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SOLAR ENERGY
Fundamentals, Economic and Energy Analysis
Saurabh Kumar Rajput
Northern India Textile Research Association
Sector-23, Rajnagar, Ghaziabad 201002
@ NITRA
All right are reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording and /or otherwise, without the prior written permission of the publisher.
First Edition: 2017
ISBN: 978-93—81125-23—6.
Price: Rs. 175//=
Foreword
The world is facing depleting natural fuel such as coal, natural gas for power generation and ever
increasing demand of electricity. In this scenario everybody is looking for non-conventional,
renewable energy sources such solar power, wind energy etc. The present book “Solar Energy –
Fundamentals, Economic & Energy Analysis” is based on present knowledge on solar energy
technology written by Mr. Saurabh Kumar Rajput, gives hands on information for practicing
engineers. This book is useful for budding engineers and researchers also. Many industries
including textiles and garment industries are installing solar power plants in large scale. This will
be useful for the energy engineers of these industries.
Dr. Arindam Basu
Director General, NITRA
(iii)
Acknowledgement
I take this opportunity to express my gratitude and thanks to the respected Director General of
NITRA, Dr. Arindam Basu for his valuable suggestions and constant encouragement, without
which this book would not have come into existence.
I am especially grateful to Dr. M.S. Parmar, Joint Director (Academics) of NITRA Technical
Campus for his time-to-time; much needed valuable guidance and support.
I would like to express my thanks to Mr. Pratik Prasun, Senior Engineer (Solar Energy
Corporation of India Limited, New Delhi) for his support and help.
I am also thankful to Mr. Vikas Sharma, Principal Scientific Officer (NITRA, Ghaziabad) and
Mr. Paurush Godhar, Scientific Officer (NITRA, Ghaziabad) for their help.
Saurabh Kumar Rajput
Assistant Professor
(iv)
Brief Contents
Chapter 1: Basics of solar energy 1
Chapter 2: Solar thermal and application 9
Chapter 3: Solar photovoltaic (PV) and application 19
Chapter 4: Economics of solar systems 34
Chapter 5: Energy analysis of solar systems 55
Chapter 6: Simulation and analysis of Photovoltaic (PV) system with Maximum power
point Tracking (MPPT)
66
Appendix 78
Bibliography 81
(v)
Table of contents
Chapter 1: Basics of solar energy (1-7)
1.1 Introduction 1
1.1.1 Primary and secondary energy 1
1.1.2 Commercial and noncommercial energy 1
1.1.3 Renewable and nonrenewable energy 1
1.2 Solar energy and Solar radiation (Direct, diffuse and total solar radiation) 2
1.3 Sun earth angles 4
1.3.1 Latitude 4
1.3.2 Declination 4
1.3.3 Hour angle 5
1.3.4 Altitude angle and Zenith angle 6
1.3.5 Surface azimuth angle and Solar azimuth angle 7
Chapter 2: Solar thermal and application (9-18)
2.1 Introduction 9
2.2 Solar thermal energy applications 9
2.2.1 Flat plate solar collector 9
2.2.1 (a) Flat plate solar water heater 11
2.2.1 (b) Flat plate solar space heater 12
2.2.2 Concentrating collector / Focusing collector 12
2.2.3 Solar thermal power plant 14
2.2.3 (a) Solar distributed collector power plant 15
2.2.3 (b) Solar central receiver power plant 16
2.3 Thermal energy storage for solar heating and cooling 16
2.3.1 Sensible heat storage 17
2.3.2 Latent heat storage 17
2.4 Limitations of solar thermal energy 18
Chapter 3: Solar photovoltaic (PV) and application (19-33)
3.1 Solar photovoltaic (PV) energy conversion / Photovoltaic effect 19
3.2 Performance analysis of solar photovoltaic (PV) Cell 20
3.2.1 Short circuit current 20
3.2.2 Open circuit voltage 21
3.2.3 Power delivered to load 21
3.2.4 Maximum current 21
3.2.5 Maximum power 21
3.2.6 Efficiency of solar cell 22
3.2.7 Fill factor 22
(vi)
3.2.8Limitation of Solar Cell 22
3.3 Solar cell material 23
3.4 Solar cell, Solar module & Solar array 24
3.5 Solar power plant 30
3.5.1 Autonomous solar power plant / off grid power plant 30
3.5.2 Grid connected Solar power plant 32
3.6 Limitations of solar photovoltaic (PV) energy conversion 33
Chapter 4: Economics of solar systems (34-52)
4.1 Economics of renewable energy system 34
4.2 Economics of solar system 34
4.3 Cash flow diagram 35
4.4 Time value of money 35
4.4.1 Equivalence formula involving time value of money 36
4.5 Salvage value 37
4.6 Profit cost analysis 38
4.6.1 Profit cost analysis by converting to future time frame 38
4.6.2 Profit cost analysis by converting to ‘t=o’time frame 39
4.7 Unit cost analysis of solar system 42
4.7.1 Estimation of unit cost of useful thermal energy delivered by a domestic solar water
heating system (DSWHS) 42
4.7.2 Unit cost analysis of electricity generated by solar PV system 45
4.8 Measures of financial (economical) performance 47
4.8.1 Payback period 47
4.8.1(a) Simple payback period 48
4.8.1(b) Discounted payback period 48
4.8.2 Net present value 49
4.8.3 Benefit to cost ratio (B/C) and internal rate of return (IRR) 51
4.9 Case study: Roof-top PV system for textile unit 52
Chapter 5: Energy analysis of solar systems (55-64)
5.1 Energy metrics 55
5.1.1 Embodied energy 55
5.1.2 Energy Pay Back Time (EPBT) 55
5.1.3 Electricity Production Factor (EPF) 56
5.1.4 Life Cycle Conversion Efficiency (LCCE) 57
5.2 Case study: Energy analysis of roof-top photovoltaic (PV) system 57
5.3 Energy analysis of solar evaporative cooling system 63
5.4 Energy analysis of solar day lighting system 64
(vii)
Chapter 6: Simulation and analysis of photovoltaic (PV) system with Maximum Power
Point Tracking (MPPT) system (66-76)
6.1 Simulation of PV system 66
6.1.1 Introduction 66
6.1.2 Model of solar cell 66
6.2 Maximum power point tracking system 69
6.2.1 Perturb and observe 70
6.2.2 Perturb and observe algorithm 71
6.3 Simulation of overall PV system 72
6.3.1 PV system without MPPT 72
6.3.2 PV system with MPPT 73
6.4 Simulation results 74
6.5 Calculation of energy metrics using MATLAB 76
Appendix: Relevant data for Solar based project 78
Bibliography 81
(viii)
1
1.1 Introduction
Energy is defined as capacity to produce an effect to do work. Energy has been an important
component to meet the day to day needs of human beings. Human society require increasing
amount of energy for industrial, commercial, domestic, agriculture, and transport uses. Different
forms of energy are defined as primary and secondary energy, commercial and noncommercial
energy, renewable and nonrenewable energy.
1.1.1 Primary and Secondary energy-
Primary energy refers to all types of energy extracted or captured directly from natural resources.
Primary energy can be further divided into two parts namely renewable and non renewable
energy.
Primary energy is transformed into more convenient form of energy such as electricity, steam
etc. these form of energy are called secondary energy
1.1.2 Commercial and Noncommercial energy-
Energy that is available in the market for a definite price is known as commercial energy. The
most important forms of commercial energy are electricity, coal, refined petroleum products and
natural gas.
Any kind of energy which is sourced within a community and its surrounding area, and which is
not normally treated in the commercial market is termed as noncommercial energy such as
firewood, cattle dung, agriculture waste etc.
1.1.3 Renewable and nonrenewable energy-
Renewable energy is obtained from natural sources. These resources can be used to produce
energy again and again eg. Solar energy, wind energy, tidal energy etc.
Non renewable resources cannot be replaced once they are used eg. Coal, oil, gas etc. these
energy resources are limited and would be exhausted within prescribed period of time.
2
1.2 Solar energy and solar radiation-
The earth receives the solar energy in the form of solar radiation. These radiations comprising of
ultra-violet, visible and infrared radiation. The amount of solar radiation that reaches any given
location is dependent on several factors like geographic location, time of day, season, land scope
and local weather. Because the earth is round, the sun rays strike the earth surface at different
angl
possible energy.
Most of the part of India receives 4 to 7 kWh of solar radiation per square meter per day. India
receives solar energy equivalent more than 5000 trillion kWh per year.
Solar radiation (Direct, diffuse and total solar radiation):
Fig. 1.1 Solar radiation
The solar radiation that reaches the surface of the earth without being diffused is called direct
beam solar radiation. It is measured by instrument named as pyrheliometer.
As sun light passes through the atmosphere, some part of it is absorbed, scattered and reflected
by air molecule, water vapours, clouds, dust and pollutants. This is called diffuse solar radiation.
The diffuse solar radiation does not have unique path.
3
The sum of the direct and diffuse solar radiations is called total radiation or global solar
radiation. Pyranometer is used for measuring the total radiation.
