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____________________________________

SEMESTER I EXAMINATIONS - 2013/2014____________________________________

School of Electrical, Electronic and Communications Engineering

EEEN40400 Wind Energy

Professor Tim Green

Professor Tom Brazil

Mr. Rick Watson*

Professor Mark OMalley

Time Allowed: 2 hours

Instructions for Candidates

Answer question 1 to 5 and any two of questions 6, 7 and 8.

Questions 1 to 5 each carry 8% and questions 6, 7 and 8 each carry 30%of the overall marks for this exam paper.

In Questions 6, 7 and 8 the distribution of marks in the right margin shown asa percentage 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

The measured mean annual wind speed at a prospective wind turbine site at

30m above ground level is 7.6 m/s. Assuming the vertical windshear follows a

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

ground level if the surface roughness around the site is a uniform 0.1 m. If the

standard deviation of the wind speed is 2.5 times the friction velocity find the

turbulence intensity at 100 m above ground level.

Question 2

If the annual wind speed distribution in Question 1 is a Rayleigh distribution

find the mean annual power density in the wind at 100 m above ground level.

Question 3

Using momentum theory, write down an expression for the thrust force on the

actuator disk where0

u is the free stream wind speed,w

u is the wind speed in

the wake, a is the axial flow induction factor andd

A is the disk area.

Show that the thrust coefficient is given by aaCf 14 and calculate the

thrust coefficient at the Betz condition.

Question 4

The mean for the Weibull distribution is given by:

C

Au1

1

Use the properties of the gamma function to show that for a Rayleigh

distribution

uA

2

Given that the most probable wind for a Weibull distribution is

C

mpC

CAu

1

1

show that the most probable wind for a Rayleigh distribution is

uump2 .

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Question 5.

It is observed that the annual wind speed distribution at a prospective wind

turbine site is a Rayleigh distribution and that the most probable wind at the

site is 6.5 m/s at 50 m a.g.l. Find the percentage time for which the winds are

above 5 m/s but less than 15 m/s.

Figure 1

Table I

Induction generator and compensation capacitors.

nominal voltage 0.69 kV, rating 2.2MVA

equivalent circuit parameters (rotor quantities are referred to stator turns)

9209.0,0155.0,0376.0,0018.0,0022.0 mrsrs XXXRR

capacitor bank ,8.0 jZc per phase

Transformer

rating 2.2 MVA, ratedvoltage MV 20kV

rated voltage LV0.69kV, uRr1%, ukr6%

Line

length 10 km, rated voltage20 kV

specific resistance0.309/km

specific reactance 0.32/km

Grid

nominal voltage 20kV, frequency 50Hz,

short circuitcapacity 50MVA,X/R =2

Question 6

A wind turbine generator is connected to an MV grid via a transformer and a

distribution line as shown in Figure 1. Details of the system components are

provided in Table I. If the wind turbine generator 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

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short circuit impedance find the voltage and the active and reactive power

exported by the wind farm as would be measured at the MV terminals of the

transformer.

Question 7

A wind farm (represented by generator G) is connected to a large power

system via a transformer as shown in Figure 2. The transformer is rated at

200 MVA with rated voltages 33 kV on the MV side and 150 kV on the HV

side. The transformer rated short circuit voltage is 20% and its rated resistive

voltage drop is 0.5%. The power system is modelled as an infinite bus

operating at a nominal voltage of 150 kV.

An ideal compensator is also connected to the MV bus of the transformer and

can provide variable compensating reactive power Qcomp to control the power

factor or the voltage at the MV bus

Figure 2

It can be shown that the steady state operation of the system is described by

the following equations:

02 222exp2exp2

expexp

24 XRQPVXQRPVV SGG

expexp

2

expexp1tan

XQRPU

RQXPV

G

G

Where GV is the wind farm voltage on the MV side of the transformer, SV is

the power grid voltage referred to the MV side of the transformer, R and X

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are the transformer resistance and reactance on the MV side and expP and

expQ are the exported active and reactive powers as measured on the MV side

of the transformer.

If the wind farm is operating at active power MW196GP and reactive power

MVAR8.39GQ and the ideal compensator is controlled to ensure unity

power factor operation at the MV side of transformer find:

(a) the reactive power supplied by the ideal compensator. 10%

(b) the wind farm voltage 50%

(c) the active and reactive power supplied to the power system as

measured on the HV side of the transformer. 30%

(d) Comment on the active and reactive power balances 10%

Question 8

(a) Explain with the aid of clearly labelled diagrams what is meant by the

axial flow induction factor and the tangential flow induction factor. 15%

(b) Draw a clearly labelled 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 these

incremental forces in the axial and tangential directions and write out the

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

blades. 30%

(d) Draw typical lift coefficient and drag coefficient versus angle of attack

for a blade airfoil section and explain the shape of these characteristics as the

blade goes into stall. 25%

(e) Explain why typical wind turbine blades are twisted and tapered along

their length from hub to tip. 15%

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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 wind

3

02

1uAP dwind

power coefficient

wind

pP

PC

torque coefficient

X

CC PT

thrust coefficient

2

02

1uA

FC

d

F

tip speed ratio

0u

R

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 powerdensity

C

C

CAu

1

2

weibull - most probable windC

mpC

CAu

1

1

energy pattern factor

3

3

u

u

mean power

duufuPP

0

error function

z

t dtezerf

0

22

incomplete gamma function

x

t dttex

0

1,

logarithmic wind profile

0

*ln

z

zuzu

turbulence intensity:

zuz

zI uu

capital recovery factor

11

1

N

N

i

ii

P

A

capacity factor

rP

P

present worth factor

NiFP

1

1

sinking fund factor

11 Ni

i

F

A

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phasor transformation

AeAtAta j cos2 inverse phasor transformation

tatA

eAeeAeA tjtj

cos2

221

active power

cos33 IVP

reactive power

sin33 IVQ

apparent powerIVS 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

V

S

2

22

11

1

R

X

R

X

j

R

X

ZZ scsc

per unit

base

pu

Z

ZZ

base

LLbase

baseS

VZ

3

2

induction machine torque:

22

2

3

rs

r

s

s

s

r

XXs

RR

V

s

R

T

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

2

3

slip for max torquemotor

22rss

rm

XXR

Rs

Generator

22 rss

rm

XXR

Rs

oOo