8a  OPTIMIZE 
8a.1  Introduction .......................................................................................................................................... 2 
8a.1.1  Offshore Vs Onshore optimization ......................................................................................... 2 
8a.1.2  The GUI tree-structure and its levels: Site>WTG>Size>Run ................................................ 2 
8a.2  Which decision to optimize? .............................................................................................................. 7 
8a.2.1  Design of layout (given park size) ......................................................................................... 8 
8a.2.2  Number of WTGs (park size) ................................................................................................. 9 
8a.2.3  Choice of turbine model ....................................................................................................... 10 
8a.2.4  Fulfillment of constraints (spacing, noise, lifetime, wake) ................................................... 11 
8a.3  Optimization algorithm ...................................................................................................................... 12 
8a.3.1  Start model .......................................................................................................................... 13 
8a.3.2  Step model ........................................................................................................................... 14 
8a.3.3  Stop criteria .......................................................................................................................... 14 
8a.3.4  Objective & Constraints ....................................................................................................... 15 
8a.4  Objectives ........................................................................................................................................... 16 
8a.4.1  AEP ...................................................................................................................................... 16 
8a.4.2  Costs .................................................................................................................................... 16 
8a.4.3  LCOE ................................................................................................................................... 18 
8a.4.4  NPV...................................................................................................................................... 18 
8a.5  Constraints ......................................................................................................................................... 20 
8a.5.1  Area & distance (sub-areas) ................................................................................................ 20 
8a.5.2  Wake loss ............................................................................................................................ 20 
8a.5.3  Noise .................................................................................................................................... 20 
8a.5.4  Component Lifetime (loads) ................................................................................................ 21 
8a.6  Practical recommendations .............................................................................................................. 22 
8a.6.1  WTG Area import ................................................................................................................. 22 
8a.6.2  Example projects ................................................................................................................. 22 
8a.7  References .......................................................................................................................................... 24 
 
   

Introduction 2

8a.1 Introduction

The Classical Optimizer in windPRO was released around year 2000. It has performed well for the tasks it was

designed to solve in the youth of the wind energy business. Since then, the development of the wind industry

has been fast, and many new requirements and challenges have become relevant. The size of wind farms and

the complexity of wind farm areas has increased dramatically. But also, the basis on which decisions are made

has matured, so that financial parameters such as costs of developing the farm and even the expectation for

future electricity prices should be included already in the windfarm design phase. In addition, new constraining

factors emerged that must be considered, such as wake effects from new wind turbines on existing wind turbines.

These developments have led to the need for a new windPRO Optimizer has been released in 2022 in windPRO

3.6. This was just the start of journey towards optimal design and operation of wind farms, and new features

have been integrated since into the new windPRO 4.0. Now, in addition to layout optimization, a long-awaited

noise curtailment optimization is offered, which is explained in detail in the Noise Curtailment Optimize manual.

The journey has not ended here; a wider range of cases will be supported, and more features will be included in

windPRO versions to come. If you experience limitations, have wishes or ideas please do not hesitate to reach

out and contact us – we are more than happy to listen to your input!

8a.1.1 Offshore Vs Onshore optimization

The New Optimizer in windPRO covers both onshore and offshore optimization. For offshore layouts the

geometry is not fixed, for this functionality the user is referred to the Classical windPRO optimizer. The key

differences between onshore and offshore optimizations lie in the setup of the wake decay constant for the

annual energy production (AEP) calculation and in the model for calculating the cost of building the wind farm (if

costs are included in the objective). Hence, for pure optimizations of AEP there is no difference in the way that

the Optimizer operates. However, the performance will of course be guided by the user-provided information

such as WTG area and resource, which typically have distinct characteristics offshore and will be reflected in

the resulting optimization solutions. A new feature that is particularly useful for offshore applications that comes

with the release of 4.0 is the integration of cost surfaces. This feature allows to better integrate costs that change

over space into the cost analysis. Further details of onshore and offshore cost models are given in section 8a.4.2.

8a.1.2 The GUI tree-structure and its levels: Site>WTG>Size>Run

A flexible graphical user interface (GUI) has been developed for the New Optimizer to accommodate several

different scenarios of use (see section 8a.2 for a description of the scenarios). This flexible GUI is represented

by a tree located on the left side of the Optimizer window. The tree will be gradually built-up by the user with the

required input information and with the different optimization scenarios run by the user. A lot of information needs

to be defined and setup prior to running the optimizations. This setup of pre-defined data and pre-calculated

information is a prerequisite for gaining sufficiently fast, yet accurate, optimization results.

Figure 1: The basic components and levels of the GUI tree: Site, WTG, Size and Run, with Run highlighted.

Building the tree, setting up and preparing the optimization, different information and decisions must be defined

and entered. When a level or item is selected and highlighted in the GUI tree (see Figure 1) the window on the

right shows the contents associated to this item, e.g. Site. Adding new levels to build the tree is done using the

three buttons below the tree. On the first occasion of adding a level the relevant button is highlighted in green.

Figure 2: Building the GUI tree for the optimization and adding levels. Next step is always highlighted in green.

The following sub-sections go through the setup that needs to be defined at each level of the GUI tree. While

setting up and running optimizations the main window of the Optimizer should be on the tab Setup & run.

Introduction 3

Figure 3: When setting up and running optimizations the tab of main window should be on ‘Setup & run’.

