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TRANSCRIPT
Mo
W
onitorin
WIND
Thng Strat
FLOWU
heory aegies a
Michae
Nicholas M
W MOUNCERnd Appnd Proj
el C Brower, Ch
M Robinson, D
Sant
February
ODELINRTAINTlicationect Des
hief Technical O
Director of Ope
ti Vila, Lead En
y 2015
NG TYn to sign
Officer
enwind
gineer
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February 2
ABSTRA
The uncertAlthough wrigorously.the variatiignored in larger‐than
This reporsome applobserved wresearch suncertaintcampaignsproject layappropriat
INTROD
The financuncertaintlarge proje
The main rlocation soconstrainesystems, binformatiotypically on
Despite thframeworka single unmast or foon the comcomparisoguessworkmay vary distance fr
The purpomodeling approach dmore costunderstand
CONCEP
Most windproject aremast than distance, sor even the
2015
ACT
tainty of wind wind flow mod This can lead on of the windthe process ofn‐expected err
rt presents a tications of thiswind flow modhows that, wity across a pros to minimize tyout to maximite for its partic
DUCTION
cial models ony, or risk, in thects involving n
role of wind floo that the wined by wind rebut where theon. At large, cone‐fourth or m
e importance k for accountinncertainty valur the project amplexity of then of measurek” than quantitwith position rom the neares
se of this reseuncertainty todescribed heret effective mading of the ove
PTUAL FRA
d resource anaea. It is commfarther away;
such as 1 or 2 e most import
resource and deling uncertaito an underesd flow modelinf designing a wrors in energy p
theoretical fras framework indeling errors foth the approproject site in a phe wind flow mze the PXX proular financing
n which wind he underlying wnumerous wind
ow modeling isd plant's overesource measuere are no meomplex sites, imore – of the to
of wind flow mng for this factoue to the modes a whole. Type terrain and thements and mtative analysis.across a projest mast. Howev
arch was to deo be taken inte should permnner, design merall uncertaint
AMEWORK
alysts recognizmonly assumed; that is why pkm, from the nant, factor?
energy produnty is often a lstimation or ong uncertaintywind project. Coproduction for
mework for un plant design sor sites spanniriate model, it physically reasmodeling unceoduction (whermodel.
project inveswind resource d turbines ‐ is r
s to estimate trall productionurements at oeasurements, tn particular, wotal uncertaint
modeling unceor in project deling uncertainpically this valuhe distance to model predict. Equally impoect area. It maver, the distan
evelop, validatto account in mit plant develmore nearly oty in energy pr
K
ze intuitively td, for exampleproject design nearest mast.
ction estimatearge contributverestimation y across a site onsequently, tecasts.
nderstanding software. The ng a range of is possible to onable and staertainty for a pre XX is any co
stments are bestimates. Anrelated to num
the wind resoun can be calculone or more the wind flowwind flow modty in the estima
ertainty, the wesign and assenty, either for ue ranges fromthe mast. Ofteions at similartant, most asay be implicitlce dependenc
e, and implema rigorous, quopers and conoptimal wind roduction.
hat wind flowe, that modelinguidelines caBut can this va
es is a critical etor to the totalof the financiis generally unhe turbine layo
wind flow mouncertainty mtopographic a(a) quantify thatistically defeparticular buildnfidence thres
ased depend n important soumerical wind flo
urce at every plated and its dmeteorologicaw model becodeling uncertaiated energy pr
ind industry cuessment. The ma group of tur
m 3% to 10% ofen, these estimar sites, and ssessments do ly assumed the is rarely qua
ment a theoretiuantitative wansultants to deturbine layout
w modeling uncng errors are ll for placing tariation be qu
Wind Flow M
element in winl uncertainty, ial risks of the nknown and, aout may not be
odeling uncertmodel is derivednd meteorologhe variation of ensible way; (bdable area; andshold such as 7
on a solid unurce of uncertow modeling.
proposed or podesign optimizal towers or omes the only inty can be a roduction.1
urrently lacks most commonrbines associatf the mean winmates are not bthus represenot consider h
hat the uncertantified or teste
ical frameworkay. Among otheploy wind mots, and develo
certainty is liksmaller close turbines no faantified? And
Modeling Uncer
nd project finait is rarely quaproject. In adas a consequee optimal, lead
ainty and illusd from an analgical conditionwind flow mob) design monid (c) optimize a75%, 90% or 95
nderstanding otainty ‐ especia
otential wind tzed. The modeother measuresource of ressignificant frac
a rigorous ana practice is to ted with a parnd speed, depebased on a thont more “eduhow the uncerainty increaseed against data
k allowing winher applicationonitoring assetop a more ac
kely to vary acto a meteororther than a cis distance the
rtainty
1
ancing. ntified dition, nce, is ding to
strates ysis of ns. Our odeling itoring a wind 5%), as
of the ally for
urbine eling is ement source ction ‐
alytical assign rticular ending orough ucated rtainty s with a.
d flow ns, the ts in a curate
cross a logical certain e only,
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February 2
At the outphysical diconditionsthe resourc
1.
2.
3.
As these egradient asapart theymeasurem
If this conc
Figure 1.
2015
tset of this stuistance over w are likely to dce distance (RD
. In nearly flrelated to wthe nearest
. In mountaisteep slopeturbines thpredictionspredictions
. In a coastashoreline (Ferrors. A dresource at
examples sugges well as on thy are, the morments at the oth
ceptual frame
An illustration omost rapid
udy, we hypotwhich the modiffer between D). Three exam
at, featurelesswind flow modt meteorologicnous terrain, e. An examplehat are even aat more distamade in flat tel region, the dFigure 2). Thiseveloper wout the coast, or t
est, how well he physical distre difficult it isher. The comb
work is correc
Relatively faresource an
of how the windchange in the w
hesized that wel must extrappoints, which
mples help illus
s terrain, the wdeling will probal tower. the wind resoe is a mast loca short distancnt points alonerrain). irection of largs is also the dld be ill‐adviseto rely on a ma
a model is liketance. The mos for the modination of reso
ct, then the ch
ast change ind modeling
d flow modeling wind resource, in
wind flow modpolate from mcan be thoughtrate the point
wind resourcebably also be sm
ource varies racated on top ce off the ridg the ridge to
gest wind resodirection a wined to rely on ast at the coast
ely to performore two points del to accurateource gradient
hallenge is to d
n wind errors
uncertainty is lik this case, direct
deling uncertameasurements,ht of as the dist.
