Analysis of pre- and post- construction wind farm energy ... · Uncertainty is involved in allof the assessment process: in the wind speed measurement, in the long-term correlation,

Analysis of pre – and post construction wind farm energy

yields with focus on uncertainties

Master Thesis

For obtaining the academic degree "Master of Science"

By Abdelbari Redouane

December 2014

REMENA Master Program

Faculty of Electrical Engineering / Computer Science

Master Thesis

Analysis of pre – and post construction wind farm energy

yields with focus on uncertainties

Improvement of Lahmeyer’s spreadsheet application

software for estimating wind farm energy yield uncertain-

ties

Author: Abdelbari Redouane

Student ID Number: 3103246

Faculty: Faculty of Electrical Engineering / Computer Science

Supervisor: Prof. Adel Khalil

Supervisor: Prof. Siegfried Heier

Co-supervisor: Dr. Kurt Rohrig

Supervisor on-site: MSc. Ren. Energies - Dipl. Ing. Nicolás Veneranda

Company: Lahmeyer International GmbH

Date of submission: 15. 11. 2014

LAHMEYER INTERNATIONAL

Abstract

The evaluation of a wind resource and the following estimation of the annual

energy production (AEP) is a very important part in wind project development.

Uncertainty is involved in all of the assessment process: in the wind speed

measurement, in the long-term correlation, in the wind flow modeling, in the

conversion from wind speed into energy (wind turbine power curve) and in the

energy losses estimation. An appropriate assessment of uncertainty is crucial

for judging the technical and commercial feasibility and the associated risk of

a wind project development.

In this manuscript, the statistical and mathematical background of uncertain-

ties related to wind energy yield estimations were investigated and the uncer-

tainty analysis tool of Lahmeyer International GmbH currently applied for wind

energy yield assessment was evaluated. A comparison between pre- and post-

construction energy yields was carried out for a limited number of wind farms

operating in several countries worldwide.

The evaluation of uncertainties is a complex topic where a typical approach is

to consider each uncertainty factor independent from the other, with each un-

certainty factor quantified on the basis of experience. An analog concept to

the uncertainty has been identified through a pragmatic approach which can

be examined in relation to some of the main uncertainty factors considered in

the wind energy yield assessment process (variability of the production).

The aim of the approach used in this work is to give a more accurate and ob-

jective comparative tool of uncertainty issued from the wind study (WS) and

the uncertainty based on production data (PD), and consequently to give a

learning tool for learning from the projects already implemented.

ملخص

المستخدمة من طرف الیقین ألداة تحلیل عدم تحلیلي ا العمل البحثي، تم تقدیم استعراضفي ھذ

صحیح لعدم الیقین في م المنھج اإلحصائي لتقدیر یقدتم ت. إذ تقییم الریاحل المایر العالمیة شركة

تقییم موارد الریاح و بالتالي حیث أن .موارد طاقة الریاح و كذا تقییم اإلنتاج الطاقي للریاح تقییم

عدم یتدخل تقدیر اإلنتاج السنوي للطاقة ھو جزء مھم جدا في تطویر مشاریع طاقة الریاح. و

قیاس سرعة الریاح إلى عدم الیقین في عدم الیقین في نمتقییم، العملیة مراحل الیقین في كل

أمر بالغ األھمیة للحكم على لعدم الیقین المناسب تقدیر الضائعات. و یعتبر التقدیر منحنى القوة و

.ر مشروع طاقة الریاحیجدوى ومخاطر تطو

عدم الیقین لكل منلمقارنة أكثر دقة وموضوعیة عطي أداةت في ھذا العمل ةالمتبع یةنھجمال

وبالتالي یعطي أداة موضوعیة .وعدم الیقین على أساس بیانات اإلنتاج من دراسة الریاح الصادر

قع،اتقییم المولالیقین عدم إلى استعراض أداة باإلضافة علم من المشاریع التي نفذت بالفعل.للت

بیانات من خالل الریحي لتغیرات اإلنتاجب الرئیسیة من الجوان اثنین ھذا البحث إلى تعرضی

الجمع بین عدم و أوال، تم تقدیم وسیلة للجمع بین المتغیرات التغیر الزماني والمكاني. :اإلنتاج

ثانیا، .المتغیرات المترابطة وغیر المترابطة بالنسبة لكل الیقین الذي یطرح نفسھ في إنتاج الریاح

ة وفقا لبیانات مزرعة الریاح والطاقة اإلنتاجیة السنویة المتاح تم تحجیم التفاوت على مستوى

.خصائص مختلفةذات الریاح م مقارنة بین نتائج العدید من مزارعیقدتم ت ثالثا، .اإلنتاج

Acknowledgement

After two years of hard work, there comes a nice moment when everything

begins to take on its finale form. And the entire struggle yields its fruitful re-

sults. In that moment the best thing to do is not to forget all the people who

participated in the process. So here I would like to extend my deepest grati-

tude to all the people who supported me and contributed to make this

achievement possible. And I would like to thank particularly:

The professors from Egypt and Germany who covered the REMENA Pro-gram pedagogically and scientifically.

The Professors from Morocco who wrote nice reference letters for me. The officers and the staff of the REMENA program: Prof. Adel Khalil,

Prof. Sayed Kaseb, Prof. Dirk Dahlhaus and M.A. Anke Aref and their teams for making this program an unforgettable experience

Lahmeyer International Wind department project engineers, managers, directors and the Head of the department, the company where I wrote my Master thesis and where I learnt a lot of things about wind engi-neering consulting but also about life.

Further I want to thank my supervisor of University Kassel, Prof. Adel Khalil,

Prof. Siegfried Heier and co-supervisor Dr. Kurt Rohrig, for agreeing to super-

vise my Master thesis. I want to thank my tutor at Lahmeyer International Dipl.

Ing. Nicolás Veneranda, for his support in shaping the scope of the thesis top-

ic and his review of the manuscript. And thanks to David for his help

Additionally, special thanks go to Patric, Dagmar, Jan, Tobias, Luis and Frieder

for making my stay at Lahmeyer agreeable. Thanks to Michael, Nicolas, Roland

for providing me the necessary data. Thanks to Gyeongil and Joerg for their

contribution in many discussions and comments about the topic. Finally I

would thank David for his review of the text of the Manuscript.

Declaration

Hiermit versichere ich, dass ich die vorliegende Arbeit selbstständig durchge-

führt und verfasst, keine anderen als die angegebenen Hilfsmittel verwendet

und sämtliche Stellen, die anderen Werken im Wortlaut oder dem Sinn nach

entnommen sind, mit Quellenangaben kenntlich gemacht habe. Desgleichen

gilt für Zeichnungen, Skizzen, bildliche Darstellungen oder Gleichungen.

Bad Vilbel, den …………

……………………………………………

Table of contents

Table of contents

Scope of the Work ................................................................................ 6

Motivation ...................................................................................... 7

History ................................................................................................ 7

Tasks ................................................................................................ 8

Introduction ......................................................................................... 9

Chapitre 1: Uncertainty Concept ..................................................... 11

1.1 Introduction ............................................................................ 11

1.2 Uncertainty types .................................................................... 12

1.3 Evaluating standard uncertainty .............................................. 14

1.3.1 Type A evaluation of standard uncertainty ........................ 16

1.3.2 Type B evaluation of standard uncertainty ........................ 16

1.4 Determining combined standard uncertainty ........................... 17

1.4.1 Uncorrelated input quantities ........................................... 17

1.4.2 Correlated input quantities .............................................. 18

1.5 Probability vocabulary ............................................................. 19

Chapitre 2: Uncertainties in wind assessment ................................. 21

2.1 General ................................................................................... 21

2.2 Expanded uncertainty ............................................................. 24

Chapitre 3: Lahemyer Uncertainties Analysis Tool and the Variability Analysis tool ................................................................................. 25

I

Table of contents

3.1 Investigation of the Lahemyer International Uncertainties Analysis Tool .......................................................................... 25

3.1.1 Wind-related uncertainty ................................................. 25

3.1.1.1 Measurement Wind Speed (cup anemometer) ....................... 25

3.1.1.2 Measurement Wind Direction (wind vane) ............................. 26

3.1.1.3 Mounting ........................................................................... 26

3.1.1.4 Data Processing .................................................................. 28

3.1.2 Energy-related uncertainty .............................................. 30

3.1.2.1 Flow modeling .................................................................... 30

3.1.2.2 Wake Effects ....................................................................... 32

3.1.2.3 Power curve ....................................................................... 32

3.1.2.4 Losses (Uncertainty of loss estimation) ................................ 33

3.2 Wind production variability ...................................................... 36

Chapitre 4: Uncertainties input data for the Model .......................... 43

4.1 General Information ................................................................ 44

4.1.1 Site 1 ............................................................................... 45

4.1.2 Site 2 ............................................................................... 47

4.1.3 Site 3 ............................................................................... 49

4.1.4 Site 4 ............................................................................... 51

4.1.5 Site 5 ............................................................................... 53

4.1.6 Site 6 ............................................................................... 55

4.1.7 Site 7 ............................................................................... 57

4.1.8 Site 8 ............................................................................... 59

4.1.9 Site 9 ............................................................................... 61

4.2 Wind Study Data ...................................................................... 63

4.2.1 Site 1 ............................................................................... 65

II

Table of contents

4.2.2 Site 2 ............................................................................... 67

4.2.3 Site 3 ............................................................................... 69

4.2.4 Site 4 ............................................................................... 71

4.2.5 Site 5 ............................................................................... 73

4.2.6 Site 6 ............................................................................... 75

4.2.7 Site 7 ............................................................................... 77

4.2.8 Site 8 ............................................................................... 79

4.2.9 Site 9 ............................................................................... 81

4.2.10 The AEP calculated in the Wind Study for all the farms .. 83

4.3 Production Data ...................................................................... 85

4.3.1 Site 1 ............................................................................... 86

4.3.2 Site 2 ............................................................................... 87

4.3.3 Site 3 ............................................................................... 88

4.3.4 Site 4 ............................................................................... 89

4.3.1 Site 5 ............................................................................... 90

4.3.2 Site 6 ............................................................................... 91

4.3.3 Site 7 ............................................................................... 92

4.3.4 Site 8 ............................................................................... 93

4.3.5 Site 9 ............................................................................... 94

Chapitre 5: Results ......................................................................... 95

5.1 Results concerning the different sites ...................................... 95

5.1.1 Site 1 ............................................................................... 97

5.1.2 Site 2 ............................................................................... 99

5.1.3 Site 3 ............................................................................. 101

5.1.4 Site 4 ............................................................................. 103

5.1.5 Site 5 ............................................................................. 105

5.1.6 Site 6 ............................................................................. 107

III

Table of contents

5.1.7 Site 7 ............................................................................. 109

5.1.8 Site 8 ............................................................................. 111

5.1.9 Site 9 ............................................................................. 113

5.2 Comparison between sites based on the type of terrain ......... 115

5.3 Improvement of Lahmeyer’s spreadsheet application software120

Conclusion ....................................................................................... 122

Annexes .......................................................................................... 124

Annex A: Example (IEC 12400-12-1) .......................................... 124

Category A uncertainties ......................................................... 125

Category A uncertainty in electric power .......................................... 125

Category A uncertainties in climatic variations ................................. 128

Category A uncertainties in the site calibration................................. 128

Category B uncertainties .......................................................... 128

Category B uncertainties in the data acquisition system .................... 129

Category B uncertainties in electric power ........................................ 129

Category B uncertainties in wind speed ............................................ 132

IV

Nomenclature

Nomenclature

AEP, Annual Energy Production

MEP, Monthly Energy Production

PoE, Probability of Exceedance

WTG, Wind Turbine

FLH, Full load hours

WS, Wind study

PD, Production data

PDA, Production Data Analysis

O&M, Operation and Maintenance

LT, Long-term

SCADA, Supervisory control and data acquisition

MCP, Measure correlate predict

Met-Mast, Meteorological Mast

TSA, Turbine Supply Agreement

ECWP, Extreme Cold Weather Package equipment

PPT, Power Performance Test

NCEP, National Centers for Environmental Prediction

NCAR, National Center for Atmospheric Research

PPA, Power Purchase Agreement

StdDev, Standard deviation

COV, Covariance

R, Correlation coefficient, Pearson coefficient

V

Master Thesis -REMENA- Abdelbari REDOUANE

Scope of the Work

The topic of the master thesis is the analysis of pre – and post-construction wind

farm energy yields with a focus on uncertainties. The scope of work was defined by

the author in agreement with the site supervisor and also with the head of the wind

energy department at Lahmeyer International GmbH.

It is in the interest of the site supervisor to understand the accuracy of the wind en-

ergy yield estimations carried out within the wind assessment study using Lahmey-

er-developed tools, by means of comparison of pre- and post-construction wind

farm energy yields. Moreover, the author of the thesis and the site supervisor are

highly motivated in identifying trends and areas of further research in connec-tion

to deviations between estimated and real annual energy production and wind speeds

which could lead to improvements in the understanding of the challenges on the

wind potential assessment and evaluation of uncertainties.

To evaluate the accuracy of the Lahmeyer International GmbH uncertainty estimation

tool, the author compares the Annual Energy Production (AEP) output of the wind

studies (pre-construction estimated AEP and uncertainties based on wind measure-

ment data) with the AEP output of PDA (post-construction Production Data Analysis

and estimated AEP and uncertainties) or AEP output of O&M monitoring studies

(post-construction measured production carried out during Operation and Mainte-

nancemonitoring of the wind farm).

In order to achieve results within the timeframe available within the Master Program,

the comparison of pre- and post-construction energy yields is limited to nine (9)

wind farm projects. The author is aware the selected project basis cannot be consid-

ered statistically sufficient for deriving final conclusions. Nevertheless, the author

considers the analysis and evaluation of pre- and post- estimated energy yields will

6


allow an internal “validation” of the company PoE (probability of Exceedance) tool,

especially the uncertainty analysis tool, which can be helpful to identify areas of im-

provement and can also show the company if its prediction of uncertainties is opti-

mistic or rather conservative.

Motivation

Improving the accuracy of the energy yield assessments, understanding better the

uncertainty estimation process and eventually reducing the total uncertainties asso-

ciated to the energy yield predictions are stated as important goals that the compa-

ny wants to aim for.

In the wind industry it is already clear that project financing is becoming increasing-

ly harder since granted tariffs for wind energy are being reduced almost worldwide

for different reasons. More accurate energy yield assessments are necessary for pro-

ject implementation. Lahmeyer might have a competitive advantage if their studies

define more accurate total uncertainties, and such an achievement will proof the

learning curve regarding AEP estimation.

History

Wind Energy Advisers have always considered the uncertainty factors as standard

deviation factors with a normal (Gaussian) distribution. Consistent with this ap-

proach, the combination of uncertainty factors (Ui) is done considering each factor

independent from any other:

Total uncertainty = �∑ Ui2

i

The topic is challenging since it aims to identify a methodology to evaluate the cor-

relation of the uncertainty factors and no results from operating wind farms are

7


proving the calculated uncertainty factors, and nor can their correlations be stated

as exact.

Tasks

A) Read available documentation

B) Define boundary conditions for the thesis

a. Investigate the methodology of uncertainty estimation used by

Lahmeyer

b. compare the AEP PoE results for many wind studies

c. Investigate the production data available for the same wind farms con-

cerned by the wind studies

d. compare the AEPPoE based on the data production and evaluate the

uncertainty generated by the spatiotemporal variabilities

e. Obtain correlation and covariance matrixes for the following the spati-

otemporal variabilities

f. Investigate the influence of the grid losses and the availability influ-

ences in the AEP.

C) Design of a new tool that respond to the requirements mentioned in the task

b)

D) Implementation of the AEP comparison tool with an ergonomic interface and

simplified data feeding

8


Introduction

The global installed capacity for wind power is increasing significantly in reaction to

the worldwide concern about low-emissions of GHG and a desire to decrease the

dependency on petroleum. The European Union directive 2009/28/EC applies the

mandatory target of a 20 % RE by 2020 aiming to increase the share of renewable

energy in overall EU energy consumption by 2020. This target may require between

30 and 40 % of the electricity in the European Union to come from renewable energy

sources by 2020 [1]. In the U.S.A, wind energy at present contributes just one per-

cent of the energy supply. However, the wind power generation share is expected to

increase to 20% in the USA by 2030 [1]. Moreover, depending on the local states

legislations’, how much ambitious renewable energy targets may change from one

state to another.