8a.1.2.1 Site

The Site level is the fundamental level of the optimization, but there can be multiple Sites in the tree to allow

studying the effect of different basic assumptions. In the Site, the following information and settings must be

defined:

Site Climate/Resources - here the pre-calculated wind resource across the site must be defined by selecting an

‘rsf’ or ‘siteres’ file. Ideally, the resource has a grid resolution of 0.5 times the turbine rotor diameter or less as

this leads to a good balance between resolution and performance.

Objective – this is the choice of what the user wants to optimize: AEP (annual energy production), LCOE (cost

of electricity) or NPV (profit of project). These are described in detail in section 8a.4. For each choice of objective

several associated decisions are required. For instance, Wake Decay constant in the PARK calculation (all

objectives), setting up a Cost Model (LCOE and NPV) or setting the expectation for the future average Electricity

Price.

Constraints - The particular requirements for the site must be defined and ALWAYS requires definition of a WTG

Area. This defines the limits of the site area or sub-areas where turbine placement is allowed, any requirements

for minimum and maximum turbine numbers or capacity in each sub-area. It also defines exclusion zones and

set-back buffers as well as minimal spacing requirements for turbines in each sub-area. In addition to this the

spacing or inter-turbine Distance defined in the WTG area may be activated or deactivated. Finally, constraints

on turbine component Lifetime, turbine noise at noise sensitive areas, and Wake constraints for new and existing

WTGs may be activated (see section 8a.5 for further details).

Connection points – Objectives which require cost calculation (LCOE and NPV) may include known connection

points for external grid and road connection. These points must be pre-defined as Control points and selected

here.

Existing WTGs – If there are known turbines in the area from other projects which will create wakes on this

project they must be defined as existing WTGs and selected here. Their wake effect on the new turbines will be

included and the additional wake that they might experience can be considered.

Noise sensitive areas – If noise constraint is activated one or more noise sensitive area (NSA) points must be

selected here.

Figure 4: Setting up the Site level of an optimization and building the GUI tree.

Introduction 4

8a.1.2.2 WTG

At the WTG level the required data must be defined for the objective and constraints selected on the Site level.

All new turbines in optimizations in this branch of the tree will be done using the selected turbine and data.

WTG & Mode - Any optimization requires the selection of a turbine model from windPRO’s WTG catalogue, a

Hub height, and the Power curve/Mode for that turbine model. This is the basis for the AEP and wake loss

calculations. For traditional power curve data the appropriate power curve is selected and for Power Matrix data

the operation mode is also selected.

Lifetime/Loads – If lifetime constraint is activated the turbine Design Standard and Design Class must be defined

as well as the Load Response Model for use in the calculation of loads and lifetime.

Noise Data – When noise constraint has been activated the noise data must be selected. For Power Matrix the

noise data are pre-defined via the selected mode.

Use individual WTG cost model - When multiple WTG types are defined for the same Site, it might be relevant

to define different cost models for each WTG type individually. In that case this option must be activated and the

cost model for the current WTG type defined here. This will override the cost model selected on the Site level.

Figure 5: Setting up the WTG level of an optimization.

8a.1.2.3 Size (and ‘Add Sizes & Runs’ button)

The Size level has no setting up on the window to the right. Instead, it is created in a single step together with at

least one Run at it its sub-level (child). This is done via the Add Sizes & Runs button (see green highlight in

Figure 5).

Once the Sizes and Runs have been created this window shows an overview of all the runs for this size. In this

regard a run is simply an optimization for the park size in question and subject to optimization settings.

The benefit from adding Sizes & Runs in a single step is mainly efficiency, so that more park sizes can be created

at once with identical optimization settings without further effort.

Define Park size(s) - Here the user can define the park sizes of interest. Note that ALL sizes from minimum

through to maximum will be created once the button Create & queue runs is pressed after which a separate

optimization will be run for each size. It is therefore recommended to limit the range of sizes such that it results

in a reasonable number of optimizations. The table above the size selection summarizes the requirements for

minimum and maximum turbine numbers in the WTG area. Limits on capacity are automatically converted to

Introduction 5

turbine numbers given the selected WTG. Alternatives, to defining a range of sizes are either to define a User

layout where the user must select the initial positions for the optimization or Fill max which will seek to fill the

maximum number of turbine units (see section 8a.3 for further details).

Run setup for each Size – This setup defines the optimization strategy for each created optimization run. Default

is Smart with the alternatives Random and Custom. The latter unlocks the lower section of the window

unleashing the full flexibility of the optimization solution (see section 8a.3 for details). The Realizations setting

available for Random simply defines how many times to repeat the experiment of starting an optimization run

from a random initial layout. Setting realizations to, for example, five will yield five different random runs for each

size.

When setup is done in the Setup & Run window the optimizations can either be put in the queue directly by

pressing Create & queue runs or be parked for now to be run later by pressing Create & park runs.

Figure 6: Setting up the Size and Run level in one go via the button ‘Add Sizes & Runs’.

Introduction 6

8a.1.2.4 Run

The deepest level of the GUI tree is the Run level. At this level each optimization run is presented and when

they are completed a resulting optimized layout can be created in the windPRO object list and map window by

pressing Realize Final Layout. Through the course of the optimization the positions of WTGs at the current step

of the optimization run are visible and updated in the Layout plot. Similarly, the Steps list will show the current

and history of the Objective. Alternatively, the Wake loss (available for all objective) or AEP, Wake loss or Cost

are plotted (only available for LCOE and NPV objectives. This information is also available in the Convergence

plot. At the top of the view is a detailed summary of the settings for the run, including a Status indication whether

it is running, done or failed.