e normally varimall and increa
apidly with poof a steep ridge are likely tp (though bot
ource gradientnd flow modea mast locatet to predict the
appears to dediffer in their
ely predict theand physical d
devise a quant
Relativelyresource
kely to increase tly down the slo
Wind Flow M
inty is driven but by the detance in resou
ies little with ase only slowly
osition, especidgeline (Figureto have greath are likely to
t tends to be pl will probablyd well inland e resource wel
epend on the r wind charactee resource at distance is the
titative measu
y slow chanand modeli
more quickly in ope from the ridg
Modeling Uncer
not so much begree to whichurce space, or s
position. Any y with distance
ially in directioe 1). Predictioter uncertaintybe less certain
perpendicular y exhibit the lto predict thell offshore.
underlying reseristics, howevone point basresource dista
ure of wind res
ge in wind ing errors
the direction ofge top.
rtainty
2
by the h wind simply,
errors e from
ons of ons for y than n than
to the argest e wind
source ver far sed on nce.
source
f the
Page | 3
February 2
differencesparameter
(i) (ii) (iii)
In additionwhat we mare many pVariations in land covmountain temperatu
Based on tpredicted frequencie
Figure 2resource
2015
s between poir should have a
It should reIt should alwIt should bmodeling e
n, the paramemean when wepossibilities, twin speed are over. Changes ingap. In addit
ure contrasts.
these considerdirectional spes between poi
. Similar to Figure and wind flow
Relativeand mod
nts, and to linat least the foll
duce to zero wways be non‐nbe bounded byrrors.
ter should cape say that twowo such featuroften linked to n direction mayion, both spe
rations, we propeed ratios beints. The speed
re 1, but for a shw modeling unce
ly slow chandeling uncer
k that measurowing general
when the two pnegative, as it ry some maxim
pture some keo points experies are certainltopographic ey also be causeed and direct
oposed two poetween pointsd deviation for
1
ND
i
SD
horeline. Here it rtainty, but the t
nge in resourtainty
e to the wind l characteristic
points are the srepresents the mum value re
ey features of ience “similar"y the directioneffects, such ased by topograption can be a
ossible measur, and the othrmula is,
)(
)()( 1
ri
tir
i v
vf
is not mainly ththermal and sur
rce
Rean
flow modelingcs.
same. width of an er
epresenting th
the wind clim" or "different"nal mean speeds acceleration phy, such as waltered by the
res of wind resher on the pre
2/12
1
he terrain that derface roughness
latively fastd modeling
Wind Flow M
g uncertainty.
rror distributioe global rang
mate represent" wind conditids and the direover a ridge, a
when a flow is cermal effects,
source variatioedicted differe
etermines the gcontrast betwee
t change in runcertainty
Modeling Uncer
To be useful, s
on. e of potentia
ting, in this coons. Althoughectional frequeas well as to chchanneled throsuch as land‐
on, one based oences in direc
radient in the wen land and wat
resource y
rtainty
3
such a
l wind
ontext, there encies. hanges ough a ‐water
on the ctional
(1)
wind ter.
Page | 4
February 2
The directi
The sums
direction ipoints, resHowever, t
It is notewmodeling, convenientWhether tfactors thamountain‐underestimapproach a
EXPERIM
We set outtowers at drelationshito represecompare it
We identifmeasuremstandard Mwere creattopped megrid (WRGresolution is done ini(WRG). Thof occurre
A softwareof calculatthe other mfor each dreference reference bias, or errturn.
The result towers is rtruly indeptarget is nThus, it waavoid inadv
2015
ion deviation f
are over ND w
, and vi is the spectively. Thethe formulas c
worthy that thewithout expltly eliminatesthe approach wat are likely tovalley circulatmate their uncare likely to be
MENTAL D
t to validate thdiverse wind pip between SDnt that relationts performance
fied 74 mastsments were avaMCP process, ated. The sites esas in Texas, G) using the Sand microscaltially without e raw WRG filence and Weibu
e program wasions. Starting wmasts (the targdirection from TAB file, and tfrequencies. Fror, for each ta
was a set of prepresented twpendent sampot exactly the as decided to rvertently biasi
ormula is,
wind directions
mean speed fe reference canan be applied
e speed and diricit reference s the need to works well, hoo affect the retions will not ertainty. The me.
DESIGN
his conceptual project sites. TD and DD and wnship. Along the against the o
at seven proailable for eacand tabular (Tspan a range and broad moSiteWind systee modeling at reference to oes contain, for ull scale and sh
s written to reawith an arbitragets) at the samthe raw WRGthen taking theFinally, the resarget mast. Th
predicted meawice in the datales is only halfsame as doingretain the duplng the results
ND
i
DD
s, where ND is
for that directin be thought oto any two poi
rection deviatito the terrarun other mo
owever, depenesource. For eonly make p
more sophistic
framework thhe main objecwind flow modhe way, we waother paramete
oject sites aroh mast. The dAB) files summof conditions
ountain gaps inem. SiteWind 50 m resolutioon‐site measureach grid poin
hape factors (A
ad the raw WRary mast (the rme project siteG file, applyinge sum of the psulting mean se process is th
n speeds and ea set (once as f as large. Howg the reverse, licate pairs of for any given p
1
)()( D
ri
ti ff
typically 12 o
ion. The superof as a mast, wints.
ions in these foin, land coverodels or perfonds on whetheexample, a simpoor predictiocated the mod
hrough a statistctives were (a) deling uncertainted to test diers.
