Obstacle-Avoiding Wind Turbine Placement for Power-Loss and

Wake-Effect Optimization

Yu-Wei WuYi-Yu Shi

Sudip RoyTsung-Yi Ho3

ASP-DAC’15

Outline• Introduction• Preliminaries• Proposed Method• Experimental result• Conclusions

Introduction• The main difficulty in designing a wind

farm is the wind turbine placement problem that would directly influence the produced power.

• The most considered factor in the wind turbine placement problem is to reduce the wake effect.

Introduction• When the wind flows through the wind

turbines, the wake effect is caused due to the fact that each wind turbine produces abnormal turbulence behind it and effects downstream indirectly.

• Hence, minimizing the wake effect can lead to maximizing the power generation.

Introduction• In the wind turbine placement problem the

blocks are in irregular shape and they can overlap without violation of the center of the wind turbine into the obstacle.

• Along with the wake effect, we additionally consider wirelength and obstacle-avoiding at the same time.

Preliminaries• Let X = {x1, . . . , xn} and Y = {y1, . . . , yn} be the

sets of x and y-coordinates of n wind turbines with m obstacles in the plane.

• We use the penalty function to incorporate the constraint and wirelength cost as

Wirelength Model• As the half-perimeter wirelength(HPWL) is not

differentiable, we use the log-sum-exp wirelength model [10] in our wirelength computation given by Eq.(2).

Bell-shaped Function• In order to smooth the non-differentiable and non-

smoothing density, we use the bell-shaped function [11] as follows

Constraints• Constraint 1: Wind turbines may be damaged

by turbulence when they are too close to each other.

• Constraint 2: An obstacle means that the location is not suitable to set up the wind turbine.

Power Output• We use the Park wake model [4] to evaluate the

wake effects.

• The expected value of power generation (η) of the whole wind farm is given by

Proposed Method• Region Separation Based on Wake Effect• Obstacle-Avoidance Method• Gradually Approximation Method• Wind Turbine Placement

Region Separation Based on Wake Effect

• We consider the wake effect block as an irregular shape in the plane. We adjust the size of wake effect block (wv) for computing the wake effect density in a bin as follows

• 12

Obstacle-Avoidance Method• After obtaining the next location of a wind turbine

by separateRegion(),the center of the wind turbine may move on to the obstacle Ob.

• In the next round, the wind turbine may escape from the obstacle Ob and again it hides.

Gradually Approximation Method• we diffuse the wind turbines through gradually

increasing the wake effect distances using a procedure increasingWakeEffect(). Fig.7 shows how the wake effect distances gradually increase.

Wind Turbine Placement

Experimental result• We implement the proposed method using C++

on a 64-bit Linux machine with 3.4-GHz processor and 8GB RAM.

Conclusion• In this paper, we have proposed an algorithm to

solve the wind turbine placement problem with the help of the analytical method and based on the gradually approximation method.

• In the best of our knowledge, for the first time, we have considered wake effect, wirelength and obstacle-avoiding all together at the same time.