Details of constraints and/or individual turbine production and wake loss information may be viewed via the

buttons Show AEP/Wake and Show Constraints to the lower left of the Optimizer window.

Figure 7: The Run level of the GUI tree. This documents the course the optimization run selected in the tree.

The current status of a run is indicated in the Status line in the Summary when the run is selected in the tree.

The status is also in the tree itself on the level of the run and via the icons shown to the left on that line. The

legend for these icons and a summary status of all current runs within the tree are shown just below the tree

(see Figure 7).

Note that shown cost values are not discounted only index corrected (if set) and summed over the lifetime.

Which decision to optimize? 7

8a.2 Which decision to optimize?

Many important decisions need to be taken when developing a wind farm. Several of these decisions can benefit

from an optimization approach but may not fit well into a traditional optimization setup. In some of the cases the

variables on which the decisions are based on (the objective) such as AEP, or financial metrics as cost-of-energy

(COE) may not be suitable or sufficiently sensitive to the decisions in question. One such example is the size of

a wind farm. The relation between the number of WTGs in the farm and the associated AEP, is simply an increase

with the number of WTGs. COE on the other hand typically decreases smoothly with the number of WTGs. This

makes AEP and COE unsuitable for determining the optimal size of a wind farm on their own [1]. To

accommodate these additional and important decisions in the optimization setup, but not directly in the actual

algorithmic optimization process, the decision of these variables is supported by the structure of the GUI. The

main use-scenarios are described in the following and includes the following key decisions in wind farm

development:

• Design of a layout

• Number of WTGs in the park

• Choice of turbine model

• Fulfillment of constraints

Section 8a.1.2 has described how to establish the tree with a Site, WTG and one or more optimization runs and

the settings and inputs needed at each level of the GUI tree. All these settings are done on the Setup & Run tab

(cf. Figure 8), which basically is the action mode of the Optimizer, where optimizations can be added and setup

and details can be viewed.

Figure 8: The Compare and Setup & Run tabs. Here Compare is selected.

To compare multiple finalized optimizations the Optimizer has a ‘comparison mode’ which is available via the

Compare tab (cf. Figure 8). In compare mode, the GUI allows for easy comparison across results for different

WTGs, sizes and runs mainly showing the results and some overall settings. Once in compare mode (i.e. on the

Compare tab) the GUI tree will behave slightly differently as it will start highlighting the runs which are being

compared in mustard color (cf. Figure 9). The highlight shows the level selected by the user below which runs

will be compared. When a site is selected results will be compared for WTGs defined for that site. For each WTG

the best run across all sizes will be chosen and highlighted in mustard color. When selecting a WTG all sizes

below that level will be compared, for each size the best run will be chosen if there is more than one run. Selecting

a size will simply compare all runs for that size.

At the current stage it is not possible to compare across sites, as they may have different objectives and

constraints which cannot easily be compared.

Figure 9: Appearance of the GUI-tree when in compare mode.

Which decision to optimize? 8

8a.2.1 Design of layout (given park size)

Designing a layout with a single fixed number of WTGs is the basic and simplest mode of use for the Optimizer.

Just one optimization needs to be set up and run once the data and settings on the Site and WTG levels have

been defined. The flexibility of the GUI tree helps to compare different strategies for the optimization, described

in further detail in section 8a.3. Such strategies could include the default, which is called Smart, a user defined

initial layout (via User Layout), or perhaps relying more on stochasticity by including random runs. In the last

case, several random runs can be started via Realizations.

Once a single run has been added for the park size in question more runs can be added by selecting the size in

the tree and pressing the button Add Runs, which in this case has replaced the Add Sizes & Runs button (shown

when the WTG level is selected). If, on the other hand, a particular run in the tree is selected, then the button

renames to Clone Run – this will allow to use the result of that run at starting point for another run. This can be

useful for continuing an optimization or doing an optimization with multiple stages. The three variants of the

‘Add…’ button are shown in Figure 10.

Figure 10: Different variants of the ’Add…’ button. The variant Add Sizes & Runs occurs when a WTG is selected

in the tree, Add Runs when a Size is selected and Clone Run when an existing finalized run is selected.

An example of a size with several runs is demonstrated in Figure 11 showing the view on Setup & Run tab.

Figure 12 shows the view on the Compare tab, which is more focused on comparing the objective for the final

layout across the runs.

Figure 11: Setup & Run tab for a park size (10 WTGs) with several runs. See Figure 12 for Compare tab.

Which decision to optimize? 9

Figure 12: Compare tab showing several runs for the same size (10 WTGs) also shown in Figure 11.

8a.2.2 Number of WTGs (park size)

The New Optimizer can be used to analyze parks with different sizes, but it does not optimize for the number of

turbines since the objectives are not well suited to optimize the park size: If the objective is to maximize the AEP,

it is generally best to place as many wind turbines as possible into the park. In such case the Fill max option can

be used. On the contrary, if the objective is to minimize the costs, it would be optimal to place none. In practice,

the problem is often to find the wind turbine positions that are optimal for the specified objective with a given

park size, and it is more useful to analyse different set-ups per park size and for different park sizes.