Fig.1.2 Direct, diffuse and total solar radiation
If,
Rb- Beam Radiation (direct solar radiation)
Rd- Diffuse Radiation (solar radiation after diffusion)
Rr- Reflected radiation (solar radiation after reflection from surface)
Rt- Total solar radiation on tilted surface
Then,
Rt = Rb + Rd + Rr --------------- (1.1)
4
1.3 Sun – Earth angles
1.3.1 Latitude (ф)
The latitude of a location is the angle made by the radial line joining the location to the centre of
the earth with the projection of the line on the equatorial plane.
-+90°
Fig. 1.3 Latitude angle
1.3.2 Declination (δ)
The declination angle is the angle made by the line joining the centre of the sun and the earth
with its projection on equatorial plane.
The declination angle varies from a maximum value of +23.45° on June 21 to a minimum value
of -23.45 on December 21.
5
--------------- (1.2)
(Where, n- number of days)
for winters in northern hemisphere
for summer in northern hemisphere
Example1: Calculate declination angle for March 22 in a non-leap year.
Solution: On March 22, n= 31 (January) + 28 (February) + 22 (22nd march)
n= 81 days
So,
= 0
On march 22 and September 22, the declination is zero so these days are called equinoxial day
Example2: Calculate declination angle for March 31 in a leap year.
Solution: On March 22, n= 31 (January) + 29 (February) + 31 (31st march)
n= 91 days
So,
= 4.016°
1.3.3 Hour angle (ω)
It is the angle through which the earth must be rotated to bring the meridian of the plane directly
under the sun
Fig. 1.4 Hour angle
6
Because it is 24 hours for 360° of rotation, so each one hour correspond to 15°
12) ---------------- (1.3)
Where, ST solar time
Example3: Calculate the hour angle at 02:30 PM.
Solution: 12)
12) = 37.5°
1.3.4 Altitude Angle (α) and Zenith angle (θZ)
Altitude angle is the angle between the incident sun ray and the projection of
horizontal plane.
Z= 90° - -------------------- (1.4)
zenith angle is the angle between the incident sun ray and the perpendicular line to the horizontal
plane.
Z ---------------- (1.5)
Fig.1.5 Altitude angle and Zenith angle
7
1.3.5 Surface azimuth angle (γ) and solar azimuth angle (γS)
of
normal on horizontal plane.
Surface azimuth angle is the angle between line due south and the projection of normal to the
surface on horizontal plane.
Solar azimuth angle is the angle between line due south and the projection of sun rays on
horizontal plane.
------------------------------ (1.6)
Fig.1.6 surface azimuth angle and solar azimuth angle
8
Example 4: st
at latitude of 23°N.
Solution: , n= 244 days
12) = 45°
= 7.724°
Z = Sin (23°) Sin (7.724°) + Cos (23°) Cos (7.724°) Cos (45°)
Z = 45.87°
9
2.1 Introduction
The Sun is most prominent source of energy in our system. The source of solar energy is process
. This energy is radiated from sun in all directions and a
fraction of this energy is reaches to the earth.
C.
Above the photosphere there is a transparent layer of gases known as chromospheres. The light
emitted by the chromospheres is of short wave length. Finally there is the corona. The corona is
in this region, prominence appear. Prominence is
immense clouds of glowing gas that erupt from upper chromospheres. The corona can only be
seen during total solar eclipse.
2.2 Solar thermal energy application
Solar thermal energy is used for water heating, space heating, electric power generation, solar
cooker for cooking of food etc.
2.2.1 Flat plate solar collector
Solar collector absorbs the incident solar radiation and converts it to the useful heat which is use
for heating a collector fluid such as water, oil or air.
Flat plate collector are used where temperature below 100°C are required.
10
The important parts of flat plate collectors are shown below
Transparent cover Absorber plate
Thermal insulation series of tubes
(Heat transfer medium)
Fig. 2.1 Flat plate solar collector
Construction
Transparent Cover-
This allows solar energy to pass through, but reduces the heat loss examples are tempered glass,
transparent plastic materials etc
Absorber plate-
Plate is blackened in order to absorb the maximum amount of solar radiations.
The absorber consists of a thin sheet. This sheet is made of conductor material (aluminum, steel,
copper etc.) because the metal is a good conductor of heat. Black coating is applied to this
conductor / metal plate in order to absorb the maximum amount of solar radiations.
Copper is best material for absorber plate because it has high thermal conductivity, adequate
tensile strength and good corrosion resistance.
Series of tubes-
The absorber plate with several parallel tubes is fabricated from copper tube and sheet by soft
soldering.
11
Heat transport fluid (Water)-
To remove heat from the absorber, fluid is usually circulated through tubes to transfer heat from
the absorber to an insulated water tank.
Thermal insulation-
It is used to provide insulation on the sides and bottom so as to prevent losses and thereby attain
high temperatures. Examples of thermal insulations are crown white wool, glass wool, calcium
silicate etc.
Working-
When solar radiation passes through the transparent cover and incident on blackened absorber
surface of high absorptivity, a large portion of this energy is absorbed by the plate and then
transferred to the fluid (Air, Water etc)
Thermal insulation is used to reduce conduction losses and transparent cover is used to reduce
convection losses.
Note when air is used as heat transport fluid, it is flat plate air collector which is used for space
heating (solar space heater) and when liquid is used as heat transport fluid, it is flat plate liquid
collector which is used for water heating (solar water heater)
2.2.1 (a) Solar flat plate collector type water heating system-
Fig. 2.2 Solar water heater
12
Cold water is pumped to the flat plate collector, collector absorbs the heat by solar radiation and
heated water is stored in the tank.
2.2.1 (b) Solar flat plate collector type space heating system-
Fig. 2.3 Solar space heater
Water is heated by incident solar radiation on flat plate collector. This heated water is collected
in a tank.
The energy is transferred to the air circulating in the house by water to air heat exchanger.
2.2.2 Concentrating collectors / focusing collectors (Cylindrical trough Solar collector)
Focusing collector has less heat loss so they operate at higher temperature. Flat plate collectors
operate on temperature about 100°C in summer and 40°C in winter. So, in order to increase the
temperature range of collectors, focusing of collectors are used.
In focusing collectors, a parabolic mirror is used. The sun rays are focused on the focal point of
the mirror by reflection from its surface.
A tube is placed along the focal line of the mirror and fluid is circulated through the tube this
fluid absorb the heat from reflected solar radiation.
13
Fig. 2.4 focusing of collector
With these collectors, temperature of 200°C - 300°C or above may be obtained. In some
mechanism, seasonal tracking of sun is also provided to get the maximum heat from sun light.
The focusing collectors can have two arrangements namely cylindrical parabolic concentrator
(100°C < T < 200°C) and parabolic mirror arrays (T > 200°C)
C = (Aa / Ab) ---------------------------- (2.1)
Aa - Aperture area, Ab - Absorber area
The C value of 20 to 100 can be achieved by a linear concentrator such as parabolic trough
concentrator and the C value of 100 to 4000 can be achieved by a point focus concentrator such
as parabolic dish.
14
Fig. 2.5 Different types of concentrating / focusing collectors
Materials for concentrators-
Reflector-
Reflector should have high reflectivity. Therefore mirror glass may be used. Glass is the most
durable with low iron content so it is a good reflector. Aluminium and silver are also good
reflecting surface. Plastics are also used as reflector now days.
Receiving material-
Glass and transparent plastic films are generally used as cover material for receivers. Glass
should have low iron content to reduce absorption by it.
Coatings are required to have strong solar absorptivity. Weather resistance, stability at high
temperature Examples are black paints, black chrome etc.
2.2.3 Solar thermal power plant-
15
In solar thermal power plants, the concentrating collectors are used for generation of electricity.
There are two types of solar thermal power plants namely solar distributed collector power plant
and solar central receiver power plant.
2.2.3 (a) Solar distributed collector power plants-
Fig. 2.6 Solar distributed collector electric power plant
In this type of power plants, collectors are used. Collectors may be parabolic trough unit with
line focus or parabolidal dishes with centre focus.
The flat plate collectors are not used in power plants because there efficiency is very poor and
operating temperature is very low.
Water is heated by the collector and stored in the storage tank. This heated water is converted
into steam by boiler and steam is provided to turbine to make it run. This turbine is coupled with
generator so rotation of turbine makes generator to rotate hence electricity is generated.
The steam is condensed in the condenser and feed water is provided to boiler for reuse.
16
2.2.3 (b) Solar central receiver power plant-
Fig. 2.7 Solar central receiver electrical power plant
In this system, a large number of linear reflectors are used. These are called heliostat. Heliostat
focus on the central receiver as shown in the figure
When solar radiations fall on heliostat, sun rays after getting reflected from the heliostat are
focused on the boiler.
The output of boiler is high temperature steam which is provided to the turbine. This will rotate
turbine. As the generator is also coupled with the turbine so with the rotation of turbine,
generator will also rotate and electricity will produce.
2.3 Thermal energy storage for solar heating and cooling-
Thermal energy storage is essential for both domestic water and space heating applications.