und the Unitedata were corrmarizing the frs, including sten the West. Foemploys a co
on for a represrements; this pnt and for eachA and k) of the
RG file and TAreference), thee. This is done, g it to the obspredicted speespeeds are comhen repeated u
errors for 990 reference‐targwever, using oespecially if thmasts in the dpair through th
2/1
2
or 16. fi refers rscripts t and rwhile the targ
ormulas are der, or other chrm other analer the wind flomple model thns in and arodel, in other wo
tical analysis oto determine inty, and (b) toistance as an in
ed States. At rected to the lrequencies in deep mountainoor each projecombination ofsentative sampproduces whath of 12 wind dspeed distribu
B files for eache program predin the usual wserved mean seds over all dirmpared with tusing each of th
mast pairs in get and once asone mast as thhe directional ata set both tohe choice of re
Wind Flow M
to the frequen
r refer to the tget is a propos
erived entirelyharacteristics lyses to estimow model is sehat cannot simound these feords, the bette
of data from a if there is a sto devise a suitandependent pr
least one yealong‐term windifferent speeous terrain in t site we creatf mesoscale mple of historicat we call a rawirections, the eution.
h site and thendicts the wind way, by calculatspeed for thatrections weightthe observed mhe other mast
all. Arguably, s target‐referehe reference afrequencies do maximize theference mast.
Modeling Uncer
ncy of occurre
target and refesed turbine loc
y from the winof the regionate the uncertensitive to themulate gap floeatures, it wier the results
large number tatistically signable functionaredictor of erro
ar of validatedd climate throd and directiothe Northeastted a wind resmodeling at 1l days. The mow wind resourcestimated freq
n perform a nuresource for eting a speed‐upt direction froted by the obsmeans to derivs as the refere
since a given pence), the numand the other iffer between e sample size a
rtainty
4
(2)
nce of
erence cation.
d flow n. This tainty. e main ows or ll also of this
of tall ificant al form or and
d wind ough a on bins t, flat‐source 1.2 km odeling ce grid quency
umber each of p ratio om the served ve the ence in
pair of mber of as the them. and to
Page | 5
February 2
In the nextand DD, wbins for eamore samdistance, SFor a suffpredictions
Through apredictor parameteralone.
The scatteour data sa
where σ is there is soOther funcwe chose approache
A multipleerror. Thusfor a reliab
Figure 3. Pl
The values
0%
2%
4%
6%
8%
10%
12%
0
Standard Error (%
of Mean
Speed)
2015
t stage of the pwas created in aach parameterples, the meanSD, and DD. Thficient samples for the given
multiple regrof the standars, both of whic
r plots in Figurample. Overlai
the uncertainme scatter, thectional forms, is that it behaes E), consisten
regression ans it was decideble combined f
ots of the modefit
s of the coeffic
0.05 0.1 0
Standard
process, a tablan Excel workbr. Bins with lesn error and ste mean error we size, the stacombination o
ression analysrd deviation och are significa
re 3 show the rd on each plot
ty, x is the spee curves fit theincluding logaaves well near nt with the con
nalysis demonsed to create a cfit, we weighte
eling uncertaintytted lines are lin
ients are as fol
.15 0.2 0.25
Speed Deviation Function
Error v. Speed Deviation
r2=0.81
e of the obserbook. It was dess than 10 samandard deviatwas virtually zeandard deviatof distance, DD
is, it was thenof errors. Insteantly correlated
relationships bt is a fitted line
E
eed or directioe data quite werithmic and exzero (where i
nstraints listed
strated that bocombined equd each deviatio
E 1B
y, expressed as anear in the recip
llows:
AB
0.3 0.35
rved and prediecided to bin t
mples (mast paion of errors wero, which is notion of errorsD, and SD.
n determined ead, it appeard with it. Cons
between the obe of the form
E 1BA
x A
n deviation, anell, with an r2 cxponential formt approaches Ein the Concep
oth SD and DDation using boon parameter
A
DD AD
a percent of mearocal of SD and
A 0.071B 0.411
0.4
0%
2%
4%
6%
8%
10%
12%
0
Standard Error (%
of Mean
Speed)
cted speeds athe data first birs) were elimwere calculateot surprising gs represents t
that distancers to operate equently, the d
bserved model
A
nd A, B, and Ecoefficient of dms, also fit theE(1-B)) and fotual Framewo
D are independoth parametersequally. This le
C
SDC
an speed, as a fuDD, as described
0.02 0.04 0.06
Standard
Wind Flow M
nd errors, alonby distance, SDinated. For thed, along with given the desigthe uncertaint
e is not a signprimarily throdata were re‐b
ling uncertaint
E are constantsdetermination e data well. Thor very large vrk section.
dently significas. Since there wed to the follow
unction of SD (lefd in the text.
0.08 0.1 0.12
Directional Deviation Functi
Error v. Directional Devia
r
Modeling Uncer
ng with distancD, and DD, witose bins with the mean valn of the experty in the mo
nificant indepeough the othebinned by SD a
ty and SD and
s of the fit. Altof 0.81 in eachhe virtue of thevalues of x (wh
ant predictors was insufficienwing equation
eft) and DD (righ
0.14 0.16 0.18
ion
ation
r2=0.81
rtainty
5
ce, SD, th four ten or ues of iment. odeling
endent er two and DD
DD for
(3)
hough h case. e form here it
of the nt data :
(4)
t). The
8 0.2
Page | 6
February 2
The predicthe r2 coef
The uncermeasuremdiffer by aamong oth
so that thealone. Wituncertaintmonitoring
For large vearlier, altstudy was
It should bflow mode
bd
i(
)
2015
cted uncertaintfficient has inc
tainty accordiment error. It iman amount of her factors. To
e uncertainty th this form ofies) can be ag equipment. T
values of SD ahough it is raractually about
be stressed thaels will general
0%
2%
4%
6%
8%
10%
12%
0%
Observed Error Margin (%
)
ty based on threased from 0.
ng to this formmplies that evthat order, robtain the mo
goes to zero. f the equationaccounted for The method of
and DD, the urely reached int 10%.
t this formula ly exhibit diffe
Figure 4. Pexpre
2%
Predicted
CDE
is equation is p.81 to 0.89.
mula goes to en if two masreflecting diffeodeling uncerta
WFM
The subscriptn, the measureseparately ac
f doing so is dis
ncertainty in En practice. The
is specific to Arent behavior.
