24
PERFORMANCE MODELING AND SIZE OPTIMIZATION OF A STANDALONE PHOTOVOLTAIC SYSTEM Abdul Qayoom Jakhrani Doctor of Philosophy (Environmental Engineering) 2013 Faculty of Engineering
PERFORMANCE MODELING AND SIZE OPTIMIZATION OF A STANDALONE
PHOTOVOLTAIC SYSTEM
Abdul Qayoom Jakhrani
Doctor of Philosophy
(Environmental Engineering)
2013
Faculty of Engineering
UNIVERSITI MALAYSIA SARAWAK
94300, KOTA SAMARAHAN, SARAWAK, MALAYSIA
CERTIFICATE
This is to certify that the thesis entitled “Performance Modeling and Size Optimization of a
Standalone Photovoltaic System” submitted by Engr. Abdul Qayoom Jakhrani for the
award of Doctor of Philosophy (Ph.D) Degree in Environmental Engineering at the
Universiti Malaysia Sarawak (UNIMAS) is an authentic work carried by him under my
supervision and guidance.
Date: 04/ 04/ 2013 Assoc. Prof. Dr. Al-Khalid Bin Haji Othman
Place: Malaysia Faculty of Engineering
University Malaysia Sarawak (UNIMAS)
94300, Kota Samarahan, Sarawak, Malaysia
i
DEDICATION
This work is dedicated to my elder brother Mr. Abdul Qadir Jakhrani who has never failed to
give me financial and moral support throughout my life, and to my mother for her kindness,
who taught me that even the largest task can be accomplished if it is done one step at a time.
It is also dedicated to my wife and children for their encouragement and patient, who have
always stood by me and dealt with all of my absence from many family occasions with a
smile.
ii
ACKNOWLEDGEMENTS
Praise is due to almighty ALLAH, who is compassionate and merciful, and Durood and
Salam upon the Holy Prophet (SAW), who gave me the power, patient and courage to
finalize my PhD thesis. First of all, I with immense gratitude acknowledge the support and
help of my supervisor, Assoc. Prof. Dr. Al Khalid Othman, his sage advice, insightful
criticisms and patient encouragement aided the writing of this thesis in innumerable ways. I
cannot find the words to express my thanks to Assoc. Prof. Ir. Dr. Andrew Ragai Henry Rigit
who served as my co-supervisor. I appreciate the guidance and invaluable cooperation,
constructive comments provided by him to enhance the quality of this thesis. I pay my
sincere thanks to Prof. Ir. Dr. Law Puong Ling and Dr. Rubiyah Baini for their co-operation
and support who served as my co-supervisors. Thanks and appreciation to all the members of
dissertation committee, especially Dr. Tay Kai Meng and Dr. Kismet Anak Hong Ping who
generously spare the time and gave fruitful comments for the betterment of this work. I must
acknowledge and appreciate the teachers, archivists, lab attendants, librarians, friends and
colleagues who helped me during my study. I need to express my gratitude and deep
appreciation to my beloved friend Shakeel Ahmed Kamboh for his valuable help for the
derivation of mathematical models and computer programming. Special thanks are also due
to Abdul Nabi Kalwar Ex: Executive District Officer Education, District Kashmore, Sindh,
Pakistan for correction of English composition of this work. My admiration is also due to the
Universiti Malaysia Sarawak (UNIMAS) for extending all facilities for conducting research
and monitoring facilities in Electronic Engineering Department.
iii
ABSTRACT
Standalone photovoltaic (SAPV) systems are emerging source of generating electrical power
especially for isolated villages. The remote villages, which cut-off from the national grid and
where extension of power transmission lines is expensive due to their geographical
conditions. Poor modelling algorithms, high initial capital cost and threat of system
breakdown due to improper sizing of SAPV systems impede its growth. The available
models were mostly validated by applying the long term (more than twenty years) solar
radiation data with small time intervals from developed countries. The procedure for
determination of input parameters required for the models was not well explained. The
available intuitive sizing methods were found to be imperfect and the numerical methods
were complicated and time consuming. Therefore, the development of an appropriate sizing
method was necessary which should fill up the gap between complex and imprecise SAPV
sizing methods.
