# 8. Economic optimization

The Layout optimization will produce the energy_curve.csv file, denoted in the GUIas E(n), for the project size  n=1,…,N, and enable Economic Optimization.

For each layout with n turbines , there is a correspondin energy yield E(n).  Parkoptimizer can optimize a range of project sizes, from n=1,…,N turbines.  The energy output thus forms the energy curve E(n) as displayed in the graph to the right when pressing the Energy Yield E(n) button (see (

The Net Present Value formula is stated in the right hand side of the GUI, and all variables are defined to the left. Position the mouse over a variable and its definition will be shown. The variables that are functions of time t or number of turbines n, are definable in an editor appearing when the corresponding button is pressed.

The example below shows that for the given economic variables, we maximize the Net Present Value of the project at about n=40 turbines. This corresponds to layout file layout040.txt/ows stored in Results_Directory\OPT_OUT ( or Results_Directory\OPT_OUT\wake_effect_adjusted ).

Monetary units

By default, the monetary units are EUR and MEUR (Millino Euro), but the monetary unit can be set to any unit, as long as consistency is provided . Pay attention to the input units, whether it is EUR/MWh, MEUR/MW etc.

## 7.1 Optimization algorithms

Three alternatives for optimization can be selected, see (1) on the figure:  Basic Optimizer, WFD cloud optimiziation and  WFD local optimiziation

Basic optimization algorithm is a heuristic algorithm based on simulated annealing, and provides near-optimal solutions.  Methods such as simulated annealing, genetic algorithms and similar trial-and error algorithms can find good results, but are slow compared to more formal optimziation techniques, and does not provide information about the quality of the solution.

The basic optimization algorithm is default and does not require extra licenses for use.

WFD cloud optimization *  is a highly specialized optimization routine based on formal operations research methods, and solved by state-of-the-art optimization solvers.  The WFD optimziation algorithm can guarantee global optimum for layout optimization problem, subject to minimum distance, elliptic distance and wake induced turbulence constraints.

To our knowledge this is the only optimizer available that guarantees global optimum with the above mentioned distance constraints.  Wake losses are however not included in the optimization, but we argue that the distances required for effective turbulence constraints dominate the importance of wake losses, see article xx

WFD cloud optimization is a cloud service, and can be called from within ParkOptimizer.  The cloud optimziation upload the problem to the WFD server (hosted on google compute engine), that runs the optimization algorithm with state-of-the-art solvers and return the results to parkoptimizer.

WFD cloud optimization can be purchased on a per use basis, or with a periodic license.  Contact klaus@windfarmdesigns.com for more information

* Requires internet access

WFD local optimization is the same optimization algorithm as WFD cloud optimization but deployed as an executable running on the client’s local server.  This alternative is intended for larger organisations for in-house use, and requires additional licenses.

Terrain inclination is not a part of the IEC standard, but is useful for practical purposes.  Terrain inclination are areas unsuitable for turbine placements because of steep slopes and/or steep road access .  These constraints are not absolute, and can be remediated by proper civil works at some increased costs.  Moreover, steep terrain causes flow inclinations as well (see next section), and these constraints often overlap.

At an early stage of the project development, it is useful to get an indicator of the problem with terrain fro screening of sites, and for initial layouts and derived energy yield estimates.

Terrain inclination is derived from the WindSim input files, \dtm\view_inclination.scl

## 7.2 Optimization settings

Number of turbines

A special feature of ParkOptimizer compared to other wind farm tools, is that you can optimize for a range of layouts, n=1..N.  If the layout size is not fixed, layout size can have as significant impact on the profitability of the project, and on the project risk, as we will explain in the economy module.  Select the Number of turbines by entering Min and Max values, see (2) in the above figure.

Distance constraints

You can specify either Minimum distance (see 3 in figure) or Elliptic distance with parameters a,b and deg, where a is the diameter in [m] along the major axis, is the diameter in [m] along the minor axis and deg is the orientation of the ellipse major axis measured in [deg].

The elliptic distance constraint (see 4 in the figure) has become a proxy for wake losses and wake induced turbulence, as these are more pronounced in the prevailing wind direction.  A typical choice of paramterers are a=5 RD, b=3 RD where RD = rotor diameter.  The orientation depends on the wind rose.

