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RISK BASED OPTIMAL ELECTRICITY GENERATION 
PLANNING USING MODERN PORTFOLIO THEORY 
LIBRARY 
jWVEHSITY OF MORATUWA. SRI IANX 
M O R A T U W A 
I. Mahakalanda 
07/8501 
Dissertation submitted in partial fulfilment of the requirements for the degree of 
Master of Science in Financial Mathematics 
Department of Mathematics ^ N V
 q C | V 
University of Moratuwa 
Sri Lanka T \A 
October 2009 
University of Moratuwa 
111 
102484 
102484 
JL&/Z>On/3o/aQS2 
D E C L A R A T I O N 
I hereby certify that this dissertation does not incorporate without acknowledgement of any 
material previously submitted for a Degree or Diploma in any University, and to the best of 
my knowledge and belief it does not contain any material previously published or written by 
another person or myself except where due reference is made in the text. 
I Mahakalanda' 
(07/8501) 
, 1 3 0 . o 9 . 3 - O I O 
Date 
We endorse the declaration by the candidate. 
3 0 - D 9 -
Dr. P.D. Nimal ~~ Date 
(Supervisor) 
Senior Lecturer 
Department of Finance. 
Faculty of Management Studies and Commerce 
University of Sri Jayawardena pura 
go . 0 9 . ^ -OTO 
Prof. R. A. Attalage Date 
(Co-supervisor) 
Department of Mechanical Engineering 
Faculty of Engineering 
University of Moratuwa 
ii 
A B S T R A C T 
At present majority of electric power systems are carbon intensive, supply driven and highly 
centralised. A high percentage of countries still have regulated monopolised markets and 
utilization of fossil fuel fed power plants proliferated rapidly to bridge the supply and demand gap. 
Least cost and merit order methods are widely used for generation expansion planning. These 
methods incorporates present value based least cost generating technologies and favoured by 
policy makers. Generally least cost method favours fossil fuel based technologies over the 
renewable technologies irrespective of many other benefits rendered by renewable technologies. 
Therefore, energy supply is susceptible to fuel price volatilities. From an energy security 
perspective, the economies rich with diverse natural resources such as coal, crude oil, hydro, wind 
and superior technologies such as nuclear transcend above others. But countries which import 
crude oil face severe hardships due to sudden price hikes. Presently the governments are 
increasingly pressurised to decarbonise their electricity generation to combat global climate 
change even though low carbon emitting generating technologies impend relatively high initial 
capital outlays, exposing the system with greater risk from generation shortfalls. 
The objectives of this dissertation are to determine the most efficient portfolios that abate cost and 
risk and to establish a quantitative framework to determine the efficient generating portfolios from 
the societal perspective. It further evaluates the sensitivity of risk and expected cost when 
incorporating a new power generating technology to existing portfolio. 
Portfolio based generation planning is used to explicate the portfolio performance not only by cost 
(return) basis but more importantly by risk basis. Markowitz's (1952) Portfolio theory is well 
established, proven and robust model used in finance to determine the optimal portfolios of assets. 
The analysis for electricity generating technologies based on modern portfolio theory lays out a 
consistent framework which provides much better view into the portfolio cost and risk. 
Therefore, it could infer that efficient portfolios (minimum expected cost and risk) determined are 
in dissonance with extant generation expansion plan of Ceylon Electricity Board. Secondly, the 
environmental adders were incorporated to find the efficient portfolio having least societal risk. A 
sensitivity analysis gives the direction that the existing portfolio will move in terms of expected 
cost and risk when adding a new generating source to the system. It is possible to use standard 
deviation as a predictor as well as a variable that measures diversification of generating 
technologies. 
iii 
AC K N O W L E D G E M E N T 
The work of this nature would not realise with out the help and kindness of many individuals 
mentioned below. Appreciat ions to those who contributed in one way or the other to make 
my effort successful: my supervisor, Senior Lecturer, Department o f Finance, University of 
Sri Jayawardenapura Dr. P D Nimal and co-supervisor, Prof. R A Attalage attached to 
Department o f Mechanical Engineering, University of Moratuwa for their continuous 
guidance, commitment and for their valuable t ime. My gratitude goes to Dr. Chandana Perera 
for his t ime and efforts spent to finding a supervisor for my research. 
I am grateful to Dr. Vathsala Wickramasinghe for all the guidance and support rendered. I 
greatly appreciate Dr. Thilak Siyambalapit iya for making available necessary data for my 
research and Mr. Darshana Mudalige for diligent support provided. I should also like to thank 
Mr. Rohana Dissanayaka, Mr. T M J Cooray for their support and guidance. I thank my 
examiners for providing constructive comments on my study. 