Figure 1: Global installed wind power capacity, end of 2013

With this increasing amount of wind generation, the future electricity markets could

be very different to those of today: instead of fossil fuel power stations dominating

9


the energy generation system, the market could be dominated by large amounts of

RE energy generation systems, combined with highly intermittent output from the

wind farms. The amount of uncertainty and variability in wind generation makes this

resource different from the traditional. At moderately low levels of RE capacity pene-

trated in the generation system, wind turbines variabilities can basically be absorbed

into the generation system without affecting the system reliability.

Figure 2: Global cumulative installed wind capacity 1996-2013

In addition to the important role of assessing uncertainty and variability from the

energy market and the technical point of view regarding the wind energy penetration

in the grid, understanding and mastering the uncertainty and variability of the wind

resource stands as a condition for the successful development of wind energy and

minimization of financial risk before starting the construction of a wind project.

References: [1] Joaquin Mur-Amada and Ángel Bayod-Rújula, Variability of Wind and Wind Power, Wind

Power, ISBN 978-953-7619-81-7, pp. 558, June 2010, INTECH, Croatia [2] GLOBAL WIND STATISTICS 2013, GLOBAL WIND ENERGY COUNCIL, 05.02.2014

10


Chapter 1: Uncertainty Concept

1.1 Introduction

Uncertainty is one of the important aspects that has been carefully considered in

science and engineering. In fact, it is not only the final result that should be consid-

ered but also how this result was reached. The word “uncertainty” means doubt, and

therefore in its large sense “uncertainty” denotes doubt about the validity of the re-

sult. Before, some time ago, error analysis was addressing the same aspects consid-

ered by the uncertainty analysis nowadays. However there is quite difference be-

tween the two concepts; indeed, when all of the known or suspected components of

error have been evaluated and the appropriate corrections have been applied, there

still remains an uncertainty about the accuracy of the stated result, that is, a doubt

about how well the result of the measurement represents the value of the quantity

being measured or calculated. [1]

In the JCGM 100:2008 [1] it was stated that the ideal method for evaluating and ex-

pressing the uncertainty of the result of a measurement should be universal so that

it applies for all kinds of measurements and to all types of input data used in meas-

urements. When the actual quantity used to express uncertainty should be: on the

one hand, internally consistent in the sense that it should be derived directly from

the components that contribute to it, as well as independent of how these compo-

nents are grouped and of the decomposition of the components into subcompo-

nents. And in the other hand transferable in the sense that it should be possible di-

rectly to use the uncertainty evaluated for one result as a component in evaluating

the uncertainty of another measurement in which the first result is used. Sometimes

and instead of this general concept of uncertainty, the uncertainty denotes some

specific quantities that provide quantitative measures of the concept, for example,

11


the standard deviation, so it is necessary to stress that the word “uncertainty” can be

used in these two different senses.

Since in this chapter the word measurand will be used frequently, it is important to

define it here according to the annex D of the JCGM 100:2008 [1]. Indeed the meas-

urand is stated as “the quantity to be measured; the measurand cannot be specified

by a value but only by a description of a quantity. However, in principle, a measur-

and cannot be completely described without an infinite amount of information.

Thus, to the extent that it leaves room for interpretation, incomplete definition of

the measurand introduces into the uncertainty of the result of a measurement a

component of uncertainty that may or may not be significant relative to the accuracy

required of the measurement”. In another paragraph the measurand is defined as a

“well‑defined physical quantity that can be characterized by an essentially unique

value. If the phenomenon of interest can be represented only as a distribution of

values or is dependent on one or more parameters, such as time, then the measur-

ands required for its description are the set of quantities describing that distribution

or that dependence”.

it is to be noted that this chapter and the next chapter are taken from standards

with slight and superficial modifications. The aim of these two chapters is simply to

put the lecture in the context of the uncertainty studies according to the interna-

tional standards mentioned in their respective references.

1.2 Uncertainty types

When speaking about the uncertainty of measurement, it is mainly defined as a Pa-

rameter, related to the result of a measurement, which characterizes the dispersion

of the values of the measurand around the mean value. The Standard uncertainty is

the uncertainty of the result of a measurement expressed as a standard deviation.

There are two types of evaluation of uncertainties:

12


Type A evaluation: Method of evaluation of uncertainty by the statistical analysis of

series of observations

Type B evaluation: Method of evaluation of uncertainty by means other than the sta-

tistical analysis of series of observations

There is also another categorization of uncertainty which differentiates between

“random” and “systematic” components of the uncertainty; this two components

generally are associated with errors coming up from random effects and known sys-

tematic effects, correspondingly. However, this categorization of components of un-

certainty can be confusing in its implementation, as a “random” component of un-

certainty in one measurement or calculation may turn into a “systematic” component

of uncertainty in another measurement if it takes as input the result of the first

measurement. Therefore, categorizing the types of evaluating uncertainty compo-

nents rather than the components themselves can overcome such confusion. How-

ever the classification of “random” and “systematic” components of the uncertainty,

as mentioned in [1], is intended to designate the two different types of the error

source and this is for the convenience of discussion only; the classification is not

meant to indicate that there is any difference in the nature of the components re-

sulting from the two types of evaluation.The two types of evaluation are derived

from probability distributions, and the variances or the standard deviations are

mainly the parameters to quantify the uncertainty associated to them.

The uncertainty mirrors the lack of knowledge of the exact value of the measurand.

The result after correction for recognized systematic effects is still only an estimate

of the value of the measurand because of the uncertainty arising from random ef-

fects and from imperfect correction of the result for systematic effects.

13


Actually, many error sources can contribute to the uncertainty of the final result,

these sources may be dependent, and some of the sources may contribute to other

sources.In the list below are some of these sources:

1. Incomplete definition of the measurand ;

2. Imperfect realization of the definition of the measurand ;

3. Non-representative sampling if a sampling is used;

4. Inadequate knowledge of the effects of environmental conditions on the

measurement or imperfect measurement of environmental conditions;

5. Personal bias in handling the instruments;

6. Finite instrument resolution or discrimination threshold;

7. Inexact values of measurement standards and reference materials;

8. Inexact values of constants and other parameters obtained from external

sources and used in the data-reduction algorithm;

9. Approximations and assumptions incorporated in method and procedure of

the data analysis;

10. Variations in repeated observations of the measurand under apparently iden-

tical conditions.

1.3 Evaluating standard uncertainty

In addition to the standard uncertainty which, as was mentioned previously, can be

defined as a parameter associated with the result that characterizes the dispersion

of the values that could reasonably be attributed to the measurand. Other important

elements to take into consideration when analyzing the standard uncertainty are:

the combined standard uncertainty, the expanded uncertainty and its Coverage fac-

tor.

The combined standard uncertainty is a standard uncertainty of the result of a

measurement when that result is obtained from the values of a number of other

14


quantities, equal to the positive square root of a sum of terms, the terms being the

variances or covariances of these other quantities weighted according to how the

measurement result varies with changes in these quantities.

The expanded uncertainty is a quantity defining an interval about the result of a

measurement that may be expected to encompass a large fraction of the distribution

of values that could reasonably be attributed to the measurand.

The coverage factor is a numerical factor which is used as a multiplier of the com-

bined standard uncertainty in order to obtain an expanded uncertainty.

In most cases, a measurand Y is not measured directly, but is determined from N

other quantities

X1X2...XN through a functional relationship f:

𝑌 = 𝑓(𝑋1,𝑋2, . . . ,𝑋𝑁 ) (E.1)

The set of input quantities X1, X2...XN may be categorized as:

⎯ Quantities whose values and uncertainties are directly determined in the cur-

rent measurement. These values and uncertainties may be obtained from, for exam-

ple, a single observation, repeated observations, or judgment based on experience,

and may involve the determination of corrections to instrument readings and cor-

rections for influence quantities, such as ambient temperature, barometric pressure,

and humidity;

⎯ Quantities whose values and uncertainties are brought into the measurement

from external sources, such as quantities associated with calibrated measurement

standards, certified reference materials, and reference data obtained from hand-

books.

15


1.3.1 Type A evaluation of standard uncertainty

In most cases, the best available estimate of the expectation or expected value µq of

a quantity q that varies randomly [a random variable], and for which n independent

observations qk have been obtained under the same conditions of measurement, is

the arithmetic mean or average of the n observations

𝑞� = 1𝑛∑ 𝑞𝑘𝑛𝑘=1 (E.2)

The individual observations 𝑞𝑘 differ in value because of random variations in the

influence quantities, or random effects. The experimental variance of the observa-

tions, which estimates the variance σ² of the probability distribution of q, is given by

𝑠𝑠²(𝑞𝑘) = 1𝑛−1

∑ (𝑞𝑗 −𝑛𝑘=1 𝑞�)² (E.3)

This estimate of variance and its positive square root s(qk), termed the experimental

standard deviation, characterize the variability of the observed values qk , or more

specifically their dispersion about their mean q�.

The best estimate of σ2(q�) = σ²/n, the variance of the mean, is given by

s2(q�) = s²(qk)/n (E.4)

Thus, for an input quantity Xi determined from n independent repetitions observa-

tions Xi,k, the standard uncertainty u(xi) of its estimate xi = X�i is u(xi) = s(X�i). For

convenience u2(xi) = s²(X�i) and u(xi) = s(X�i) are sometimes called a Type A variance

and a Type A standard uncertainty respectively.

1.3.2 Type B evaluation of standard uncertainty

For an estimate xi of an input quantity Xi that has not been obtained from repeated

observations, the associated estimated variance u2(xi) or the standard uncertainty

u(xi) is evaluated by scientific judgment based on all of the available information on

the possible variability of Xi. The pool of information may include

16


• Previous measurement data;

• Experience with or general knowledge of the behavior and properties of rele-

vant materials and instruments;

• Manufacturer’s specifications;

• Data provided in calibration and other certificates;

• Uncertainties assigned to reference data taken from handbooks.

The proper use of the pool of available information for a Type B evaluation of stand-

ard uncertainty calls for insight based on experience and general knowledge, and is

a skill that can be learned with practice. It should be recognized that a Type B evalu-

ation of standard uncertainty can be as reliable as a Type A evaluation, especially in

a measurement situation where a Type A evaluation is based on a comparatively

small number of statistically independent observations.

1.4 Determining combined standard uncertainty

1.4.1 Uncorrelated input quantities

This sub-clause treats the case where all input quantities are independent. When

two or more input quantities are related, input quantities are said to be interde-

pendent or correlated.

The standard uncertainty of y, where y is the estimate of the measurand Y and thus

the result of the measurement is obtained by appropriately combining the standard

uncertainties of the input estimates X1, X2... XN .This combined standard uncertainty

of the estimate y is denoted by uc(y).

The combined standard uncertainty uc(y) is the positive square root of the combined

variance u2c(y), which is given by

𝑢𝑐2(𝑦) = ∑ �𝜕𝑓𝜕𝑥𝑖�2

𝑁𝑖=1 𝑢2(𝑥𝑖) (E.5)

17


The partial derivatives 𝜕𝑓

𝜕𝑥𝑖are equal to 𝜕𝑓

𝜕𝑋𝑖evaluated at Xi = xi. These derivatives, often

called sensitivity coefficients, describe how the output estimate y varies with chang-

es in the values of the input estimates x1, x2, ..., xN. In particular, the change in y

produced by a small change Δxi in input estimate xi is given by (∆𝑦)𝑖 = �𝜕𝑓𝜕𝑥𝑖� (∆𝑥𝑖). If

this change is generated by the standard uncertainty of the estimate xi, the corre-

sponding variation in y is �𝜕𝑓𝜕𝑥𝑖�𝑢(𝑥𝑖). The combined variance u2c(y) can therefore be

viewed as a sum of terms, each of which represents the estimated variance associat-

ed with the output estimate y generated by the estimated variance associated with

each input estimate xi. Sometimes the sensitivity coefficients are noted ci.

1.4.2 Correlated input quantities

The previous Equation is valid only if the input quantities Xi are independent or un-

correlated. If some of the Xi are significantly correlated, the correlations must be

taken into account.

When the input quantities are correlated, the appropriate expression for the com-

bined variance u2c(y) associated with the result of a measurement is

𝑢𝑐2(𝑦) = ∑ ∑ 𝜕𝑓𝜕𝑥𝑖

𝜕𝑓𝜕𝑥𝑗

𝑁𝑗=1 𝑢�𝑥𝑖 ,𝑥𝑗�𝑁

𝑖=1 (E.6)

Or,

𝑢𝑐2(𝑦) = ∑ �𝜕𝑓𝜕𝑥𝑖�2

𝑁𝑖=1 𝑢2(𝑥𝑖) + 2∑ ∑ 𝜕𝑓

𝜕𝑥𝑖

𝜕𝑓𝜕𝑥𝑗

𝑁𝑗=𝑖+1 𝑢�𝑥𝑖 ,𝑥𝑗�𝑁−1

𝑖=1 (E.7)

Or,

𝑢𝑐2(𝑦) = ∑ (𝑐𝑖)2𝑁𝑖=1 𝑢2(𝑥𝑖) + 2∑ ∑ 𝑐𝑖𝑐𝑗𝑢(𝑥𝑖)𝑢�𝑥𝑗�𝑁

𝑗=𝑖+1 𝑟�𝑥𝑖 ,𝑥𝑗�𝑁−1𝑖=1 (E.8)

Where xi and xj are the estimates of Xi and Xj and u(xi, xj) = u(xj, xi) is the estimated

covariance associated with xi and xj. The degree of correlation between xi and xj is

characterized by the estimated correlation coefficient

18


𝑟�𝑥𝑖 ,𝑥𝑗� =𝑢�𝑥𝑖,𝑥𝑗�

𝑢(𝑥𝑖)𝑢�𝑥𝑗� (E.9)

Where r(xi, xj) = r(xj, xi), and −1 ≤ 𝑟�𝑥𝑖 ,𝑥𝑗� ≤ 1. If the estimates xi and xj are inde-

pendent, r(xi, xj) = 0, and a change in one does not imply an expected change in the

other.

There may be significant correlation between two input quantities if the same meas-

uring instrument, physical measurement standard, or reference datum having a sig-

nificant standard uncertainty is used in their determination.

Correlations between input quantities cannot be ignored if present and significant.

The associated co-variances should be evaluated experimentally if feasible by vary-

ing the correlated input quantities, or by using the pool of available information on

the correlated variability of the quantities in question (Type B evaluation of covari-

ance). Insight based on experience and general knowledge is especially required

when estimating the degree of correlation between input quantities arising from the

effects of common influences, such as ambient temperature, barometric pressure,

and humidity. Fortunately, in many cases, the effects of such influences have negli-

gible interdependence and the affected input quantities can be assumed to be un-

correlated. However, if they cannot be assumed to be uncorrelated, the correlations

themselves can be avoided if the common influences are introduced as additional

independent input quantities.