The aim of this work was to improve the prediction of SAPV system performance by
proposing an appropriate sizing method. The original contribution of this work was the
development of two mathematical models namely a model for determination of global solar
radiation and a model for the estimation of PV module power output. Furthermore, a novel
analytical size optimization method was formulated involving load demand on the basis of
power reliability and system cost. The adapted global radiation model is different from
available models as it incorporates the site specific and environmnetal parameters, which
considered as influential input variables. It was found from the study that the adapted global
solar radiation model performed well and displayed less than 10% RMSE and 8% MBE as
compared to the examined models. The power outputs of PV modules were estimated by
iv
development of a single diode equivalent electrical circuit model. The values of input
parameters for developed model were computed analytically. The expression for output
current from PV module was determined explicitly by Lambert W function and the voltage
output was computed numerically by Newton-Raphson method. The developed model
executed ± 2% error with the rated power output of a PV module provided by the
manufacturers. Furthermore, SAPV components sizing method was formulated with a non-
linear unconstrained optimization technique by using first derivative method. The proposed
optimal sizing method determines the required PV array area and battery storage capacity for
the system load with least possible cost and predefined power reliability.
The results of the adopted models and developed sizing method were validated by
conducting sensitivity analysis of model parameters. It was revealed that the most important
and sensitive input variable was the total solar radiation with 2.5 times influence over the
output results with a sensitivity index of 0.8. The lowest sensitive variable was wind speed
with a sensitivity index of less than 0.1. The carbon footprints from diesel generators were
estimated and compared with SAPV system emissions for environmental analysis. It is
because the diesel generators are most common power producing units in remote areas of
Sarawak. The analysis reveals that the power generated by SAPV systems will help to avoid
111 tonnes of CO2 to the atmosphere as compared to a 5kW rated power diesel generator
with a load demand of 6.3kW/day. However, the estimated net energy cost occurred from
SAPV system was found to be 20 times higher than average electricity tariff in Malaysia.
It was found from the study that proposed sizing method is precise and easy to implement
than previously available methods. It requires average solar radiation data, which is almost
available in every place. It gives a complete procedure for determination of required model
v
parameters and incorporates the load demand besides system cost and power reliability. It is
concluded that the proposed optimal sizing method can be successfully implemented for the
design, development, size optimization and feasibility study of SAPV systems for the supply
of reliable power in isolated villages.
vi
ABSTRAK
Sistem kendiri fotovolta (SAPV) muncul sebagai sumber penjana kuasa elektrik terutamanya
bagi keperluan kampung-kampung di kawasan pedalaman. Keadaan geografi kampung-
kampung di kawasan pedalaman yang berada jauh dari lingkungan grid nasional
menyebabkan sambungan capaian talian penghantaran kuasa melibatkan kos yang tinggi. Di
samping model algoritma yang tedak cekap, kos modal yang tinggi dan ancaman kerosakan
sistem yang disebabkan oleh pengiraan saiz sistem SAPV yang tidak sesuai telah
menghalang pertumbuhan teknologi tersebut. Model-model yang sedia ada kebanyakannya
disahkan dengan menggunakan data sinaran suria jangka masa panjang (lebih daripada dua
puluh tahun) dengan selang masa yang kecil. Tatacara untuk penentuan masukan parameter
yang diperlukan untuk model yang sediada tidak dibincangkan dengan lanjut. Kaedah intuitif
bagi pengiraan saiz yang sedia ada, didapati tidak sempurna manakala kaedah berangka pula
merupakan kaedah yang rumit dan memakan masa. Oleh itu, pembangunan kaedah pengiraan
saiz yang sesuai adalah penting bagi mengisi jurang di antara kaedah pengiraan saiz SAPV
yang rumit dan tidak tepat.