Plot of the predissed as a percen
4%
Pre
and Observed
C 0.097D 0.423E 0.121
plotted against
0.02 when SDts are at exacterences in theainty alone, the
2 0.02
t WFM denoteement uncertaccording to thscussed later.
Eq. 4 goes to e maximum er
AWS Truepowe
cted and observnt of mean spee
R² = 0.8
6%
edicted Error Mar
Wind Flow M
t the observed
D=DD=0. This tly the same le performancee residual shou
22
es the uncertaainty (as well he particular
0.12. This is trror band for t
er’s wind mode
ved modeling uned, according to
8938
8%
rgin (%)
odeling Uncer
Wind Flow M
d uncertainty in
value is interpocation, their e and mountinuld be remove
ainty due to thas other non‐characteristics
the global uncthe binned cas
eling system, S
ncertainty, Eq. 4.
10%
rtainty
Modeling Uncer
n Figure 4. Not
preted as a remeasurementng of anemomd as follows,
he wind flow ‐wind‐flow‐mos of the mast
certainty referses evaluated
iteWind. Othe
12%
rtainty
6
te that
esidual ts may meters,
(5)
model odeling ts and
red to in this
r wind
Page | 7
February 2
IMPLEM
The resultsdescribe te
UncertaThe first anmeasuremwith respecorrespondshown in F
Figure 5. shows theblack dots
B
Note that reference ttowers A aridge as thit. Similarlyconsistent
A
2015
MENTATIO
s of the foregoechnical aspect
inty Maps nd simplest ap
ment tower. Sucect to the towding modelingFigure 5.
An example of fe topography: a s and labeled A, lue to green colo
in each of thtower and to fand B, located he correspondiy, for towers with the conc
A
N
oing research ts of the imple
Derived fropplication of thch maps are cr
wer location fo uncertainty. A
four uncertaintyridgeline (light bB, C, and D. In tors represent sm
he four uncertfollow the conton either side ng tower, andC and D, the eptual model d
C
D
have been imementation.
om a Singlee wind flow mreated by usingr every point A set of four s
y maps created fbrown to white)he four panels omaller uncertain
tainty maps, ttours of terrainof the ridge, t
d the uncertainarea of relativdiscussed earli
B
plemented in
e Mast modeling uncertg Eq. 1 and Eq.in the area, asuch maps, alo
rom four separa) tapering into a on the right, the ties, while pink t
he area of lown that is similarhe area of relanty increases mvely low unceer (see Figure
A
the Openwind
tainty is creati 2 to derive thnd then by usong with the c
ate masts at a wplain (dark browuncertainty mato red colors rep
wer uncertainr to where theatively low uncmuch more raprtainty follows1).
D
Wind Flow M
d software. Th
ng an uncertahe directional asing Eq. 4 andcorresponding
ind project site. wn to red). Fourp generated forpresent larger u
ty tends bothe tower is locatcertainty is on tpidly towards ts the ridge to
Modeling Uncer
he following se
inty map for a and speed devi Eq. 5 to derivtopographic m
The map on ther masts are show each mast is shncertainties.
h to be close tted. For exampthe same side the ridge thanp. These resu
C
B
rtainty
7
ections
single iations ve the map, is
e left wn as own.
to the ple, for of the along lts are
Page | 8
February 2
CombinIn recent yTypically inrun presenhow shoul
The genermultiple mdifferent ngroups of s(and usual
In applying“measuremto be indepartially co
IndepenWe start b
associatedassumed to
where the
The quest
produce thvariance o
variance of
To find the
to w1 and s
(Though th
apparent b1 and 2 sw
2015
ing Resourcyears it has bn such cases, ants a somewhad the different
al approach wmeasurements nights, or seversubjects. In ealy more accura
g this approacment.” In the fpendent of evorrelated, estim
ndent Estimy supposing th
uncertainties o be a weighte
last term take
ions posed at
he value of e wof the estimate
f e correspond
e value of w1 w
set the result t
he first form of
below.) The cowitched. After in
ce and Uncbecome comma separate winat different pict estimates be
we use to answof various kinral laboratoriesch case, it is poate) estimate o
ch, we treat thfollowing sectioery other meamates.
mates hat there are tw
σ1 and σ2. (Foed average of t
es advantage of
the start of
with the smales (the square
ding to Eq. 6 is
where the tota
to zero. With s
f the equation
rresponding vanserting this ex
certainty Eson to install md flow modelincture of the wicombined, and
wering these qnds – for exams measuring thossible to comof the paramet
he wind resouon, we start wasurement.2 La
wo independen
or example, ethe two estima
e w1e1 w2
f the fact that
w
this section b
lest uncertainte of their unce
2 w12
l variance is m
ome reorganiz
w1
12
is simpler, the
alue of the secxpression into
e
stimates fromore than onng run or modnd resource vad what is the u
questions hasmple, an obserhe effectivenesmbine the resulter being sough
rce estimate aith the simple ater, we addres
nt measureme
could be the ates,
2e2 w1e1 in a weighted
w1 w2 1
oil down to t
ty, and what iertainty) rathe
12 1w1
minimized, we t
zation, the resu
22
22
1
11
2
e second provid
cond weight, wEq. 6, we have
e1
12 e2
22
11
2 1 2
2
om Differene meteorologdel adjustmentariation acrossuncertainty of t
been developrvatory measuss of a new druts of well‐desiht.
at any point dcase where eass the more ge
ents of a quant
average wind
1w1e2
average, the w
his: What we
is that uncertaer than uncert
2 22
take the deriva
ult is
11
2
1 2
2
des more insig
w2, is given by te
Wind Flow M
nt Masts ical tower at t is performed s the site. For the final result
ped to handle uring the diamug in treating agned experime
derived from oach such measeneral case of
tity e, referred speed.) The b
weights must su
ights in the a
ainty? It is eastainty itself. T
ative of this eq
ght into what is
the same equa
Modeling Uncer
a wind projecfor each mastany particular t?
