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___________________________________

SEMESTER I EXAMINATIONS - 2011/2012____________________________________

School of Electrical, Electronic and Communications Engineering

EEEN 40400 Wind Energy

Professor Stephen McLaughlin

Professor Tom Brazil

Professor Mark OMalley

Mr. Rick Watson*

Time Allowed: 2 hours

Instructions for Candidates

Answer any threequestions. All questions carry equal marks. Thepercentages in the right margin give an approximate indication of the relative

importance of each part of the question.

Instructions for Invigilators

Non-programmable calculators are permitted.No rough-work paper is to be provided for candidates.

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Question 1(a) Show that the wind speed at which the maximum power density in the

wind occurs for a Weibull distribution is:

C

C

CAu

1

2

25%

(b) The V80-2MW wind turbine (whose power curve is shown in Figure 1) isoperating at a site where the hub height wind speed distribution is aWeibull distribution with scale parameter 13 m/s and shape parameter 2.2.If the wind turbine is operating at a wind speed corresponding to themaximum of the power density probability density function, find the Cpofthe wind turbine at this operating point.

0 5 10 15 20 25

wind speed [ms-1]

0

0.5

1

1.5

2

power[MW]

Vestas V80-2MW

diameter 80 m

swept area 5027 m2

cut in 4 m/s

rated 16 m/s

cut out 25 m/s

Figure 1

25%

(c)

(i)

(ii)(iii)(iv)

Assuming the V802MW wind turbine (whose power curve and otherrelevant details are shown in Figure 1) has a mechanical availability of100% estimate the percentage time in the year that the wind turbineis not generating because of low winds

is not generating because of excessive windsis generating rated poweris generating below rated power

at a site where the hub height wind speed distribution is a Weibulldistribution with scale parameter 13 m/s and shape parameter 2.2

40%

(d) Describe briefly the MCP method used in wind resource assessment.10%

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Question 2(a) Given that the axial thrust of a wind turbine from momentum theory

considerations is given by

00 1 uaAuuF dw

where u0 is freestream wind speed, uw is wake wind speed and Ad is thedisk area show that the thrust coefficient is

aaCf 14

What is the thrust coefficient at the Betz condition?20%

(b) Show for a wind turbine based on the concept of a sail moving straight

before the wind that

27

4max pC

40%

(c) Describe and compare (with the aid of clearly labelled diagrams) powerregulation in wind turbines using stall regulation, pitch regulation and activestall regulation.

40%

Question 3(a) The 82.4 m diameter wind turbine WT in Figure 2 drives a three phase, 4

pole, 2.6 MVA, 690 V induction generator IG via a step up gearbox G ofgear ratio 1:91. The induction generator is connected to the 50 Hz grid viaa transformer T (2.6 MVA, 0.69kV/20kV, ukr=5%). The grid is modelled asan infinite bus at 1 p.u. voltage.

Figure 2

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The per phase equivalent circuit parameters of the induction machine areas follows:

001065.0,00150,66.0,002963.0,00116.0 rrmss X.RXXR (all quantities in ohms with rotor quantities referred to stator turns).

The generator is operating at a slip of -0.4%. Neglecting friction andwindage losses in the generator determine the generator shaft mechanicalpower at this operating point.

50%

(b) If the hub height wind speed is 10 m/s at this operating point find the Cpatwhich the turbine is operating (ignore all losses in the drive train andgearbox).

15%

(c) Find the tip speed ratio at which the turbine is running. 10%(d) Find the active power exported to the grid and reactive power imported

from the grid as measured at the grid terminals. Explain the differencebetween values found for the exported active power to grid and thegenerator shaft mechanical power.

25%

Question 4

Figure 3

Figure 3 shows a wind farm connected to a grid via a wind farmtransformer TW and an overhead line OHL. The wind farm injects complex

power S into the MV busbar W of transformer TW. The HV busbar T of the

transformer TW is connected to the overhead line. The overhead line is

connected to the grid at PCC. The transformer is represented by an

impedance ZT, the overhead line by a series impedance ZLand the grid by

an ideal voltage source US behind the grid short circuit impedance ZSC.

With all quantities in per unit and taking the source voltage as the reference

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voltage and generator convention for the direction of injected power and

current it can be shown that the following quadratic equation in wind farm

voltage squared2

WU

02 2222224 QPXRUXQRPUU SWW

describes the operation of the system where TLSC ZZZjXRZ

and jQPS

(a) Details of the different components of the system are provided in Table I.

Table I

grid overhead line transformer

4MVA2000S

kV110

''

k

R

X

Un

km40

/km41.0176.0

kV110

l

jz

Un

%5.0%20

MVA150S

kV20kV110

Tr

Rrkr

MVrHVr

uu

UU

Calculate the impedances of the components in per unit on a commonpower base equal to the rating of the wind farm transformer TW.

20%

(b) If the system voltage is 1 pu and the wind farm is exporting active power of1 p.u. at upf into the MV busbar of the wind farm transformer find the windfarm voltage

20%

(c) What reactive power must be exported or imported by the wind farm inorder to maintain the wind farm voltage at 1 p.u. whilst still exporting 1 p.u.active power.

50%

(d) Comment on the results obtained in parts (b) and (c).10%

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List of physical constants & useful formulae

density of air:

1.225kg/m3

von Karman constant:

4.0

power in the wind3

02

1uAPdwind

power coefficientwind

p P

PC

torque coefficientX

CC PT

thrust coefficient

2

02

1uA

FC

d

F

tip speed ratio

0u

RX

weibull distribution

CC

A

u

A

u

A

Cuf exp

1

probability of wind u uFuG 1 rayleigh distribution

2

2

2 4exp

2 u

u

u

uuf

properties of gamma function

2

11

weibull mean of mth power

C

mAu mm 1

energy pattern factor3

3

u

u mean power duufuPP

0

error function

z

tdtezerf

0

22

incomplete gamma function

x

t dttex0

1,

logarithmic wind profile

0

* lnz

zuzu

turbulence intensity:

zuz

zI uu

capital recovery factor

11

1

N

N

i

ii

P

A

capacity factor

rP

P

present worth factor NiF

P 11 sinking fund factor 11 Ni

i

F

A

phasor transformation

AeAtAta j

cos2

inverse phasor transformation

tatA

eAeeAeA tjtj

cos2

221

active power

cos33 IVP

reactive power

sin33 IVQ

apparent power

IVS 33

where V is the phase voltage

complex power:

phph

j

phphph jQPeIVIVS 33*

3 33

synchronous speed:pp

sn

f

2

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SCC

sc

LLn

SCZ

VS

2

22

11

1

R

X

R

X

j

R

X

ZZ scsc

per unit

base

puZ

ZZ

base

LLba se

base

S

VZ

3

2

induction machine torque:

22

2

3

rsr

s

s

s

r

XXs

RR

V

s

RT

induction machine slip:

s

rss

induction machine max torque

motor

srss

s

sm

RXXR

V

T

22

2

2

3

generator

srss

s

sm

RXXR

V

T

22

2

23

slip for max torque

motor

22 rss

rm

XXR

Rs

generator

22 rss

rm

XXRRs

oOo