Tujuan penyelidikan ini adalah untuk meningkatkan ramalan prestasi sistem SAPV dengan
mencadangkan satu kaedah pengiraan saiz yang lebih sesuai. Sumbangan penyelidikan ini
adalah untuk membina dua model matematik iaitu model bagi penentuan radiasi global solar
dan model bagi penganggaran kuasa pengeluaran modul PV. Tambahan pula, kaedah baru
untuk menganalisis saiz optimum yang melibatkan permintaan beban berasaskan reabiliti
kuasa dan kos sistem juga diformulakan. Model sinaran global yang sesuai adalah berbeza
daripada model yang sedia ada kerana ia menggabungkan lokasi secara khusus dan parameter
persekitaran, yang dianggap akan mempengaruhi pembolehubah masukan. Hasil daripada
vii
kajian menunjukkan bahawa model radiasi solar yang dicadangkan menunjukkan prestasi
yang baik dan memaparkan peratusan RMSE kurang daripada 10% dan peratusan 8% bagi
MBE berbanding dengan model-model lain yang diperiksa. Kuasa pengeluaran modul PV
juga dianggarkan dengan pembinaan model litar elektrik diod tunggal. Masukan parameter
bagi model yang dibina diperolehi melalui kajian analisis. Ungkapan bagi keluaran arus dari
PV modul ditentukan dengan menggunakan fungsi W Lambert dan keluaran voltan pula
dikira dengan menggunakan kaedah berangka Newton-Raphson. Model yang dibina
menghasilkan ralat ± 2% dengan keluaran kuasa modul PV yang disediakan oleh pengeluar.
Tambahan pula, kaedah pensaizan komponen SAPV dirumuskan dengan menggunakan
teknik pengoptimuman tak-linear dengan kaedah terbitan pertama. Kaedah pensaizan
optimum yang dicadangkan menentukan keperluan tatasusunan kawasan modul PV dan
sistem beban penyimpanan kapasiti bateri dengan kos yang paling kurang dan proses
pratakrif keandalan kuasa.
Keputusan dari model yang telah diaplikasi dan kaedah pensaizan analisis disahkan dengan
menjalankan analisis model sensitiviti parameter. Hasil keputusan menunjukkan bahawa
pembolehubah masukan yang paling penting dan sensitif adalah jumlah radiasi solar, ia
mempunyai 2.5 kali pengaruh ke atas keputusan keluaran dengan indeks sensitiviti sebanyak
0.8. Pembolehubah sensitif yang terendah adalah kelajuan angin dengan indeks sensitiviti
kurang daripada 0.1. Jejak karbon dari generator diesel telah dianggar dan dibandingkan
dengan pelepasan karbon sistem SAPV untuk tujuan analisis persekitaran. Ini adalah kerana
generator diesel merupakan penjana kuasa yang umum untuk menghasilkan tenaga di
kawasan pedalaman di Sarawak. Analisis tersebut mendedahkan bahawa kuasa yang
dihasilkan oleh sistem SAPV dapat membantu untuk mengelakkan 111 tan CO2 dibebaskan
ke atmosfera berbanding kepada penjana kuasa 5kW diesel dengan permintaan beban
viii
6.3kW/day. Walau bagaimanapun, anggaran kos tenaga bersih daripada sistem SAPV
didapati 20 kali lebih tinggi daripada purata tarif elektrik di Malaysia.
Hasil kajian menunjukkan kaedah pensaizan yang dicadangkan ini adalah lebih tepat dan
mudah dilaksanakan berbanding dengan kaedah didapati sedia ada. Ia memerlukan data
purata sinaran suria, yang hampir boleh didapati di setiap tempat. Ia juga memberikan satu
tatacara yang lengkap bagi penentuan parameter model yang diperlukan dan menggabungkan
permintaan beban selain daripada kos dan keandalan sistem kuasa. Sebagai kesimpulan,
kaedah saiz optimum yang dibangunkan dapat digunakan dengan mudah bagi tujuan reka
bentuk, pembangunan, saiz pengoptimuman dan kajian kebolehlaksanaan sistem SAPV bagi
bekalan kuasa boleh diperbaharui di kawasan pedalaman dengan mudah.