## 7.3 Effective turbulence

Effective turbulence can be specified by checking Use Effective Turbulence (see 5 in figure) and editing the Setup as follows:

• Effective turbulence is calculated based on the .tws mast file, also used in the IEC constraints module, see (1) on figure below.
• If a measurement mast is to be used for turbulence calculations, check (2) on the figure below
• Set the the Wöhler coefficient in (3) and check the terrain complexity index (4) if needed.  See also discussion in section 6.4 Turbulence

Turbulence GUI

Characteristic turbulence should be checked for a range of wind speed intervals, ranging from $0.2V_{ref} \dots 0.4V_{ref}$ where the charactistic turbulence $\sigma_c$ should not exceed the 90th percdentile of the standard deviation of the turbulence, $\sigma_{\sigma}$, ie $\sigma_c \le \sigma_{\sigma}$

At this moment, the velocity range to check for the effective turbulence is considered in the IEC exclusion area map (i.e. the ambient effective turbulence) (point 6 on figure)  whereas for the wake induced effective turbulence, the constraint is only checked for one wind speed interval (see (7) on figure).

Method of turbulence extrapolation

The default method for turbulence extrapolation , is by scaling the map with the mast, where the wind map is adjusted by the ratio of the measured wind speed and the simulated wind speed at the mast point and sector, extrapolated  to each map point, see

An alternative method, more precise but also more time consuming, is to also scale mast according to various wind speed bins (see (8) on figure).

## 7.4 Wake losses

Wake losses

Wake loss calculations are preferably applied after a layout satisfying the minimum distances are created.  For wake loss calculations, N.O Jensens model is applied:

$dV(s) = dV(s) = v_0 \cdot (1-\sqrt{1-C_t(v_0)}) \cdot (\frac{D}{D+2kx})^2$

where is the down stream distance of the rotor with diameter R, and \alpha  is the wake decay coefficient, also denoted as k (see (6) in figure 7.1 layout optimization module)

The parameters for the wake model, rotor diamter D, wake decay coeffefficient k=0.075 (default) and the number of iterations are defined by the user (see (6) in figure 7.1 layout optimization module), and indicates how many attempts the simulated annealing algorithm will check to find better turbine placements.

Start optimizer

We recommend to not use wake loss calculations for the optimization, the wake loss adjustments can be run later to adjust a layout where the distance constraints are satisfied.

To start the optimizer, press Start Optimizer button (see (7) on figure 7.1 )

## 7.5 Improve layouts

Improve layouts

Once a layout satisfying the distance constraints are establishe, we recommend to run optimized layouts using with wake effects, (see (8) on figure 7.1 ), where the number in the dropdown menu defines the number of  times the simulated annealing process is run for wake effect adjustments.  For each run , there will be a new folder with layout files.

Performing wake effect adjustment will modify the layouts and write the files to Results_Directory\OPT_OUT\wake_effect_adjusted. The following method is employed for each layout :

Let PC and Ct be the turbine specific power-curve and thrust-coefficient, as defined in the Turbine File ( set in the Energy Map module) and let A(s), k(s), f(s) be the Weibull parameters for sector s of points in the Wind Resource file.
The energy production at each point , incorporating wake effects, is calculated as follows

• A dV – change in wind speed due to wake – matrix is constructed for each sector accounting for each turbine position p. Let $v_0 = A(s,p)$ at a turbine position p ( we are using the A parameter as an approximation to the average wind speed ).
Then dV for sector s , dV(s), due to turbine at position p is

$dV(s) = v_0 \cdot (1-\sqrt{1-C_t(v_0)}) \cdot (\frac{D}{D+2kx})^2$,

where $\alpha=0.075$ and D = Rotor Diameter,  and where the calculation is done for values of x within a cone downwind of the turbine position p inside +/- 15 deg (if the data-set has 12 sectors; correspondingly less for 16 and 24 sectors) of the sector s direction and radius $10RD$. If a point is affected by more than 1 wake, the $dV(s)$ values are added.

• The energy at each point , incorporating wake effects, is the sum over the sectors s of $\int_v( wbl(v, A(s) - dV(s) , k(s)))\cdot PC(v)\cdot f(s) \cdot dv$, over $v=v_{in},\dots,v_{out}$where wbl is the Weibull probability distribution function

This wake effect adjusted energy map is then used to move turbines so that the total energy production will be higher. The optimization method is based on Simulated Annealing.

The figure below illustrates the wake adjustment. Press the Figure button  (see (11) in above figure) in the gui to produce the figures ( note that the circles are markers, and do not indicate distance ). The layout size can  be chosend from the nearby dropdown menu (see 10 on the above figure)

Open layouts

All optimization results are stored in the folder OPT_OUT, containing

Layout0001.txt, ….

Layout0002.txt,…

Layout00NN.txt

in the form of text files with turbine coordinates, as well as an energy_curve.txt file containing the corresponding energy yield for each layout size.