Thermal energy can be stored in well insulated fluids or solids.
17
There are two ways for thermal energy storage namely sensible heat storage and latent heat
storage.
2.3.1 Sensible heat storage-
In sensible heat storage the temperature of the medium changes during charging and discharging
of the storage
In this, there is no change in phase. The basic equation for energy storage is given by
Q = mcp -------------------------------- (2.2)
Where
Q- Total thermal capacity
m- Mass of storage medium
cp- Specific heat
Heat stored per unit volume (Q/Vs) is given by
------------------------------------ (2.3)
Where Vs is the volume of the given storage container
Water is generally used for storing thermal energy at low temperature. Heat transfer oils are used
in sensible heat storage system for temperature range 100 - 300°C
Solid materials like rocks, metals, concrete, sand and bricks etc. are also used for thermal
storage.
Water is also used as heat transfer fluid for heat flow to and from (but the temperature range is
limited)
2.3.2 Latent heat storage-
In latent heat storage, the temperature of the medium remains more or less constant, since it
undergoes a phase transformation ie. The transition from solid to liquid or liquid to vapour
In a latent heat storage system, the heat is stored in a material when it melts and heat is extracted
from material when it freezes example of such materials are paraffin wax, calcium chloride
hexahydrate, magnesium nitrate hexahydrate, ice, sodium hydroxide etc.
18
For latent heat storage charging, phase transition solid- liquid (melting) is most suitable and for
storage discharging, liquid- solid (solidification) is most suitable.
The basic equation for energy storage is given by
Q= m [Cs(tm tmin) + hm + CL(tmax tm)] joule ----------------------------------(2.4)
Where
m- Mass of phase change material (PCM) storage medium
Cs- Specific heat of PCM solid state (J/KgK)
CL- Specific heat of PCM liquid state (J/KgK)
hm Specific melting enthalpy of PCM storage medium (J/Kg)
tmin- Minimum storage temperature (°C)
tmax- maximum storage temperature (°C)
tm- Melting temperature of PCM storage medium (°C)
the latent heat storage charging process comprises three stages-
First stage is heating of the phase change material in solid state
Second stage is melting of phase change material at constant temperature for pure substance or in
the range of temperatures for mixed composition
Third stage involve heating of the molten phase change material to the maximum temperature
(tmax)
2.4 Limitations of Solar thermal energy
Low energy density 0.1 to 1 KW/ m2
Large area is required to collect solar thermal energy
Direction of rays changes continuously with time
Energy not available during night and during clouds
Energy storage is essential
It has high cost
Solar central power plants in MW range are not economical
19
3.1 Solar photovoltaic (PV) energy conversion (Photovoltaic effect) -
Fig. 3.1 Photovoltaic effect
A solar cell is nothing but a PN junction diode under light illumination. Sun light can be
converted into electricity due to photovoltaic effect. Sun light composed of photons (packets of
energy). These photons contain various amount of energy corresponding to different wave
lengths of light. When photons strike a solar cell they may be reflected or absorbed or pass
through the cell. When solar radiation is absorbed in PN junction diode, electron-hole pairs
(EHP) are generated.
Electron hole pair (EHP) generated in depletion layer-
Electrons of EHP will be repealed towards N side because of electric field and holes of
EHP will be repealed towards P side because of electric field.
20
Electron hole pair (EHP) generated in quasi neutral region-
In this region, the electron and holes of EHP will wander around in the region randomly.
There is no electric force to guide them in any direction.
Minority carriers of P and N regions-
The minority carrier near the depletion region will also get direction by electric field.
In this way there will be increase of positive charge at P side and increase of negative charge at
N side. This build up of positive and negative charge causes a potential difference to appear
across the PN junction due to light falling on it. This generation of photo voltage is known as
photovoltaic effect.
3.2 Performance analysis of photovoltaic (PV) cell –
Fig. 3.2 Photovoltaic cell performance
Consider a PN junction with resistive load as shown in figure. When solar cell is illuminated,
electron hole pair is generated in the depletion region. This electron hole pair when separated
from each other across junction then a current (IL) flows in external circuit by photovoltaic
effect.
This photo current (IL) produces a voltage drop across resistive load and this voltage will forward
bias the PN junction. Forward bias voltage produces forward current (I1).
So the net current will be, I = IL I1
------------------- (3.1)
3.2.1 Short circuit current (ISC)-
21
When R=0 and V = 0 then I1 =0
so I = IL = ISC ----------------------------------------- (3.2)
3.2.2 Open circuit voltage (VOC)-
--------------------------------------------------- (3.3)
3.2.3 Power delivered to load-
P= V.I
P= V.
for maximum power delivered to load,
By solving, 1 +
=
------------------------- (3.4)
Where Vm is the voltage which produces maximum power
3.2.4 Maximum Current -
If we put the value of
from equation 4 to equation 1, we get the maximum value of
current (Im)
3.2.5 Maximum Power -.
the maximum power is obtained by multiplying vm and Im
Pm = Vm.Im =
--------------------------------------- (3.5)
22
Fig. 3.3 I-V characteristics of solar cell
3.2.6 Efficiency of solar cell-
Conversion efficiency of solar cell is defined as the ratio of output power to incident optical
power. For maximum power output,
------------------------------------------- (3.6)
Where, Pm- maximum power(watt), Pin- input power(Watt), Vm- maximum voltage(Volt), Im-
maximum current(Amp), I- solar intensity(watt/m2), A- area(m2)
3.2.7 Fill Factor (FF)-
It is the ratio of maximum power to the product of Voc and Isc
-------------------------------------------------- (3.7)
3.2.8 Limitation of solar cell -
There are several factors that limit the efficiency of solar cells, these are:
23
Photons with energy below the band gap energy, cannot generate electron hole pair so there
energy is not converted into useful output. These electron generate only heat and reduces the
electrical efficiency of solar cell
Photons with energy above the band gap energy, only a fraction of energy is used for generating
free electrons for conduction. Remaining energy will produce heat and reduce electrical
efficiency of solar cells.
When sun light fall on solar cell, some part of it is reflected back, some part is absorbed and
some part is transmitted, only absorbed solar light is converted into electricity so its efficiency is
poor
Example 1: Calculate Fill factor, maximum power and cell efficiency with following
parameters- Voc= 0.24 volt, Isc= 10mAmp, Vm= 0.14 volt, Im= 6.5 mAmp., Intensity = 24
W/m2, Area= 4 cm2
Solution-
Pm = Vm × Im = 0.91 m Watt
= 9.48 %
3.3 Solar cell material -
The solar cells are made of various materials. Silicon is the most commonly used material for
solar cells. The electrical properties of silicon depend on the type and amount of dopants.
Phosphorous and boron are most widely used doner and accepter dopant respectively.
The choice of material depends upon the energy gap, efficiency and cost. In order to reduce the
cost, the level of efficiency should be high. The cost can be reduced by using thin film
technology. A variety of compound semiconductor are to be used to manufacture thin film solar
cell. These materials are CdS, CdTe, InP, GaAs, ZnTe, AlSb (Aluminium Antimonide).
24
Table 3.1 Energy Gap of some materials
Material
Energy Gap (ev)
Si
1.1
CdTe
1.44
CdS
2.42
GaAs
1.40
InP
1.27
ZnTe
2.2
AlSb
1.63
According to types of crystal, the solar cells are of three types
First is mono crystalline silicon cells (Maximum efficiency= 24%)
Second is poly crystalline silicon cells (Maximum efficiency= 17.8%)
Third is amorphous silicon cell (Maximum efficiency= 13%)
3.4 Solar Cells, Solar Modules and Solar Array-
Solar cell is basic unit of solar electricity generator. It is made up of semiconductor material.
When sun light falls on solar cells, it produces electricity by photovoltaic effect. One solar cell
produces 0.5 Volt DC voltages.
Fig. 3.4 Series connection of three solar cells
When solar cells are connected in series to produce high voltage, it is called as solar module. The
number of solar cells in solar module is determined by the required voltage. Generally solar
modules are made to produce output voltage of 18 Volt DC voltage
(Voltage of one solar cell) × (Number of solar cells) = Output of solar module ------------- (3.8)
25
By using this formula, we can say that 36 solar cells of 0.5 Volt each will be required for
producing 18 Volt output voltage module. These 36 solar cells will be connected in series as
shown in the figure
3.5 (a) Opaque PV Module 3.5(b) Semitransparent PV Module
Solar modules are of two types namely Opaque module and Semitransparent module. In opaque
modules, front side is transparent glass cover and back side is insulating tedler material which is
not transparent.
In semitransparent type module, both the front and back side is transparent glass cover (ethyle
vinyl acetate).
Packing factor (PF) is defined as the ratio of area covered by solar cell to the area of PV module.
In case of rectangular solar cells, packing factor is 1.
Area covered by solar cell = Area of PV module × Packing Factor -------------------------- (3.9)
Non packing factor area (Area between two solar cells) = (1 - PF) × Module Area ------- (3.10)
The efficiency of semitransparent module is higher than opaque module because in
semitransparent PV module only un-used solar energy by cell is responsible for raising the cell
temperature and energy received by space between two solar cells is transmitted outside so it is
not responsible for increment in temperature ie. Top heat loss and bottom heat loss is more in
semitransparent PV module.