ix
TABLE OF CONTENTS
Page
Dedication i
Acknowledgements ii
Abstract iii
Abstrak vi
Table of Contents ix
List of Figures xiv
List of Tables xix
Nomenclature xxi
Abbreviations xxvii
List of Papers xxix
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Statement of problems 2
1.3 Objectives of thesis 4
1.4 Original contributions 5
1.5 Structure of thesis 6
Chapter 2 Background and Literature Review 8
2.1 Introduction 8
2.2 Standalone photovoltaic systems 9
x
2.2.1 Charge controllers 9
2.2.2 Batteries 13
2.2.3 Power Inverters 17
2.3 Modeling of SAPV systems 19
2.3.1 Global solar radiation on horizontal surfaces 19
2.3.2 Solar radiation on PV module surface 22
2.3.2.1 Diffuse radiation component on horizontal surface 22
2.3.2.2 Solar radiation on tilted surfaces 24
2.3.2.3 Absorbed solar radiation on plane of array 31
2.3.3 PV module generator model 35
2.3.3.1 PV module temperature models 36
2.3.3.2 PV module power output models 39
2.4 Calculation of load demand 44
2.5 Estimation of energy output from PV systems 45
2.6 Design and sizing of SAPV systems 47
2.6.1 Meteorological data generation 48
2.6.2 Optimization scenarios based on different meteorological data 50
2.6.3 Optimization of tilt angle 50
2.6.4 Criteria for size optimization 52
2.6.4.1 Power reliability analysis 52
2.6.4.2 System cost analysis 53
2.6.5 Optimal sizing methods 53
xi
2.7 Sensitivity analysis 57
2.7.1 Methods of sensitivity analysis 57
2.7.2 Sensitivity analysis of PV system parameters 59
2.8 Economic Analysis 62
2.8.1 Economic factors 63
2.8.2 Economic measures for cost estimation 64
2.9 Environmental benefits of PV systems 69
2. 9.1 Diesel generators 70
2. 9.2 Fuel consumption model of diesel generators 72
2. 9.3 Environmental impacts of diesel generators 73
2. 9.4 Estimation of carbon footprints from diesel generators 74
2.10 Summary 75
Chapter 3 Performance Modeling of Photovoltaic Module 76
3.1 Introduction 76
3.2 Model for estimation of global solar radiation 77
3.3 Model for PV module power output 79
3.3.1 Determination of unknown parameters of model 82
3.3.1.1 Light-generated current 82
3.3.1.2 Reverse saturation current 83
3.3.1.3 Shape factor 84
3.3.1.4 Series Resistance 86
3.3.2 Determination of optimum power output parameters of model 88
3.3.3 I-V and P-V characteristic curves of a PV module by improved model 89
xii
3.4 Solar resource data 95
3.5 Comparison of adapted global solar radiation model with selected models 98
3.6 Comparison of selected tilted surface radiation models 104
3.7 Selection of tilted surface model 112
3.8 Comparison of selected PV module temperature models 116
3.9 Selection of PV module temperature model 119
3.10 Comparison of adapted PV module power output model with other models 121
3.11 Error analysis of PV module power output models 124
3.12 Summary 126
Chapter 4 Size Optimization of Standalone Photovoltaic System 129
4.1 Introduction 129
4.2 Size optimization method 130
4.2.1 Methodology of developed size optimization method 131
4.2.2 Developed analytical model for determination of optimal PV array capacity
and optimal battery storage capacity 133
4.2.3 Developed analytical model for determination of optimal PV array area and
useful battery storage capacity 140
4.3 Comparison of developed size optimization method with other methods 146
4.4 Sizing of SAPV system based on optimal PV array and battery storage capacity 151
4.5 Sizing of SAPV system based on optimal PV array area and useful battery
storage capacity 153
4.6 Size optimization of SAPV system with different scenarios 155
4.7 Summary 160
xiii
Chapter 5 Sensitivity Analysis and Economic Evaluation 162
5.1 Introduction 162
5.2 Sensitivity analysis 162
5.2.1 Differential sensitivity analysis method 163
5.2.2 Methodology for sensitivity analysis of SAPV system parameters 166
5.2.3 Results and discussions of sensitivity analysis 168
5.3 Determination of system cost 186
5.4 Results and discussions of cost analysis 187
5.5 Standalone diesel power systems 192
5.5.1 Estimation of carbon footprints from emissions of diesel generators 193
5.5.2 Environmental benefits of SAPV systems 198