Finally, I wish to express thanks to my wife who is my best friend for encouraging me and 
taking care of family matters and my parents for all their support through out my life. 
iv 
T A B L E OF C O N T E N T S 
T A B L E OF C O N T E N T S 
D E C L A R A T I O N ii 
A B S T R A C T iii 
A C K N O W L E D G E M E N T iv 
T A B L E O F C O N T E N T S vi 
L I S T O F T A B L E S vi 
L I S T O F F I G U R E S v 
L I S T O F E Q U A T I O N S vi 
L I S T O F A C R O N Y M S vi 
L I S T O F S Y M B O L S vi 
I N T R O D U C T I O N 1 
1.1 B A C K G R O U N D 1 
1.3 C O N T E X T O F T H E P R O B L E M A N D O B J E C T I V E S 5 
1 .4 M E T H O D O L O G Y 6 
1.5 S C O P E A N D L I M I T A T I O N S 6 
1 .6 S I G N I F I C A N C E 7 
1 .7 C H A P T E R O U T L I N E 8 
L I T E R A T U R E R E V I E W 9 
2 . 1 I N T R O D U C T I O N 9 
2 . 2 F U N D A M E N T A L S O F P O R T F O L I O T H E O R Y : T H E E F F I C I E N T P O R T F O L I O S E T W H E N 
A L L S E C U R I T I E S A R E R I S K Y 1 0 
2 . 3 I N T E R P R E T I N G C O R R E L A T I O N C O E F F I C I E N T 1 4 
2 . 4 P O R T F O L I O T H E O R Y A N D E N E R G Y 1 8 
2 . 6 M O D E L D E S C R I P T I O N : M E A N V A R I A N C E P O R T F O L I O F R A M E W O R K F O R P O W E R 
S Y S T E M P L A N N I N G 1 9 
2 . 7 P O R T F O L I O F R A M E W O R K F O R P O W E R S Y S T E M P L A N N I N G 2 1 
2 . 8 A S S U M P T I O N S A N D L I M I T A T I O N S 2 2 
2 . 9 D E T E R M I N A T I O N O F C O N S T R U C T S A N D V A R I A B L E S 2 2 
2 . 1 0 P O R T F O L I O C H O I C E 2 6 
2 . 1 1 E N V I R O N M E N T A L R I S K A N D S O C I E T A L R I S K 3 4 
2 . 1 2 C H A P T E R S U M M A R Y 3 5 
S E C T O R H I G H L I G H T S - SRI L A N K A E L E C T R I C I T Y G E N E R A T I O N 3 7 
3 . 0 I N T R O D U C T I O N 3 7 
3 . 1 S E C T O R R E V I E W - F R O M 1 9 9 0 T O 2 0 0 8 3 8 
3 . 2 G E N E R A T I O N E X P A N S I O N P L A N N I N G 4 0 
3 . 4 S R I L A N K A S ' R E N E W A B L E E N E R G Y P O L I C Y 4 4 
3 . 5 C H A P T E R S U M M A R Y 4 5 
M E T H O D O L O G Y 4 6 
4 . 1 I N T R O D U C T I O N 4 6 
4 . 2 C O N C E P T U A L F R A M E W O R K 4 6 
4 . 3 M E T H O D S O F D A T A C O L L E C T I O N 5 0 
4 . 4 M E T H O D S O F E V A L U A T I N G V A L I D I T Y A N D R E L I A B I L I T Y O F D A T A 5 2 
4 . 5 M E T H O D S O F D A T A A N A L Y S I S 5 3 
4 . 6 C H A P T E R S U M M A R Y 5 4 
D A T A A N A L Y S I S A N D S C E N A R I O D E S I G N 5 5 
5 . 0 I N T R O D U C T I O N 5 5 
5 . 1 P O R T F O L I O R I S K E S T I M A T I O N F O R S R I L A N K A E L E C T R I C I T Y G E N E R A T I N G M I X E S 
5 5 
vi 
T A B L E OF C O N T E N T S 
5 . 2 S C E N A R I O D E S I G N : P O R T F O L I O A N A L Y S I S A N D I N T E R P R E T A T I O N O F G R A P H I C A L 
O U T P U T 6 6 
5 . 3 E L E C T R I C I T Y G E N E R A T I O N P O R T F O L I O O P T I M I Z A T I O N U S I N G I N D I F F E R E N C E 
C U R V E S F O R SRI L A N K A 7 2 
5.4 S O C I E T A L R I S K S A N D E N V I R O N M E N T A L R I S K S 7 5 
5 . 7 C H A P T E R S U M M A R Y 7 9 
S U M M A R Y O F F I N D I N G S A N D D I S C U S S I O N 8 0 
6 . 0 I N T R O D U C T I O N : I N T E R P R E T A T I O N O F F I N D I N G S V E R S U S O B J E C T I V E S 8 0 
6 .1 O B J E C T I V E 0 1 : D E T E R M I N A T I O N O F E F F I C I E N T E L E C T R I C I T Y G E N E R A T I O N 
P O R T F O L I O 8 0 
6 . 2 O B J E C T I V E 0 2 : E S T I M A T I O N O F E N V I R O N M E N T A L / S O C I E T A L R I S K 8 2 
