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___________________________________

SEMESTER I EXAMINATIONS - 2012/2013____________________________________

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) Outline a procedure to fit a Weibull distribution to a measured set of wind

data. 30%

(b) Given that the most probable wind speed for the Weibull distribution is

C

mpC

CAu

1

1

show that the most probable wind speed for the Rayleigh distribution is

uump

2

where is the mean wind speed for the Rayleigh. 25%

(c) (i) The measured mean annual wind speed at a prospective wind turbine site

is 8 m/s at 50 m above ground level. Assuming the vertical wind profile is

logarithmic estimate the mean annual wind speed at 100 m above ground

level if the surface roughness around the site is a uniform 0.2 m.

15%

(ii) If the measured standard deviation of wind speed is approximately two

and a half times the friction velocity estimate the turbulence intensity at 100

m above ground level. 15%

(d) Describe briefly the WASP/wind atlas method for wind resource assessment.

15%

Question 2

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

before the wind that

274max pC 40%

(b) Draw a velocity diagram for a wind turbine airfoil section showing the axial

and tangential components of the relative wind speed vector and distinguish

clearly between the angle of incidence, the blade pitch angle and the angle of

attack. 15%

(c) Draw a clearly labelled force diagram for a wind turbine airfoil section

showing the incremental lift and drag forces and the components of theseincremental forces in the axial and tangential directions and write out the

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equations for axial force and the torque produced by a wind turbine with B

blades 20%

(d) The induction generator rotor of the 2MW wind turbine (whose power curve,

technical specifications and operational details are show in Figure 1) is

rotating at 1512 rpm when the hub height wind speed is 17 m/s. Find the

power coefficient and the tip speed ratio at which it is operating (assume no

losses in the drive train or generator). 25%

0 5 10 15 20 25

uhub[m/s]

0

0.5

1

1.5

2

P [MW]

Prated2 MW

ucutin3 m/s

urated16 m/s

ucutout25 m/s

turbine rotor diameter 76 mgearbox ratio 1:93

Figure 1

Question 3

(a) A fixed pitch wind turbine is directly coupled to a permanent magnet AC

generator which feeds a controllable resistive load as shown in Figure 2. The

generator voltage magnitude and angular frequency are both proportional to

the rotational speed of the turbine. Assuming no losses in the drive train or

generator find the control law for the resistive load so as to ensure: (i)

operation of the wind turbine at max Cpup to the rotational speed at which

rated generator current is reached and (ii) regulation of the generator

current to its rated value above this speed up to a higher furling speed. Note

the wind generator is furled out of the wind above the furling speed by a

separate mechanism. Plot typical plots of load resistance, power and torque

versus rotational speed for operation in regions (i) and (ii) above.

60%

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Figure 2

(b) A wind turbine whose power curve, technical specifications and operational

details are shown in Figure 1 is operating at a site where the annual wind speed

distribution is a Rayleigh distribution with mean annual windspeed at hub height

equal to 8.5 m/s. Assuming 100% mechanical availability estimate the % time the

wind turbine generator is not generating due to (i) low wind and (ii) high wind and

estimate the % time the wind turbine generator is generating (iii) at rated power and

(iv) between cut in and rated wind speed. 40%

Figure 3

Question 4

A wind farm of three wind turbines is connected to a grid via a HV overhead line

(ohl) shown in Figure 3. The output from each induction generator (gi) is stepped up

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from low voltage to medium voltage by a transformer (t i) and fed via a medium

voltage cable (ki) to the wind farm transformer (tw). Each generator is compensated

by a capacitor bank (ci). Details of the system components are shown in Table I. If

each of the wind turbine generators is operating at a slip of s= -0.008 p.u. and the

grid is represented as a 1 p.u. voltage source behind its short circuit impedance find:

(a) the voltage and (b) the active and reactive power exported by the wind farm as

would be measured at the HV terminals of the wind farm transformer (tw), i.e at bus

hvw.

Table I

inductiongenerator

(gi)

nominal voltage 0.69 kV, rating 2.2 MVAequivalent circuit parameters (rotor quantities are referred to stator

turns)

9209.0,0155.0,0376.0

0018.0,0022.0

mrs

rs

XXX

RR

capacitor bank (ci) 8.0jZc per phase

transformer

(ti)

rating 2.2 MVA

rated voltage MV 10 kV

rated voltage LV 0.69kV

uRr1 %, ukr6 %

distribution

cable (ki)

nominal voltage 10 kV, length

0.4 km

specific resistance 0.3 /km

specific inductive reactance0.35 /km

wind farm

transformer

(tw)

rating 10 MVA

rated voltage MV 10 kV

rated voltage HV 38 kV

ukr 9.34 %, uRr 0.38 %,

HV

overhead

line (ohl)

nominal voltage 38 kV, length

20 km

specific resistance 0.368

/km

specific inductive reactance

0.392 /km

grid nominal voltage 38 kV, frequency 50 Hz, short circuit capacity 100

MVA, X/R =2

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List of physical constants & useful formulae

density of air:

1.225 kg/m3

von Karman constant:

4.0

power in the wind3

02

1

uAP dwind power coefficient

wind

pP

PC

torque coefficientX

CC PT

thrust coefficient

2

02

1uA

FC

d

F

tip speed ratio0u

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

weibullmean of mth power

C

mAu mm 1

weibullwind speed for highest wind power density

C

C

CAu

1

2

weibull - most probable wind

C

mpC

CAu

1

1

energy pattern factor3

3

u

u

mean power

duufuPP

0

error function

z

t dtezerf0

22

incomplete gamma function

x

tdttex

0

1,

logarithmic wind profile

0

* lnz

zuzu

turbulence intensity:

zuz

zI uu

capital recovery factor

11

1

N

N

i

ii

P

A

capacity factorrP

P

present worth factor NiF

P

1

1

sinking fund factor

11

Ni

i

F

A

phasor transformation

AeAtAta j

cos2

active power

cos33 IVP

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inverse phasor transformation

tatA

eAeeAeA tjtj

cos2

221

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

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

baseS

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

ss

m

RXXR

VT

22

2

2

3

slip for max torque

motor

22 rss

rm

XXR

Rs

generator

22 rss

r

mXXR

R

s

oOo