M. Bawe Gerard Nfor, Jr. a soutenu sa thèse de Doctorat/Phd en Physique, option Mécanique-Énergétique ce 19 mai 2016 dans la salle des conférences de l'Université de Dschang. A l'issue de la soutenance, le jury présidé par le Prof. Anaclet Fomethe lui a décerné, à l'unanimité de ses membres, la mention très honorable. Voici la présentation powerpoint qu'il a effectuée dans le cadre de cette soutenance.

1. DEPARTEMENT DE PHYSIQUE
DEPARTMENT OF PHYSICS
UNIVERSITY OF DSCHANG
***************
POSTGRADUATE SCHOOL
*************
DOCTORAL TRAINING UNIT
FUNDAMENTAL SCIENCES AND
TECHNOLOGY
***********
Laboratory of Mechanics and Modelling of Physical Systems (L2MSP)
Contribution to the investigation of wind characteristics and
assessment of wind energy potential for some regions in Cameroon
THESIS
Submitted in partial fulfillment of the requirements for the award of
Doctorat/PhD in Physics
Option: Mechanics-Energetics
By
BAWE Gerard NFOR, Jr.
Registration number: CM04-09SCI4256
MSc (Exploration Geophysics)
Under the co-supervisions of
TALLA Pierre Kisito YEMELE David
Associate Professor Associate Professor
University of Dschang University of Dschang
1
UNIVERSITÉ DE DSCHANG
************
ECOLE DOCTORALE
*************
UNITE DE FORMATION DOCTORALE
SCIENCES FONDAMENTALES ET
TECHNOLOGIE
**************

2. Plan
Introduction
Problematic
Energy Meteorology
Methodology
Results & Discussions
Conclusions & Perspectives
2

3. Introduction
 Energy permeates all the fabrics of our daily
activities
 And primordial as the live wire of industries
 Industries offer employment opportunities and
better standard of living
 However, mostly fossil based fuels are used and
are identified with undesirable characteristics
 Emission of GHG (global warming), SO2 (acid
rain) and also used as instruments of coercion
(blackmail and wars) and depletion,
3

4. Introduction
4 Fig. 0.1. Temperature changes since 1880

5. Study Location
5 Fig. 0.2. Map of Cameroon showing study sites

6. Energy Demand Factors
6
0.0
5.0
10.0
15.0
20.0
25.0
1970 1980 1990 2000 2010 2020
population(millions)
year
Population growth
Fig. 0.3. Population growth

7. 0.00
1.00
2.00
3.00
4.00
5.00
1975 1980 1985 1990 1995 2000 2005 2010 2015
Energy(BkWh)
year
Total Hydroelectricity Net Generation
Energy Situation in Cameroon
7 Fig. 0.4. Hydroelectricity production

8. 8
HE station
Capacity
(MW)
Year
completed
Name of
reservoir
River
Edea PS
204 1953 Edea Reservoir
Sanaga
River
Song Loulou
PS
384 1981 & 1988 Song Loulou Reservoir
Sanaga
River
Lagdo PS
72 1982 Lagdo Reservoir
Benue
River
Memve'ele
PS
200 2013 Memve'ele Reservoir Ntem Rive
8
Energy Situation in Cameroon

9. 0.0
50.0
100.0
150.0
200.0
1970 1980 1990 2000 2010 2020
Production(Thsnd
barrels/day
year
Cameroon: Production of Crude Oil
Energy Situation in Cameroon
9 Fig. 0.5. Crude oil production

10. Leaders in wind installation in the world
Fig. 1. Leading World Countries in installed Wind Power
10Fig. 0.6. World wind energy installations

11. 11
Country Turbines Capacity (MW)
Algeria 1 11
Cape Verde 5 31
Egypt 9 745
Eritrea 1 1
Ethiopia 3 325
Gambia 1 1
Libya 1 20
Mauritania 2 36
Mauritius 1 2
Morocco 13 885
Mozambique 1 1
Namibia 1 1
Nigeria 1 11
Seychelles 1 6
South Africa 21 1,670
Tanzania 1 50
Tunisia 3 243 Table 0.1. Wind installation in Africa

12. Problematic
 Frequent electricity cuts
 We create wind speed data bank of these areas
 Carry out comparative studies of best representative
of some PDFs, introducing the new MEP-type
probability density function
 Estimate wind energy potential at study sites
 Produce wind speed and Power density atlases
12

13. Chapter one:
ENERGY METEOROLOGY
PHYSICS METEOROLOGY
 Stratified atmosphere, ours is the troposphere
 Earth surrounded by a blanket of air
 Interested in air in the lower 100m; the ABL
 Wind is Air in motion
 Produced by differential heating of the earth
13