6 . 3 O B J E C T I V E 0 3 : T O E V A L U A T E T H E S E N S I T I V I T Y O F R I S K A N D E X P E C T E D C O S T 
W H E N D E C I D I N G T O I N C O R P O R A T E N E W P O W E R G E N E R A T I N G T E C H N O L O G Y T O 
E X I S T I N G P O R T F O L I O . . 8 6 
C O N C L U S I O N S A N D F U R T H E R R E S E A R C H 8 7 
7 . 0 I N T R O D U C T I O N 8 7 
7 .1 C O N T R I B U T I O N S O F T H E S T U D Y 8 7 
7 . 2 C O N C L U S I O N S 8 7 
7 . 3 I M P L I C A T I O N S 8 8 
7.4 F U R T H E R R E S E A R C H 8 9 
R E F E R E N C E S 9 0 
A P P E N D I X Al: E L E C T R I C I T Y G E N E R A T I N G P O R T F O L I O 9 2 
vii 
L IST OF T A B L E S 
L I S T O F T A B L E S 
Table 2.1 Correlation coefficients for different technologies 
Table 2.2. Variance-covariance matrix 
Table 3.1 Capacity shares 
Table 3.2. Generation expansion plan 2008 -capacity additions 
Table 3.3. NCRE Parameters 
Table 3.4. Generating technologies and their state of maturity 
Table 3.5. Energy share of each generation technology 
Table 4.1. Secondary data sources and description of data acquired 
Table 5.1. Cost of fuel types used for different plants 
Table 5.2. Historic fuel prices 
Table 5.3. Holding period return for different fuel types 
Table 5.4. Covariance-variance matrix of different fuel types 
Table 5.5. Estimated fuel correlation matrix 
Table 5.6. Economic attributes of existing generation plants 
Table 5.7. Estimated economic costs of candidate plants 
Table 5.8. Covariance - Variance matrix for generating technologies 
Table 5.9. Present and future generation mix 
Table 5.10. Resource Limitations 
Table 5.11. Possible generating portfolios 
Table 5.12. Feasible, 2008 and 2019 electricity generating portfolios 
Table 5.13. Expected cost, standard deviation and b 
Table 5.14. Life cycle emission for different generating mixes 
Table 6.1. Proposed emission standards for larger plants 
Table 6.2. GHG emissions per capita 
Table 6.3. Capacity shares, H index and Variance 
L IST OF F I G U R E S 
L I S T OF FIGURES 
Figure 2.1 The principle of diversification 9 
Figure 2.2. Mean-standard deviation portfolio frontier: risky assets only 13 
Figure 2.3. Perfectly positively and negative correlated returns 14 
Figure 2.4. Risk and return for two-asset portfolio given different correlation coefficients 16 
Figure 2.5. Possible risk-cost impacts Figure 2.6. Portfolio combinations for available m-assets 16 
Figure 2.7. An illustration of a revenue efficient frontier 17 
Figure 2.8. Markowitz efficient frontier 17 
Figure 2.9. Risk-return diagram 18 
Figure 2.10. An illustration of a cost efficient frontier 20 
Figure 2.11. Cost-risk diagram 20 
Figure 2.12. Variables of the study 23 
Figure 2.13. Wealth and utility 28 
Figure 2.14. Characteristics of the functions with different risk-aversion coefficients 28 
Figure 2.15. Indifference curves for a risk-averse investor 29 
Figure 2.16. Indifference curves for different type and risk averse investors 30 
Figure 2.17. Optimal portfolio selection 30 
Figure 2.18. Mean and variance of four alternatives 31 
Figure 2.19. Energy portfolio choice 34 
Figure 2.20. Life Cycle C02 emissions 35 
Figure 3.1. Growth rates of GDP and Electricity sales 37 
Figure 3.2. Gross electricity generation 38 
Figure 3.3. Energy generation by source (GWh) - 2002 and 2003 40 
Figure 4.1. Conceptual Model developed for the study 47 
Figure 4.2. Electricity generating portfolios 48 