To analyze the park size, simply set the appropriate range of sizes from min to max in the Add Sizes & Runs

setup as shown in Figure 13. Then choose the preferred setup of the runs which will be created for each size

(see section 8a.1.2.3 for further details). The Optimizer uses parallelization so several runs will start and run

simultaneously to speed-up performance.

Figure 13: Setting a range of park sizes in the Add Sizes & Runs window. An optimization run (or more via

Realizations) will be created for each size.

Once completed, the results can be visualized and analyzed on the Compare tab and by selecting the relevant

WTG in the tree.

Which decision to optimize? 10

Figure 14: Example Compare view for a range of sizes. The optimizations are run using LCOE objective.

In some cases, the runs for the largest park sizes will fail before all turbines could be placed by the start model.

This can indicate the maximum number of turbines which is possible to place, but care must be taken as several

factors influence this outcome. One thing is making sure that the grid resolution is not too coarse, generally

around 0.5 RD ensures good performance. Another possibility is that the default start model (Smart) places

turbines according to the objective – but that the maximum is determined by a constraint, hence placement may

not be ideal regarding minimizing constraint exceedance. Section 8a.2.4 describes a procedure that improves

chances of finding a valid layout in such cases.

8a.2.3 Choice of turbine model

To analyze the choice of WTG model, simply add all the relevant WTG models to the Site. In such cases setting

the maximum allowed capacity of the grid in the WTG area is beneficial as this will automatically influence the

maximum number of turbines for each model, given its capacity. It may also be relevant to set individual cost

models for each WTG if detailed cost information is available. However, this is not required as the default cost

model will automatically account for the difference in rotor size and generator capacity of each WTG type.

Figure 15: Setting individual cost models for each WTG type.

The results across the WTGs may be compared on the Compare tab by selecting the relevant site in the tree. If

there are more sizes and runs for each WTG the best run (with regard to the selected objective) is chosen to

Which decision to optimize? 11

represent each WTG type. Figure 16 shows an example of comparing NPV optimizations across three turbine

types.

Figure 16: Compare tab showing results for three different WTG models for a site.

8a.2.4 Fulfillment of constraints (spacing, noise, lifetime, wake)

In some cases, the optimization is more driven by the constraints (noise or loads) than by the objective (AEP,

LCOE or NPV). This does not mean that the objective is irrelevant, but rather that the design space is very

difficult to navigate in for the Optimizer because large parts are invalid due to the constraints. In some cases,

this may lead to runs failing for particular sizes because the start model cannot generate a valid layout, i.e.

place all turbines without violating the constraints. If this happens it can be beneficial to add several runs with

the Random run setup for a failed size and with the setting Allow invalid start model activated. This will allow

the start model to place all the required turbines but disregard the constraints (except the WTG area). The step

model will then seek to minimize the constraint exceedance first, and if that succeeds then optimize the

objective function.

Figure 17: Setup of a run showing how Allow invalid start model is activated. This option is only supported for

Random start models.

Optimization algorithm 12

8a.3 Optimization algorithm

The wind farm optimization problem is a difficult problem mainly due to the occurrence of several local minima

and so-called non-linearity and interaction in the objective functions, chiefly arising from the turbine wake

interaction. If one turbine is moved the optimum position for all other turbines in the park may change or they

may exceed a constraint they did not before. These effects may be accentuated by too coarse a resource grid

and too coarse a directional resolution in the wake model or simply by multi-directional wind roses. When

constraints are included, these may also prevent otherwise beneficial layout changes and effectively split the

solution space into many smaller un-connected “islands” (in a high dimensional sense), which are extremely

difficult to navigate for an optimization algorithm. The supported objectives and constraints are described in

section 0.

The structure of the New Optimizer reflects the structure of the underlying solution approach, which is a classical

iterative search, but with many built-in smart features that improve its performance and efficiency. In this

framework, an optimization needs a Start model, an initial ‘first guess’ and then a Step model that subsequently

seeks to make iterative, incremental improvements to further improve and optimize the Start model. As the final

optimal model is not known a priori, one or more Stop criteria are needed to decide when to halt the search of

the Step model. This could be once a maximum time or a maximum number of fruitless attempts to take a new

step improvement have been tried.

The better the initial Start model the more focused the iterative Step model can perform its search. In fact, the

wind farm optimization problem is so complex that with many turbines it is very difficult for an iterative solution

to find a good optimum. Increasing the likelihood of ending up in an only modestly good local optimum. In this

sense the old saying “Well begun is half done” is extremely pertinent and the reason for the development of the

Smart Start models described in section 8a.3.1.

Figure 18 shows the basic options available for setting up optimization runs. The Optimizer includes multiple

options both for the Start model, Step model and Stop criteria and is quite flexible in this sense. However, the

basic options shown represent the main recommended combinations of Start and Step models.

Figure 18: The basic setup options for optimization runs.

The full flexibility is available when choosing the Custom option where all the Start, Step and Stop options

become available. These options are summarized in the bullet points below including the two additional options,

Seed and Realization, which are explained in their respective parentheses.