situations invmeter of a plana disease in difents to derive
one mast as a surement is asssemi‐depende
to as e1 and e2
best estimate
um to one:
bove equation
siest to considhe equation f
quation with re
s going on, as w
ation with subs
rtainty
8
ct site. t. Each point,
volving net on fferent a new
single sumed ent, or
2, with
of e is
(6)
(7)
ns will
er the or the
(8)
espect
(9)
will be
scripts
(10)
Page | 9
February 2
In other w(The denoblended un
Note that estimate isone measu
These resucreate a neand so on
where ei ablended unis in fact thmeant by t
It is intereresource prelatively luncertaint
Furthermodifferent mthe same correspondresource g
Partial lyWhile the decreases example, osecond towthe model
The reasoexample, tpoint basebiased in t
Other situaFor examp
2015
words, the optiominator is a ncertainty is de
when the twos the average ourement divide
ults are easily gew estimate, wuntil the last m
and σi are the ncertainty is nhe smallest pothe “best estim
esting to take apredicted by a arge weight iny, the mast wi
ore, this appromasts accordinas assuming ding mast. Thiradient on the
y Correlateequations deswith the addione could placwer would adding uncertainty
n the equatiothe modeling eed on one of the same direct
ations can be iple, suppose o
mal weights anormalization erived by repla
o uncertaintieof the two indeed by the squa
generalized to which can thenmeasurement i
ith estimates oever larger (anossible uncertamate.”)
a moment hermast has a lo
n the final estimll be given com
oach provides g to the inversthat the unces assumption, e wind flow mo
ed Estimatescribed above ition of more e two towers d no value (excy at points awa
ns fail in this errors from thehe masts weretion, and by ex
imagined wheonly tower C w
re inversely prfactor which
acing Eq. 9 in E
2 11
2
s are equal, tependent measre root of 2.
many measuren be combineds reached. The
e
of the paramend is usually smainty that can
re to reflect oow uncertaintymate. Conversmparatively litt
a fresh perspese of the distanertainty of eaas we have n
odeling uncerta
es are fairly simptowers. It is eright next to ecept to reduceay from the tow
situation is the two masts we biased highxactly the same
re the correlatwas initially pr
roportional to ensures that q. 8 and reorg
1 2 2
22 1
11
2
he equations surements, an
ements, as thed with the nexte general result
2
2
1
i
i
ie
2
2
11
i
eter and its uncmaller) than thbe obtained b
n the meaningy compared tosely if the resole weight. This
ective on the nce squared toach estimate oted, fails to aainty.
ple, they haveeasy to imagineach other. Sine the measuremwers. Eq. 13, h
hat the measuwould be perfeor low, then ae amount.
tion would be,esent in Figur
the squared u the weights ganizing:
1
1 2
2
reduce to thed the combine
e first pair of mt measurement is:
certainty, resphe smallest of y combining t
g of these equo that of otherource predicteds makes intuitiv
common praco each mast. Nis strictly proaccount for th
e a significant ne situations wce they measument error), ahowever, says t
urements are ctly correlatedan estimate ba
, if not 1, at lere 5. Would th
Wind Flow M
uncertainty of sum to one.)
e familiar caseed uncertainty
measurements nt to create an
pectively. It canthe constituenhe measureme
uations. At poir masts, that md by the mast ve sense.
ctice of weighow we can seeportional to te important in
drawback: thewhere this wouure exactly thend should resuthat it would.
not, in fact, id, meaning thaased on the o
ast significanthe addition of
Modeling Uncer
each measure The correspo
e where the ois the uncerta
can be combiother new est
n be shown thnt uncertaintieents. (This is w
ints where themast will be ghas a relativel
ting estimatese that this metthe distance tnfluence of the
e uncertainty auld not happee same resourcult in no decre
ndependent. at if an estimatother mast wo
ly greater thanf a tower at p
rtainty
9
ement. onding
(11)
ptimal inty of
ned to imate,
(12)
(13)
hat the es, and what is
e wind given a ly high
s from thod is to the e wind
always en. For ce, the ease in
In this te at a uld be
n zero. oint D
Page | 10
February 2
reduce themeasure tbiased in a
Finding thethe same tequation f
Here, r12 is
written comeasuremmeasurempositive).
After takinsolve for th
In the spegoes to zeuncertaintno value.
These equsystem of mast, whic
subject to
(Note thatthe systemand all oth
For N=3 (i.
Once A and
2015
e uncertainty ahe ridge‐top rea similar way.
e optimal blentechnique useor the combine
s the correlati
ov(1,2). Notements were indments is always
ng the derivativhe weight that
cial case wherro. No mattery of one meas
ations can be N equations rech can be writt
the constraint
t when i=j, them solvable throher terms on th
e., three masts
d b are known
at, say, point Aesource rather
nd of partially d for indepened variance is
on of the two
that when tdependent. Thilarger than th
ve of this expre produces the
w1
re r12=1 and σr what values wurement alone
extended to aepresenting then,
,
en rij=1 and σough matrix invhe other, we ha
s), for example
, then the solu
A by as much r than the reso
correlated windent estimateas follows (com
1
measuremen
the covarianceis shows direce combined un
ession with reslowest uncert
22 r12
12 2
2 2r
σ1=σ2, the weiwe give them,e; in other wor
ny number N ohe derivatives o
∑ ∑
iσj=σi2.) The c
version. In matave
e, the matrix A
2
ution for the ve
as the square ource in the va
nd resource eses. Starting witmpare with Eq
2
ts, and the ex
e is positive, ctly that the concertainty if th
spect to the weainty in the co
1 2
r121 2
11
2
ghts w1 and w, however, Eq.rds, when perf
of measuremeof the total va
1
onstraint redutrix notation, a
and vector b a
ector of weight
root of two? alley, and hen
stimates, thougth the relative. 8):
1
xpression r12σ1
the combineombined uncehey are indepe
eight and settimbined estima
11
2 r12
1 2
1 2
2 2r12
1
w2 are undefin. 14 states thafectly correlate
ents (or towersariance with re
0
uces the numbafter grouping
are as follows:
2
ts is given by
Wind Flow M
Probably not,ce their valley
gh more compely simple case
1σ2 is their coved variance isertainty of twoendent (assumi
ng the result eate. The result
2
2
ned, as the deat the total uned, the second
s). The solutionespect to the w
ber of equationall terms conta
Modeling Uncer
since both C y predictions m
plicated, is base of two tower
variance, some
s larger than o partially corring the correla
equal to zero, wt is
nominator in certainty equad measuremen
n involves creaweight given to
ns to N‐1, renaining w on on
rtainty
10
and D may be
sed on rs, the
(14)
etimes
if the related ation is
we can
(15)
Eq. 15 als the nt adds
ating a o each
(16)
dering ne side
(17)
(18)
(19)
Page | 11
February 2
following s
CorrelatIt remains point. With
Lacking a gthe concepsame ridgeare much mthe two mthat of theerrors are
Resource dmasts and SD and DD
The correla
Figure 6.estimate o
2015
standard matri
t ion Coefficto determine hout this inform
general model pt of resource eline were usemore similar toasts are likely e point than tolikely to be un
distance (RD) between each
D are treated as
ation coefficien
. Three illustratioof the correlatio
x inversion me
cients the correlatiomation, we can
of the correladistance. This ed to predict tho one anotherto be correlato that of the otcorrelated.