Figure 4.3. Efficient electricity generating portfolios 48 
Figure 4.4 Determination of optimal portfolio 49 
Figure 4.5. Optimal electricity generating portfolio 49 
Figure 4.6. Sensitivity analysis 50 
Figure 5.1. NAPHTHA price trends 57 
Figure 5.2. Holding period returns for NAPHTHA 58 
Figure 5.3. GAS Oil price trend 58 
Figure 5.4. Holding period returns for GAS Oil 58 
Figure 5.5. HFO trend 59 
Figure 5.6. Holding period returns for HFO 59 
Figure 5.7. Holding period returns for Coal 60 
v 
L IST OF F I G U R E S 
Figure 5.8. Fuel use for electricity generation 61 
Figure 5.9. Gross generation by fuel type 62 
Figure 5.10. Coal price trend 65 
Figure 5.11. Expected cost versus standard deviation for 3 technologies 67 
Figure 5.12. MATLAB window - Constructing efficient frontier 67 
Figure 5.13. MATLAB window - Efficient portfolios 68 
Figure 5.14. MS Excel Solver output 70 
Figure 5.15. Combinations of electricity generating technologies 71 
Figure 5.16. Indifference curves in mean variance plane 74 
Figure 5.17. Life Cycle C02 emissions 76 
Figure 5.18. C02 emissions for different portfolios 77 
Figure 5.19. Portfolio C02 emissions, Expected cost and Risk 78 
Figure 6.1. National ambient air quality standards 83 
Figure 6.2. Behaviour of H value against Standard Deviation 85 
Figure 6.3. Sensitivity analysis 86 
vi 
L IST O F E Q U A T I O N S 
L I S T OF EQUATIONS 
Equation 2.1 
Equation 2.2 
Equation 2.3 
Equation 2.4 
min o»TQ(o 
L = <aTfia> + 8i(uP-(oTu) + 52(l-<oTi), 1 1 
2Q(D -8 , u -8 2 i = 0 1 1 
<Dp = g + hUp 
.2 
11 
Equation 2.5 <7 
2 Cfi -2A/I + B 
D 
Equation 2.6 
Equation 2.7 
Equation 2.8 
Equation 2.9 
>0 d
lol _2C 
dp.1 ~ D 
_ \(Cn2 -2Ap. + B~) 
=V D a 
fi = fi + — -JDC(a2 -<r 2) 
C 
Cov(Rp,Rr) 
C 
D c 
+ • 
c 
Equation 2.10 Holding period return, rt = 
EVl-BVl-CF^ 
BV, 
Equation 2.11 
Equation 2.12. 
Equation 2.13 
Equation 2.14 
Equation 2.15 
Equation 2.16 
Equation 2.17 
Equation 2.18 
Equation 2.19 
Equation 2.20 
Equation 2.21 
Equation 2.22 
Equation 3.1 
Equation 3.2 
Equation 3.3 
Equation 3.4 
Equation 3.5 
Equation 3.6 
Equation 4.1 
<?k =(°>k ak ) +(Q)k <*k ) k ) O&M O&M \2 
12 
12 
.12 
.12 
.13 
.21 
.21 
.22 
Levelised cost calculation 24 
Single index portfolio selection 27 
Cut-off rate 27 
Percentage of investment in each security 27 
Expected utility 31 
Mean of mix strategy aQ 32 
Variance of mix strategy aQ 32 
U ^p-b^a2 +bxM3 -b2M4 +b,M5 - 33 
lrn\ 
.33 
2" 
U = E(x)-f(a2) 33 
= £ ( ^ - ^ + ^ + ^ + ^ > ^ 7 ) 4 2 
Minimum B{ among all j 42 
Calculation of Capital investment costs and salvage value 42 
Fuel cost calculations 43 
Fuel inventory cost 43 
Operations and maintenance costs 43 
min o)TQco 48 
4 vi 
L I S T OF A C R O N Y M S A N D S Y M B O L S 
L I S T OF ACRONYMS 
C C Y Combine cycle power plant 
C E B Ceylon Electricity Board 
C P C Ceylon Petroleum Corporation 
DSM Demand Side Management 
G H G Green House Gases 
G o S L Government of Sri Lanka 
G W h Giga Watt Hour 
IEA International Energy Agency 
IPP Independent Power Producer 
kWh Kilo Watt Hour 
LKR Sri Lanka Rupees 
LNG Liquefied Natural Gas 
LOLP Loss of Load Probability 
MPT Modern Portfolio Theory 
MW Mega Watt 
M W h Mega Watt Hour 
N C R E Non Conventional Renewable Energy 
PV Present Value 
us$ United States Dollar 
USCents United States Cents 
W A S P Wein Automatic System Planning Package 
L I S T OF SYMBOLS 
Expected cost, mean 
a Standard deviation 
CO Weights 
Q Covariance matrix 
EV, Previous value 
BV, Current value 
5 Lagrange multipliers