• Custom

o Start: Fill; Manual; Resource Greedy; Random; Smart

o Step: Random, Local; Random, Regional; Random, Global

▪ Resolution: Discrete (Limit to grid points), Continuous

o Stop: Max runtime, Max fruitless tries, (exhausted neighborhood)

o Stochastic (use of random numbers)

o Seed (to ensure reproducibility of stochastic methods)

o Realizations (how many runs to generate for a stochastic method)

Optimization algorithm 13

The last listed Stop criterion, exhausted neighborhood, is in parentheses as it is never selectable for the end-

user and always applied when the optimization runs with the Discrete resolution setting, where turbine positions

are limited to the grid points in the resource grid. This Resolution setting with options Discrete or Continuous is

a property of the step model as it is referred to as Limit to grid points in the basic options setup (i.e. not Custom).

Figure 19: The detailed setup options available when choosing the Custom option.

To keep the GUI user-friendly, we have pre-defined combinations of Start model and Step model (cf. Figure 18)

that are known to perform well together. Above all the Smart option which is the default option will perform the

best in the majority of cases. The pre-defined (default) combinations are listed below indicating the Start and

Step models

• User Layout

o Start: Manual (i.e., user defined)

o Step: Random, Regional

• Fill max

o Start: Fill

o Step: Random, Local

• Smart

o Start: Smart

o Step: Random, Local

• Random

o Start: Random

o Step: Random, Regional

The following sections describe the Start, Step and Stop options in further detail.

8a.3.1 Start model

The purpose of the Start model is to define the initial guess of the optimization solution and to make that guess

as good as possible. As described earlier, for complex optimization problems “well begun really is half done”,

and most likely much more than just half done. A poor starting model will be more likely to end up in modest

local optimal solutions. All the start models operate strictly on the resource grid. If this grid is excessively coarse

relative to the rotor diameter of the turbine model, that is to say >1RD, the performance of the Start models may

deteriorate, in particular the more advanced ones like the Smart Start model. The optimal trade-off between

speed and resolution lies around 0.5RD for the resource grid spacing relative to the turbine rotor diameter.

Unless the Allow invalid start model is activated the Start model will respect all activated constraints. The option

can only be activated for the Random start model. See section 8a.2.4 for further information.

The Smart Start model picks the optimal position (approximately) for each new WTG it places, regarding the

actual chosen objective and the effects of already-placed turbines. If stochastic is activated a measure of

randomness is added in the placement of each individual turbine.

The Random Start model is fully stochastic and picks the positions at random across the entire grid. More than

one Realization is recommended for this model, typically 7-8 or more, which simply means doing several similar

runs with different sets of random numbers. This model can be beneficial particularly if the optimization is strongly

Optimization algorithm 14

influenced by restrictive constraints. A fixed Seed may be set to exactly reproduce random numbers as this seed

is used both for the start and step models to ensure full consistency. A fixed seed cannot be used with multiple

realizations.

The Resource Greedy option is mainly included for historic reasons and for comparisons with the Classical

windPRO Optimizer. It picks each turbine position according to the best available resource position disregarding

wake effects and any objective function. This option performs well for sites with strong resource variation (e.g. a

ridge) using the AEP objective.

The Fill Start model will simply disregard the resource and start filling turbines from one corner only respecting

the constraints until the required number have been placed. If selected via the Fill max option, the filling will

continue until no more turbines can be placed due to the constraints – this option is particularly vulnerable to too

coarse a resource grid.

The Manual Start model is defined by the user who selects the turbine’s starting positions.

8a.3.2 Step model

The Step model iteratively seeks to improve the Start model until a Stop criterion is met. All the Step models are

stochastic, which means that they rely on random numbers. This means that both a turbine is selected at random

and that a new position for that turbine is selected at random. The main difference between the Step models is

the pool of positions from which these new positions are drawn.

The Random, Local Step model assumes that the current layout and turbine positions are relatively close to the

optimum. The assumption is typically valid for Smart Start models and Manual user defined Start models. The

local step model draws random positions from a local area around the turbine.

The Random, Regional Step model draws the random positions from a relatively large region around the turbine,

expecting improvements to be found further away, and the optimum position is not in the direct neighborhood.

The Random, Global Step model draws new positions from the entire domain. It is not utilized in any of the

standard options as convergence is inefficient. However, as a first broad search phase it can be useful followed

by a Random, Regional step model initiated via a Clone run, for example.

When grid spacing is finer than the expected optimal trade-off at around 0.5RD, the default option is Limit to grid

points (Discrete). When grid spacing exceeds 0.5RD, the default option is Continuous, which will allow turbines

to move away from grid points and prevent local optima due to a grid that is too coarse which is important. The

drawback is that the most natural Stop criterion cannot be used as will be described in the next section.

The main difference between the local, regional, and global set-up is the areas around the turbines considered

for steps. In a local step, the local area is 5D at the start of the optimization run and becomes iteratively smaller

until it reaches 1D at the end of the run in the discrete case or 0.5D in the continuous case. The distance that

defines the regional area is a square root of the vertical and horizontal distance of the whole WTG area, but at

least 5D in case of small WTG areas, at the start of the optimization run. It also ends up at 1D in the discrete

case and 0.5D in the continuous case. In the global step, the whole area is constantly considered during the run.

8a.3.3 Stop criteria

The purpose of the Stop criteria is to detect if an optimization is converged or so close to being converged that

further improvement will be insignificant. Another purpose is to give the user a chance to set a maximum waiting

time (with the risk of stopping prematurely far from an optimum).

Max runtime is the maximum time Step model is allowed to run. When the time is up the optimization is stopped.

The time to generate the starting model is not included in the timing.