1.5 Probability vocabulary

Distribution function: Function giving, for every value, the probability that the ran-

dom variable X be less than or equal to:

𝐺𝑥(𝜉) = Pr (𝑋 ≤ 𝜉) (E.10)

Probability density function PDF: Derivative, when it exists, of the distribution func-

tion

19


𝑔𝑥(𝜉) = 𝑑𝐺𝑥(𝜉)/𝑑𝜉 (E.11)

Note:𝑔𝑥(𝜉)𝑑𝜉 is the probability element

𝑔𝑥(𝜉)𝑑𝜉 = 𝑃𝑟(𝜉 < 𝑋 < 𝜉 + 𝑑𝜉) (E.12)

Normal distribution: Probability distribution of a continuous random variable X hav-

ing the probability density function

𝑔𝑥(𝜉) = 1𝜎√2𝜋

exp �− 12�𝜉−𝜇

𝜎�2� (E.13)

Expectation for a continuous random variable X characterized by a PDF 𝑔𝑥(𝜉),

𝐸(𝑋) = ∫ 𝜉𝑔𝑥(𝜉)𝑑𝜉∞−∞ (E.14)

The expectation of the random variable Z = F(X), for a given function F(X), is

Variance: For a continuous random variable X characterized by a PDF 𝑔𝑥(𝜉)

𝑉(𝑋) = ∫ [𝜉 − 𝐸(𝑋)]2𝑔𝑥(𝜉)𝑑𝜉∞−∞ (E.15)

Standard deviation: Positive square root of the variance

References:

[1] JCGM 100:2008: Evaluation of measurement data – Guide to the expression of uncertainty in measurement (ISO/IEC Guide 98-3)

[2] JCGM 101:2008 Evaluation of measurement data – Supplement 1 to the "Guide to the ex-pression of uncertainty in measurement" – Propagation of distributions using a Monte Carlo method (ISO/IEC Guide 98-3-1)

[3] ISO 3534-1:1993: International vocabulary of basic and general terms in metrology, second edition, 1993, International Organization for Standardization (Geneva, Switzerland)

20


Chapter 2: Uncertainties in wind assessment

2.1 General

In its most general form, the combined standard uncertainty of the power in

bin i, uc,ican be expressed by

𝑢𝑐,𝑖2 = ∑ ∑ 𝑐𝑘,𝑖𝑢𝑘,𝑖𝑐𝑙,𝑖𝑢𝑙,𝑖𝜌𝑘,𝑙,𝑖,𝑗

𝑀𝑙=1

𝑀𝑘=1 (E.16)

Where

ck,i is the sensitivity factor of component k in bin i;

uk,i is the standard uncertainty of component k in bin i;

M is the number of uncertainty components in each bin;

ρk,l,i,j Is the correlation coefficient between uncertainty component k in bin i

and uncertainty component l in bin j (in the expression the component

k and l are both in bin i).

The uncertainty component is the individual input quantity to the uncertainty

of each measured parameter. The combined standard uncertainty in the esti-

mated annual energy production, uAEP, can in its most general form be ex-

pressed by

𝑢𝐴𝐸𝑃2 = 𝑁ℎ2 ∑ ∑ ∑ ∑ 𝑓𝑖𝑐𝑘,𝑖𝑢𝑘,𝑖𝑓𝑗𝑐𝑙,𝑗𝑢𝑙,𝑗𝜌𝑘,𝑙,𝑖,𝑗𝑀𝑙=1

𝑀𝑘=1

𝑁𝑗=1

𝑁𝑖=1 (E.17)

Where

Fi is the relative occurrence of wind speed between Vi–1 and Vi:F (Vi)–F

(Vi–1) within bin i;

F (V) Is the Rayleigh or site specific cumulative probability distribution

function for wind speed;

N is the number of bins;

21


Nh is the number of hours in one year ≈8760 h.

It is seldom possible to deduce explicitly all the values of the correlation coef-

ficients ρk,l,i,j and normally significant simplifications are necessary. To allow

the above expressions of combined uncertainties to be simplified to a practical

level, the following assumptions may be made:

– uncertainty components are either fully correlated (ρk,l,i,j=1, implying

linear summation to obtain the combined standard uncertainty ) or inde-

pendent (ρk,l,i,j= 0, implying quadratic summation, i.e. the combined

standard uncertainty is the square root of summed square s of the uncer-

tainty components );

– all category A uncertainty components are mutually independent and cat-

egory A and B uncertainty components are independent (they are either

from the same bin or they are from different bins), while category B uncer-

tainty components are mutually fully correlated (e.g. uncertainty in power-

transducer in different bins).

Using these assumptions, the combined uncertainty of the power within a bin,

uc,i, can be expressed by

𝑢𝑐,𝑖2 = ∑ 𝑐𝑘,𝑖

2 𝑠𝑠𝑘,𝑖2𝑀𝐴

𝑘=1 +∑ 𝑐𝑘,𝑖2 𝑠𝑠𝑘,𝑖

2𝑀𝐵𝑘=1 = 𝑆𝑖2 + 𝑢𝑖2 (E.18)

Where

MA is the number of category A uncertainty components;

MB is the number of category B uncertainty components;

sk,i is the category A standard uncertainty of component k in bin i;

Si are the combined category A uncertainties in bin i;

Ui are the combined category B uncertainties in bin i.

It should be noted that uc,i2 is not independent of bin size due to the depend-

22


ency of sP,ion the number of data sets in the bin, see Annex.

The assumptions imply that the combined standard uncertainty in energy pro-

duction, uAEP, is:

𝑢𝐴𝐸𝑃2 = 𝑁ℎ2 ∑ 𝑓𝑖2 ∑ 𝑐𝑘,𝑖2 𝑠𝑠𝑘,𝑖

2𝑀𝐴𝑘=1

𝑁𝑖=1 +𝑁ℎ2 ∑ �∑ 𝑓𝑖𝑐𝑘,𝑖𝑢𝑘,𝑖

𝑁𝑖=1 �2𝑀𝐵

𝑘=1 (E.19)

The significance of the second term in this equation is that each individual cat-

egory B uncertainty component progresses through to the corresponding AEP

uncertainty, applying the assumption of full correlation across bins for the in-

dividual components. Finally, the cross-bin combined uncertainty components

are added quadratically in to a resulting AEP uncertainty.

Furthermore, certain components of category A uncertainty can not necessari-

ly be conveniently derived or estimated on a bin-wise basis. For example the

climatic variation and site calibration method category A components which

may have been derived by a sensitivity analysis on the AEP calculation. In this

case, these components should be added quadratically to the resulting AEP

uncertainty. Refer to equation E.8 for an example of this.

In practice, it may not be convenient to sum category B uncertainty components

across the bins before they are individually combined. An approximation, all

owing the category B uncertainty components to be combined within bins be-

fore they are combined across bins (i.e. siand ui can be used), leads to the

more convenient expression:

𝑢𝐴𝐸𝑃2 = 𝑁ℎ2 ∑ 𝑓𝑖2 ∑ 𝑐𝑘,𝑖2 𝑠𝑠𝑘,𝑖

2𝑀𝐴𝑘=1

𝑁𝑖=1 +𝑁ℎ2 �∑ 𝑓𝑖��∑ 𝑐𝑘,𝑖

2 𝑢𝑘,𝑖2𝑀𝐵

𝑘=1 �𝑁𝑖=1 �

2

=

𝑁ℎ2 ∑ 𝑓𝑖2𝑆𝑖2𝑁𝑖=1 +𝑁ℎ2�∑ 𝑓𝑖𝑢𝑖𝑁

𝑖=1 �2(E.20)

The uAEP, obtained by this expression is always equal to or larger than that ob-

tained using equation (E.12).

23


2.2 Expanded uncertainty

The combined standard uncertainties of the power curve and the AEP may addition-

ally be expressed by expanded uncertainties. Referring to the ISO guide and assum-

ing normal distributions, intervals having levels of confidence shown in Table E.1

can be found by multiplying these combined standard uncertainties by a coverage

facto r also shown in the table.

Table 1: Expanded uncertainties

Level of confidence

Coverage factor

68,27

90

95

95,45

99

99,73

1

1,645

1,960

2

2,576

3

References:

[1] IEC 61400-1: Wind turbines – Part 1: Design requirements [2] IEC 61400-12-1 Wind turbines – Part 12-1: Power performance measurements of electricity

producing wind turbines

24


Chapter 3: Lahemyer Uncertainties Analysis Tool and the

Variability Analysis tool

3.1 Investigation of the Lahemyer International Uncertainties Analysis Tool

3.1.1 Wind-related uncertainty

3.1.1.1 Measurement Wind Speed (cup anemometer)

This uncertainty parameter covers amongst others the abrasion (e.g. the anemome-

ter is covered by sand, dirt, etc.), the technical characteristics and the calibration

procedure of the sensors.

The anemometers have to be calibrated preferably according to the MEASNET stand-

ards. A non-MEASNET calibration is considered less certain than a calibration fol-

lowing the MEASNET standards. In such a case, a higher calibration uncertainty has

to be considered.

The total uncertainty calculated for the wind speed cup anemometer is usually situ-

ated in the range of 1%-4%.

In order to calculate this total uncertainty the following sub uncertainties are used:

• Anemometer condition (abrasion), it indicates the physical conditions of the

measurement instrument (e.g. the anemometer is covered by sand, dirt, etc.), the

value of this uncertainty is in general considered in the range of 1.0 - 2.5 %.

• Anemometer measuring uncertainty, this uncertainty designates if the measure-

ment instrument was calibrated or not, the value of this uncertainty is generally

considered to be in the range of 0.9 - 3.0 %. Two main cases are to be consid-

ered:

25


o If the anemometer is without calibration, then the uncertainty is to be

found in the anemometer brochures, generally its value is in the range of

1.5 - 3.0%)

o If the anemometer is with calibration, then the uncertainty can be calcu-

lated from calibration results, generally its value is in the range of 0.9-

1.5%)

• Data logging and resolution, this uncertainty outlines the uncertainties regarding

the sampling interval in the data logger, the data logger type etc. The value of

this uncertainty is in general considered in the range of 0.1 - 1.0 %

• Quality of correction method. If any correction of systematical errors in the

measurements is applied to meet the calibration data logger setting (Slope +

Offset), uncertainties related to this correction should be taken in consideration.

A value in the range of 0.0 - 1.0 % should be estimated. See also the data integ-

rity uncertainty.

3.1.1.2 Measurement Wind Direction (wind vane)

This uncertainty designates the influence of the wind direction measurements on

the frequency distribution. This uncertainty parameter covers amongst others the

offset to the North of the sensor in respect to the real geographic North. For the

measurement systems, state-of-the-art devices have to be used in order to limit the

uncertainties.

In practice, a total Wind vane measurement uncertainty between 1.0 - 1.5 % is to be

considered.

3.1.1.3 Mounting

This uncertainty category covers deviations of the measurement setup to the IEC

standard as well as influences to the measurements from the tower itself, booms

and mounting clamps.

26


A site visit carried out by experts is therefore recommended to check the vertical

alignment of the measurement masts and if the orientations of booms are in ac-

cordance to the standard specifications.

The anemometer mounting can introduce uncertainties equally as significant as

those caused by calibration and design. A total uncertainty between 1.1- 3.6 % is to

be expected for the category mounting. In order to calculate this total uncertainty

the following sub-uncertainties are used:

• Top Anemometer, Alternative mounted anemometers depending on how the

mounting is compliant with IEC 61400-12-1,the uncertainty in this sub category

varies in the range of 1.0 - 3.0 %.

• Deviation to vertical alignment depending on how the mounting is compliant

with IEC 61400-12-1, the uncertainty in this sub category varies in the range of

0.0 - 1.0 %.A deviation of+/-5° from a setup of 90° vertically is considered ac-

ceptable.

• Influence of the Mast, this uncertainty concerns the orientation of the booms in

respect to the main wind direction and the type of mast (tubular/lattice tower). It

varies in the range of 0.2 - 1.0 %.

• Influence of the booms and clamps, It is quite clear that if an anemometer is op-

erating in the wake of the host meteorological mast then its indication will not

be a true reflection of the free field wind speed. Less obvious is the fact that flow

distortion upstream of the tower or above amounting boom can be significant

and adequate separation must be allowed between the rotor and the host struc-

ture to keep such effects to an acceptably low level. This uncertainty varies in the

range of 0.2 - 1.0 %. Depending on how the mounting is compliant with IEC

61400-12-1, the uncertainty due to the influence of the clamps can be estimat-

ed in the range of 0.0 - 1.0 %.

27


3.1.1.4 Data Processing

• Data Integrity, this subcategory of uncertainty is related to the measurement

campaign traceability and it is meant to identity how well the measurement

equipment is documented. Normally a value between 0.0 - 5.0 % is to be consid-

ered

• Data Analysis, it covers the uncertainty in the data processing and it is applied

for parameters as duration of the measurement campaign, data coverage, meas-

urement consistency, data processing and the methodology in fitting the actual

wind frequency distribution to Weibull distribution.

Due to the application of MCP or other procedures to complete the statistics, an

additional uncertainty is to be included in the assessment. An uncertainty be-

tween 1.1 - 6.1 % has to be calculated and it is considered to sufficiently cover

any deviations or errors related to data processing. This uncertainty includes the

following sub-uncertainties:

o Duration of the measurement campaign can originate in an uncertainty

estimated to be between 1.0 - 4.0%. Normally a duration higher than 3

years implies an uncertainty of 1%, else if the duration is superior than 1

year the uncertainty is to be as high as 2.0%, in some special cases and

when there is the possibility to use other data sources the data of a dura-

tion less than 1 year can be used with an uncertainty of 4.0%. If no data

source with duration higher than 1 year is available, no final wind study

should be prepared.

o Data Coverage, this uncertainty concerns the data gaps and the measure-

ment material availability. Generally it varies in the range of 0.0 - 1.5 %.

The data coverage should be 100% or at least higher than 95%. In some

special cases withdata coverage below 95%, in such a case the uncertainty

is higher. The data coverage of each month should be higher than 75%.

o Consistency of measured data, concerns the Change on the measurement

setup and equipment, or relocation of the Met-Mast. In general a value

between 0.0 - 1.5 % should be considered.

28


o Data synthesis, this uncertainty is sometimes also called internal adjust-ments uncertainty. It should be considered when data generation through MCP (e.g. Alkinoos) (for more information see [4]), has to be made to complete wind speed and direction data, and to substitute few implausible values detected in the time series. An uncertainty between 0.0 - 3.0 % is to be applied for this uncertainty. In the special cases mentioned in the previous paragraphs, generally internal adjustment is needed. The im-portance of this uncertainty dependents on the aspects mentioned below:

Overlapping periods, amount of predicted / reconstructed values, Corre-lation coefficients, etc.

Wind Shear extrapolation, a sub uncertainty between 0.0 - 2.0 % can be considered

If the extrapolation was not done by flow model Terrain complexity If the measurement of wind speed took place in at a height superior than

2/3 of the Hub Height Wind Frequency Distribution and Weibull Fit, a sub uncertainty between

0.5 - 2.0 % can be considered Compare Vmeasured vs. Vweibull Compare different Weibull fits regarding applicability

• Long-term Correlation, Uncertainty of the long-term assessment considers qual-

ity, consistency and representativeness of the reference data as well as the cor-

relation between site and reference data and the uncertainty of the applied

methodology.

For instance, the number of NCEP grid points and meteorological stations that

have been considered and the quality of their correlation with the on-site wind

measurements are among the important aspects to be taken in consideration

when assessing this uncertainty.

The uncertainty of the long-term correlation is to be estimated within the range

of 0.7 - 6.4 % in terms of standard deviation to the long-term adjustment of the

short term wind data. This uncertainty can be broken down into the sub-

categories:

29


o Representativeness of long-term data, this uncertainty varies between 0.2 - 2.5 %. The value depends on how much the source of the reference data is representative of the site (the distance, the topography etc.)

o Quality and Consistency of long term data, this uncertainty concerns the data coverage, the measurement period, if the location of the source of the data has been changed in the measurement period. In general the val-ue of this uncertainty is in the range of 0.0 - 4.0 %.

o Representativeness of long-term period, depending on how long the total period of the reference data was (10a, 20a, 30a)this uncertainty varies in the range 0.5 - 2.5 %

o Correlation Met-Mast data vs. Reference, a good indicator is the correla-tion coefficient but also the scatter plot should be checked visually. These uncertainty values are generally estimated between 0.5 - 3.0 %.

o Applied Methodology, depending on the methodology used (Linear re-gression MCP, Matrix MCP, Index MCP etc., see [4]) the uncertainty related is estimated to be in the range 0.0 - 2.0 %.

• Variability of the prediction horizon, for a certain period of interest the wind

speed may also fluctuate in the long-term. The uncertainties in terms of stand-

ard deviation of this fluctuation around the long-term average wind velocity for

periods of interest of 1 and 10 years have to be determined.

3.1.2 Energy-related uncertainty

As the wind speed related uncertainties were discussed in Section 3.1., the following

uncertainties allocated to the flow model and mathematical algorithms lead to a re-

duction of the calculated energy yield at higher confidence levels. They are quanti-

fied according to international practice.

3.1.2.1 Flow modeling

The uncertainty in the mathematical wind flow modeling is estimated to be between

3.2 and 12.4 % in terms of standard deviation. This value includes uncertainties in

roughness, orography (topographical description) as well as the transfer of wind

30


conditions from the measurement mast to the turbine positions. In the breakdown

of this category, the following sub-uncertainties are found:

• Topographical complexity and accuracy of data, this sub-category characterizes

the complexity of the terrain, the accuracy of topographical description (rough-

ness & orography). Typical value for equidistance between high contour lines of

10m and semi-complex terrain is found between 3 and 6 %. When the maps res-

olution used is low or the terrain is complex, the uncertainty in this sub-category

is high.