14. Physics Meteorology
Wind at higher heights governed by:
𝑣𝑧 =
𝑣∗
𝜅
𝑙𝑛
𝑧−𝑑
𝑧 𝑑
+ 𝜓 𝑧, 𝑧0, 𝐿 (1.1)
14

15. Wind shear profile
Fig. 1.1. Wind shear profile
15

16. Vertical Extrapolation of Wind speed
 Many expressions but most prominently used are:
 (i): The log-law
 𝑣 𝑧 𝑟
= 𝑣(𝑧)
𝑙𝑛 𝑧 𝑟
𝑧 𝑜
𝑙𝑛 𝑧
𝑧 𝑜
(1.3)
 (ii): The power law
 𝑣𝑧 = 𝑣𝑟
𝑧 𝑣
𝑧 𝑟
𝛼
(1.4)
16

17. Types of wind turbines
Fig. 1.2. Horizontal axis turbine (HAWT) Fig. 1.3. Vertical axis turbine (VAWT)
17

18. Wind turbine characteristics power curve
18
Fig. 1.4. Power curve characteristics of a wind turbine

19. Wind power equation
 Formulation of transformation of kinetic energy of
the wind to electrical power
 𝑘𝑒 𝑤𝑖𝑛𝑑 =
1
2
𝑚𝑣2 (1.5)
 𝑚=𝜌𝐴𝑣 (1.6)
 𝑃𝑜 =
1
2
𝜌𝐴𝑣3 (1.7)
 Eqn (1.7) is the available power presented to turbine
 However, Betz’s law limits it to a maximum of 𝐶 𝑝= 59.3%
of 𝑃𝑜
𝑃𝑒= 𝐶 𝑝 𝑃𝑜 (1.8)
19

20. Chapter Two:
Materials and Methodology
 Materials mostly software:
Matlab R2013b, MS Excel 10 and QGIS
 Sites found on next page
 Two years (731 days) of daily mean wind speed, using
cup anemometers, from 22 sites and in Excel format
 Hard copies of 7 years of 3-hourly separation time
steps, from 6am to 6pm, daily, from Bafoussam
Airport, using Beaufort scale
 Preprocessing of wind speed for completeness,
 Statistical analysis and Modeling of wind speed
20

21. Data Processing
Vertical extrapolation:
Where necessary, and for convenience, we use the power law
𝑣ℎ = 𝑣0
ℎ 𝑣
ℎ0
𝛼
(2.1)
Statistical Analysis
(i) Mean wind speed:
𝑣 =
1
𝑛 𝑖=1
𝑛
𝑣𝑖 (2.2)
(ii) Standard deviation:
𝜎 = 𝑖
𝑛
𝑣 𝑖− 𝑣 2
𝑛−1
(2.3)
22

22. Weibull and Rayleigh PDF Models
(i) Weibull PDF & CDF
𝑓(𝑣) =
𝑘
𝑐
𝑣
𝑐
𝑘−1
𝑒𝑥𝑝 −
𝑣 𝑘
𝑐
(2.4)
𝐹 𝑣 = 1 − 𝑒𝑥𝑝 −
𝑣
𝑐
𝑘
(2.5)
(ii) Rayleigh PDF & CDF
𝑓 𝑣 =
𝑣
𝑏2 𝑒𝑥𝑝 −
1
2
𝑣
𝑏
2
(2.6)
F 𝑣 = 1 − 𝑒𝑥𝑝 −
1
2
𝑣
𝑏
2
(2.7)
22

23. Gamma PDF Model
 Gamma PDF
 𝑓 𝑣|𝑎, 𝑏 =
1
baΓ 𝑎
𝑣 𝑎−1
𝑒𝑥𝑝 −
𝑣
𝑏
(2.9)
 Gamma CDF
 𝐹 𝑣 = 1 − 𝑘=1
𝑎−1
𝑣
𝑏
𝑘
exp −
𝑣
𝑏
𝑘!
(2.10)
23

24. Lognormal PDF Model
 The Lognormal given by equation (2.11)
 𝑓 𝑣 =
1
𝑣𝜎 2𝜋
𝑒𝑥𝑝 −
1
2
ln(𝑣)−𝜇
𝜎
2
(2.11)
 𝜎 and 𝜇 are the standard deviation and mean of
the logarithm of the wind speed
24

25. Maximum Entropy Principle (MEP)
 With constraints equated to 1, mass, momentum and
kinetic energy, respectively, we obtain these equations:
0
𝑣 𝑚𝑎𝑥
𝑒𝑥𝑝 −𝜆0 − 𝜆1 𝑣 − 𝜆2 𝑣2
− 𝜆3 𝑣3
𝑑𝑣 = 1 (2.14)
0
𝑣 𝑚𝑎𝑥
𝑣𝑒𝑥𝑝 −𝜆0 − 𝜆1 𝑣 − 𝜆2 𝑣2
− 𝜆3 𝑣3
𝑑𝑣 = 𝑣 (2.15)
0
𝑣 𝑚𝑎𝑥
𝑣2
𝑒𝑥𝑝 −𝜆0 − 𝜆1 𝑣 − 𝜆2 𝑣2
− 𝜆3 𝑣3
𝑑𝑣 = 𝑣2
(2.16)
0
𝑣 𝑚𝑎𝑥
𝑣3
𝑒𝑥𝑝 −𝜆0 − 𝜆1 𝑣 − 𝜆2 𝑣2
− 𝜆3 𝑣3
𝑑𝑣 = 𝑣3
(2.17)
25