26
While in case of opaque module, energy received by space between two solar cells is reflected
back so it also responsible for increment in temperature ie. Top heat loss and bottom heat loss is
less in opaque PV module.
From semitransparent PV module, we get electrical energy, space heating and illumination while
from opaque PV module, we get electrical energy and space heating only.
When sun rays falls on PV module, heat s transferred inside by convection. To regulate this heat,
we have to provide force movement of air from top to bottom. For this, use a DC fan.
When solar modules are electrically connected in series or parallel, the arrangement is called
solar array / solar generator. For series connection of two solar modules, the plus terminal of one
module is connected to the minus terminal of second module. When two modules are connected
in series then total output voltage will be 24 Volt.
Fig. 3.6 Series connection of two PV Modules to form a PV array
For increasing output current and power, a number of modules are connected in parallel. The
modules which are being connected in parallel, they must have same output voltage.
------------- (3.11)
------------- (3.12)
Total no. of modules in solar generator= Ns × Np --------------------------- (3.13)
27
Example 2: The semitransparent and opaque PV modules are tested under sun light in order to
measure the module parameters. The intensity of sun light is measured by solarimeter, which is
746 W/m2 and the area of each module is 0.61 m2.
The module voltage, current and power is measured by multimeter under variable load condition.
These measurements are shown below in observation tables
Semitransparent module
Opaque module
V (Volt)
I (Amp.)
P (Watt)
V (Volt)
I (Amp.)
P (Watt)
0.0
2.4
0.0
0.0
1.8
0.0
2.7
2.1
5.67
0.2
1.7
0.34
8.9
2.0
17.80
1.5
1.6
2.40
12.0
1.8
21.60
7.1
1.5
10.65
14.1
1.7
23.97
9.6
1.4
13.44
14.6
1.6
23.36
12.8
1.3
16.64
15.4
1.5
23.10
14.2
1.2
17.04
16.8
1.0
16.80
14.6
1.0
14.60
17.0
0.8
13.60
14.9
0.8
11.92
18.0
0.0
0.0
15.6
0.0
0.0
(I) Draw Current vs Voltage & Power vs Voltage characteristics for both the modules
(II) Find open circuit voltage & short circuit current for both the modules
(III) Calculate Fill factor for both the modules
(IV) Calculate the efficiency of both the modules
Solution
(I) Current vs Voltage & Power vs Voltage characteristics of semitransparent module:
0
10
20
30
40
50
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20
Power (Watt)
Current (Amp.)
Voltage (Volt)
I (Amp.)
P (Watt)
28
Current vs Voltage & Power vs Voltage characteristics of opaque modules:
(II) Open circuit voltage: it is the voltage when the current flowing through the PV
module is zero ie. It is the voltage measured when no load is connected with PV
circuit.
The open circuit voltage is measured across the open terminals of circuit.
By observation table of semitransparent module, when current (I) is zero then voltage
measured is 18 vollt.
So, Voc = 18 Volt (for semitransparent module)
Similarly Voc = 15.6 Volt (for opaque module)
Short circuit current: it is the current when the voltage across the PV module
terminal is zero ie. It is the current measured with
PV circuit.
The short circuit current is measured across the shorted terminals of circuit.
By observation table of semitransparent module, when voltage (V) is zero then
current measured is 2.4 Amp.
So, Isc = 2.4 Amp. (For semitransparent module)
Similarly Isc = 1.8 Amp (For opaque module)
(III) Fill Factor:
For semitransparent module:
From the characteristics curve of semitransparent PV module,
Vm. Im = Pm= 24 Watt, Voc = 18 Volt, Isc = 2.4 Amp.
Hence,
= 0.55
0
10
20
30
40
50
0
0.5
1
1.5
2
0 5 10 15 20
Power (Watt)
Current(Amp.)
Voltage (Volt)
I (Amp.)
P (Watt)
29
For opaque module:
From the characteristics curve of opaque PV module,
Vm. Im = Pm= 20 Watt, Voc = 15.6 Volt, Isc = 1.8 Amp.
Hence,
= 0.71
(IV) Electrical efficiency of modules:
Electrical efficiency of module is given by
m =
For semitransparent module:
m =
× 100 = 5.27 %
For opaque module:
m =
× 100 = 4.39 %
The output power of opaque PV module is less than semitransparent PV module because in
opaque PV module, the glass cover is used on front side of module and insulating material
(white tedlar) is used on back side of module. In opaque PV module, the unused solar energy
in solar cells of module is responsible to raise the solar cell temperature and the energy
received by the space between two solar cells (non packing area) is also responsible for
increasing the cell temperature. In semi transparent PV module, the glass cover is used on
both front and back side of module. In it whatever solar energy falls on non packing area
goes directly out which is called as direct gain. So in such modules, only unused solar energy
is responsible to raise the cell temperature. The bottom heat loss is less in opaque module in
comparison to the semitransparent module because of insulating material (white tedlar) at its
back surface and this is responsible for increasing the cell temperature of opaque PV
modules. When the cell temperature increases, the saturation current also increases with
intrinsic carrier concentration so the open circuit voltage of module reduces and the short
circuit current of module increases. But the effect of increasing module temperature on short
circuit current is small than open circuit voltage so the overall effect of increased module
temperature is a reduction in output power of module hence the efficiency of module
reduces.
30
3.5 Solar power Plant-
Solar cell power plants are of two types namely autonomous power plant (Off grid power plant)
and Grid connected power plants.
3.5.1 Autonomous Solar Power Plant-
Fig. 3.7 Block diagram of off grid / autonomous solar plant
Description of different components of Installed PV System:
PV Array
In this system, PV modules are connected in parallel and mounted on an inclined structure. The
inclination of the system is kept at latitude of location to receive maximum annual insolation.
Charge Controller
This device regulates rates of flow of electricity from the PV Array to the battery and the load.
This controller keeps the battery full charged without over charging it. When the load is drawing
power, the controller allows the charge to flow from the PV Array into the battery, the load or
31
both. When the controller senses that the battery is fully charged, it reduces or stops the flow of
electricity from the PV Array.
A charge controller may be used to power DC equipment with solar panels. The charge
controller provides a regulated DC output and stores excess energy in a battery as well as
monitoring the battery voltage to prevent under /over charging, it will also perform maximum
power point tracking.
Inverter
An inverter converts the DC electricity from sources such as battery to AC electricity. The
electricity can be at any required voltage; in particular it can operate AC equipment designed for
mains operation, or rectified to produce DC at any desired voltage.
A solar inverter or PV inverter is a critical component in a photovoltaic system. It converts the
variable DC output of the solar panel into a utility frequency alternating current that can be fed
into the commercial electrical grid or used by a local, off-grid electrical network. Solar inverters
have special functions adapted for use with PV arrays, including maximum power point tracking
Stand-alone inverters, used in isolated systems where the inverter draws its DC energy
from batteries charged by photovoltaic arrays. Many stand-alone inverters also incorporate
integral battery chargers to replenish the battery from an AC source, when available.
Maximum power point tracking is a technique that solar inverters use to get the maximum
possible power from the PV array. Solar cells have a complex relationship between solar
irradiation, temperature and total resistance that produces a non-linear output efficiency
known as the I-V curve. It is the purpose of the MPPT system to sample the output of the
cells and apply a resistance (load) to obtain maximum power for any given environmental
conditions. Essentially, this defines the current that the inverter should draw from the PV in
order to get the maximum possible power (since power equals voltage times current).
Battery
A battery stores electricity produced by a solar electric system. The energy storage capacity of a
battery is measured in watt-hours, which is the amp-hour rating times the voltage.
32
Kerosene Generator
Generators are useful appliances that supply electrical power during a power outage and prevent
discontinuity.
An electric generator is a device that converts mechanical energy obtained from an external
source into electrical energy as the output.
Working of Installed PV System:
PV Modules use light energy (photons) from the sun to generate electricity through
the photovoltaic effect. The output of PV Array is given to the charge controller. Charge
controller regulates rates of flow of electricity from the PV Array to the battery and the load.
This controller keeps the battery full charged without over charging it. The output of charge
controller is given to the Battery. This stores electricity produced by a solar electric system. Now
the battery output is connected with inverter input. An inverter converts the DC electricity from
This AC output of Inverter is now provided to the load connected with it.
When battery is not sufficiently charged to supply the loads, Generator is used.
3.5.2 Grid connected solar power plants-
Fig.3.8 Grid connected solar power plant
33
In grid connected system power is fed into the grid during day time and taking power from the
grid during night. PV array supplies the current only when sun light fall on it, Photovoltaic array
produces DC power and this must be converted into ac power for local use and feeding into grid
so inverters are used along with PV array. Inverter converts DC supply into AC and feeds the
solar power to grid or supply to the consumer. In case of low power availability from PV
generator, the local load can be fed from the grid (as shown in diagram)
At the time of excessive generation, the energy can be stored and maybe used at the time of low
generation. Regulation and dispatch unit regulates the flow of power from photovoltaic power
system into grid and vice-versa.