• Transfer of wind data to hub height, this uncertainty is applicable if an extrapo-

lation is done by the flow model and not during the data processing, then during

the adjustment of the model at the mast position this uncertainty can be derived.

Its value varies in the range of 0.0 - 5.0 %.

• Limitation on applied flow model, this uncertainty considers the exceeding of the

limitations of the flow model. For example, when using WEG (Wind Energy Gen-

erator) with hub heights above 100m and modeling with WAsP, un uncertainty of

2.0% should be considered. Normally the value of this uncertainty is between 0.0

and 2.0 %

• Thermal stratification, when the vertical stratification of the atmosphere is stable

and the wind speeds are low, this uncertainty is high.Stable stratifications are

common during clear and calm night, associated with marine environments near

cold water currents. Unstable stratification of the atmosphere is common in hot

terrain surfaces during warm days. This uncertainty takes values between 1.0

and 5.0%

• Transfer of wind data to turbine position, depending on the distance between

the Met-Mast and the WTG positions this uncertainty varies in the range of 0.0 -

8.0 %.

31


3.1.2.2 Wake Effects

The uncertainty related to the Wake effect is estimated to be in the range of 0.0 -

10.0 %. Taking in consideration both the internal wake effects and the wake effects

from the nearby existing wind farm as it follows:

• New and existing WTGs, this uncertainty concerns the estimation of the losses

caused by the WTGs under assessment (new) and by non-under-assessment

WTGs (existing). Existing WTGs are either already operating or under installation.

In the flow modeling new and existing WTGs have to be considered. The loss

value is calculated by the wake model (e.g. "Input_WindPRO_Results"). The value

of this uncertainty varies in the range of 1.0 - 15.0 %.

• Future wake effects, this uncertainty accounts the subsequent losses from au-

thorized for construction WTGs which will be located within a distance less than

5km to the site under study. If there is no evidence of wind farm development,

then 0.0 % should be considered for this uncertainty. The value of this uncertain-

ty varies in the range of 0.0 - 2.0 %.

3.1.2.3 Power curve

A calculated power curve is usually used for the estimation of the AEP; this power

curve is provided by the manufacture under a guarantee of performance. However

this guarantee is site-specific and it is only valid and applicable for similar sites like

where the measurement of the power curves has been performed. The uncertainty

related to this category is generally estimated between 4.0 and 10.4 %. The main

subcategories included in the breakdown of this category are:

• Measurement Uncertainty, this uncertainty value is normally found in the power

curve measurement report (PPT, Power Performance Test), it concerns the AEP

and its typical range is 4- 10%. The higher the wind speeds on site (annual aver-

age) the lower the uncertainty for this sub category. If no PPT is available for the

concerned WTG, then the uncertainty from a similar WTG PPT of the same manu-

facturer can be used. Depending on the annual wind speed average of the site, if

32


no data is available for the site under study, 7% is a good estimation if the site

has low annual wind speed average (less than 6m/s at hub height) and 5% is a

good estimation if the site has a high annual average wind speed (more than

8m/s at hub height).

• Deviations from IEC Guideline, this uncertainty is related to there being any devi-

ation of the Power Curve measurement from the IEC 61400-12-1that is docu-

mented in the PPT. Normally the value of this uncertainty is between 0.0 and 2.0

%.

3.1.2.4 Losses (Uncertainty of loss estimation)

As the values of the losses are generally approximated and/or generic values, each

loss position is subject to an uncertainty in its assessment. Below is a list of the

subcategories found in the losses uncertainties.

• Availability o Turbine (unavailability + scheduled maintenance), losses that are general-

ly mentioned in the TSA (Turbine Supply Agreement). If no TSA available and no records from similar turbine of the same manufacturer a generic value is to be used. Else the following formulas are to be used: Unavaila-bility = 100% -Turbine contractual availability % (as specific in TSA). Scheduled maintenance = maximum hours of scheduled maintenance consider available (see Maintenance Agreement).

o Balance of Plant (substation and internal cabling), losses due to downtime in components between the turbine main breaker to an including project substation transformer and project specific transmission line.

o External grid, losses due to downtime of power grid external to the wind power facility

o (Turbine + BoP) during 1st operational year, Other availability losses not accounted for above or in other categories below

• Underperformance (deviation to advertised power curves) o Power performance guarantee % (as specified in TSA), losses due to the

turbine not producing to its advertised power curve.

33


o High wind speed hysteresis, losses due to shut down between high wind cut out and subsequent cut back in.

• Electrical o Electrical losses, it is recommended to request the Client for the electrical

losses calculations. Losses between the low‐voltage terminals of the tur-bine (where the output is measured in a power curve test) and the revenue meter located on the high‐voltage side of the on‐site substation, includ-ing: transformers; collection wiring; substation; transmission.

• Environmental losses, it is to be noted that some of the environmental losses can also be covered under availability

o Performance degradation not due to icing, losses due to blade degrada-tion over time and blade soiling. Only in areas with extreme conditions of dust (like MENA region) a value of 5.0% can be considered. Intervals of blade cleaning are important (6 months-1year). Stall regulated turbines in MENA region could have losses above 20% if blade cleaning is not done regularly (every 3 months).

o Performance degradation and shut down due to icing, Losses due to temporary ice accumulation on blades, reducing their aerodynamic per-formance, and sometimes due to icing. If WTG is equipped with ECWP (Ex-treme Cold Weather Package equipment), than losses due to icing should be neglected.

o Shutdown due to lightning and hail, losses due to turbine shutdowns (re-quested by turbine controller, or by an operator) associated with lightning and hail.

o High and low temperature, losses due to ambient temperature outside the turbine's operating range. Estimate by neglecting the turbine production for time periods where ambient temperature was outside turbine's opera-tional range.

o Site access, Losses due to difficult site access for the performance of maintenance due to ice, snow or remote location.

• Curtailment o Wind sector management, losses due to commanded shutdown of closely

spaced turbines to reduce physical loads on the turbines. If there is no ev-idence of necessary sector management, then these losses are to be ne-glected.

34


o Power curtailment, losses due to nominal power curtailment of the wind farm or turbines.

o Shadow flicker mitigation, losses due to curtailments to avoid shadow flickering effects on sensitive areas.

o Noise mitigation, losses due de-rating of wind turbine Power Curve to comply with noise limitations.

o Birds, bats and other animal protections, losses due to curtailments due to birds, bats and other animals

o Grid curtailment and ramp-up-rate, Losses due to limitations on the ex-ternal grid, both due to limitations on the amount of power delivered at a given time, as well as limitations on the rate of change of power deliver-ies.

• PPA curtailment (Power Purchase Agreement), losses caused if the power pur-chaser decides to not take the power generated by the facility.

• Through the whole process of wind assessment a number of uncertainties are

present. The idea of the uncertainty analysis is to properly gather these different

uncertainties in one overall uncertainty, with respect to the statistics background

of the notion of uncertainty.

35


3.2 Wind production variability

In this work the uncertainty of the AEP calculated during the wind study will be faced

up to the “actual” variability manifested during the production period. For conven-

ience this “actual” variability will be called variability.

To simplify the concept of the approach utilized in this work, it may be adequate to

regard the Wind Farm as a measurement setup for measuring the AEP; this setup is

recording measurements with a well-defined time stamp, and consisting of many

measuring devices (wind turbines) installed at the site of interest. After getting the

records every time-stamp, the AEP is scaled accordingly to the number of devices

and the measurement period. Accordingly, this variability reflects the same charac-

teristics of the uncertainty.

This overall variability, as the definition implies, is composed of two variabilities:

temporal variability and spatial variability.

• The temporal variability, this variability includes the instantaneous variation of

the wind resource. It includes also the seasonal and the inter-annual variability

in the wind resource. Indeed, since the production data used in this study is

monthly records, the estimated AEP based on the data set can vary dramatically,

depending on the representativeness of the data set and on the data cover of the

recorded production data. However, it is assumed that a one year production da-

ta can overtake the seasonal effect. More than one year data production can

overtake the inter-annual effect.

• The spatial variability, this variability concerns the variations in the AEP between

all the turbines in the Wind Farm. Depending on the position of each turbine

within the wind farm and the performance of each turbine during the production

period, the estimated AEP based on the data set can vary, but this variation is

normally smaller.

36


As the monthly production data of the turbines are very well correlated, the square

root of the sum of covariance equals the square of the sum of the standard devia-

tion for the spatial variation.

Concerning the monthly spatial variation, this is considered depending on the wake

effect and the availability of the turbines and the internal grid, under the assump-

tion that the spatial variation independent from the temporal variation, and then it

can be considered constant. In fact this variability reflects somehow the perfor-

mance of the park, since if all the turbines work in the same conditions and without

any wake effect this variability tends to zero. Therefore it can be stated that this

variability can be ameliorated within a good O&M and it may be interesting to figure

out statistically its relationship with the availability of the turbines and of the park.

The temporal variation within the months can be predicted statistically, since it in-

cludes mainly the variation caused by the seasonal effect and inter-annual variation

of the wind resources. However, because of the whole wind farm availability, if all

the turbines have some problems in an extended time period, it can effect the over-

all production of a month and therefore the temporal variation even if such effect is

not detected by the spatial variability, For this reason, the information about the

wind turbine status of the wind farm should be checked carefully, especially when

there is a remarkable deviation of the AEP. Such a case is often observed in the first

year of operations, and may cause this year in the data set to be ignored.

Spatial variability: for every month the production (MEP) of all turbines is correlated

Variability temporal: for every turbine the MEP of all months is correlated

In the comparison tool, four methods have been used to calculate the uncertainty:

• First method is simply to calculate the standard deviation of the monthly energy

production of a set of turbines for example

37


• Second method is to calculate the different standard deviation and then average

them and scale the average to AEP level

• Third method is to sum the root square of the individual standard deviations

• Fourth method consists of using the correlation and the covariance matrices

it is assumed that the overall variation of the AEP of a wind farm is composed of a

spatial variation and a temporal variation and these two variations are independent,

nevertheless that is not always true, because it may be that some seasonal effects

favoring condition directionally and the production of wind turbine may also change.

To assess that it is important to have wind directions records in the same period of

data production to study statistically if any dependence is existing (bins method,

see chapter II). This assumption allows us to add the variances and to deduct the

overall variance for every month.

To include all independencies in the production data, the overall variability was cal-

culated using the correlation and the covariance matrices. The aim is to have a

standard deviation that takes also in consideration to the correlation between the

turbines of the park and between the months of the year. These matrices are based

on the production data of all the available months. It was also defined as an annual

variation for the farm with production data for more than one year.

For the farms where no data is available for individual turbines, the monthly average

of the production of all the farms is used. There are two cases: the case where the

production data represents the sum of the individual production of each turbine,

and the case where the production data is recorded in the connection point with the

grid. For this kind of production data, it is not possible to calculate the spatial varia-

tion, and only the temporal variation is calculated.

When the production data contains only the overall data of the farm without the in-

dividual production data of every turbine, in this case the square root of the sum of

38


the variances of each turbine for every month of the farm can’t be calculated be-

cause of a lack of data and the standard deviation of the monthly production equals

the square root of the sum of the variance of the monthly production of every tur-

bine which is in this case like only one wind Turbine.

It is to be noted that when the number of the months increases (the considered pe-

riod), the uncertainty tends to decrease because more knowledge is brought by

more data. For the small periods the uncertainty increases gradually, because of the

data set representativeness.

In order to be consistent in the comparison of variability of post-construction ener-

gy yield and pre-construction energy related uncertainty, total energy related uncer-

tainties in the wind study will be scaled to meet the same time period of the evalua-

tion of variability.

The model of the variability and the uncertainty are described by the following dia-

grams.

Figure 3: Diagram of the wind study uncertainty calculation

39


Figure 4: Diagram of the energy production variability calculation

The plausibility check aims to assess the consistency of the model with respect to

expected behavior. Many aspects should be assessed such as the fact that the over-

all variability should reflect the reality in a statistical sense, for example it is ex-

pected to have less variability for long periods of data production and vice versa,

also the seasonal effect should be consistent from one year to another, also that the

spatial variability should be smaller than the temporal variability.

40


References:

[1] IEC 61400-1: Wind turbines – Part 1: Design requirements [2] Wind speed measurement and use of cup anemometry- . 1st Edition. International Energy

Agency. 1999. [3] MEASNET - Evaluation of Site-Specific Wind Conditions - Version 1, November 2009. [4] M. L. Thøgersen et al., Measure-Correlate-Predict Methods: Case Studies and Software Im-

plementation, EWEC, 2007 [5] WAsP-CFD Validation Report, Lasse Svenningsen, PhD, EMD ([email protected]) [6] EFFECTS OF TUBULAR ANEMOMETER TOWERS ON WIND SPEED MEASUREMENTS, Jack Kline,

RAM Associates, [7] Analyse und Evaluierung der Unsicherheiten bei der Energieertragsprognose von WEA, Dip-

lomarbeit, Hochschule Darmstadt, Fachbereich EEU, Ahmed Mahmoud Ould Sidahmed [8] On the Uncertainty of Wind Power Predictions—Analysis of the Forecast Accuracy and Statis-

tical Distribution of Errors, Matthias Lange, DOI: 10.1115/1.1862266 [9] Large Scale Wind Energy Potential Evaluation in Complex Terrain, Internal publication,

Lahmeyer International GmbH [10]The NumericalWind Atlas - the KAMM/WAsP Method, Helmut P. Frank, Ole Rathmann, Niels

G. Mortensen, Lars Landberg, Risø National Laboratory, Roskilde, Denmark June 2001 [11]WIND RESOURCE ASSESSMENT A Practical Guide to Developing a Wind Project Michael C.

Brower AWS Truepower, LLC, Albany, New York, USA, ISBN 978-1-118-02232-0 [12]Guidelines for design of wind turbines DNV/Risø pages [13]Baptiste Ruille, How do we measure the wind on a site, Theolia, May 2011 [14]Validation of wind turbine wake models Using wind farm data and wind tunnel measure-

ments, Douwe J. Renkema, June 11, 2007, Faculty of Aerospace Engineering • Delft Universi-ty of Technology

[15]Comparing existing wake models with CFD offshore, Rebecca Barthelmie et al, Project Up-Wind, Deliverable 8.2

[16]Søren Ott, Jacob Berg and Morten Nielsen, Linearised CFD Models for Wakes, Risø National Laboratory, Roskilde, Denmark, December 2011

[17]J.F. Ainslie, Calculating the flow field in the wake of wind turbines, Journal of Wind Engineer-ing and Industrial Aerodynamics, 27 (1988) 213-224 213 Elsevier Science Publishers B.V., Am-sterdam -- Printed in The Netherlands

[18]Lars Landberg, Wind Resources and Wakes, Vindforsk projects, a survey of the development and research needs. Elforsk, June 2012 // 12_38_report.pdf

[19]Philippe Beaucage et al. Overview of six commercial and research wake models for large off-shore wind farms, Proceedings ewea, 2012, //926_EWEA2012presentation.pdf

[20]B. Buffard, Regional Wind Speed Evolution Identification and Long- term Correlation Applica-tion, DEWI MAGAZIN NO. 41, AUGUST 2012

[21]http://www.emd.dk [22]Aviation Weather For Pilots and Flight Operations Personnel FAA Advisory Circular AC 00-6A

Revised 1975 [23]http://www.cpc.ncep.noaa.gov/products/wesley/reanalysis.html

41


[24]Agnès FONTAINE, Peter ARMSTRONG, UNCERTAINTY ANALYSIS IN ENERGY YIELD ASSESS-MENT, proceedings EWEA, Milano Convention Centre, Milan, Italy 7-10 May 2007

[25]Christian Léger et al., Évaluation de l’incertitude sur le calcul de production d’énergie éolienne, The Fourth Montreal Industrial Problem Solving Workshop took place from August 15 to 19, 2011

[26]Matthew A. Lackner et Al, Uncertainty Analysis in Wind Resource Assessment and Wind En-ergy Production Estimation, American Institute of Aeronautics and Astronautics, Aerospace Sciences Meetings, 2007

[27]J. M. Marco et al. How to determine the Portfolio Effect based on wind regime dependency: European examples, EWEC Proceedings, Marseille, 2009

[28]Guidelines for Design of Wind Turbines, publication from DNV/Risø, Second Edition, Denmark 2002, ISBN 87-550-2870-5

[29]J.T.G Pierik, et al, European wind turbine standards II (EWTS-II), Wind energy for the next mil-lennium. Proceedings. ed. / E.L. Petersen; P. Hjuler Jensen; K. Rave; P. Helm; H. Ehmann. London: James and James Science Publishers, 1999. p. 568-571.