Max fruitless tries simply defines the maximum number of unsuccessful attempts to take a step which accepted

before stopping. Both invalid steps (i.e., failed constraints) and steps without improved objective values are

counted.

Exhausted neighborhood is an option hidden from the user which is the most efficient stopping criterion. It can

only be used for runs with the resolution set to Limit to grid points (Discrete). It is a memory that tests if all

possible positions in the search neighborhood for all turbines have been tried in vain – and if so, the current

Optimization algorithm 15

layout is by definition an optimum and the run is stopped. For continuous runs the search neighborhood is always

infinite no matter how small it is, and this Stop criterion cannot be employed.

8a.3.4 Objective & Constraints

Put simply, the Objective of an optimization is what we seek to optimize. The design variables are the degrees

of freedom given to the Optimizer, which are allowed to be modified to find the best possible objective. In this

Optimizer only the turbine positions, their X and Y coordinates are explicit design variables. The number of

turbines and the turbine models are implicit design variables which the user can analyze and optimize via the

flexible structure of the GUI-tree. The choice of objective may differ for different users, the supported objectives

are described in next section.

Constraints are known limitations which must be fulfilled for a solution to be accepted, hence, we call a solution

which fulfills all constraints Valid. A solution where at least one constraint is violated is Invalid (and will not be

accepted).

Objectives 16

8a.4 Objectives

An optimization needs a quantity that must be optimized, the Objective, given a set of design variables that may

be varied. For some objectives optimization implies maximization, which is the case when wind farm production

(AEP) or project profit is the objective. For other objectives optimization implies minimization, which is the case

for cost-of-energy optimization.

8a.4.1 AEP

AEP is simply the Annual Energy Production including wake losses. The AEP calculation is based on the

resource data in the selected .rsf or .siteres file, containing sector-wise Weibull parameters (A and k) and

frequencies (f). Wake effects are calculated using the PARK2 wake model and the user-defined wake decay

constant.

Wind farm layout optimizations using AEP as the objective have a drawback, particularly if the available WTG

area is large: The optimization may lead to very spread-out layouts that would incur excessive costs for building

roads and grid connection. This is the main motivation for choosing other objectives, in particular, objectives

which include the costs of building the wind farm.

8a.4.2 Costs

Costs are not included as an objective on its own in the New Optimizer, at least not directly. However, the

estimation of costs is an important input to financial objectives such as cost-of-energy (COE) or profit (NPV), to

account for the balance between the created value (i.e., AEP) and the expected costs required to realize that

potential. Costs in the New Optimizer are estimated using the windPRO Cost tool. This tool estimates costs

using parameterized formulas fitted to a large amount of real historic costs and based on extensive literature

reviews. As an example, turbine costs scale with generator capacity (MW), specific capacity (MW/m

), rotor size

) and hub height (m) via an elaborate regression expression. The cost tool comes with six predefined cost

models, three price levels ‘high’, ‘mid’ and ‘low’ for onshore and offshore, respectively.

Figure 20: Selection of the cost model showing the two default cost models for onshore and offshore

respectively.

In the cost tool, the costs are divided into four main categories as listed below.

• Devex: development expenditure

• Capex: capital expenditure

• Opex: operational expenditure

• Abex: abandonment expenditure

Development expenditures (Devex) quantify the cost associated with developing the project, getting permissions

to build the wind farm etc. Capital expenditures (Capex) represent the main investment of building the wind farm.

Operational expenditures (Opex) represent the costs of keeping the wind farm running through its lifetime, and

abandonment expenditures (Abex) quantify the estimated amount of money to eventually remove the wind park.

Capex is the only cost category which depends on the actual design of the layout via the costs for the internal

grid connection between the turbines (and roads for onshore).

For each cost a Cost Index may be defined to account for expected future trends in the price development. This

index should exclude the effect of the general baseline inflation.

Objectives 17

Figure 21: Extract from the Cost tool showing the possibility to enter Price Indices for each cost component, but

also the possibility to include replacement costs, e.g. for gearboxes.

In Figure 21 please note the possibility to insert adjustments to the baseline costs via entries in the table column

Cost function value. It is via values in this column that the high and low alternative cost models are defined, by

an increase or decrease of these factors.

In the Optimizer the wind farm is assumed to be built and put into operation the year after the current year, which

for 2023 would be 2024. Devex is assumed to occur the year before the installation, i.e. the current year. When

the reference year defined in the cost tool deviates from the year that a cost occurs the price index (if set) will

be used to adjust the costs accordingly. The default cost index is zero through the lifetime.

Note that the total cost values shown in the optimizer are not discounted only index corrected (if set by the user)

and summed over the lifetime.

For the grid (offshore and onshore) and road connection costs (onshore only) an additional sub-optimization is

solved for finding the shortest possible way to connect the turbines in the layout. Either to each other or to any

of the Connection points if defined for the Site. The resulting inter-connection distance is what enters the cost

calculation. The solution to this sub-optimization relies on graph theory and the optimization problem is referred

to as the minimum spanning tree. The connections of the minimum spanning tree are visualized in the Layout

plot for each run as the black connection lines between the WTGs (and connection points, if any).

Figure 22: Layout plot from for a run with LCOE optimization showing the black connection lines.