is measured bh mast and pois orthogonal, a
nt is then given
ons of different on coefficient. Thbetween the po
ethods.
on (or more prnnot create or
tions of wind fextends the lohe resource inr than either ised at that pointher mast, or i
by the combinnt. In a manneand the total R
RD
n by the ratio
arrangements ohe resource distaoint and either m
recisely, the cosolve the syst
flow modelingogic of the earln the valley. Ws to that of thent. Conversely if all three poi
ed directional er analogous toD is given by:
SD DD
,
,
of two towers, A ance ratio is themast. For further
ovariance) betem of equatio
g errors, we adier example, in
We posit that ife point in quesif the resourcnts have differ
and speed deo the x and y co
/
and B, relative te ratio of the RD2
r explanation, se
Wind Flow M
tween any twons in Eq. 16.
opt a practican which two tof the wind resostion, then thece of either marent resources
eviations DD aomponents of
to a point P, and2 between mastee the text.
Modeling Uncer
o towers for a
l approach basowers located oources at two modeling erroast is more sims, then the mo
and SD betweedistance on a
d the corresponds to the smallest
rtainty
11
a given
sed on on the masts ors for milar to odeling
en the plane,
(20)
(21)
ding t RD2
Page | 12
February 2
Here, p is athe RD be(smallest R
its most sim
The conceother thancorrelated mostly indillustrationthem that
The effect is to be expblend of th
TowardsThe final suncertaintdiscussion simple trea
For conveuncorrelat
A
Figure 7.created
2015
an index repretween the maRD) mast is com
milar mast, the
pt is illustratedn they are to t(r ~1). On the
dependent. Thens show the phcounts.
of this approapected, the unhe correspondi
s a Complestage of the Oy, which can inof these souratment that ca
nience, we aed or correlate
. The map on thed using the meth
esenting the poasts establishempared. When
en rij will be clo
d in Figure 6. Ohe point, withe right, the poe situation in thysical positio
ach on a real‐wncertainty has bing areas from
te UncertaOpenwind impnclude sensor crces, which is an be adapted
ssume that aed.3 Uncorrelat
C
D
e left is the blenhod described he
oint (e.g., a gries the scale agn the RD betw
ose to zero. W
On the left of h the result thaint is betweenthe middle is bns of the tow
world case is illbeen reduced the original m
inty Modelplementation calibration, shecovered well ito many situat
ny source of ted sources ar
B
ded uncertaintyere. The individu
those s
id coordinate),gainst which thween masts is m
When the oppos
this figure, theat modeling ern the two towebetween the twwers and point
ustrated in Figat all points, a
maps.
l was to extendear, MCP, and in other referetions.
uncertainty ce independent
A
y of mean wind sual uncertainty mhown in Figure 5
, and i and j rehe RD betweemuch larger th
site is true, the
e masts are asrrors from theers, and the mwo extremes. . However, it
gure 7 for the nd the areas o
d the methodother factors. ences. Instead
can be classift between mea
A
C
speed estimatesmaps are shown5).
Wind Flow M
epresent a paien the point ahan the RD bet
en rij will be clo
ssumed to be e two masts armodeling errorsNote that, foris the resourc
same site as sof low uncertai
d to encompa This is not the we will conte
fied as being asurement poi
s from the four mn on the right (an
Modeling Uncer
r of masts. In nd the most stween the poin
ose to one.
much closer tore likely to be s are assumedr convenience,ce distance be
hown in Figureinty now repre
ss other soure place for a deent ourselves w
one of two ints. Examples
B
D
masts A, B, C, annd are the same
rtainty
12
effect, similar nt and
o each highly
d to be these tween
e 5. As esent a
ces of etailed with a
types: might
d D, as
Page | 13
February 2
include mehowever, tcharacterisin the samtowers at aerror cause
Both typeuncorrelatcovariance
where theuncorrelatrelative tomasts. In twind flow quality, pethe matrixuncorrelat
A consequ100% evenuncertaintthat mast uncorrelatnot quite mthat no me
The correla
This compo
APPLICA
With the imnumber ofcampaign d
Cost‐EffThe optimUnderstansystematic
Figure 8 illwind resouSubsequengood or buncertain, uncertaint
Somethingexperiencemeasurem
2015
easurement ethat some meastic, such as th
me way. An exaa site span a sed by the choic
es of uncertaied uncertainties unchanged.
e subscript WFed sources of the covariancthis way, the rmodeling unc
eriod of recordx A in Eq. 17 ed uncertainty
ence of includn at that masy is consideredbecomes the oed uncertaintimatch the obseeasurement is
ated uncertain
onent increase
ATIONS
mplementationf applications bdesign, and op
ective Monmal monitoringding the spatc and cost‐effec
ustrates how turce is along thnt wind flow mbetter resourcand should bey over a large
g like the deced analyst woument. The key
rrors due to vasurement errohe same instruample of a souimilar period oce of period or
nty are incores, this is accoFor a given tow
FM refers to thuncertainty. Tces in the A anrelative imporcertainty, but d, and so on. Inless prone to y when using th
ding uncorrelatst’s location. Td, the uncertaionly one that ces are includeerved at that tperfect, and al
nty is dealt with
es all uncertain
n of the uncertbeyond simply ptimizing layou
nitoring Camg campaign shial variation octive way.