[30]U. Bunse, H. Mellinghoff, O. Haack, Uncertainty of annual energy production for a specific turbine model based on a set of IEC 61400-12 measurements German Wind Energy Institute GmbH (DEWI).

42


Chapter 4: Uncertainties input data for the Model

The uncertainty analysis is executed as one main part of a wind resource assessment

and is of particular importance for risk analysis for investors and project develop-

ment. Understanding and accruably estimating the uncertainty can increase the cer-

tainty of the estimation of the annual energy production and therefore provide the

correct inputs for the feasibility study of any project development, and improve the

quality of overall energy yield predictions.

The uncertainties in the wind assessment have two main sources: the uncertainty in

measurement and the estimation in methodology, and the wind resource variability.

The first ones as was discussed in the present chapters reflect the errors originating

in equipment selection, measurement, analysis and modeling. The wind resource

variability nevertheless is an independent factor leading to uncertainty in long-term

wind resource estimations.

In this chapter, a general overview of the different sites investigated in this study is

presented. In this work, nine different farms were investigated, as well as, the main

input data of the wind assessment uncertainties analysis and the production data for

all the sites. Table 2 indicates the sites considered in this study.

Table 2: The list of the investigated sites

Farm Location Designation Site1 Italy Confidential Site 2 Italy Confidential Site 3 Italy Confidential Site 4 France Confidential Site 5 France Confidential Site 6 France Confidential Site 7 Portugal Confidential Site 8 Pakistan Confidential Site 9 Italy Confidential

43


4.1 General Information

The aim of this part is to give a comprehensive summary of every site to introduce

the main elements that characterize it. For the reason that every wind assessment is

very site specific, and within changes between sites the energy yield can change con-

siderably. Also this general information is important to find common traits between

sites and hence allow conclusions to be derived based on well-informed assump-

tions.

For every site, the same master schema is respected in all the following subtitles of

this chapter. Four tables outline, respectively, the main information elements of the

wind farm, the wind data sources, the modeling and the turbines installed. Two fig-

ures are then given to illustrate the nature of the site and the final layout of the tur-

bines.

The first table gives the number of wind turbines, their nominal power and their hub

height. The second table shows the wind data sources specifications such as the

Met-Mast height, the number of met-masts available, the distance between the main

Met-Mast and the position of the wind farm and the extension of the climate data

input which designates the period of measurement available.

In the third table some important information about other input data of the wind as-

sessment is given, for instance the farm nominal power, the type of terrain, the num-

ber of neighboring farms existing or authorized for construction, the source and type

of the wind data used for the long term correlation, the flow model and the type of

production data available. The fourth table outlines the characteristics of the turbines

installed at the site.

44


4.1.1 Site 1

Table 3: Wind farm data

Farm Site 1 Number of WTG 19 Nominal Power MW 2 Hub height m 78

Table 4: The wind data source

Farm Site 1 Mast with measurement height 50 m Number of Met-Masts 3 Distance from mast to WTGs On Site Extension of the climate data input 4 years 8 months

Table 5: Modeling characteristics

Farm Site 1 Farm Nominal Power 38 Terrain complexity flat, hilly Neighboring Farms 2 existing 2 authorized Data for the LT adjustment 4 NCEP/NCAR ts Flow modeling WAsP Production data Monthly

Table 6: Turbine specifications

Turbine specifications Manufacturer Gamesa Turbine Type G97 Nominal power [kWh] 2000 Rotor diameter [m] 97 Hub height [m] 78 Control system Pitch Cut-in and Cut-off wind speed [m/s] 3.0/25 Opertating range rotational speed [rpm] 9.0-19.0 Rated wind speed [m/s] 13 Number of WTG 19

45


Figure 5 : A map displaying the location of site 1

Figure 6: The final layout of the turbines in site 1

6 8

30 31 32 35 37 38 39 40 41

42

43 44 48

54 55

56 57

4560000

4562000

4564000

4566000

4568000

4570000

2569000 2570000 2571000 2572000 2573000 2574000 2575000 2576000 2577000 2578000

46


4.1.2 Site 2


Farm Site 2 Number of WTG 15 Nominal Power MW 2.5 Hub height m 100


Farm Site 2 Mast with measurement height 30 m.50 m Number of Met-Masts 2 Distance from mast to WTGs On site Extension of the climate data input 4 years


Farm Site 2 Farm Nominal Power 37.5 Terrain complexity flat (modestly hilly) Neighboring Farms 1 existing Data for the LT adjustment 1 meteorological stationand 1 NCEP/NCAR ts Flow modeling WAsP Production data Monthly


Turbine specifications No. of WTG 15 Type of WEC GE WIND ENERGY GE 2.5/100-

2.500/2.5MW/100m hub height Nominal Power [MW] 2 Hub height [m] 100 Rotor diameter 92.5 Wind Farm Capacity [MW] 37.5

47




1

2 3

4

5

6

7 8

9

10 11

12 13 14

15

4568500

4569000

4569500

4570000

4570500

4571000

4571500

2571200 2571400 2571600 2571800 2572000 2572200 2572400 2572600 2572800 2573000 2573200

48


4.1.3 Site 3




Farm Site 3 Mast with measurement height 30 m40 m53 m Number of Met-Masts 4 Distance from mast to WTGs On site Extension of the climate data input 6 years


Farm Site 3 Farm Nominal Power 96 Terrain complexity Complex Neighboring Farms 0 Data for the LT adjustment NCEP / NCAR wind data Flow modeling WAsP Production data Monthly


Turbine specifications No. of WTG 48

Type of WEC VESTAS V80-2.0MW/2MW/67m hub

height Nominal Power [MW] 2 Hub height [m] 67 Rotor diameter 80 Wind Farm Capacity [MW] 96

49




1 2 3 4

5 6

7 8

9 10 11 12 13 14 15

16 17

18 19

20

21 22 23

24 25

26 27 28 29

30 31 32

33 34

35

36

37 38

39 40 41

42 43

44 45

46 47 48

4392000

4393000

4394000

4395000

4396000

4397000

4398000

4399000

537000 538000 539000 540000 541000 542000 543000 544000 545000 546000 547000

50


4.1.4 Site 4


Farm Site 4 Number of WTG 5 Nominal Power MW 2 Hub height m 78.3


Farm Site 4 Mast with measurement height 49.5 Number of Met-Masts 1 Distance from mast to WTGs On site Extension of the climate data input 1 year


Farm Site 4 Farm Nominal Power 10 Terrain complexity flat, hilly Neighboring Farms 0 Data for the LT adjustment 2 Weather Station +NCEP Flow modeling WAsP Production data Monthly



Type of WEC Enercon E82-NH 78.3 m Nominal Power [MW] 2 Control system: Pitch Rotor diameter: 82 m Cut-in and Cut-off wind speed: 2 / 25 m/s Rated wind speed: 12-13 m/s Hub height

78.3 m

51




1

2

3

4

5

5366600

5366800

5367000

5367200

5367400

5367600

5367800

5368000

704300 704350 704400 704450 704500 704550 704600 704650 704700

52


4.1.5 Site 5




Farm Site 5 Mast with measurement height 85.0 m, 66.0 m and 42.0 m Number of Met-Masts 1 Distance from mast to WTGs On site Extension of the climate data input 1 year (16 months)


Farm Site 5 Farm Nominal Power 12 Terrain complexity flat, hilly Neighboring Farms 1 Data for the LT adjustment 1 Weather Station +NCEP Flow modeling WAsP Production data Monthly



Type of WEC Vestas V90 2.0MW Nominal Power [MW] 2 Control system: Pitch Rotor Rotor diameter: 90 m Cut-in and Cut-off wind speed: 3 / 23 m/s Rated wind speed: 13 m/s Hub height 80 m

53




1

2

3

4

5

6

5495400

5495600

5495800

5496000

5496200

5496400

5496600

5496800

5497000

639800 639900 640000 640100 640200 640300 640400 640500 640600

54


4.1.6 Site 6




Farm Site 6 Mast with measurement height 49.5 Number of Met-Masts 1 Distance from mast to WTGs On site Extension of the climate data input 1 year


Farm Site 6 Farm Nominal Power 11.5 Terrain complexity Complex Neighboring Farms 0 Data for the LT adjustment Weather Station Flow modeling WAsP Production data Monthly



Type of WEC ENERCON E-70 E4 Nominal Power [MW] 2.3 Control system: Pitch Rotor diameter: 71 m Cut-in and Cut-off wind speed: 2 / 25 m/s Rated wind speed: 16 m/s Hub height Pitch

55




1

2

3

4

5

4896000

4896200

4896400

4896600

4896800

4897000

4897200

4897400

954900 955000 955100 955200 955300 955400 955500

56


4.1.7 Site 7




Farm Site 7 Mast with measurement height 81, 40 m Number of Met-Masts 2 Distance from mast to WTGs On site Extension of the climate data input 8.5, 5.5


Farm Site 7 Farm Nominal Power 12 Terrain complexity Simple Neighboring Farms 0(repowering) Data for the LT adjustment NCEP/NCAR ts Flow modeling WAsP Production data Monthly



Type of WEC VESTAS V90-2,000/2MW/80m hub

height Nominal Power [MW] 2 Hub height [m] 80 Rotor diameter 90 Wind Farm Capacity [MW] 12 (limited to 10 - grid requirement)

57




1

2 3

4

5

6

4107400

4107600

4107800

4108000

4108200

4108400

4108600

4108800

4109000

4109200

4109400

509800 509900 510000 510100 510200 510300 510400 510500

58


4.1.8 Site 8




Farm Site 8 Mast with measurement height 31, 50 m Number of Met-Masts 2 Distance from mast to WTGs 1 On site, 1 22km Extension of the climate data input 4.5 months, 5 years


Farm Site 8 Farm Nominal Power 49.5 Terrain complexity Flat Neighboring Farms 2 authorized Data for the LT adjustment NCEP/NCAR Flow modeling WAsP Production data Monthly



Type of WEC Nordex S77 1500 kW 80 m hub

height Nominal Power [MW] 1.5 Hub height [m] 80 Rotor diameter 77 Wind Farm Capacity [MW] 49.5

59




1 7

8

19

21 22

23

24 25

14 15

16 20

26

27 28

29

32

12

13

17

18 30

31

2

3 4

5

6

9

10 11

33

396000

396500

397000

397500

398000

398500

399000

399500

400000

400500

401000

2771000 2771500 2772000 2772500 2773000 2773500 2774000 2774500 2775000

60


4.1.9 Site 9




Farm Site 9 Mast with measurement height N/A Number of Met-Masts 1 Distance from mast to WTGs On site Extension of the climate data input 2 years


Farm Site 9 Farm Nominal Power 34 Terrain complexity Complex Neighboring Farms 2 Data for the LT adjustment NCEP/NCAR Flow modeling WAsP Production data Monthly



Type of WEC Gamesa G58 - 850 kW

55 m hub height Nominal Power [MW] 0.85 Hub height [m] 55 Rotor diameter 58 Wind Farm Capacity [MW]

34

61




1 5

6

8

10 12

14 16 19

25 26

27 28

33 34

36 37 38

41 43

45 46 48

49

52 55 56

57 58

60 62

11 17

40

3

59

54

50

29

9

4119000

4119500

4120000

4120500

4121000

4121500

4122000

4122500

4123000

4123500

4124000

4124500

387500 388000 388500 389000 389500 390000 390500 391000

62


4.2 Wind Study Data

In this part, the results of the uncertainty analysis of the wind study are presented for

every site. The wind assessment methodology is fully described in many articles giv-

en in the references of chapter III. The description and the methodology for calculat-

ing the uncertainties in wind assessment are presented in chapter III.

Actually, the AEP calculated by the modeling software may include the wake effect

and in this case the wake effect is not to be considered in the energy losses. In the

case where the wake effect was not calculated in the software, it should be estimated

and considered in the calculation of the AEP NET, this AEP Gross is generally de-

scribed as Free Flow AEP Gross. The following table shows whether the AEP Gross

calculated for each farm includes the wake effect or not.

Table 39: The type of AEP Gross calculated for each farm

Farm AEP Gross Site 1 Free-Flow Site 2 Gross Site 3 Gross Site 4 Gross Site 5 Gross Site 6 Gross Site 7 Free-Flow Site 8 Free-Flow Site 9 Free-Flow

For every farm, six tables gather the relevant information needed and used as inputs

for the comparison tool. In the first table the uncertainties regarding the wind meas-

urement are shown and in the second table the data processing uncertainties are

combined with them. In the third table, the results of converting these wind related

uncertainties to energy, via the sensitivity analysis, are presented and also combined

to the other energy related uncertainties.

63


The fourth table gathers the estimated losses that allow the estimation of the Net

annual energy production based on the gross annual energy production. These losses

are assumed to be in the same range for a one-year and a ten-year prediction hori-

zon for almost all of the studied wind farms.

The fifth and the sixth tables give the gross and net predicted annual energy produc-

tion for one and ten years within the probabilities of exceedance 50%, 75% and 90%.

The calculation of the predicted AEP on the different levels of the PoE is function of

the average AEP estimated and the uncertainty related to its estimation.

64


4.2.1 Site 1

Table 40: Uncertainties related to the measurement of wind

Measurement - wind speed related Site 1 [%] Wind Speed (cup anemometer) 1.8% Wind Direction (wind vane) 1.5% Mounting 2.0% Subtotal (measurement) 3.1%

Table 41: Uncertainties related to measurement and data processing

Measurement and Data Processing - wind speed related Site 1 [%] Measurement 3.1% Data Integrity 1.0% Data Analysis 2.9% Long-term correlation 2.2% Subtotal (Measurement and Data Processing) 4.9%

Table 42: Uncertainties related to the annual energy production

Turbine Model G 97 [%] Total Uncertainty of Measurement and Data Processing 8.5% Prediction horizon [years] 10 1-year wind deviation 8.0% 10-year wind deviation 2.5% Modeling 8.1% Power curve 6.0% Reference WEC 0.0% Total Uncertainty on Gross(free flow) Production (1-year) 15.5% Total Uncertainty on Gross (free flow) Production (10-year) 13.5% Losses (uncertainty of loss estimations) 1.2% Total Uncertainty on NET Production (1-year) 15.5% Total Uncertainty on NET Production (10-year) 13.5%

65


Table 43: The estimation of the energy losses for one and 10 years

Operational Year 1st 2nd - 10th [%] [%] GrossAEP P50 [MWh/a] 123 937 123 937 Wake Effects 7.8% 7.8% Availability 3.2% 3.2% Turbine Performance 0.3% 0.3% Electrical 2.1% 2.1% Environmental 0.1% 0.1% Curtailment 0.0% 0.0% Energy Losses 12.9% 12.9%

Net AEP P50 [MWh/a] 107 894 107 894

Table 44: The gross and the net annual energy production

GROSS (free flow) PoE AEP Full Load Farm Nominal Power [MWh] 38.0 [MWh/a] [h/a] 1-year period

Production [MWh/a] 123 937 50% 123 937 3 261 Uncertainty 15,5% 75% 111 010 2 921 Standard Deviation [MWh] 19 165 90% 99 376 2 615 10-year period

Production [MWh/a] 123 937 50% 123 937 3 261 Uncertainty 13,5% 75% 112 691 2 966 Standard Deviation [MWh] 16 673 90% 102 569 2 699

Table 45: The AEP within the different probabilities of exceedance

NET PoE AEP Full Load Farm Nominal Power [MWh] 38.0 [MWh/a] [h/a] 1-year period Production [MWh/a] 107 894 50% 107 894 2 839 Uncertainty 15,5% 75% 96 607 2 542 Standard Deviation [MWh] 16 734 90% 86 448 2 275 10-year period