Grid connected system require additional components to regulate voltage, frequency, and
waveform to meet the requirement of feeding the power into grid
3.6 Limitations of solar photovoltaic energy conversion-
High initial cost
Irregular supply of solar energy
Require battery storage for supply power at night
Low efficiency
Require large area
Do not generate power during cloudy season
34
4.1 Economics of renewable energy system-
Economics of any system is based on cost and benefit analysis.
Cost of system involve
Initial cost ie. Capital cost (Co at t = 0). It include cost of purchase, installation, training
to be given to user
Cost of operation
Cost of maintenance and replacement of items
Incremental cost (property) - tax
Benefits which we get from the system are of two types namely tangible benefits and intangible
benefits. Tangible benefits can be converted in to monetary terms but intangible benefits cannot
be converted in to monetary terms.
Tangible benefits of system are monetary worth of fuel saved, temporal & spatial dimension
(besides being user specific). While intangible benefits are reduced environment emission,
employment generation etc.
4.2 Economics of solar system-
Economics of solar system is based on cost and benefit analysis of solar system. The costs of
solar energy system are-
Capital cost- Solar energy harnessing will involve high capital cost because a large area
needs to be used for PV installation
Cost of operation is low
Repair and maintenance will also be low
Property tax will increase annually so solar energy sources are cost intensive
The benefits of solar energy system are-
35
If solar energy replacing straw then it is not lucrative, generally solar energy installation
are set to live long life span (about 40 years). These benefits are called tangible benefits
this means the benefits which can be converted in to monetary worth.
While intangible benefits are reduced environment emission, employment generation etc.
4.3 Cash Flow diagram-
A pictorial representation of cash flow of a project is used for economical analysis of system.
This representation includes both cost and benefits as shown in the cash flow diagram below
Fig.4.1 Cash flow diagram for benefit – cost analysis
Money has time value ie. Value of money for user changes with time, value at t=T is less than
Hence benefits or costs cannot be algebraically added over the total period in the cash flow
diagram instead bring benefits and costs in a common time frame then add all benefits together
and add all costs together then subtract total benefits with total costs.
4.4 Time value of money-
X X {1 + r}
(At t=0) (At t=1)
one year it will become (1 + I)
express the time value of money from one reference frame to another reference frame.
36
If , it will become X (1 + d) after one
year
So, X (1 + d) =
at t=0 & t=1, taking into account the rate of
inflation. Rupees 100 today in bank returned at a discounted rate of 10% would give Rs 110
where both 100 & 110 hold values what Rs 100 holds today.
me to time.
4.4.1 Equivalence formula involving time value of money:
A single cash flow at present (t=0)
to
An
expected in future at t=T
to
An equivalent present (t=0) value of expected cash flow in future
A series of cash flows at regular periodic intervals of time between present t=0
and t=T in future
to
An equivalent single value in future at t=T
A single cash flow expected in future at t=T
to
An equivalent series of uniform cash flows from present (t=0) to time (t=T) in
future
st year = P (1+d)
2nd year = P (1+d) + P (1+d) d
= P (1+d) 2
Equivalent value th year = P (1+d) T
37
Single cash flow compound amount factor,
T
Single cash flow present worth factor,
T
Example1: solar plant construction
Generally the time from which the solar plant starts working is taken as t=0. But before this a lot
of money is invested at different years as shown in the cash flow diagram below
Fig. 4.2 Cash flow analysis for construction of a solar plant
C0 = A5 + A4 (1+d) + A3 (1+d)2 + A2 (1+d)3 +A1 (1+d)4 --------------------------------- (4.1)
Where C0 is the cost at time t=0
A1, A2, A3, A4, A5 are the expenditure on construction of plant
4.5 Salvage value:
It is the value of a project at the end of useful life. If the salvage value at the end of useful life (at
T
38
Salvage value is converted to t=0 time frame so that it can be compared with the cost invested.
This is also termed as equivalent present value of expected cash flow in future and is given by
formula- S / (1+d)T.
(th year)
The salvage value of a project may also be negative for example in case of solar PV system, to
dispose a lot of lead acid battery safely; we need to spend money for it instead of getting the
same.
4.6 Profit cost analysis:
The profit cost analysis can be done either by bringing everything to present or by bringing
everything to future.
4.6.1 Profit cost analysis by converting to future time frame
Consider a cash flow diagram as shown below
Fig. 4.3 Cash flow diagram
The installation cost of solar power plant is C0. After completion of one year from the
installation, the benefit is B1 and maintenance cost is C1 so the net profit will be A1 (=B1 C1).
Similarly at the end of second year the net profit is A2 (=B2 C2) and so on.
Now converting all the values into future time frame , cumulative future worth of all series cash
flows at t = T
F= A1 (1+d) T-1 + A2 (1+d) T-2 + -------- + Aj (1+d) T-j + ------- + AT
F= T-j
39
Special case: if Aj = A (uniform series of cash flow)
F= A (1+d) T-1 + A (1+d) T-2 + -------- + A (1+d) T-j + ------- + A
F=
F=
Uniform series compound amount factor:
=
----------------------------------- (4.2)
Uniform series sinking fund factor:
=
------------------------------------------- (4.3)
be generated.
-------------------------------------------- (4.4)
Where there is replacement cost such as batteries of PV system which has to be replaced every 5
fter 5 years
4.6.2 Profit cost analysis by converting to ‘t=0’ time frame
Consider a cash flow diagram as shown below
Fig. 4.4 Cash flow diagram
40
The installation cost of solar power plant is C0. After completion of one year from the
installation, the benefit is B1 and maintenance cost is C1 so the net profit will be A1 (=B1 C1).
Similarly at the end of second year the net profit is A2 (=B2 C2) and so on.
Now converting all the values into time t=0 frame, cumulative present worth of a series of cash
flows,
P =
+
+
P =
[
]
Special case: if Aj = A (uniform series of cash flow)
P = A [
] ---------------------------------------------- (4.5)
Uniform series present worth factor
= [
] ---------------------------------------- (4.6)
Uniform series capital recovery factor
= [
] --------------------------------------- (4.7)
It is used for EMI calculations
Example 2: Capital cost of box type solar cooker is Rs. 2500. Its net annual benefit is Rs. 800
for expected life of 10 years and discount rate is 0.10. By considering its zero salvage value,
draw the cash flow diagram and calculate cumulative present value.
Solution: C0=Rs.2500, A= Rs. 800, d=0.10, T=10 years, S=0
41
P = A [
]
P = 800 [
]
= Rs 4915
Example 3: 1 kW (rated) wind turbine of capital cost C0= Rs. 1, 20,000/= has useful life of 15
years and discount rate of 12%. If annual cost of operation & maintenance is 1% of its capital
cost and capacity utilization factor is 25%, calculate unit cost of electricity produced by wind
turbine in Rs / kWh.
Solution: Annual electricity output = 0.25 × 1 × 365 × 24
= 2190 kWh
42
Total annual cost = Annual capital cost + annual cost of operation & maintenance
= {A= P [
]} + {1% of 1,20,000}
= {A= 1,20,000 [
]} + {0.01 × 1,20,000}
= Rs. 18,818.9
Hence unit cost of electricity = 18818.9 / 2190
= Rs 8.6 / kWh.
4.7 Unit cost analysis of solar systems-
Unit cost analysis of solar system means the cost of energy produced by solar system. In case of
solar thermal system, it involves the calculation of cost of thermal energy produced by the
system and in case of solar photovoltaic (PV) system; it involves the calculation of cost of
electrical energy produced by the system.
4.7.1 Estimation of unit cost of useful thermal energy delivered by a domestic solar water
heating system (DSWHS).
Unit cost analysis of domestic solar water heating system involves the estimation of total annual
cost of system and annual thermal energy output of the system. It is calculated in Rs/MJ.