5.6 Summary 199
Chapter 6 Conclusion and Future Works 201
6.1 Conclusion 201
6.2 Summary of contributions 204
6.3 Recommendations for future works 206
References 207
Appendix-A 238
Appendix-B 249
Appendix-C 250
Appendix-D 252
xiv
LIST OF FIGURES
Page
Figure 2.1 Operating principle of overcharge and over-discharge protection of
MPPT controller 10
Figure 3.1 Equivalent electrical circuit model of a PV module 81
Figure 3.2 Typical I-V characteristic curve of a selected PV module 90
Figure 3.3 Typical P-V characteristic curve of a selected PV module 91
Figure 3.4 I-V characteristic curves at various solar radiation levels 91
Figure 3.5 I-V characteristic curves at various ambient temperatures 92
Figure 3.6 I-V characteristic curves for various set of solar radiation and ambient
temperature 93
Figure 3.7 P-V characteristic curve at constant temperature of 25°C 94
Figure 3.8 P-V characteristic curve at constant solar radiation of 1000 W/m2
94
Figure 3.9 P-V characteristic curve at various set of solar radiation and ambient
temperature 95
Figure 3.10 Measured global solar radiation data at Kuching by MMS and NASA 96
Figure 3.11 Estimated monthly mean daily global solar radiation at Sri Aman 99
Figure 3.12 Estimated monthly mean daily global solar radiation at Sibu 100
Figure 3.13 Estimated monthly mean daily global solar radiation at Bintulu 100
Figure 3.14 Estimated monthly mean daily global solar radiation at Limbang 101
Figure 3.15 Estimated RMSE and MBE of global radiation by different models at various
cities of Sarawak 103
Figure 3.16 Estimated percentage RMSE and MBE of different models at various cities of
Sarawak 103
Figure 3.17 Estimated amount of (a) incident (b) absorbed solar radiation on tilted surface
by different models with MMS data 107
xv
Figure 3.18 Estimated amount of (a) incident (b) absorbed solar radiation on tilted surface
by different models with NASA data 109
Figure 3.19 Estimated amount of incident solar radiation on tilted surface by different
models with MMS and NASA data 110
Figure 3.20 Estimated amount of absorbed solar radiation on tilted surface by different
models with MMS and NASA data 110
Figure 3.21 Mean and standard deviation of absorbed solar irradiation of different models
with MMS and NASA data 114
Figure 3.22 SEM and Range of absorbed solar irradiation at confidence interval of
95% by different models 115
Figure 3.23 Estimated yearly mean daily PV module temperature by different models
with MMS data 117
Figure 3.24 Estimated yearly mean daily PV module temperature by different models
with NASA data 117
Figure 3.25 PV module temperature mean and standard deviation by different models
with MMS and NASA data 120
Figure 3.26 PV module temperature SEM and Range at confidence interval of 95%
by different models 120
Figure 3.27 Estimated yearly mean hourly PV module power output by different
models with MMS data 122
Figure 3.28 Estimated yearly mean hourly PV module power output by different
models with NASA data 123
Figure 3.29 PV module power output mean and standard deviation by different models
with MMS and NASA data 125
Figure 3.30 PV module power output SEM and Range at confidence interval of 95%
by different models 125
Figure 4.1 Isoreliability lines with three different LLP values 136
Figure 4.2 LLP curve with various combinations of PV array capacity and battery
storage capacity in terms of different cost lines 138
Figure 4.3 Isoreliability lines with three different LLP values 141
Figure 4.4 LLP curve and cost lines with various combinations of A and uC 143
xvi
Figure 4.5 Comparison of analytical methods with developed model at LLP of 0.1 147
Figure 4.6 Comparison of analytical methods with developed model at LLP of 0.01 147
Figure 4.7 Comparison of numerical methods with developed model at LLP of 0.1 148
Figure 4.8 Comparison of numerical methods with developed model at LLP of 0.01 149
Figure 4.9 Comparison of Markvart method with developed model 150
Figure 4.10 Battery storage capacity versus PV array capacity at LLP of 0.01 152
Figure 4.11 Useful battery storage capacity versus PV array area at LLP of 0.01 154