Production [MWh/a] 107 894 50% 107 894 2 839 Uncertainty 13,5% 75% 98 065 2 581 Standard Deviation [MWh] 14 573 90% 89 219 2 348

66


4.2.2 Site 2


Measurement - wind speed related Site 2 [%] Calibration 1.0% Type of Anemometer 1.8% Mounting 2.0% Subtotal (measurement) 2.9%




Turbine Model GE 2.5 [%] Total Uncertainty of Measurement and Data Processing 10.6% Prediction horizon [years] 10 1-year wind deviation 8.7% 10-year wind deviation 2.7% Flow modeling 3.0% Wake modeling 1.8% Power curve 5.0% Total Uncertainty on GrossProduction (1-year) 15.0% Total Uncertainty on Gross Production (10-year) 12.5% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 15.0% Total Uncertainty on NET Production (10-year) 12.5%

67



Operational Year 1st 2nd - 10th [%] [%] GrossAEP P50 [MWh/a] 100 971 100 971 Unavailability 4.2% 4.2% Electrical Losses 2.3% 2.3% Icing/rotor blade degradation 0.1% 0.1% Cut out wind speed hysteresis 0.1% 0.1% Grid unavailabilty 0.0% 0.0% Curtailment 0.0% 0.0% Energy Losses 6.6% 6.6% Net AEP P50 [MWh/a] 94 316 94 316


GROSS PoE AEP Full Load Farm Nominal Power [MWh] 37.5 [MWh/a] [h/a] 1-year period

Production [MWh/a] 100 971 50% 100 971 2 693 Uncertainty 15.0% 75% 90 767 2 420 Standard Deviation [MWh] 15 128 90% 81 584 2 176 10-year period Production [MWh/a] 100 971 50% 100 971 2 693 Uncertainty 12.5% 75% 92 435 2 465 Standard Deviation [MWh] 12 656 90% 84 752 2 260


NET PoE AEP Full Load Farm Nominal Power [MWh] 37.5 [MWh/a] [h/a] 1-year period Production [MWh/a] 94 316 50% 94 316 2 515 Uncertainty 15,0% 75% 84 785 2 261 Standard Deviation [MWh] 14 131 90% 76 207 2 032 10-year period Production [MWh/a] 94 316 50% 94 316 2 515 Uncertainty 12,5% 75% 86 343 2 302 Standard Deviation [MWh] 11 822 90% 79 166 2 111

68


4.2.3 Site 3






Turbine Model V 80 [%] Total Uncertainty of Measurement and Data Processing 6.0% Prediction horizon [years] 10 1-year wind deviation 9.2% 10-year wind deviation 2.9% Flow modeling 7.0% Wake modeling 1.3% Power curve 5.0% Total Uncertainty on GrossProduction (1-year) 11,9% Total Uncertainty on Gross Production (10-year) 9,7% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 11,9% Total Uncertainty on NET Production (10-year) 9,7%

69






Production [MWh/a] 234 944 50% 234 944 2 447 Uncertainty 11,9% 75% 216 040 2 250 Standard Deviation [MWh] 28 027 90% 199 027 2 073 10-year period Production [MWh/a] 234 944 50% 234 944 2 447 Uncertainty 9,7% 75% 219 637 2 288 Standard Deviation [MWh] 22 695 90% 205 859 2 144


NET PoE AEP Full Load Farm Nominal Power [MWh] 96.0 [MWh/a] [h/a] 1-year period Production [MWh/a] 219 779 50% 219 779 2 289 Uncertainty 11,9% 75% 202 095 2 105 Standard Deviation [MWh] 26 217 90% 186 180 1 939 10-year period Production [MWh/a] 219 779 50% 219 779 2 289 Uncertainty 9,7% 75% 205 460 2 140

Standard Deviation [MWh] 24,091 90% 192 572 2 006

70


4.2.4 Site 4






Turbine Model E 82 [%] Total Uncertainty of Measurement and Data Processing 5.3% Prediction horizon [years] 10 1-year wind deviation 12.7% 10-year wind deviation 4.0% Flow modeling 8.0% Wake modeling 1.4% Power curve 5.0% Total Uncertainty on GrossProduction (1-year) 16.7% Total Uncertainty on Gross Production (10-year) 11.6% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 16.7% Total Uncertainty on NET Production (10-year) 11.6%

71



Operational Year 1st 2nd - 10th [%] [%] Gross AEP P50 [MWh/a] 26 747 26 747 Unavailability 3.0% 3.0% Electrical Losses 3.5% 3.5% Icing/rotor blade degradation 0.1% 0.1% Cut out wind speed hysteresis 0.0% 0.0% Grid unavailabilty 1.0% 1.0% Curtailment 0,6% 0,6% Energy Losses 8.0% 8.0% Net AEP P50 [MWh/a] 24 613 24 613






72


4.2.5 Site 5






Turbine Model V 90 [%] Total Uncertainty of Measurement and Data Processing 5.6% Prediction horizon [years] 10 1-year wind deviation 11.3% 10-year wind deviation 3.6% Flow modeling 9.0% Wake modeling 0.5% Power curve 6.0% Total Uncertainty on GrossProduction (1-year) 16.6% Total Uncertainty on Gross Production (10-year) 12.7% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 16.6% Total Uncertainty on NET Production (10-year) 12.7%

73



Operational Year 1st 2nd - 10th [%] [%] Gross AEP P50 [MWh/a] 32 422 32 422 Unavailability 3.0% 3.0% Electrical Losses 2.5% 2.5% Icing/rotor blade degradation 0.5% 0.5% Cut out wind speed hysteresis 0.0% 0.0% Grid unavailabilty 0.0% 0.0% Curtailment 0.0% 0.0% Energy Losses 5.9% 5.9% Net AEP P50 [MWh/a] 30 510 30 510






74


4.2.6 Site 6






Turbine Model E 70 [%] Total Uncertainty of Measurement and Data Processing 5.1% Prediction horizon [years] 10 1-year wind deviation 6.4% 10-year wind deviation 2.0% Flow modeling 9.0% Wake modeling 0.1% Power curve 5.0% Total Uncertainty on Gross Production (1-year) 13.2% Total Uncertainty on Gross Production (10-year) 11.7% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 13.2% Total Uncertainty on NET Production (10-year) 11.7%

75









76


4.2.7 Site 7


Measurement - wind speed related Site 7 [%] Wind Speed (cup anemometer) 3.5% Wind Direction (wind vane) 0.0% Mounting 1.5% Subtotal (measurement) 3.8%


Measurement and Data Processing - wind speed related Site 7 [%] Measurement 3.8% Data Integrity 1.0%

Data Analysis 1.0% Long-term correlation 2.0% Subtotal (Measurement and Data Processing) 4.5%


Turbine Model V 90 [%] Total Uncertainty of Measurement and Data Processing 9.0% Prediction horizon [years] 10 1-year wind deviation 7.5% 10-year wind deviation 2.4% Flow modeling 2.0% Wake modeling 0.1% Power curve 5.0% Total Uncertainty on Gross(free flow) Production (1-year) 12.9% Total Uncertainty on Gross (free flow) Production (10-year) 10.7% Losses (uncertainty of loss estimations) 1.0% Total Uncertainty on NET Production (1-year) 12.9% Total Uncertainty on NET Production (10-year) 10.8%

77



Operational Year 1st 2nd - 10th [%] [%] Gross AEP P50 [MWh/a] 40 579 40 579 Wake Effects 4.2% 4.2% Availability 4.1% 4.1% Turbine Performance 2.5% 2.5% Electrical 2.1% 2.1% Environmental 0.3% 0.3% Curtailment 4.4% 4.4% Energy Losses 16.3% 16.3% Net AEP P50 [MWh/a] 33 949 33 949






78


4.2.8 Site 8


Measurement - wind speed related Site 8 [%] Calibration 6.0% Type of Anemometer 5.0% Mounting 8.0% Transfer to the wind farm( WindPro/WAsP) 4.0% Subtotal (measurement) 11.9%


Measurement and Data Processing - wind speed related Site 8 [%] Measurement 11.9% Data Integrity 8.0% Data Analysis 0,0% Long-term correlation 0,0% Subtotal (Measurement and Data Processing) 14.3%


Turbine Model S 77 [%] Total Uncertainty of Measurement and Data Processing 14.3% Prediction horizon [years] 10 1-year wind deviation 7.7% 10-year wind deviation 2.4% Flow modeling 0,0% Wake modeling 0,0% Power curve 0,0% Total Uncertainty on Gross(free flow) Production (1-year) 16.3% Total Uncertainty on Gross (free flow) Production (10-year) 14.5% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 16.3% Total Uncertainty on NET Production (10-year) 14.5%

79



Operational Year 1st 2nd - 10th [%] [%] GrossAEP P50 [MWh/a] 168 616 168 616 Wake Effects 10,9% 10,9% Availability 5,0% 5,0% Turbine Performance 0,2% 0,2% Electrical 1,80% 1,80% Environmental 0,2% 0,2% Curtailment 0,0% 0,0% Energy Losses 6.9% 6.9% Net AEP P50 [MWh/a] 139 601 139 601





NET PoE AEP Full Load Farm Nominal Power [MWh] 49.5 [MWh/a] [h/a] 1-year period Production [MWh/a] 139 601 50% 139 601 2 820 Uncertainty 16,3% 75% 124 294 2 511 Standard Deviation [MWh] 22 695 90% 110 516 2 233 10-year period Production [MWh/a] 139 601 50% 139 601 2 820 Uncertainty 14,5% 75% 125 926 2 544 Standard Deviation [MWh] 19,412 90% 113 618 2 295

80


4.2.9 Site 9




Measurement and Data Processing - wind speed related Site 9 [%] Measurement 3.0% RIX number variability 2.0% Vertical extrapolation 3.0% Inter-annual and thermal 4.0% Subtotal (Measurement and Data Processing) 6.2%


Turbine Model G 58 [%] Total Uncertainty of Measurement and Data Processing 8.0% Prediction horizon [years] 10 1-year wind deviation 7.7% 10-year wind deviation 2,4% Flow modeling 0,0% Wake modeling 0,0% Power curve 0,0% Total Uncertainty on Gross(free flow) Production (1-year) 11.1% Total Uncertainty on Gross (free flow) Production (10-year) 8.4% Losses (uncertainty of loss estimations) Total Uncertainty on NET Production (1-year) 11.1% Total Uncertainty on NET Production (10-year) 8.4%

81



Operational Year 1st 2nd - 10th [%] [%] GrossAEP P50 [MWh/a] 71 680 71 680 Wake Effects 8.6% 8.6% Availability 0.0% 0.0% Turbine Performance 0.0% 0.0% Electrical 0.0% 0.0% Environmental 0.0% 0.0% Curtailment 0.0% 0.0% Energy Losses 8.6% 8.6% Net AEP P50 [MWh/a] 65 544 65 544






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4.2.10 The AEP calculated in the Wind Study for all the farms

In the following table the different results of the calculation of the AEP in the Wind

Study are presented.

Table 94: Different AEP calculated in the wind study

Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Site 7 Site 8 Site 9

AEP Gross Type Free-

Flow Gross Gross Gross Gross Gross

Free-

Flow

Free-

Flow

Free-

Flow

[%] [%] [%] [%] [%] [%] [%] [%] [%] Total Uncertainty of Measurement and Data Processing

8,5 10,6 6,0 5,3 5,6 5,1 9,0 14,3 8,0

Prediction horizon [years]

10 10 10 10 10 10 10 10 10

1-year wind devia-tion

8,0 8,7 9,2 12,7 11,3 6,4 7,5 7,7 7,7

10-year wind devia-tion

2,5 2,7 2,9 4,0 3,6 2,0 2,4 2,4 2,4

Modelling 8,1 3,0 7,0 8,0 9,0 9,0 2,0 0,0 0,0 Power curve 6,0 1,8 1,3 1,4 0,5 0,1 0,1 0,0 0,0 Reference WEC 0,0 5,0 5,0 5,0 6,0 5,0 5,0 0,0 0,0 Total Uncertainty on GrossProduction (1-year)

15,5 15,0 11,9 16,7 16,6 13,2 12,9 16,3 11,1

Total Uncertainty on Gross Production (10-year)

13,5 12,5 9,7 11,6 12,7 11,7 10,7 14,5 8,4

Losses (uncertainty of loss estimations)

1,2 0,0 0,0 0,0 0,0 0,0 1,0 0,0 0,0

Total Uncertainty on NET Production (1-year)

15,5 15,0 11,9 16,7 16,6 13,2 12,9 16,3 11,1

Total Uncertainty on NET Production (10-year)

13,5 12,5 9,7 11,6 12,7 11,7 10,8 14,5 8,4

In order to compare the Wind Study AEP with the actual AEP resulted from the data production recorded, it is important to calculate the AEP NET without considering the

83


electrical losses, since the data is recorded in the WTG level in the SCADA system and summed for all the farms.

Table 95: Energy Losses with electrical Losses Excluded

Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Site 7 Site 8 Site 9 Energy Losses with electrical Losses Excluded [%]

11,1 4,4 4,5 4,6 3,5 3,0 14,5 15,7 8,6

84


4.3 Production Data

In this section of the master thesis manuscript is presented a summary of the pro-

duction data used as input for the comparison tool. The production data available for

the considered wind farm site differs significantly from one to the other. The produc-

tion data available is either monthly records or daily records, depending on the sites,

but even when it is daily it is summed to monthly energy production. The production

data of every wind farm is provided either for every turbine or for the whole wind

farm

This section aims to show a good visualization of the energy production of every site.

To fulfill this objective, a compilation of graphs showing different aspects of energy

production variability are presented for every site.

Every compilation of graphs displayed contains as a function of months or turbines

the average values, the maximum value, the standard deviation, the variability which

is the standard deviation divided by the average, the sum of the covariance calculated

based on the correlation and the covariance matrices.

85


4.3.1 Site 1

86


Figure 23: Graphs illustrating the monthly production and the variability related to it

87


4.3.2 Site 2


88


4.3.3 Site 3


89


4.3.4 Site 4


90


4.3.1 Site 5


91


4.3.2 Site 6


92


4.3.3 Site 7


93


4.3.4 Site 8


94


4.3.5 Site 9


95


Chapter 5: Results

5.1 Results concerning the different sites

A common way of reporting wind assessment uncertainties is by giving the proba-

bilities of exceedance in terms of annual expected wind farm energy output or full

load hours, for different periods, usually 1 year and 10 years. The idea of this work

is to perform similar calculation based on variability of the actual energy production.

The calculation of the AEP at different PoE levels is based on the standard deviation.

The standard deviation is derived from the uncertainty for the wind assessment

study and calculated based on the combined variability for the production data.

The presentation of the results follows the same schema for every site similar to the

logic followed in the previous parts. In this part are a set of tables presenting the

main results of the AEP estimated in the wind assessment study and the AEP calcu-

lated based on the energy production and the calculation of the standard deviation.

The results are also presented in the form of graphs.

The first table gives the AEP and the average energy production. The process of

converting data from monthly production data to annual production data goes

through an averaging according to the data set used. In fact, for the turbines the

average concerns the same number of turbines when the production data is availa-

ble for every turbine, otherwise the wind farm production is averaged only according

to the months. For the temporal variability, the number of months considered de-

pends on the production data cover and on the timestamp of the data available

which can be 10 min scada data or daily production or monthly. And therefore the

time period may be more or less than one year depending on the site. The total en-

ergy-related uncertainties in the wind study are scaled to meet the same time period

96


of the evaluation of variability in terms of years. This is the reason why quantities

described as “Uncertainty WS [%]” in the following pages do not directly match the

quantities designated as “Total Uncertainty on NET Production” from section 4.2.

In the table, the calculated values of the whole available period are presented and

scaled to 12 months to correspond to the AEP. Other statistical information is pre-

sented such as the standard deviation of the production data, the square root of the

sum of the squares of the standard deviations and the sum of the sum of the covari-

ances which are calculated based on the correlation matrix and the covariance ma-

trix. Also the average of the correlation coefficients between the production data is

given for both the months and the turbines. In the second table the calculated AEP

in the wind assessment study is given with its uncertainty and the derived standard

deviation. And the AEP calculated based on the production data is given with its

standard deviation and the derived variability. In the third table the estimated and

the actual AEP are calculated for different PoE levels.