the process cahe upwind (somodeling basee. However, te confirmed. Ppart of layout.
ision‐making puld likely recogadvantage of
variations in thors can be corrment mountinurce of correlatof record and ar reference is li
rporated easilymplished by inwer i, the com
he wind flow he effect of adnd b matrices rtance of eachon other comncluding the usingularities. he uncertainty
ted uncertaintThis is contrarnty associatedcounts in the bed, the uncertaower. This is dll measuremen
h by combining
σ
nties without c
tainty model dcreating uncerts to consider
mpaign Deshould minimizof wind flow m
n unfold in prauthern) edgesd on these tothe uncertaintlacing masts in
process descrignize that thef uncertainty m
he sensitivity orelated betweeng.) Correlatedted uncertaintare adjusted toikely to affect a
y into the frncreasing the vbined variance
, ,
modeling uncdding the uncoin Eq. 17. Thi mast in the f
mponents of ununcorrelated uFor both reasy model in the
ties is that the ry to commond with a particublended resourainty does not discomforting ants, within reas
g it with the fin
σ σ
hanging the re
escribed in thertainty maps. Hresource unce
sign e the uncertamodeling unce
actice. At this ss of the mesa, owers indicatesty map on thn the locations
ibed here couwind resourcmapping is th
of anemometeen towers if thd sources of unty might be theo the same lonall towers mor
ramework desvariance of eace is
ertainty and torrelated unceis, in turn, chafinal resource ncertainty sucncertainty termsons, it is alwaOpenwind soft
weight given n practice. Whular mast goes rce estimate atgo to zero, anat first, but is tson, have some
nal blended un
elative weights
e previous sectHere we discusertainty.
ainty for the ertainty can al
site, the develoand so initiallys the downwihe left showss indicated on
uld easily occue in the indicahat the effects
Wind Flow M
ers and other he measuremencertainty affee MCP processng‐term referere or less equa
scribed in prech measureme
the subscript Urtainty is to inanges the weigestimate depe
ch as the mastm has the addays recommentware.
to a single mahen only the wto zero at the t that point. Hnd thus the blethe logical conse value.
ncertainty, i.e.,
s assigned to di
tion, it is possiss two: cost‐eff
most productlow this to be
oper at first asy deploys monnd (northern) that this prethe right subst
ur without unated area shous on uncertain
Modeling Uncer
instruments. nts share a comct all measures. In most caseence. Thus, anylly.
evious sectionnt while keepi
U refers to all crease the varghts assigned ends not only t height, instruded virtue of mnded to includ
ast may never wind flow momast, and theowever, whenended resourcsequence of th
ifferent masts.
ble to considefective monito
tive possible le accomplishe
ssumes that thnitoring masts edges may ha
ediction is relatantially reduc
ncertainty mapuld be confirmnty of change
rtainty
13
(Note, mmon ments es, the y MCP
s. For ng the
(22)
other riances to the on its ument making de the
reach odeling erefore n other ce may he fact
(23)
.
r a oring
ayout. d in a
he best there. ave as atively ces the
ps. An med by es in a
Page | 14
February 2
monitoringadditional of trade of
In additionachieve thbased on tsuch guideare optimatop, even ttowers at dparallel to
A tool forsoftware.4 from a singin the comsensing syuncertaintand so on,
In this waylevel of unmodel for increment
Figure 9 ilnumber ouncorrelatout markethe non‐w(implying a
Area prresourc
Figure 8focusedwould be
2015
g campaign demeasurementff must be don
n, uncertainty e greatest redthe maximum delines can leadally placed. Fothough many tdifferent distathe shore, alb
r using uncertThe program gle tower). Thembined uncertystem) were py, and then seuntil it is told
y, the tool can ncertainty. Or,the project, al reduction in
lustrates both of towers deped and correladly as each adind‐flow‐relatea debt service
edicted to havce but relatively
8. Illustration of d on the upwind e windier, but th
uncertaint
esign can be qts might be cose subjectively,
maps provideduction in uncedistance betwe to false confir example, onturbines mightnces from the eit the same d
tainty maps infirst calculatesen it searches aainty for a paplaced there. earches for anoto stop.
help the deve knowing the the developer
n uncertainty is
approaches. ployed at a sated errors noditional towered uncertaintiecoverage ratio
ve a good windy high uncerta
how uncertainty(southern) edgehe uncertainty thty was substanti
quantified andst effective. W and different
useful informertainty. This iseen turbines adence that thee could satisfyt be placed weshore will prodistance apart.
n monitoring s the blended all allowed locarticular layoutOnce that lo
other location
loper determincost of each r can find thes outweighed b
In this chart, site and the ot associated wr produces a smes begin to doo of 1.23 based
inty
y maps can be uses of this mesa. There was relativeally reduced acr
d used to deteWithout uncertaanalysts will li
mation on the os in contrast tond towers in dere are enougy the distance ell off the ridgeduce a lower o
campaign desuncertainty baations to find tt or buildable ocation is chothat would pr
ne the smallestadditional mee point of dimby the cost of t
the blue curveestimated totwith the wind fmaller decreasminate. If the d on the P99 –
Unceareas
sed to inform mThe wind resourely high (ellipse)ross the mesa, a
ermine, in an ainty maps bakely arrive at d
optimal placemo the commondifferent types h towers for arequirement be. The same gooverall uncerta
sign has beenased on existinthe one that warea assuminosen, the proroduce the nex
t number of toeasurement anminishing retuthe next tower
e represents atal uncertaintyflow model). Ase in the wind goal is to redu– a typical crite
ertainty is redus with the add
monitoring camparce map (not sho). Right: After thnd especially in
Wind Flow M
objective wased on rigoroudifferent concl
ment of measn practice of eof terrain. Thea given layout by placing all toes for coastal ainty than plac
n implementeng measuremewould produce g an additionaogram recalculxt largest decr
owers needed nd armed withrns where ther.