As a final remark it is important to stress that the cost model is deliberately kept relatively simple with a minimum

of assumptions which are calibrated against actual project costs. Hence, the user does not need, in fact cannot,

set a large range of particular cost items such as the cost of crossing a stream or railway. Although that degree

of flexibility might appear beneficial, if the input quantities are not known the values will be associated with a

very large uncertainty, as will the resulting overall cost estimates.

The current cost tool seeks to strike an ideal balance between accuracy and detail/flexibility, but with a

preference for accuracy over detail. In the end what is important is getting the right order of magnitude of costs

as input to the financial objectives described in the following sections.

Objectives 18

8a.4.2.1 Offshore Vs Onshore costs

The onshore and offshore cost setups share many cost components, and both include costs for the internal grid

connection, but with very different price constants. A main difference is that the onshore cost model includes the

cost of connecting roads where the offshore model includes the cost of a main grid connection (to the shore).

Also, the foundation and area are calculated differently. See the manual for the Cost tool for further details

(windPRO BASIS manual, chapter 2 section 18).

8a.4.3 LCOE

Levelized cost of energy (LCOE) is often preferred as an objective in optimizations, as on the one hand it includes

the effect of costs, in particular Capex, the cost of building the wind farm project. On the other hand, LCOE does

not require further assumptions of uncertain quantities such as the future development of the electricity price. In

addition, a discount rate must also be assumed for the costs to calculate LCOE, to discount future costs to

present day values. The discount rate is a baseline interest rate often representing the average interest rate for

secure investments such as bonds or set as the baseline return of investment in a company. windPRO uses the

so-called real discount rate, which is corrected for the general inflation (i.e., it excludes inflation). Hence, future

costs in the windPRO cost tool should not account for inflation.

In LCOE the future AEP is discounted similarly, which might seem counter-intuitive. However, the AEP of each

year through the lifetime will lead to a cash flow via the sale of the produced electricity. In this regard the AEP

produced next year is worth more than AEP produced in say 15 years (for positive discount rates), assuming a

constant electricity price. Thus, LCOE accounts for the discount effect of both future costs and future sale of

electricity and calculates the average cost of electricity from these, as expressed in the equation below (e.g. [2]

or [3]):

 



















  













  





In the above expression, costs are condensed to a single sum for each year. In practical terms, the Capex will

occur in year zero, the installation year, and the Opex occurs in all the following years until end of lifetime,

possibly increasing over time if the user has set a cost index for the future years.

The LCOE has the drawback in that it tends to increase (i.e., deteriorate) with increasing size of a wind farm, as

the best resource positions get taken first and wake effects tend to increase with park size. The total profit of the

project on the other hand would typically increase with the size of the wind farm. Hence, LCOE will generally

lead to too small a wind farm if used as an objective to determine the wind farm size. When comparing wind

farms of equal capacity LCOE does not suffer from this shortcoming.

8a.4.4 NPV

The Net Present Value (NPV) for a wind farm project is simply put the total profit of the wind farm through its

lifetime converted to present day value. NPV bares many similarities with the LCOE, and addresses the main

drawback of LCOE, that it under evaluates the value of larger projects. Still NPV includes the penalizing effect

of Capex costs for spread-out layouts. The main difference between NPV and LCOE is the fact that the AEP in

future years is explicitly converted to a cash flow. This requires the assumption of a future electricity price (P) in

addition to the discount rate (d), which by default is constant, but may include future projections via a price index

similar to the cost components. The equation below summarizes the calculation of NPV (e.g. [3]).

  



 





 



 





  





NPV is the most flexible objective function of the three objectives supported in the Optimizer. In fact, NPV can

give similar results to both AEP optimizations and LCOE optimizations. The performance is controlled by the

trade-off between costs and AEP, which is defined by the assumed electricity price. For very high electricity

prices, costs lose importance and the NPV objective approaches the AEP objective. For very low electricity

prices AEP loses its importance and the optimization will be driven mainly by costs to minimize expenses. If the

Objectives 19

electricity price is set to be equal to the LCOE from another optimization, then the performance of the NPV

objective will yield results very similar to the LCOE optimization.

The NPV has several advantages compared to AEP and LCOE and addresses their shortcomings. NPV also

works well as an objective for determining the size of a wind farm as it will seek to maximize the lifetime profit of

the project. But as profit in absolute terms tend to grow with project size, the optimal size will often be the

maximum allowed park size, as is the case for AEP. The main drawback when using NPV as an objective is that

an assumption of a future electricity price is required, and that this assumption is associated with a large or even

very large uncertainty. At the same time the assumed electricity price may significantly influence the performance

of the NPV objective as described above.

Constraints  20 
 
 
© EMD International  •  www.emd.dk •  windPRO 4.0  •  September 2023 
8a.5  Constraints 
The following sections describe the constraints supported by the New Optimizer. The supported constraints are 
shown in Figure 23. Note that including Lifetime or Noise constraints are subject to additional windPRO license 
requirements  as  they  draw  on  calculation  functionality  in  the  LOAD  RESPONSE  and  DECIBEL  modules, 
respectively. 
 