The compilation of graphs displays the results in a form that simplifies the visuali-

zation and the comparison between different aspects of the AEP calculated in the

wind assessment and derived from actual energy production.

Within the PoE50 the wind farm produces the average AEP(P50), from a theoretical

point of view many cases can arise depending on the values of the AEP estimated in

the wind assessment and calculated based on the production data and depending on

the uncertainty and the variability values.

The AEP(50) based on the production data is higher than the AEP(50) based on the wind assessment and the production variability is lower than the uncertainty of the wind assessment. In this case it is most probable that the wind farm will reach or even exceed the predicted production at all the probability levels, however this case is rare and may reflect an under-estimation of the AEP in the wind assessment, and so on.

97


5.1.1 Site 1

Table 96: The AEP and its statistical characteristics calculated for the complete production period

Site 1 Site 1

Correlation Turbines Correlation Months

AEP PD [kWh] 87 722 129 87 722 129 Average Monthly PD [kWh] 4 616 954 7 310 177 StdDev Monthly PD [kWh] 3 546 014 1 228 586 Average StdDevPD [kWh] 544 615 1 633 887 SQRT(Sum(StdDev²)) PD [kWh] 699 796 2 493 177 SQRT(Sum(Sum COVi))PD [kWh] 748 245 5 614 522 Average R 75% 48%

Table 97: Different NET AEP and their standard deviation

Site 1 Site 1

PD WS

AEP NET [kWh/a] 87 722 129 110 208 538 StdDev 6 640 563 16 095 082 Variability[%] 8% Uncertainty WS[%] 15%

Table 98: The AEP predicted and actual at different PoE levels

Site 1 Site 1

WS PD

PoE AEP NET [kWh/a] AEP NET [kWh/a] 50% 110 208 538 87 722 129 75% 99 352 570 83 243 137 90% 89 581 860 79 211 905

98


Figure 32: Graphs showing different aspects of the predicted and actual AEP

99


5.1.2 Site 2


Site 2 Site 2


AEP PD [kWh] 69 730 606 69 730 606 Average Monthly PD [kWh] 4 648 707 5 810 884 StdDev Monthly PD [kWh] 1 622 521 1 216 678 Average StdDevPD [kWh] 424 612 405 696 SQRT(Sum(StdDev²)) PD [kWh] 475 011 656 613 SQRT(Sum(Sum COVi))PD [kWh] 453 407 2 004 528 Average R 97% 38%


Site 2 Site 2

PD WS



Site 2 Site 2

WS PD


100



101


5.1.3 Site 3


Site 3 Site 3


AEP PD [kWh] 187 662 330 187 662 330 Average Monthly PD [kWh] 3 909 632 15 638 527 StdDev Monthly PD [kWh] 3 519 073 5 328 976 Average StdDevPD [kWh] 715 524 3 632 876 SQRT(Sum(StdDev²)) PD [kWh] 1 438 095 6 033 838 SQRT(Sum(Sum COVi))PD [kWh] 1 351 815 14 076 294 Average R 87% 36%


Site 3 Site 3

PD WS



Site 3 Site 3

WS PD


102



103


5.1.4 Site 4


Site 4 Site 4


AEP PD [kWh] 23 743 078 23 743 078 Average Monthly PD [kWh] 23 743 078 1 978 590 StdDev Monthly PD [kWh] - 337 477 Average StdDevPD [kWh] 337 477 - SQRT(Sum(StdDev²)) PD [kWh] 337 477 - SQRT(Sum(Sum COVi))PD [kWh] - - Average R 100% No Data


Site 4 Site 4

PD WS



Site 4 Site 4

WS PD


104



105


5.1.5 Site 5


Site 5 Site 5




Site 5 Site 5

PD WS



Site 5 Site 5

WS PD


106



107


5.1.6 Site 6


Site 6 Site 6




Site 6 Site 6

PD WS

AEP NET [kWh/a] 21 549 852 25 187 804 StdDev 959 134 2 970 314 Variability[%] 4% Uncertainty WS[%] 12%


Site 6 Site 6

WS PD


108



109


5.1.7 Site 7


Site 7 Site 7




Site 7 Site 7

PD WS



Site 7 Site 7

WS PD


110



111


5.1.8 Site 8


Site 8 Site 8


AEP PD [kWh] 126 925 843 126 925 843 Average Monthly PD [kWh] 3 846 238 10 577 154 StdDev Monthly PD [kWh] 3 116 703 6 825 491 Average StdDevPD [kWh] 2 718 842 3 949 303 SQRT(Sum(StdDev²)) PD [kWh] 4 524 039 3 991 563 SQRT(Sum(Sum COVi))PD [kWh] 4 550 907 8 570 932 Average R 99% 51%


Site 8 Site 8

PD WS



Site 8 Site 8

WS PD


112



113


5.1.9 Site 9


Site 9 Site 9


AEP PD [kWh] 57 379 146 57 379 146 Average Monthly PD [kWh] 1 434 479 4 781 596 StdDev Monthly PD [kWh] 1 182 039 1 165 712 Average StdDevPD [kWh] 121 484 524 866 SQRT(Sum(StdDev²)) PD [kWh] 222 982 980 933 SQRT(Sum(Sum COVi))PD [kWh] 222 274 3 865 190 Average R 93% 54%


Site 9 Site 9

PD WS



Site 9 Site 9

WS PD


114



115


5.2 Comparison between sites based on the type of terrain

In this part of the results, is a comparison of the full load hours of every site esti-

mated in the wind study and calculated based on the production data. The ad-

vantage that this quantity brings is that it allows the comparison between farms

which do not have the same capacity. A comparison between the variability calculat-

ed based on all the energy production data available and the wind study uncertainty

was also performed based on the terrain nature of the sites. This comparison is dis-

played in figure 41 for better visualization.

Table 123: Full load hour estimated in the WS and calculated based on the PD

Farm Terrain FLH WS [h] FLH PD [h] Site 1 flat 2 900 2 308 Site 2 flat 2 574 1 859 Site 3 Complex 2 336 1 955 Site 4 flat 2 551 2 374 Site 5 flat 2 608 1 776 Site 6 Complex 2 190 1 874 Site 7 Flat 2 890 3 014 Site 8 Flat 2 872 2 564 Site 9 Complex 1 928 1 688

Table 124: Uncertainty of the WS and Variability in the PD

Farm Terrain WS Uncertainty [%] PD Variability [%] Site 1 flat 15% 8% Site 2 flat 13% 4% Site 3 Complex 12% 8% Site 4 flat 12% 4% Site 5 flat 13% 5% Site 6 Complex 12% 4% Site 7 Flat 12% 7% Site 8 Flat 16% 8% Site 9 Complex 9% 7%

116


Figure 41: Comparison between wind study and production data

Figure 41in the top-right shows that for all the sites there is an overestimation of

the FLH in the wind studies. This overestimation varies from -4% to 32% and has an

average of 15%. The figure also shows that for the complex terrain the overestima-

tion follows the same trend line. Figure 41 in the top-left shows that the estimated

uncertainty in the wind study is higher for most the sites than the Variability calcu-

lated based on the production data. The relative difference varies between 23% and

73% and has an average of 51%.

These figures give an easy way of comparing different sites; however they should be

interpreted carefully. Indeed, because of the assumptions made during the process

and the quantity of production data used in this study, it may not be correct to de-

rive conclusions about the performance of the parks based only on the visualization

117


of these results. Many other parameters whish are not included in this study may be

crucial in the overall performance of the park. Moreover, this tool cannot be used for

predicting the performance of the parks.

For the site 8, planned in flat terrain, from the production data it is noticed that the

turbines are well correlated between them, however the uncertainty related to the

wind study is in fact high, the reason being that for this site no long term correlation

was done, the Met-Mast used was more than 20km from the site and some other

uncertainty factors as well.

In the following three graphs some new results are presented concerning the esti-

mation of the AEP estimated within the Wind Study faced with the actual AEP calcu-

lated based on the Production Data. The PoE(50%) of the Wind Study AEP (PoE(50%)

WS AEP) estimation is overestimating the PoE(50%) of the Production Data AEP

(PoE(50%)PD AEP) with +15%. The PoE(90%) of the Wind Study AEP estimation is

reached within a relative deviation of -2% if the production data variability was not

included which corresponds to the P(50) PD AEP. In the case where the production

data variability is included in the calculated production data AEP, the PoE(90%) of the

Wind Study estimation stays ahead of the actual AEP by +15% again.

118


Figure 42: PoE(50%) WS AEP PoE(50%) PD AEP -> Average estimation relative deviation of +15%

Figure 43: PoE(90%) WS AEP PoE(50%) PD AEP -> Average estimation relative deviation of -2%

119


Figure 44: PoE(90%) WS AEP PoE(90%) PD AEP -> Average estimation relative deviation of +15%

The following graph shows that the uncertainties related to the wind assessment

study are found between 9% and 15%, and most of them are close to 13%. The varia-

bilities are found between 4% and 8% and the average is 6%.

The deviation between the WS and of the Production Data AEPs are found to be be-

tween 35% and 10%, which is a big range. It turns out that three of the parks are

mainly behind this big disparity, for instance when the average relative deviation

between PoE(50%) WS and AEP PoE(50%)of the Production Data is calculated for all

the farms it gives a value of +15% with a standard deviation of 10%, but when the

three farms are excluded this value decrease to +9% with a standard deviation of

only 7%. And the effect of these three farms is more important when calculating the

average relative deviation between PoE(90%) of the Wind Study and PoE(50%) of the

Production Data which it turns from an under estimation of -2% with the standard

deviation of 12% to an underestimation of -8% with the standard deviation of 9%.

120


Figure 45: Different variabilites vs. uncertainties of each farm and the relative deviation of the AEP

5.3 Improvement of Lahmeyer’s spreadsheet application software

From the evaluated wind farm site available pre- and post-construction AEP the it

was observed a need of correcting the best estimate net annual energy production

(AEP P50) with a more conservative approach. The analyzed data shows an overesti-

mation of 15 % on average; this average drops to only 9% if three farms with high

overestimation are excluded.

Probable reasons for this difference could be overestimation of the wind potential of

the sites (wind shear, long-term, flow modeling), optimistic turbine power perfor-

mance (power curve), optimistic energy losses scenarios (turbine availability, wake

losses). Due to time constraints the study did not cover the reason of the overesti-

mation of the wind potential on the analyzed wind farm projects, however many

121


pathways were investigated and opened for further development concerning the un-

certainty in wind assessment and from this study it turned out that the covariance

method is a robust method to deal with related and unrelated uncertainties and var-

iabilities. And also for detecting systematic errors that can contribute to a general

overestimation of the wind yield. Thus, it is suggested to implement the method for

the Long Term correlation uncertainty, since there is a huge potential to improve the

selection of the nodes and also of the reference station and to eliminate the ele-

ments that not only increase the uncertainty but can implicitly cause some error in

the resource assessment.

It was also remarked that opposite to the intuitive perception, the wind energy esti-

mation in the complex terrain is better than in the flat and hilly terrain, this can be

explained by the fact that in the complex terrains the assessor is more conservative

in his wind assessment, and therefore it is recommended to be more conservative

also in simple terrains.

In order to find out the origins of the observed overestimation of the annual energy

production, one idea is to investigate the wind resources in every farm. It is usual to

make a Production Data Analysis using LT wind data from reference stations and

satellite data to assess the wind energy production post-construction and to predict

the future trend of it. Similarly, this study suggests making a wind resource assess-

ment using the same kind of data and to use the correlation method to compare it

with the LT data used in the wind assessment study pre-construction and with the

wind Met-Mast data separately. Such an analysis will enable detecting if the wind

resources were overestimated.

One important parameter that can influence the deviation between the AEP estimat-

ed in the Wind Study and the calculated AEP from the wind data is the losses estima-

tion. It is highly recommended to survey the Actual Power Curve performance for all

the wind farms and to detect if any overestimation of the guaranteed Power Curve

occurs and the rank of the manufacturers accordingly. This analysis also can be

done using the correlation method. The same method is recommended to be ap-

plied for analyzing the technical availability, the curtailment and the other different

categories of losses.

122


Conclusion

In this manuscript a new approach for uncertainty learning curve was implanted

providing a powerful tool for comparing wind assessment uncertainties and the pro-

duction data variabilities. Two components of the variability were calculated as cor-

related uncertainties using the correlation and the covariance matrices.

In addition to the review of the uncertainty analysis tool, two main aspects of varia-

bility of production data are presented here, temporal and spatial variability. First, a

method is presented for combining the variabilities combining uncertainty that aris-

es in wind production as correlated and uncorrelated variabilities. Second, the varia-

bility at the wind farm level and annual energy production is scaled according to the

available production data. Third, a comparison between the results of many farms

with different characteristics is presented.

Because of the time constraints and the lack of previous similar studies, to achieve

such a study was a challenging task. Further research potential in this topic is ob-

served as necessary. In the list below some research areas are given:

Correct the NET estimated PD AEP with the Long Term of Wind Resources

correction

Include more sites and deep analysis of the different aspects of every site,

and even better if some aspects could be quantified and statistically pro-

cessed.

Resolution of the PD and the time stamp for shorter than monthly production

data.

Uncertainties details of the wake modeling and availability of the turbines vs.

spatial variability.

Include nacelle wind data in the analysis for directional behavior investiga-

tion.

123


For all the sites an overestimation of the pre-construction AEP (wind studies) was

identified when comparing with post-construction AEP (real production data). This

overestimation varies from -4% to 32% and has an average of 15%.

Estimated uncertainty in the pre-construction AEP is higher for most the sites than

the post-construction production variability. The relative deviation varies between -

23% and 73% and has an average of 51%.

124


Annexes

Annex A: Example (IEC 12400-12-1)

The following example goes through an estimate of the category A and B un-

certainties for each bin of a measured power curve. The uncertainty of the

power curve is derived, and finally the uncertainty of AEP is estimated.

The example follows the IS O guide and the assumptions made above. Using

the combination of the category B uncertainty components according to

equation (E.20),all uncertainty components within each bin can be combined

first to express the combined category B uncertainty of each measured pa-

rameter, as for example for the wind speed:

𝑢𝑉,𝑖2 = 𝑢𝑉1,𝑖

2 + 𝑢𝑉2,𝑖2 +⋯ (E.1)

Where uncertainty components refer to the uncertainty components in Table

E.2, using symbols and indices as indicated in the table.

Secondly, the standard uncertainties of the measurands can be expressed by

the uncertainties of the measurement parameters in bin i:

𝑢𝑐,𝑖2 = 𝑠𝑠𝑃,𝑖

2 + 𝑢𝑃,𝑖2 + 𝑐𝑉,𝑖

2 𝑢𝑉,𝑖2 + 𝑐𝑇,𝑖

2 𝑢𝑇,𝑖2 + 𝑐𝐵,𝑖

2 𝑢𝐵,𝑖2 (E.2)

𝑢𝐴𝐸𝑃2 = 𝑁ℎ2 ��𝑓𝑖2𝑠𝑠𝑃,𝑖2

𝑁

𝑖=1

+ 𝑠𝑠𝑤2 + 𝑠𝑠𝑠𝑐2 + ��𝑓𝑖�𝑢𝑃,𝑖2 + 𝑐𝑉,𝑖

2 𝑢𝑉,𝑖2 + 𝑐𝑇,𝑖

2 𝑢𝑇,𝑖2 + 𝑐𝐵,𝑖

2 𝑢𝐵,𝑖2 + 𝑐𝑚,𝑖

2 𝑢𝑚,𝑖2

𝑁

𝑖=1

�

2

�

(E.3)

Where uncertainties due to the data acquisition system are part of the uncer-

tainty of each measurement parameter and flow distortion due to terrain is

included in the uncertainty of wind speed. The uncertainty related to climatic

variations, sw, is evaluated separately.

The example only considers the uncertainty components, which shall be in-

cluded in the uncertainty analysis of the measured power curve. The power

curve is extrapolated with a constant power, which is the power in the last bin,

125


to the cut-out wind speed of 25m/s.

Category A uncertainties

Category A uncertainties in measured and normalized electric power and due

to climatic variations and the site calibration (if conducted) need to be con-

sidered.