a typical relatiy in plant prAfter two towflow modelinguce the uncerteria employed
uced in the targition of 3 towe
aign design. Leftown) suggested e installation ofthe areas of inte
Modeling Uncer
y, when and us analysis, thiusions.
urement systeemploying guide blind applicatand that the ttowers along asites, where ping the same t
d in the Opeents (which cothe largest decal tower (or relates the comrease in uncert
to achieve a dh a suitable fine value of the
onship betweeroduction (incers, the curve g uncertainty, aainty below, saby banks), the
get ers
t: Initial monitorthe northern edf 3 more towers,erest.
rtainty
14
where is type
ems to delines tion of towers a ridge placing towers
enwind uld be crease emote mbined tainty,
desired nancial e next
en the cluding levels and as ay, 8% e chart
ring dge , the
Page | 15
February 2
indicates iuncertaint
The red cutower (incby the expbased on increment
Figure 9 is
OptimizA second iproductionapproach financing t
In the expeP50 produshown) is sP50 layout
Figure 9. T
2015
t can be accoy model.
urve shows theluding equipmpected benefit a simple finaal cost:benefit
merely an illus
ing Layoutsinteresting apn at a desired may be desiraterms. The aim
eriment shownction (blue posmaller in the t.
Typical dependenu
omplished with
e correspondinment, installatioof that towerncial model, ratio of 1.0, th
stration. Every
s to Maximplication of thconfidence levable if a lend is to maximize
n in Figure 10, oints), and (b) northern part
ence of plant promber of towers
h 4 towers, as
ng incrementaon, maintenanr (assumed to with a 25% chis is satisfied w
y project will di
mize PXX he uncertainty vel, rather thaer or investore the value of t
a 40‐turbine pto maximize tof the region,
oduction uncertaor other measu
ssuming they a
l cost:benefit nce, and analysbe $2,000,000chance of projwith 7 optimal
ffer.
mapping metan merely to mr discounts ththe project un
project layout he P99 produc, the P99 layou
ainty (blue curverement systems
are placed in
ratio, i.e., the sis, assumed t0 per percentaject success). lly‐placed towe
thod is to optimaximize the ehe expected pder the lender
was optimizedction (red poinut has more tu
e) and marginal s for a large wind
Wind Flow M
an optimal w
cost of each ato be $100,000age point decrIf the goal isers.
imize turbine expected, or Pproduction whrs’ or investors
d in two ways:nts). Because turbines in the
cost‐benefit ratd project site.
Modeling Uncer
way according t
additional add0 per tower) drease in uncerts not to exce
layouts to ma50, productionen determinins’ own assumpt
(a) to maximithe uncertaintnorth than do
tio (red curve) on
rtainty
15
to the
itional divided tainty, eed an
ximize n. This ng the tions.
ize the ty (not oes the
n the
Page | 16
February 2
The impacP99 layoutproject des
CONCLU
This resear
1. Spbo
2. Thm
2015
cts on energy pt offers a lowesign may have
Table
USIONS AN
rch has establis
patial variationoth monitoring
he concept of wmodeling uncer
Figure 10to m
productlayout bec
production at er P50 producta significantly
e 1. Mean speed
ND DISCUS
shed the follow
n in the wind flg campaigns an
wind resource tainty.
. Predicted annumaximize the P50tion (red points)cause the uncer
different conftion, but a grehigher value.
and energy pro
SSION
wing:
ow modeling und wind projec
similarity is us
ual mean wind s0 production (bl. The P99 layoutrtainty is expecteresource comp
idence levels feater P99 prod
oduction for the
uncertainty is acts.
seful for under
peed overlaid byue points), and tt includes more ted to be smallerared to that of t
for the same cduction. Depen
two layouts sho
an important f
rstanding the s
y two turbine lathe other to maturbines in the nr there based onthe tower.
Wind Flow M
case are tabulnding on the f
own in Figure 10
factor to consid
spatial variatio
youts, one desigximize the P99 north than the Pn the similarity o
Modeling Uncer
ated in Table financing term
.
der in designin
n of wind flow
gned
P50 f the
rtainty
16
1. The ms, this
ng
w
Page | 17
February 2
3. A hiho
4. Thtoes
ACKNO
Julien Boug
1 Wind Reso2 Estimates
another, i.e3 In generaldescribed hthe problemfor each towthey do not4 The procelocations. Oresource is v
2015
model relatingigh degree of sowever, is spec
he uncertaintyool to support stimates, and o
WLEDGEM
get and Erik Ha
ource Assessmen
or measuremen
., to be wrong in
, it is possible to
ere to work, them reduces to idewer. The uncorre need to be defi
ss is best carried
Otherwise, new mvery different fr
g observed winskill at several scific to the Site
y model derivedcost‐effective optimize wind
MENTS
ale contributed
nt: A Practical Gu
nts are said to be
n the same direc
o split every sour
e correlated comntifying a single elated uncertainned individually
d out for a specif
masts may be prom that of the e
nd flow modelsites encompaeWind model.
d from this reswind monitoriplant layouts.
d useful ideas a
uide to Developi
e independent if
ction. rce of uncertaint
mponents must bcorrelated unce
nty for each towey. fied turbine layo
roposed in clearlexisting towers.
ing errors to a ssing numerou
search has beeng campaign d
and insights to
ing a Wind Proje
f there is no tend
ty into correlate
be the same, i.e.ertainty for all toer may itself be
out, or after first
ly undesirable lo
measure of wus reference‐ta
n implementedesign, improv
o this work.
ect, Chapter 14,
dency for their e
ed and uncorrela
., they must appowers, and a seta combination o
t limiting the bu
ocations, such as
Wind Flow M
wind resource sarget mast pai
d in the Openwve production u
Michael C. Brow
errors to be corr
ated component
ply to all measuret of uncorrelatedof uncorrelated
ildable area to p
s valleys, merely
Modeling Uncer
imilarity exhibrs. This relatio
wind software uncertainty
wer (ed.), Wiley 2
related with one
ts. For the equat
ements equally.d uncertainties, ouncertainties, b
prospective turb
y because their
rtainty
17
bits a nship,
as a
2012.
e
tions
Thus one ut
bine