3, density = 7850 kg/m^{3}, yield strength = 250 MPa, and allowable stress = 175 MPa).

The FE model in

Here,

1) Seismic response spectrum analysis

The seismic response spectrum analysis was performed as per the RRS of SSE 5% (Required Response Spectrum of Safe Shutdown Earthquake with 5% damping) prescribed in KBC 2009 [

ground acceleration is

The seismic spectrum response of a wind turbine structure represented in the Equation (1) is obtained with the spectrum-mode analysis [

seismic responses per single mode with high participation factors are determined, and then combined using the SRSS (Square Root of the Sum of the Squares) method to find the total response. The number of modes considered in the seismic response analysis is determined in the order of participation factors with the total modal mass accounting for more than 90% of the total mass of the structure. The ANSYS [

2) Static analysis to dead weight and wind load

The static analysis of the FE model in

3) Total stress and total deformation

The maximum stress and the maximum deformation determined by the foregoing seismic response analysis and static structural analysis were combined using the SRSS(Square Root of the Sum of the Squares) to yield the total stress (

For seismic qualification of the wind turbine, total stresses of the wind turbine components are compared with their allowable stresses.

The design optimization problem of the small wind turbine structure is to determine the best design variables that meet the seismic qualification while minimizing the weight of the wind turbine structure. As in

The design optimization problem of the wind turbine meeting the seismic qualification and minimizing the total weight of the structure was formulated as follows.

Find

To minimize

Design variables | Search space (mm) |
---|---|

1.5, 1.6, 1.7, | |

1 ,2, 3, |

Subject to

where,

Here,

The GA (Genetic Algorithm) based optimization search program [

Fitness function:

Penalty function:

where,

is amount of violation with their weighting factors of

To test the robustness of the design optimization based on the genetic algorithm, each of 4 different initial designs underwent the design optimization, and then the results were comparatively analyzed. The 4 initial designs were as follows.

Number of generation | Population size | Crossover rate | Mutation rate | Selection strategy |
---|---|---|---|---|

200 | 50 | 0.8 | 0.03 | Roulette wheel |

No. of initial design | Objectives | Design variables (mm) | ||||
---|---|---|---|---|---|---|

Weight [kg] | Acc. Response Gain | |||||

1 ( | 470 | 1.720 | 4.8 | 6 | 6 | 9 |

2 ( | 460 | 1.721 | 4.8 | 6 | 6 | 7 |

3 ( | 470 | 1.71 | 5 | 6 | 6 | 8 |

4 ( | 470 | 1.71 | 5 | 6 | 6 | 8 |

Max. deviation (%) | 1.6 | 0.3 | 2.0 | 0 | 0 | 12.5 |

For the seismic qualification and lightweight of a small vertical-axis wind turbine structure, in this study, the GA-based structural design optimization was performed. First, the wind turbine structure was FE modelled. Then, the seismic load, static load and wind load specified in the seismic design criteria of KBC 2009 and ASCE 7 - 10 were applied to the seismic qualification analysis of the wind turbine. Next, the design optimization was performed to minimize the objective functions, i.e. the wind turbine’s structural weight and acceleration response gain, using the genetic algorithm. As the design constraints, the allowable total stress, allowable total deformation and allowable acceleration response gain values were selected. The design variables were the thickness of the wind turbine blades and that of the hollow pole. To verify the robustness of the optimum search algorithm, each of the 4 different initial designs underwent the design optimization. It was found the maximum deviations of the object functions and design variables fell within 2% and 12.5%, respectively, which supported the robustness of the proposed genetic algorithm and search. The present findings will be conducive to the effective seismic design of the vertical axis wind turbine by decreasing the time and cost of design and production.

“This research is financially supported by Changwon National University in 2016- 2017”.

Choi, Y.-H. and Kang, M.-G. (2016) Structural Design Optimization of a Vertical Axis Wind Turbine for Seismic Qualification and Lightweight. World Journal of Engineering and Techno- logy, 4, 158-167. http://dx.doi.org/10.4236/wjet.2016.43D019