Category A uncertainty in electric power

The standard deviation of the distribution of normalized power data in each

bin is calculated by the equation:

𝜎𝑃,𝑖 = � 1𝑁𝑖−1

∑ �𝑃𝑖 − 𝑃𝑛,𝑖,𝑗�2𝑁𝑖

𝑗=1 (E. 4)

Where

σP,i is the standard deviation of the normalized power data in bin i;

Ni is the number of 10 min data sets in bin i;

Pi is the normalized and averaged power output in bin i;

Pn,i,j is the normalized power output of data set j in bin i.

126

TableE.1–List of categories B and A uncertainties

Category B:Instruments Note Standard Uncertainty Sensitivity

power output

Current transformers*

Voltage transformers*

power transducer or*

Power measurement device*

a

a

a

c

IEC60044-1

IEC60044-2

IEC60688

uP,i

uP1,i

uP2,i

uP3,i

uP4,i

cP,i=1

Wind speed

Anemometer *

Operational characteristics *

Mounting effects *

Flow Distortion / site Calibra-

tion *

Wind Shear Correction (or lack

of wind shear correction)

Wind Veer Correction (or lack

of wind veer correction)

b

cd

c

c/d

c

c

uV,i

uV1,i

uV2,i

uV3,i

uV4,i

uv5,i

uv6,i

𝑐𝑉,𝑖 ≈ �𝑃𝑖 − 𝑃𝑖−1𝑉𝑖 − 𝑉𝑖−1

�

Air density

Temperature

Temperature sensor*

Radiation shielding*

Mounting effects*

Air pressure

Pressure sensor*

Mounting effects*

Relative Humidity

Humidity sensor

Mounting effects

a

cd

a

c

a

cd

ISO 2533

uT,i

uT1,i uT2,i

uT3,i uB,i

uB1,i uB2,i

𝑐𝑇,𝑖 ≈𝑃𝑖

288.15𝐾

𝑐𝐵,𝑖 ≈𝑃𝑖

1013ℎ𝑃𝑎

data acquisition system

Signal transmission*

System accuracy*

Signal conditioning*

b

cd

ud,i

ud1,i

ud2,i

ud3,i

Sensitivity factor is de-

rived from actual uncer-

tainty parameter

127

Category B:Terrain

Flow distortion due to terrain

*

bc uV4,i cV,i (see above)

Category B:Method

Method

Air density correction

Turbulence Correction (or lack

of turbulence correction)

cd

cd

cd

um,i

um1,i

um2,i

cT,i and cB,i

cP,i=1 (see above)

cV,i (see above)

Category A: Statistical

electric power *

Climatic variations

site Calibration *

e

e

e

sP, i

sw

ssc

cP,i=1

𝑐𝑉,𝑖 ≈ �𝑃𝑖 − 𝑃𝑖−1𝑉𝑖 − 𝑉𝑖−1

�

*parameter required for the

uncertainty analysis

NOTE Identification of uncertainties :

a = reference to standard ;

b = calibration;

c = other "objective" method;

d = "guestimate";

e = statistics.

The standard uncertainty of the normalized and averaged power in the bin is

estimated by the equation:

𝑠𝑠𝑖 = 𝑠𝑠𝑃,𝑖 = 𝜎𝑃,𝑖

�𝑁𝑖 (E. 5)

Where

sP,i is the Category A standard uncertainty of power in bin i;

σP,i is the standard deviation of the normalized power data in bin i;

Ni is the number of 10 min data sets in bin i.

128

Category A uncertainties in climatic variations

The power performance test may have been carried out under special atmos-

pheric conditions that affect the test result systematically, such as very stable

(large vertical shear and low turbulence) or unstable (little shear and high tur-

bulence) atmospheric stratification or frequent and /or large changes in wind

direction. The degree of magnitude of this climatic uncertainty, sw, can be

tested by

a) Subdividing the data record into segments, each long enough to have small

(statistical) uncertainty on power;

b) Estimate annual energy production for each of the derived power curve s

c) Calculate the standard deviation of the annual energy production estimates

Category A uncertainties in the site calibration

The residuals between the site calibration corrected and measured wind speed

at the turbine mast are used to define the Category A uncertainty of the site

calibration, ssc.

Category B uncertainties

The category B uncertainties are assumed to be related to the instruments,

the data acquisition system, and the terrain surrounding the power perfor-

mance test site .If the uncertainties are expressed as uncertainty limits, or

have implicit, non-unity coverage factors, the standard uncertainty must be

estimated or they must be properly converted into standard uncertainties.

Consider an uncertainty expressed as an uncertainty limit ±U. If a rectangular

probability distribution is assumed, the standard uncertainty is:

𝜎 = 𝑈√3 (E. 6)

129

If a triangular probability distribution is assumed, the standard uncertainty is:

𝜎 = 𝑈√6 (E. 7)

Category B uncertainties in the data acquisition system

There may be uncertainties from transmission, signal conditioning, analogue

to digital conversion, and data processing in the data acquisition system. The

uncertainties may be different for each measurement channel. The standard

uncertainty of the data acquisition system for the full range of a certain meas-

urement channel, ud,i, can be expressed as:

𝑢𝑑,𝑖 = �𝑢1,𝑖2 + 𝑢2,𝑖

2 + 𝑢3,𝑖2 (E. 8)

Where

ud1,i is the uncertainty in signal transmission and signal conditioning in bin

i;

ud2,i is the uncertainty in digitization in bin i, for example from quantization

resolution;

ud3,i is the uncertainty in other parts of the integrated data acquisition sys-

tem (software , storage system)in bin i.

We assume in this example the data acquisition system to have a standard un-

certainty ud,i of

0.1% of full range of each measurement channel.

Category B uncertainties in electric power

The uncertainty of the power sensor has uncertainty contributions from the

current and voltage transformers and from the power transducer. Uncertainties

of these subcomponents are normally stated by their classification.

130

The standard uncertainty of the electric power for each bin, uP,i, is calculated

by combining the standard uncertainties from the power transducer, the cur-

rent and voltage transformers and the data acquisition system:

𝑢𝑃,𝑖 = �𝑢𝑃1,𝑖2 + 𝑢𝑃2,𝑖

2 + 𝑢𝑃3,𝑖2 (E. 9)

Where

uP1,i is the uncertainty in current transformers in bin i;

uP2,i is the uncertainty in voltage transformers in bin

i;

uP3,i is the uncertainty in the power transducer in bin

i;

udP,i is the uncertainty in the data acquisition system for the pow-

er channel in bin i.

In the example, the current and voltage transformers and the power transducer

are all assumed to be of class 0.5.

The current transformers of class0.5 (nominal loads of the current transform-

ers are here designed to match the nominal power, 1000kW, and not200% of

nominal power). They have uncertainty limits, referring to IEC60044-1, of

±0.5% of the current at 100% load. At 20% and 5% loads, though, the uncertainty

limits are increased to ±0.75% and ±1.5% of the current, respectively. For pow-

er performance measurements on wind turbines, the most important energy

production is produced at a reduced power. Thus, the uncertainty limits of

±0.75 % of the current at 20% load are anticipated to be a good average. The

uncertainty distribution is assumed to be rectangular. It is assumed that the

uncertainties of the three current transformers are caused by external influ-

ence factors such as air temperature, grid frequency, etc. and they are there-

fore assumed fully correlated (an exception from the general assumption) and

131

are summed linearly. As each current transformer contributes by one-third to

the power measurement, it follows that the uncertainty of all current trans-

formers is proportional to the power as follows:

𝑢𝑃1,𝑖 = 0.75% 𝑃𝑖[𝑘𝑊]√3

13

3 = 0.43% 𝑃𝑖[𝑘𝑊] (E. 10)

The voltage transformers of class 0,5 have uncertainty limits, referring to

IEC60044-2, of

±0, 5% of the voltage at all loads. The uncertainty distribution is assumed to be

rectangular. The grid voltage is normally rather constant and independent of

the wind turbine power. The uncertainties of the three voltage transformers

are as for the current transformers assumed to be caused by external influence

factors such as air temperature, grid frequency, etc. and they are therefore as-

sumed fully correlated (an exception from the general assumption) and are

summed linearly. As each voltage transformer contributes by one-third to the

power measurement, it follows that the uncertainty of all voltage transformers

is proportional to the power as follows:

𝑢𝑃2,𝑖 = 0.5% 𝑃𝑖[𝑘𝑊]√3

13

3 = 0.29% 𝑃𝑖[𝑘𝑊] (E. 11)

If current and voltage transformers are not operated within their secondary

loop operational load limits, additional uncertainties shall be added.

The power transducer of class 0, 5, referring to IEC60688, with a nominal

power of 2000kW (200% of the nominal power, 1000kW, of the wind turbine)

has an uncertainty limit of 10kW. The uncertainty distribution is assumed to be

rectangular. The uncertainty of the power transducer is thus:

𝑢𝑃3,𝑖 = 10 𝑘𝑊√3

= 5.8 𝑘𝑊 (E. 12)

Considering the electric power range of the measurement channel to be

2500kW and an uncertainty of the data acquisition system of 0, 1% of this

range, the standard uncertainty from the electric power sensor for each bin is:

132

𝑢𝑃1,𝑖 = �(0.43% 𝑃𝑖[𝑘𝑊])2 + (0.29% 𝑃𝑖[𝑘𝑊])2(5.8𝑘𝑊)2(0.1%2500𝑘𝑊)2 =

�(0.52% 𝑃𝑖[𝑘𝑊])2 + (6.3𝑘𝑊)2 (E. 13)

Category B uncertainties in wind speed

The uncertainty of the wind speed measurement is a combination of several

uncertainty components. Usually, the most operational character is tics of the

anemometer, the mounting effects on the anemometer, and the uncertainty of

the anemometer calibration. If the terrain complies with the terrain require-

ments, the flow distortion due to the terrain is determined as 2% or 3 %, de-

pendent on the distance of the meteorological mast from the wind turbine. If an

experimental site calibration is under-taken, the standard uncertainty derived

from the site calibration shall be used. The flow distortion due to mounting

effects might be considerable unless the anemometer is mounted on a tube on

top of the mast. The uncertainty of the anemometer calibration and the uncer-

tainty due to operational characteristics might dominate in the measurement.

The category B uncertainty from wind speed in bin i, uV,i, can be expressed as:

𝑢𝑉,𝑖 = �𝑢𝑉1,𝑖2 + 𝑢𝑉2,𝑖

2 + 𝑢𝑉3,𝑖2 + 𝑢𝑉4,𝑖

2 + 𝑢𝑉5,𝑖2 + 𝑢𝑑𝑉,𝑖

2 (E. 14)

Where

uV1,i is the uncertainty of the anemometer calibration in bin i;

uV2,i is the uncertainty due to operational characteristics of the an-

emometer in bin i;

uV3,i is the uncertainty of flow distortion due to mounting effects in

bin i;

uV4,i is the uncertainty of flow distortion due to the terrain in bin i;

uV5,i is the uncertainty due to lack of shear measurement in bin i;

133

udV,i is the uncertainty in the data acquisition system for

the wind speed in bin i.

The sensitivity factor is determined as the local slope of the meas-

ured power curve:

𝑐𝑉,𝑖 = �𝑃𝑖−𝑃𝑖−1𝑉𝑖−𝑉𝑖−1

� (E. 15)

The standard uncertainty of the anemometer calibration is estimated to be 0,

1m/s. uncertainty due to operational characteristics of the anemometer being

derived from the classification which is estimated to be a class 1, 2A. Assuming

a rectangular uncertainty distribution, the class corresponds to a standard un-

certainty of 0, 034m/s+0, 0034

Vi. The standard uncertainty of the flow distortion due to mounting effects is

estimated to be 1% of the wind speed. Considering a wind speed range of

30m/s of the measurement channel and an uncertainty of the data acquisition

system of 0, 1% of this range, the standard uncertainty from data acquisition is

0, 03 m/s. In this example, it is assumed that site calibration is not under-

taken, and the flow distortion due to the terrain is estimated to be 3% of the

wind speed. The uncertainty of each wind speed bin is:

𝑢𝑉,𝑖 =

�(0.1𝑚/𝑠𝑠)2 + (0.034𝑚/𝑠𝑠 + 0.0034 𝑉𝑖[𝑚/𝑠𝑠])2 + (0.01 𝑉𝑖[𝑚/𝑠𝑠])2 + (0.03 𝑉𝑖[𝑚/𝑠𝑠])2 + (0.001 × 30𝑚/𝑠𝑠)2 =

�(0.104𝑚/𝑠𝑠)2 + (0.032 𝑉𝑖[𝑚/𝑠𝑠])2 + (0.034𝑚/𝑠𝑠 + 0.0034 𝑉𝑖[𝑚/𝑠𝑠])2 (E. 16)

In the case where a site calibration has been undertaken, the uncertainty from

the site calibration shall be included as the uncertainty of the flow distortion

due to the terrain uV4, i, instead of the fixed value (2% or 3%).

The category A component of uncertainty, ssc, due to site calibration shall be

evaluated.

134

The category B components of uncertainty uv1, i, uv2, i, uv3, iand uv6, is hall be

evaluated.

The site calibration uncertainty for each wind direction bin j can be expressed

as:

𝑢4𝑣,𝑖 = �𝑢𝑉1,𝑖2 + 𝑢𝑉2,𝑖

2 + 𝑢𝑉3,𝑖2 + 𝑢𝑑𝑉 ,𝑖

2 + 𝑢𝑉6,𝑖2 + 𝑢𝑉7,𝑖

2 + 𝑢𝑉8,𝑖2 + 𝑢𝑉9,𝑖

2 + 𝑢𝑉10,𝑖2 (E. 17)

Where

uV1,I is the uncertainty of anemometer calibration in bin i;

uV2,i is the uncertainty due to anemometer operational character-

istics

uV3, i is the uncertainty due to anemometer mounting effects

udV, i is the uncertainty in data acquisition system for the wind

speed in bin i

uV6, i is the uncertainty arising due to the convergence check

uV7, i is the uncertainty arising due to correlation check

uV8, i is the uncertainty arising in the event of a change in

correction

uV9, i is the uncertainty caused by the removal of the di-

rection sensor

uV10,i is the uncertainty due to seasonal variation

Ssc is the Category A uncertainty of the site calibration

135

Table 3–Suggested assumptions of correlation s of measurement uncertainties

in different measurement heights16

Component

Correlation Coefficient of

uncertainties Between Dif-

ferent measurement

Heights

Explanation

Wind shear measurement by cup anemometers

Wind tunnel calibration 1

Calibration in same wind tunnel is re-

quired; high correlation of uncertain-

ties of calibration s of different cup

anemometers

Cup anemometer classi-

fication 1

Anemometers at different heights

measure under very similar climatic

condition s

Cup anemometer

mounting 1, 0

1, if boom mounted and same boom

configuration ;

0, if one anemometer top mounted

and the other Boom mounted

Data acquisition system 0 Different input channels applied

site effects due to dis-

tance between the ref-

erence mast and the

test turbine

1

As a first approximation, the site ef-

fects may be assumed to be identical

for the rotor height range.

Uncertainty due to lim-

ited number of meas-

urements over rotor

height range

1

to a first approximation, this uncer-

tainty is fully correlated between the

measurement heights

Wind shear measurement by remote sensing device

Verification test 1

Normally, very similar condition s of

reference sensors at different heights

present.

Sensitivity of accuracy of remote

136

sensing device on measurement

height may be ignored.

Sensitivity analysis/

classification 1

Classification performed under very

similar conditions at different heights.

Dependency of sensitivity of remote

sensing device on environmental con-

ditions on measurement height may

be ignored.

uncertainty resulting-

from control with Met-

Mast

1 Same uncertainty assumed for all

heights

uncertainty due to

flow variation in

different probe

volumes at same height

1

Normally, quite similar effect ex-

pected at different measurement

heights. Sensitivity of error on meas-

urement height may be ignored.

Mounting 1 Similar effect of system mounting in-

different measurement heights

site effects due to dis-

tance between the

measurement and the

test turbine

1

As a first approximation, the site ef-

fects may be assumed to be identical

for the rotor height range.

uncertainty due to

limited number of

measurements over ro-

tor height range

1

to a first approximation, this uncer-

tainty is fully correlated between the

measurement heights

137

Documents

Analysis of pre- and post- construction wind farm energy ... · Uncertainty is involved in allof the assessment process: in the wind speed measurement, in the long-term correlation,