By this analysis, the unit cost of different systems can also be compared to find a system which
provide the highest thermal energy (MJ) output with minimum cost (Rs)
Example 4: The design and operation parameters of DSWHS are listed in table 4.1 below
Table 4.1 Operation parameter of DSWHS
43
Term
Value
Nominal capacity of DSWHS
100 liter/day
Initial water temperature
10°C
Delivery water temperature
60°C
Useful life of system
30 years
Capital cost
Rs 30,000/=
Discount rate
12%
Annual cost of operation and maintenance
Rs 1000
Annual capacity utilization factor of DSWHS
0.8
(Initial water temperature and delivery water temperature are design values; it also includes solar
radiation on collector)
For comparative study of unit cost for DSWHS with unit cost of other water heating systems
(operated by electricity / LPG / Fuel wood), the data is given below in table 4.2
Table 4.2 Unit cost, efficiency of utilization and calorific value of different fuels
Fuel
Unit cost
Efficiency of utilization
CV
Electricity
Rs. 4 /kWh
0.95
3.6 MJ/kWh
LPG
Rs. 26 /kg
0.65
44 MJ/kg
Fuel wood
Rs. 3 /kg
0.15
18 MJ/kg
Calculate: (I) Unit cost of useful thermal energy provided by DSWHS
(II) Compare unit cost of DSWHS with Electricity, LPG and Fuel wood
(III) Find net annual benefit due to electricity saving by DSWHS
Solution:
Calculation of unit cost of useful thermal energy provided by DSWHS:
Total annual cost = Annual capital cost + annual cost of operation & maintenance
= {A= P [
]} + {1000}
= {A= 30000 [
]} + {1000}
= Rs 4724/=
44
Annual thermal energy output = ) × 365 days × CUF
= (100 kg) × (60 10 °C) × (4.2 kJ / kg°C) × (365 days) × (CUF)
= 6132 MJ
Unit cost of useful thermal energy delivered = 4724 / 6132 = Rs 0.77 / MJ
Now we will compare the unit cost of electricity, LPG and fuel wood with DSWHS:
Comparison with electric geyser:
(Neglecting capital cost compared to operational cost)
Useful energy = 3.6 × 0.95
= 3.4 MJ/kWh
Unit cost = 4 / 3.4
= Rs. 1.17 /MJ
Comparison with LPG water heater:
Useful energy = 44 × 0.65
= 28.6 MJ/kg
Unit cost = 26 / 28.6
= Rs. 0.9/MJ
Comparison with 1kg fuel wood water heater:
Useful energy = 18 × 0.15
= 2.7 MJ/kg
Unit cost = 3 / 2.7
= Rs. 1.11/MJ
Table 4.3 Comparison chart
Fuel
Solar
Electricity
LPG
Fuel wood
Unit cost
Rs 0.77 / MJ
Rs. 1.17 /MJ
Rs. 0.9/MJ
Rs. 1.11/MJ
Net annual benefits:
= 1793 kWh
Annual benefits due to electricity saving = (1793 kWh) × (Rs 4/ kWh)
= Rs. 7172
Net annual benefits = 7172 1000 = Rs. 6172
45
P = A [
]
P = 6172 [
] = Rs. 49716 /=
So the worth of the savings made is Rs. 49716 whereas the investment was only Rs.
30,000. Hence the process of installing a DSWHS is still profitable.
Also the unit cost of electricity may increase every year from present unit cost of Rs.
4/kWh
Fig. 4.5 cash flow diagram considering escalation in the price of the electricity
P =
+
P =
[
]
Present worth with fuel price escalation-
------------------------------------- (4.8)
4.7.2 Unit cost analysis of electricity generated by solar PV system
Unit cost analysis of solar Photovoltaic (PV) system involves the estimation of total annual cost
of system and annual electrical energy output of the system. It is calculated in Rs/kWh.
46
By this analysis, the unit cost of different systems can also be compared to find a system which
provides the highest electrical energy (kWh) output with minimum cost (Rs).
Example 5: Consider a solar plant, installed with initial investment of Rs. 5 × 106. Out of which
44% was used in PV array, 10% was used in battery systems, 8% were used in installation cost
and 38% was used in system balance.
The individual components of PV system have different life span as shown below in table 4.4
Table 4.4 Components and their life span
Component
Life span
PV modules
20 years
Batteries
7 years
Solar inverter
15 years
System balance
15 years
Calculate: (I) Annualized total cost of solar PV system
(II) Calculate the unit cost of electricity generated by PV system
(Consider average energy output of 75kWh / day from PV array for one year)
Solution:
Because individual components have different life span, we need to calculate the annualized
capital cost separately.
If consider the interest rate of 5% then
Annualized capital cost of PV modules = A1= P [
]
A1= (0.44 × 5 × 106) [
]
A1 = Rs. 176533.7
Annualized capital cost of batteries = A2= P [
]
47
A2= (0.1 × 5 × 106) [
]
A2 = Rs. 86409
Annualized capital cost of solar inverter = A3 = P [
]
A3 = (0.08 × 5 × 106) [
]
A3 = Rs. 38537
Annualized capital cost of system balance = A4 = P [
]
A4 = (0.38 × 5 × 106) [
]
A4 = Rs. 183050.3
So total annualized cost = Rs. 634530.86/=
A 1 kW photovoltaic module will produce 1 kW output power if it is irradiated by 1000 W/m2
and the temperature is maintained at 25°C.
Average energy output of 75kWh / day from PV array
Total annual average energy output = 75 × 365
Unit price of electricity generated =
= 23.18 /kWh
Unit cost of electricity delivered is more than unit cost of electricity generated due to T & D
charges and losses. In remote areas where resource is available, we can locally generate
electricity by PV system and cut down T & D losses and cost.
4.8 Measures of financial (economical) performance -
4.8.1 Payback period
48
It is the time elapsed between the point of initial investment and the point at which accumulated
savings (benefits) net of other accumulated costs become equal to the capital cost. In simple
words, it is the time period in which the invested money on the system is recovered by getting
profits from the system.
Payback period can be of two type namely simple payback period and discounted payback
period.
4.8.1 (a) Simple payback period (Tsp)
It is payback period without considering time value of money.
= C0
If (Bj Cj) is same every year ie. uniform net annual benefit then Tsp (B C) = C0
(For uniform net annual benefit) -------------------------------- (4.9)
4.8.1 (b) Discounted payback period (Tdp)
It is payback period with consideration of time value of money.
= C0
Special case: if (Bj Cj) = (B C) (For uniform net annual benefit)
C0 = (B C) [
]
1 (1+d) Tdp =
(1+d) Tdp = 1 -
=
(1+d) +Tdp =
------------------------------------------------------ (4.10)
When we do discounted payback analysis, the payback period will be longer than simple
payback period (Tdp > Tsp).
49
The acceptability criteria for any project is that the payback period should be less than
useful life of project
The payback period should be as minimum as possible
In case of both simple and discount payback analysis, payback period does not
necessarily take entire useful life into account because in most of solar energy projects,
the life time is long.
Simple payback is tool which emphasizes rapid recovery of initial capital investment.
4.8.2 Net Present Value (NPV)
+
- C0 --------------------------------------------- (4.11)
life of system
Fig. 4.6 Cash flow diagram for Net Present Value
This method takes care of entire life
It takes care of time value of money
It gives value in terms of money (units of money)
A system will be acceptable if NPV > 0
For mutually exclusive projects, select one with highest positive NPV
Demerits of NPV:
Consider two projects with initial cost (C0) and NPV as shown below in table 4.5
Table 4.5 Projects with their initial cost and NPV
50
Project
C0
NPV
A
1000
50000
B
100000
50000
but unfortunately NPV does not consider for what
C0 we are getting. It does not distinguish projects with equal NPV
Key points:
+
- C0
= -C0
NPV curve
Fig. 4.7 NPV Curve
If (Bj Cj) = B C
NPV = (B C) [
] +
- C0
across the useful life of project.
NPV =
[1
] C [
] +
- C0
51
4.8.3 Benefit to cost ratio (B/C) and internal rate of return (IRR):
Benefit to cost ratio:
=
---------------------------------------- (4.12)
Key points:
Merit:- In this method, C0 of project is considered
Demerit: - in this method, added benefit and reduced cost is not considered.
Internal rate of return (IRR):
It is the value of discount rate for which NPV is zero.
If the is less than breakdown value
(d)NPV=0 > d (for profitable project)
Fig. 4.8 IRR Curve
Now economist comes up with one idea that instead of purely guessing a value, we can
approximately get an initial value
NPV = {
+
+ - - - - -} C0
NPV =
] - C0
NPV =
(4.13)
At d=IRR, NPV= 0,
= 0
52
IRR =
(4.14)
4.9 Case Study: Roof-top PV system for textile unit
Following is a case study of a textile unit located in New Delhi. The unit has contracted demand
of 100kVA. Total available roof top area is 280m2. Hence, management has decided to install a
grid connected rooftop PV plant of 25kWp. Solar is preferred source of energy, energy available
from the solar plant is utilized first and the remaining requirement is fulfilled by grid supply.