Figure 4.12 Optimum points at different values of load demand with constant
and 155
Figure 4.13 Optimum points at different values of with constant and load
demand 156
Figure 4.14 Optimum points at different values of with constant and load
demand 156
Figure 4.15 Optimum points at constant load demand with different values of
and 157
Figure 4.16 PV array area versus useful battery storage capacity with MMS data 158
Figure 4.17 PV array area versus useful battery storage capacity with NASA data 159
Figure 5.1 Model for sensitivity analysis of SAPV system parameters 167
Figure 5.2 Sensitivity analysis of output parameters with respect to slope 168
Figure 5.3 Comparative values of various sensitivity indices for output parameters
w.r.t. slope 170
Figure 5.4 Sensitivity analysis of output parameters with respect to solar azimuth
angle 171
Figure 5.5 Comparative values of various sensitivity indices for output parameters
w.r.t. solar azimuth angle 172
Figure 5.6 Sensitivity analysis of output parameters with respect to hour angle 173
Figure 5.7 Comparative values of various sensitivity indices for output parameters
xvii
w.r.t. hour angle 174
Figure 5.8 Sensitivity analysis of output parameters with respect to ground
reflectance 175
Figure 5.9 Comparative values of various sensitivity indices for output parameters
w.r.t. ground reflectance 176
Figure 5.10 Sensitivity analysis of output parameters with respect to total solar
Radiation 177
Figure 5.11 Comparative values of various sensitivity indices for output parameters
w.r.t. total solar radiation 178
Figure 5.12 Sensitivity analysis of output parameters with respect to ambient
temperature 179
Figure 5.13 Comparative values of output sensitivity indices for output parameters
w.r.t. ambient temperature 180
Figure 5.14 Sensitivity analysis of output parameters with respect to wind speed 181
Figure 5.15 Comparative values of various sensitivity indices for output parameters
w.r.t. wind speed 182
Figure 5.16 Sensitivity coefficient variance of output parameters versus different
input variables 183
Figure 5.17 Sensitivity indices of output parameters versus different input variables 184
Figure 5.18 Correlation coefficient of output parameters versus different input
variables 185
Figure 5.19 Item-wise cost of PV system components with MMS data 188
Figure 5.20 Category-wise cost of PV system components with MMS data 188
Figure 5.21 Percentage-wise cost of PV system components with MMS data 189
Figure 5.22 Item-wise cost of PV system components with NASA data 190
Figure 5.23 Category-wise cost of PV system parameters with NASA data 190
Figure 5.24 Percentage-wise cost of PV system components with NASA data 191
Figure 5.25 Efficiency, fuel consumption and carbon footprints of diesel generator
versus rated power 194
xviii
Figure 5.26 Carbon footprints (kgCO2/day) at various emission factors and rated power
of diesel generators 195
Figure 5.27 Carbon footprints (kgCO2/kWh) at various emission factors and rated
power of diesel generators. 196
xix
LIST OF TABLES
Page
Table 2.1 Description of selected empirical models for determination of global
solar radiation on horizontal surface 21
Table 2.2 Description of selected models for determination of diffuse components
from global solar radiation 23
Table 2.3 Description of selected isotropic sky models for determination of tilted
surface radiation 27
Table 2.4 Description of selected anisotropic sky models for determination of tilted
surface radiation 28
Table 2.5 Values of constants )( i for various types of PV cells/ modules 33
Table 2.6 Values of constants )( ib for various types of PV cells/modules 34
Table 2.7 Description of selected PV module temperature models 38
Table 2.8 Description of selected PV module power output models 41
Table 2.9 Equations to obtain the optimum slope of the modules )( at LLP of 0.1
and 0.01 for methods A and B 51
Table 2.10 Overview of economic measures applying to social investment features
and decisions 66
Table 2.11 Merits and limitations of main economic tools for calculation of LCC 66
Table 3.1 Description of parameters for determination of location constant 79