Figure 23: Constraint options. 
8a.5.1 Area & distance (sub-areas)  
Defining a WTG area object is a prerequisite for all optimizations. The WTG area object serves the purpose to 
define the area limitations for turbine placement. A site may be split into arbitrarily many sub-areas and each 
sub-area may have individual limitations on minimum and maximum numbers of turbines or installed capacities. 
Sub-areas may also have individual requirements for turbine spacing typically defined as an elliptical constraint 
in terms of rotor diameters oriented along the prevalent wind direction. The Optimizer will always adhere to the 
areal requirements defined in the selected WTG area, whereas minimum requirements for inter-turbine distances 
must be separately activated via the Distance constraint. Even if no distance constraint is activated the Optimizer 
will not accept a turbine spacing below 1RD. Some tips and considerations to the WTG area import are available 
in section 8a.6.1, and detailed information about the WTG area object is available at Appendix 8 OPTIMIZE 
Classic in section 8.0.1.5. 
8a.5.2 Wake loss 
The maximum wake loss constraint is a new feature in windPRO 4.0 (cf. Figure 23). It allows to define maximum 
wake  losses  for  both  new  WTG  and  existing  WTG  objects;  the  maximum  wake  losses  can  be  specified 
independently from each other. 
8a.5.3 Noise 
The noise constraint requires an activated license for the DECIBEL module. The calculation is a stripped-down 
version of the ISO 9613-2 standard. The noise constraint is defined for a single wind speed selected in the Model 
settings for the noise requirement (Figure 24). Noise sensitive areas must be selected on the Site level (Figure 
25) and WTG source noise data on the WTG level (Figure 26). 
 
Figure 24: Model settings for the Noise constraint (Site level), showing the selection of wind speed. 

Constraints 21

Figure 25: Selection of noise sensitive areas (NSAs) on the Site level in the tree.

Figure 26: Selection of noise data on the WTG level in tree.

8a.5.4 Component Lifetime (loads)

The lifetime constraint requires an active license for the LOAD RESPONSE module and sets a constraint on

required minimum lifetimes for selected turbine components for each WTG position.

The calculation of lifetimes and activation of the lifetime constraint requires a resource file including all the siting

parameters for fatigue calculation, i.e., a .siteres file. Such a file may be calculated using the RESOURCE

calculation in windPRO drawing upon the IEC61400-1 ed. 4 calculation functionality in SITE COMPLIANCE, or

can be downloaded from the free online GASP dataset. The calculation options are a stripped-down version of

LOAD RESPONSE as can been from the Model settings in Figure 27.

Figure 27: Model Settings for the Lifetime constraint accessed on the Site level.

The lifetime calculation also requires the setup of the wind turbine Design Standard and Class as well as

selection of the Load Response Model which can be either a generic model or a specific model provided by a

manufacturer. For the response model, a set of sensors must be selected for the constraint, here it is

recommended to focus on the key components such as blade root and tower bottom, and perhaps low speed

shaft (LDD).

Figure 28: Turbine design class and response model selection on WTG level.

Practical recommendations 22

8a.6 Practical recommendations

8a.6.1 WTG Area import

A convenient approach is to import pre-defined WTG Areas (cf. Figure 29: WTG area Import from file.) as

shapefile format (.shp). Each feature of the shapefile a WTG area is handled separately for which properties can

be defined, e.g., whether the area is an exclusion zone or a WTG area, the minimum and maximum number of

WTGs to be placed, the minimum distance between WTG (cf. Figure 29). Moreover, a buffer zone can be

specified (cf. Figure 30) for the optimization.

Figure 29: WTG area Import from file.

Figure 30: WTG area settings.

The WTG area object handling is quite strict. In windPRO 4.0, WTG area intersections are not allowed, neither

are features within features (so-called islands). If such features must be imported, it is necessary to use

Geoinformation Systems to cut a part of the outer ring of the polygon feature (cf. Figure 31). An enhanced and

user-friendly version of WTG area import is planned for future versions.

Figure 31: Feature within feature (island). The yellow part of the feature has been cut out of the outer ring and

is handled as a third WTG area object. This prevents an intersection error message in the optimization.

8a.6.2 Example projects

Three sample projects are provided to show the range of utilities of the optimizer tool: a sample on-shore project,

a sample off-shore project, and a sample project for the new noise curtailment optimizer.

The onshore sample project Aparados da Serra.w40p provides a variety of optimization scenarios. These include

runs with AEP, LCOE and NPV objectives, runs with different constraints and on different WTG area structures.

Lastly, it shows a performance comparison for different turbine types and a performance comparison for different

optimization configurations.

Practical recommendations 23

The offshore sample Cost model offshore.w40p showcases the new option of including cost maps in the cost

set-up that can be used to represent a whole variety of costs, e.g., bathymetry-based costs, soil structure

foundation costs, or travel costs.

The noise curtailment Curtailment optimizer demo project.w40p shows how a non-compliant wind farm layout

can be made compliant with noise regulations while still obtaining the maximum possible energy yield from

optimal curtailment strategies.

References 24

8a.7 References

[1] A. P. J. Stanley, O. Roberts, J. King, and C. J. Bay, “Objective and algorithm

considerations when optimizing the number and placement of turbines in a wind power

plant,” Wind Energy Sci., vol. 6, no. 5, pp. 1143–1167, 2021, doi: 10.5194/wes-6-1143-

2021.

[2] T. Rubert, D. McMillan, and P. Niewczas, “A decision support tool to assist with lifetime

extension of wind turbines,” Renew. Energy, vol. 120, pp. 423–433, 2018, doi:

10.1016/j.renene.2017.12.064.

[3] W. Short, D. J. Packey, and T. Holt, “A manual for the economic evaluation of energy

efficiency and renewable energy technologies,” 1995. doi: NREL/TP-462-5173.