TOPFARM: Multi-fidelity Optimization of Offshore Wind Farm

Pierre-Elouan Réthoré, Peter Fuglsang,

Gunner C. Larsen, Thomas Buhl,

Torben J. Larsen and Helge A. Madsen

Wind Energy Division

Risø DTU - National Laboratory for Sustainable Energy

Technical University of Denmark

ISOPE – 19-24 June 2011

Outline

• Introduction – Vision and Philosophy• The TOPFARM Modules• The Wake “engine”• The Load and Production “Engine”• Cost Functions ... and Objective Function• Results

o Generic Offshore Wind Farmo Middelgrunden Offshore Wind Farm

• Conclusion• Outlook

Conclusions

• Vision: A “complete” wind farm topology optimization taking into account • Loading- and production aspects in a realistic and

coherent framework• Financial costs (foundation, grid infrastructure, ...)

... and subjected to various constraints (area, spacing,...)

• Philosophy: The optimal wind farm layout reflects the optimal economical performance as seen over the lifetime of the wind farm

Introduction – Vision and Philosophy

ConclusionsThe TOPFARM Modules

Conclusions

• Only variable costs (i.e. costs depending on the wind farm topology) are included in the objective function (OF)

• OF formulated as a financial balance expressing the difference between the wind farm income (power production (WP)) and the wind farm expenses (i.e. O&M expenses (CM), cost of turbine fatigue load degradation (CD), and financial expenses (C) – in this case including grid costs (CG) and foundation costs (CF))

Cost Functions … and Objective Function (1)

LXN

L

icn N

rrCWPFB

11

LXN

L

ic

N

rrCWPFB

11

Gunner Larsens cost model

CGCFC

Foundation cost

Electrical infrastructure cost

Degradation cost

• Maximize Finance balance• Maximize power production• Minimize cost

• Minimize foundation cost

• Minimize cable cost

• Minimize maintenance

• Minimize degradation

Maintenance cost

Cost Functions … and Objective Function (2)

,CMCDWPWPn

Electrical Production Sales

Simple wake model

From: G. C. Larsen, ”A simple stationary semi-analytical wake model. Risø-R-1713

Fast and Simple Wake Model

Conclusions

• The dynamic wake meandering (DWM) model (“poor mans LES”) is an efficient model providing a realistic description of wake affected flow fields within wind farms

• The core of the DWM model is a split in scales in the wake flow field, with large turbulent scales being responsible for stochastic wake meandering (passive tracer analogy), and small scales being responsible for wake attenuation and expansion in the meandering frame of reference as caused by turbulent mixing (… LES sub-scale analogy)

The Wake ”Engine” (1)

Conclusions

DWM main ingredients (2):

• Wake down-stream transportation (meandering) by passive tracer analogy (... LES large-scale analogy)

• A sequence of “deficit-releases” is considered ... and described in space and time

The Wake ”Engine” (2)

Conclusions

• Does it work? ... a full-scale verification (based on LiDAR measurements)

The wake ”engine” (4)

Conclusions

• Dynamic wake meandering (DWM) model (“poor mans LES”) – module1 – combined with aeroelastic simulations of the individual turbines – modules 2, 3

The load and production ”engine” (1)

Conclusions

• Does it work? ... a full-scale verification (based on WT7)

The load and production ”engine” (2)

• Damages costs (CD) are accumulated damage of an element ’s’ (Ds) X the price of the element (Ps).

• Ds is a linear function of the fatigue loads.

• Maintenance Costs are based on the probability of occurrence of a failure multiplied by the replacement cost.

Damages Costs (CD) & Maintenance Costs (CM)

,TN S

SSDPCD

,TN S

SCMCM

,,;,;1

,,1,1,

R

jjSjSSSRSRSSSRS DFPDFPNCM

rr

,Sd

SaS L

LD

• Different models investigated.

• Discontinuous model chosen (green):• 20 % of turbine price• For each meter above 8 meters

an additional cost of 2%• Above 20 meters very

expensive (20% pr m)

• Simple and fast

• Could be refined easily

Foundation Costs (CF)

• Simple model for electrical grid costs:• Finding the shortest

connection between all the turbines.

• Fixed cost per meter: • C=675 €/m

Electrical Grid Costs (CG)

• Genetic Algorithm (SGA)• Structured grid • Slow (Many iterations necessary)• Global optimum

• Gradient Based Search (SLP)• Unstructured grid (good for refinements)• Faster (Few iterations for converging)• Local minimum

• SGA+SLP:• Good combination for finding a refined

global optimum.

Optimization Algorithms

Example of Structured grid

LXN

L

icsf N

rrCpWPFB

111

Multifidelity Approach

Fidelity Level 1st 2nd 3rd

Electricity salesStationary wake +

Power curveHAWC2-DWM

DatabaseHAWC2-DWM

Simulations

Fatigue costs NoHAWC2-DWM

DatabaseHAWC2-DWM

Simulations

Foundation costs Yes Yes Yes

Electrical Grid costs Yes Yes Yes

Optimization algorithm SGA SLP or SGA+SLP SLP

Domain discretization Coarse Fine Fine

Wind speed and direction bin size Coarse Fine Fine

Results – Generic Offshore Wind Farm (1)

0.002 0.004

0.006

30

210

60

240

90270

120

300

150

330

180

0Wind rose

Gray color: Water depth [m]Yellow line: Electrical grid

Wind direction probabilitydensity distribution

• 6 5MW offshore wind turbines.• Water depth between 4 and 20 m

Results – Generic Offshore Wind Farm (2)

Result of a gradient based optimization (SLP)

Results – Generic Offshore Wind Farm (3)

Result of a genetic algorithm + gradient based optimization (Simplex)

Results - Middelgrunden (1)

Photo: Andreas Johansen

Results - Middelgrunden (2)

Allowed wind turbine region

Middelgrunden layout

Results - Middelgrunden (3)

• Ambient wind climate:

Results - Middelgrunden (4)

Optimum wind farm layout (left) and financial balance cost distribution relative to baseline design (right).

Iterations: 1000 SGA + 20 SLP

Results - Middelgrunden (5)

Before

After

Conclusions

• The baseline layout was largely based on visual considerations

• The optimized solution is fundamentally different from the baseline layout ... the resulting layout makes use of the entire feasible domain, and the turbines are not placed in a regular pattern

• The foundation costs have not been increased, because the turbines have been placed at shallow water

• The major changes involve energy production and electrical grid costs ... both were increased

• A total improvement of the financial balance of 2.1 M€ was achieved compared to the baseline layout

Results - Middelgrunden (4)

Conclusions

• A new optimization platform has been developed that allow for wind farm topology optimization in the sense that the optimal economical performance, as seen over the lifetime of the wind farm, is achieved

• This is done by:o Taking into account both loading (i.e. degradation),

operational costs (i.e. O&M) and production of the individual turbines in the wind farm in a realistic and coherent framework .... and by

o Including financial costs (foundation, grid infrastructure, etc.) in the optimization problem

• The performance of the platform has been demonstrated for offshore and on-shore example sites

Conclusion(s)

Conclusions

• (Possible) future model extensions:o Inclusion of atmospheric stability effects (… important for

production; cf. L. Jensen & R. Barthelmie)o Full DWM based optimization (presently only the closest

upstream turbine is considered load generating) ... o Better foundation cost modelo Parallization of the code … improved computational speedo Aeroelastic computations in the frequency domain …

improved computational speedo Cheapest rather than shortest cabling between turbineso Inclusion of extreme load aspects o Eddy viscosity model consistent with the DWM split in

scales … improved description of the wake deficit

Outlook