Table 3.2 Calculated amount of tilted surface radiation at Kuching from MMS
data sources 105
Table 3.3 Calculated amount of tilted surface radiation at Kuching from NASA
data sources 105
Table 3.4 One-sample statistical analysis of MMS and NASA data by different
tilted surface models 114
Table 3.5 One-sample statistical analysis of MMS and NASA data by different
PV module temperature models 119
xx
Table 3.6 One-sample statistical analysis of MMS and NASA data by different
PV module power output models 124
Table 4.1 Equations to estimate parameters r and s, for LLP of 0.1 and 0.01 for
methods A and B 135
Table 4.2 Optimum unit cost of PV system at different values of and 158
Table 5.1 Estimation of fuel consumption and carbon footprints from diesel
generators 193
Table 5.2 Carbon footprints (kgCO2/day) at various emission factors and rated
power of diesel generator 194
Table 5.3 Carbon footprints (kgCO2/kWh) at various emission factors and rated
power of diesel generator 195
xxi
NOMENCLATURE
Notation Description Unit
A ideality factor (1 for ideal diodes and between 1 and 2 for
real diodes)
PV array area
-
m2
iA anisotropy index -
optA
optimum PV array area m2
PVA effective area of a single PV module m2
a and b location constants -
B radiation distribution index -
pB
batteries connected in parallel -
sB
batteries connected in series -
C
total capital cost of the PV system installation US$
aC
ratio of PV array capacity to the daily mean energy
demand
-
0aC
optimum PV array capacity -
bC ratio of the useful battery storage capacity that can be
taken out from the batteries to the daily mean energy
demand
-
bnC nominal capacity of a battery Wh
0bC
optimum battery storage capacity -
0C
total constant costs including the cost of design and
installation
US$
CO2 carbon dioxide -
optC
optimum cost of SAPV system US$
uC
useful battery storage capacity Wh
ubnC maximum energy that can be extracted from a single
battery
Wh
optuC , optimum useful battery storage capacity Wh
D diode diffusion factor -
d discount rate -
acD total AC demand kWh/day
dcD total DC demand kWh/day
eqdcD , total equivalent DC demand kWh/day
maxDOD maximum depth of discharge of a battery %
dn nominal discount rate -
dr real discount rate -
DS daylight saving Minutes
weekD number of days the load is used during a week Day
E equation of time, Minutes
xxii
energy output of SAPV system kWh/day
e inflation rate -
AE energy of the PV array available to the load demand and
battery
kWh/day
eE annual energy available for export from the onsite
generation
kWh/year
PVE energy delivered by a PV array kWh/day
F fuel consumption rate of diesel generator Liters/hr
f modulating function,
number of failures,
frequency of diesel generator
-
-
Hz
scgchzc FFF ,,, ,,
view factors from PV collector to horizon, ground and sky
respectively
-
FF fill factor,
fractional factorial
-
-
Fm current dollar cash flows US$
Fn constant dollar cash flows US$ 'F modulating factor-clearness index -
TG solar radiation W/m2
refTG , solar radiation at reference conditions W/m2
GW gigawatt -
H monthly average global solar radiation on a horizontal
surface
MJ/m2
bH average daily beam radiation on horizontal surface for a
month
MJ/m2
bTH average daily beam radiation on tilted surface for a month MJ/m2
cH
monthly mean daily total radiation on a horizontal surface
on a clear sky day
MJ/m2
dH average daily diffuse radiation on horizontal surface for a
month
MJ/m2
dayH
number of hours the load is consuming power in a day Hours
dTH average daily diffuse radiation on tilted surface for a
month
MJ/m2
oH daily extraterrestrial radiation on horizontal surface MJ/m2
oH
monthly average daily extraterrestrial radiation on
horizontal surface
MJ/m2
TH monthly mean daily incident solar radiation on a tilted
surface
MJ/m2
TdHTrHTbH ,,
monthly mean daily beam, reflected and diffuse radiation
on a tilted surface respectively
MJ/m2
isoTdH
csTdHhzTdH
,
,,,,
monthly mean daily horizon brightening, circumsolar and
isotropic diffuse radiation on a tilted surface respectively
MJ/m2
I output current of a PV cell or module Ampere