The specifications of rooftop PV system are:
PV Panel Specification-
Panel rated power
Maximum power (Pm)
Open circuit voltage (Voc)
Maximum power voltage (Vm)
Power tolerance
Maximum power current
Solar intensity
Temperature
Dimension
Maximum system voltage (Vm)
305 Wp
305 Wp
44.9 Volt
36.6 Volt
8.73 Amp.
8.33 Amp.
1000 W/m2
25°C
(1956*992*40) mm3
1000 Volt
Number of panels
84
Inverter rating
30 kVA
Solar PV plant capacity
25 kWp
Roof-top area
275 m2
Annual unit generation
31700 kWh
Degradation of solar output
3% in first year & 0.7% in second year onwards
Life time of system
25 years
capacity utilization factor (CUF)
14.5%
Electricity price escalation
2% (per year)
Structure weight
27 kg
Overall system cost (including
PV array, inverter, mounting
structure, cables, metering
instruments)
Rs. 18,75,000/=
53
The PV system is in operation for 360 days in a year with capacity utilization factor
(CUF) of 14.5%. Then,
Unit (kWh) generation = kW output × CUF × 24hours × 360days
Benefit is the amount which is saved by generating kWh electricity units by PV system
Operation, maintenance and insurance cost is considered as 2.5% of initial investment on
system
Annual saving = Annual benefit (O&M+ Insurance) cost
Table: Benefit-Cost analysis
System
%
Output
kW
output
kWh
(Unit)
generation
Unit
cost-Rs
(Delhi)
Benefit
(Rs)
(O&M+
Insurance)
Cost
Savings
(Rs)
1st year
100
25
31320.0
8.400
263088
46875
216213
2nd year
97
24.250
30380.4
8.568
260299.27
46875
213424.27
3rd year
96.321
24.080
30167.7
8.739
263646.72
46875
216771.72
4th year
95.647
23.912
29956.6
8.914
267037.9
46875
220162.9
5th year
94.977
23.744
29746.8
9.092
270470.67
46875
223595.67
6th year
94.312
23.578
29538.5
9.274
273948.45
46875
227073.45
7th year
93.652
23.413
29331.8
9.460
277471.98
46875
230596.98
8th year
92.997
23.249
29126.7
9.649
281041.97
46875
234166.97
9th year
92.346
23.087
28922.8
9.842
284656.1
46875
237781.1
10th year
91.699
22.925
28720.1
10.039
288314.96
46875
241439.96
11th year
91.058
22.765
28519.4
10.240
292025.56
46875
245150.56
12th year
90.42
22.605
28319.5
10.444
295779.06
46875
248904.06
13th year
89.787
22.447
28121.3
10.653
299582.58
46875
252707.58
14th year
89.159
22.290
27924.6
10.866
303436.95
46875
256561.95
15th year
88.535
22.134
27729.2
11.084
307339.54
46875
260464.54
16th year
87.915
21.979
27535.0
11.305
311291.02
46875
264416.02
17th year
87.299
21.825
27342.0
11.531
315292.08
46875
268417.08
18th year
86.688
21.672
27150.7
11.762
319347.08
46875
272472.08
19th year
86.082
21.521
26960.9
11.997
323456.94
46875
276581.94
20th year
85.479
21.370
26772.0
12.237
327614.97
46875
280739.97
21st year
84.881
21.220
26584.7
12.482
331829.48
46875
284954.48
22nd year
84.286
21.072
26398.4
12.732
336093.48
46875
289218.48
23rd year
83.696
20.924
26213.6
12.986
340415.65
46875
293540.65
24th year
83.111
20.778
26030.4
13.246
344797.02
46875
297922.02
25th year
82.529
20.632
25848.1
13.511
349230.16
46875
302355.16
54
Table: Saving and Payback calculation
Saving
after 1
year
Saving
after 2
years
Saving
after 3
years
Saving
after 4
years
Saving
after 5
years
Saving
after 6
years
Saving
after 7
years
Saving
after 8
years
Saving
after 9
years
216213
216213
+
213424.27
216213
+
213424.27
+
216771.72
216213
+
213424.27
+
216771.72
+
220162.90
216213
+
213424.27
+
216771.72
+
220162.90
+
223595.67
216213
+
213424.27
+
216771.72
+
220162.90
+
223595.67
+
227073.45
216213
+
213424.27
+
216771.72
+
220162.90
+
223595.67
+
227073.45
+
230596.98
216213
+
213424.27
+
216771.72
+
220162.90
+
223595.67
+
227073.45
+
230596.98
+
234166.97
216213
+
213424.27
+
216771.72
+
220162.90
+
223595.67
+
227073.45
+
230596.98
+
234166.97
+
237781.1
Rs.
216213
Rs.
429637.267
Rs.
646408.98
Rs.
866571.885
Rs.
1090167.55
Rs.
1317241
Rs.
1547838
Rs.
1782005
Rs.
2019786.1
The overall cost of roof-top PV system is Rs. 18,75,000/= and total saving after 9 years is Rs.
2019786.1/= hence the payback time for this rooftop PV system for generation of 25kWp power
is 8.5 years.
A system is said to be economical if the payback time is less than life time of system. Also the
payback time should be as minimum as possible. In the case study as discussed above, the pay-
back time is one third of life time of the system so the system is economical.
55
5.1 Energy Metrics-
In order to study the economical aspects of the PV system, a careful energy analysis of the
system is required. This includes Energy payback time (EPBT), Electricity production factor
(EPF), Life cycle conversion efficiency (LCCE). These three terms combinely called as Energy
Metrics.
5.1.1 Embodied Energy
The concept of embodied energy is relatively new area of environmental assessment that has
started to be included in life cycle energy calculations of buildings. Embodied energy is defined
including the relative proportions consumed in all activities upstream to the acquisition of natural
resources and the share of energy used in making equipments and in other supporting functions
analysis is to quantify the amount of energy used to manufacture a material or component. This
involve the assessment of the overall expenditure of energy required to extract the raw material,
manufacture a product or components, installation and maintain the component element
whichever is being assessed.
5.1.2 Energy payback time (EPBT)
EPBT is the period in which embodied energy is recovered.
The EPBT depends on the energy spent to prepare the materials used for fabrication of the
system and its components, i.e. embodied energy and the annual energy yield (output) obtained
56
from such system. To evaluate embodied energy of various components of system, the energy
densities of different materials are required. It is the total time period required to recover the total
energy spent to prepare the materials (embodied energy) used for fabrication of the hybrid PVT
systems. It is the ratio of embodied energy and the annual energy output from the system
Which can be expressed as,
Ein Embodied energy (kWh)
Eaout Total annual output (kWh/ Year)
5.1.3 Electricity production factor (EPF)
It is used to predict the overall performance of the system. It is defined as the ratio of the output
energy to the input energy.
It can also be expressed as the inverse of EPBT,
Energy production factor is defined by two types
On annual basis
It is the ratio of annual energy output to the energy input.
On life time basis
It is the ratio of energy output to the energy input on life time basis.
Where
Eout Total net energy output over life of the system (kwh).
Ein Embodied Energy of the system(kwh).
57
TLS Life time of the system (years).
5.1.4 Life cycle conversion efficiency (LCCE)
LCCE is the net energy productivity of the system with respect to the solar input (radiation) over
the life time of the system
=
=
= (1 -
)
Energy metrics of an energy efficient system:
EPBT should be less than the life time of system. For an energy efficient system, EPBT should
be as minimum as possible.
LCCE is always less than one. For an energy efficient system, LCCE should approach to 1.
EPF is greater than one and for an energy efficient system, EPF should be as maximum as
possible.
Energy metrics of a system in which total output energy from a system is equal to
embodied energy of that system then
EPBT = Life time of system, LCCE = 0, EPF = 1
5.2 Case Study: Energy analysis of rooftop photovoltaic (PV) system
A roof-top PV system is designed to supply the domestic load. The system contains 12 PV
modules (area of each PV Module is 0.61 m2), a charge controller (efficiency 84%), a battery
58
(150 Ah), an inverter (efficiency 85%) and load (single phase AC operated). The block
diagram of this system is shown below in the fig. 5.1
Fig. 5.1 Block diagram of rooftop photovoltaic (PV) system
Observations: The solar intensity, short circuit current and open circuit voltage of
installed roof-top PV system is observed. The solar insolation (intensity) is measured by
solarimeter from 09:00 AM to 04:00 PM on daily hourly basis and corresponding open
circuit DC voltage and short circuit DC current by the PV array is measured by
multimeter. These observations are as shown in table 5.1
Table 5.1 Average hourly data of installed solar system
S.N.
Time
Intensity
(W/m2 )
Short Circuit Current, Isc
(Amp.)
Open Circuit Voltage,
Voc (Volt)
1
09 am
500
23.20
19.80
2
10 am
640
34.60
19.60
3
11 am
820
42.50
19.40
4
12 noon
895
46.50
19.60
5
01 pm
860
47.60
19.40
6
02 pm
740
44.60
19.40
7
03 pm
620
34.20
19.50
8
04 pm
360
18.20
19.20
PV
Array
Charge
Controller
Battery
Inverter
Load
59
Embodied Energy data:
The embodied energy of different material used in making of solar panels is as given
below in table 5.2
Table 5.2 Embodied energy
S N
Material
Embodied Energy (kWh/m2)
1
Silicon Purification and Processing
(Metallurgical grade silicon production / Electronic grade
silicon production / Silicon crystal growth)
670.00
2
Solar Cell Production
120.00
3
PV Module Lamination and Assembly
(Steel infrastructure / Ethyle vinyl acetate / Tedler
production / Glass Sheet production / Aluminum frame
production / Other materials)
190.00
The embodied energy and weight of items used in supporting structure is as shown
below in table 5.3
Table 5.3 Embodied energy
S.N
Item
Embodied Energy
Total Weight (kg) / Total Area(m2)
1
Support Structure
(Iron stand / Screw)
7.70 (kwh/kg)
8.63 (kwh/kg)
40 kg.
1.00 kg.
2
Charge Controller
210.00 (kwh/kw)
0.36 kw.