26. Goodness of fit (GoF) tests
(i): Coefficient Of determination (COD) or R2
 𝑅2 = 1 − 𝑖
𝑛
𝑋 𝑖−𝑣 𝑖
2
𝑖
𝑛 𝑋 𝑖− 𝑣 2 (2.23)
(ii): Root-mean square error
 RMSE=
1
𝑛 𝑖
𝑛
𝑋𝑖 − 𝑣𝑖
2 (2.24)
(iii): Chi square
 𝜒2 = 𝑖
𝑘
𝑂 𝑖−𝐸 𝑖
2
𝐸 𝑖
(2.25)
 Highest R2, lowest RMSE and X2 implies good accord of the model for the
wind speed regime 26

27. Modeling Power density
(i): Weibull power density
 𝑊𝑃 = 0.5𝐶𝑒 𝜌𝑐3
Γ 1 +
3
𝑘
(2.26)
(ii): Rayleigh power density
 𝑅𝑃 =
3𝜌𝑐 𝑟
𝜋
𝜋
4
(2.27)
 𝐶𝐹 =
𝑃 𝑜𝑢𝑡
𝑃 𝑟𝑎𝑡𝑒𝑑
=
𝑒
−
𝑣 𝑐
𝑐
𝑘
−𝑒
−
𝑣 𝑟
𝑐
𝑘
𝑣 𝑟
𝑐
𝑘
−
𝑣 𝑐
𝑐
𝑘 − 𝑒
−
𝑣 𝑓
𝑐
𝑘
(2.28)
27

28. Chapter Three
Results and discussions
 This chapter presents the results of the computations and
simulations for the parameters theoretically explored in
the former chapter.
 For ease of presentation, legibility and comprehension
they shall mostly be graphics and tabulations followed by
commentaries or explanations.
 However, only the results of Yoko are presented in detail
 For the remaining sites, only some results displayed,
particularly for comparison and general appraisal
 Most of the tables and figures are relegated to the
appendix

29. Time series variations Yoko
Fig. 3.1. Time series wind speed variations for Yoko for 6769 data

30. Weibull and Rayleigh PDFs
Fig. 3.2. Histogram & PDFs for Yoko for 6769 data

31. Weibull and Rayleigh CDFs
Fig. 3.3. Monthly CDFs for Yoko for 6769 data

32. Numerical results for Yoko
Model
PDF
k
c M S
RMSE R2 X2
PD WP RP ∆WP ∆RP
m/s W/m2 %
Weibull 4.1 4.0
3.7 0.9
0.0439 0.9959 0.0033
33.8 34.7 54.2 2.6 60.5
Rayleigh 2.0 2.7 0.1497 0.9524 0.0388

33. Monthly PDFs for 1st Year data set
Fig. 3.4. Monthly PDFs for Yoko for 6768 data

34. Monthly CDFs for 1st Year data
set for 1st Year data set
Fig. 3.5. Monthly CDFs for Yoko for 6768 data

35. Wind Regime Pattern Assessment
Fig. 3.5. Comparing PDFs for Wind Regime Pattern representativeness

36. Wind rose plots for Bafoussam
Fig. 3.6. Wind rose plot for Bafoussam for 2007

37. Surface roughness of Bafoussam

38. Power density atlas of Cameroon

39. Conclusion
 Cameroon suffers from severe power crisis and there is dire need for a solution.
In an attempt to curb with the situation, Cameroon has embarked on thermal
plants. However, there is an outcry against the use of fossil fuels because of
environmental concerns. There is therefore need to search for sustainable
alternatives such as wind energy.
 Based on available data, we studied the wind energy potential of 22 sites and
also carried out wind regime representativeness comparing five probability
density functions. Finally we produced the power density map of the country.
 Based on the data, our results show that Cameroon is a very poor candidate for
commercial wind energy exploitation; for all the sites fell under category 1 of
the wind speed and/or power density class. However, Yoko, Betare Oya and
Bafia prove to be exploitable for low electric power appliances and water
pumping. It was also observed that any of the PDFs could be used to describe
the wind regime as the overall least R2 was 94%.
 Wind rose plots determined winds in Bafoussam mostly flow in from angle 10o,
in accordance with its surface roughness.

40. Perspectives
 Using the old and the new data from Bafoussam, we shall use neural
network to try to generate and obtain the present from the former so as
increase the reliability of using the former today
 A reliable power density map should be produced from data
from as many sites as possible. Hence, it is imperative to obtain
data from many sites so as to give the density atlas a better
meaning.
 Only two years data length was used in this study. This is highly
insufficient for a any exploration for commercial exploitation.
Hence, if not now, this exercise should be repeated, at least in
the next ten years for better statistically sane picture of the
results.
 Proper siting of the meteorological stations is of paramount
importance. This point is pertinent because Bamenda is in a
fence, while Dschang’s is found amidst very tall buildings.

41. Thank
you
for
your
keen
attention