3
Battery
46.00 (kwh/m2)
7.32 m2.
4
Inverter
210.00 (kwh/kw)
0.50 kw.
5
Wires
3.00 (kwh/m2)
7.32 m2.
60
The embodied energy used in human labor and transportation is 9.84 kWh/ m2 and 53.50
kWh/ m2 respectively.
Calculations:
Calculation of electric power output of PV array:
SN
Time
Intensity
(W/m2 )
Short Circuit
Current, Isc
(Amp.)
Open Circuit
Voltage, Voc (Volt)
Electrical Power
Generated (Watt)
1
09 am
500
23.20
19.80
367.49
2
10 am
640
34.60
19.60
542.53
3
11 am
820
42.50
19.40
659.60
4
12 noon
895
46.50
19.60
714.24
5
01 pm
860
47.60
19.40
738.75
6
02 pm
740
44.60
19.40
692.19
7
03 pm
620
34.20
19.50
533.52
8
04 pm
360
18.20
19.20
279.55
2 .
Total Electrical Energy generated by the PV Array (E) = 4.53 kwh. (Per day).
Total Electrical Energy provided to the load for one day, E per day
E per day = E × Efficiency of Charge Controller × Efficiency of Inverter
E per day = 4.53 × 0.84 × 0.85 = 3.24 kwh.
Total Electrical Energy provided to the load for one year, E per year
E per year = E per day × No. of clear days.
E per year = 3.24 × 300
E per year = 971.05kwh.
Calculation of Embodied Energy of Installed PV System:
Calculation of material production Energy (Empe):-
61
SN
Material
Embodied
Energy (kwh/m2)
Total
Area (m2)
Total Embodied
Energy (kwh)
1
Silicon Purification and Processing
(Metallurgical grade silicon
production / Electronic grade silicon
production / Silicon crystal growth)
670.00
7.32
4904.40
2
Solar Cell Production
120.00
7.32
878.40
3
PV Module Lamination and
Assembly (Steel infrastructure /
Ethyle vinyl acetate / Tedler
production / Glass Sheet production /
Aluminum frame production / Other
materials)
190.00
7.32
1390.80
Total Material Production Energy (Empe ) = 7173.60 kwh.
Calculation of PV System Installation Energy (Einst):-
S.No
Item
Embodied
Energy
Total Weight
(kg) / Total
Area(m2)
Total
Embodied
Energy (kwh)
1
Support Structure
(Iron stand / Screw)
7.70 (kwh/kg)
8.63 (kwh/kg)
40 kg.
1.00 kg.
308.00 (kwh)
8.63 (kwh)
2
Charge Controller
210.00 (kwh/kw)
0.36 kw.
75.60 (kwh)
3
Battery
46.00 (kwh/m2)
7.32 m2.
336.72 (kwh)
4
Inverter
210.00 (kwh/kw)
0.50 kw.
105.00 (kwh)
5
Wires
3.00 (kwh/m2)
7.32 m2.
21.96 (kwh)
Total Material Production Energy (Einst) = 855.91 kwh.
62
Calculation of energy used in maintenance (Emain):-
S.No
Item
Embodied Energy
(kwh/m2)
Total Area (m2)
Total Embodied
Energy (kwh)
1
Human Labor
9.84
7.32
72.03
Calculation of energy used in administration (Eadmin):-
S.No
Item
Embodied Energy
(kwh/m2)
Total Area (m2)
Total Embodied
Energy (kwh)
1
Transportation
53.50
7.32
391.62
Total manufacturing energy (Emfg) = Empe + Emain
= 7173.60 + 72.03
= 7245.63 kwh.
Calculation of embodied energy of complete PV system:
Total Material Production Energy (Einst) = 855.91 kwh.
Total Energy Used in Administration (Eadmin) = 391.62 kwh.
Embodied Energy (Ein) = Emfg + Einst + Eadmin
= 7245.63 + 855.91 + 391.62
= 8493.16 kwh.
Calculation of Energy Metrics of Installed PV System
(I) Energy Pay Back Time (EPBT) =
Tepb =
Tepb = 8.75 Years
63
(II) Electricity Production Factor (EPF) =
0.12 per year
(III) Life Cycle Conversion Efficiency (LCCE)
0.12
5.3 Energy analysis of solar evaporative cooling system
For energy analysis of solar evaporative cooling system, costs and embodied energy involved
to wet the roof for day time (say from 10:00 AM to 04:00 PM) are given below in table 5.4
Table 5.4 cost and embodied energy of items used in evaporative cooling
SN
Item
cost
Embodied energy
1
Jute cloth
J
E1
2
Spray
S
E2
3
Water
W
E3
4
Electricity (by PV system)
E
E4
The embodied energy is calculated by equation
shows that how many the items are replaced with new items during the total life of
system)
If reference temperature TR0 is reduced to TR1 by evaporative cooling, energy saved par day
is calculated by measuring hourly energy saving (from 10:00 AM to 04:00 PM) as shown
below in table 5.5
Table 5.5 Average hourly energy saving
64
Time
TR0
TR1
Q = (MC)eff
10:00 AM
11:00 AM
.
.
.
04:00 AM
Q daily = Q10AM + Q11AM + Q12NOON + Q01PM + Q02PM + Q03PM + Q04PM
By this process, monthly and yearly saving can be calculated
Now the energy back time of solar evaporative cooling system can be calculated by using the
formula:
5.4 Energy analysis of solar day lighting system
Consider a room without any glass window ie. There is no provision for providing the day light
inside the room. Now by designing a window of 1 m2 area and thickness 5 mm, the day light is
provided in the room. Providing day lighting is simply related to saving of electrical power. If
window is there, no need of bulb of 40 Watt for lighting. If it is used for 10 hours per day then
Energy saved annually = 40 (Watt) × 10 (hours per day) × 250 (working days in a year)
= 100 kWh.
65
If the life of building is 100 years (in India), the life of glass is assumed to be infinite (if it is not
broken), cost of maintenance can be assumed zero; the embodied energy of glass is considered as
50 kWh / m2 (Ein = 50 kWh).
The energy output of system for life time of 100 years is -
Eout,T = 100 (kWh yearly) × (100 years)
Eout,T = 104 kWh
If consider the average intensity 500 W / m2 then yearly solar energy can be calculated as
E solar (yearly) = 500 (W / m2) × 1 (m2) × 250 (days) × 10 (hours per day)
E solar (yearly) = 125000 kWh
The energy metrics of the system is now calculated as:-
Life Cycle Conversion Efficiency (LCCE)
Electricity Production Factor (EPF) =
66
6.1 Simulation of PV Systems-
6.1.1 Introduction
Nowadays simulation based analysis is very common in all engineering fields in order to
minimize the cost incurred during physical testing of systems. In renewable energy systems PV
modules are one of the most important components. Recently there are a number of component
based simulation packages available for simulation based studies of renewable energy systems.
However the most commonly used software package for research and educational purpose is
MATLAB. In MATLAB/ Simulink, the simulation environment Simpower system toolbox
provides all necessary block sets for simulation power system.
6.1.2 Model of Solar Cell
Solar cell are basically a p-n junctions fabricated in a thin wafer or layer of semiconductor. The
electromagnetic radiation of solar energy can be directly converted electricity through
photovoltaic effect. Being exposed to the sunlight, photons with energy greater than the band-
gap energy of the semiconductor are absorbed and create some electron-hole pairs proportional
to the incident irradiation. Under the influence of the internal electric fields of the p-n junction,
these carriers are swept apart and create a photocurrent which is directly proportional to solar
radiation. PV system naturally exhibits a nonlinear I-V and P-V characteristics which vary with
the radiant intensity and cell temperature.
67
Fig. 6.1: Equivalent circuit of PV cell
The simplest equivalent circuit of a solar cell is an ideal current source in parallel with a diode as
shown in figure 1. The current source represents the current generated by photons (often denoted
as Iph) and its output is constant under constant temperature and constant incident radiation of
light. The diode determines the I-V characteristics of the cell. Increasing sophistication, accuracy
and complexity can be introduced to the model by adding in turn
Temperature dependence of the diode saturation current.
Saturation current contribution due to diffusion process.
Saturation current contribution due to recombination in the space layer effect dominant at
higher bias region.
In small size solar cells leakage current has an effect on the low bias region.
Temperature dependence of the photo current Iph
Shunt resistance RSh in parallel with the diode. Series resistance RS, which gives a more accurate
shape between the maximum power point and the open circuit voltage. Either allowing the diode
ideality factor A to become a variable parameter (instead of being fixed at either 1 or 2) or
introducing two parallel diodes (one with A=1, one with A=2) with independently set saturation
currents. The voltage-current characteristic equation of a solar cell is given as Eq. (6.1).
I= Iph ( IS exp ( q (V + IRs) / kTcA ) 1) ( V + IRs) / Rsh -------------------------------- (6.1)
68
Where Iph is the photocurrent or light generated current
q is charge of an electron (1.6 × 10-19 C)
-23 j/K)
Tc is the cell working temperature in Kelvin
A ideality factor
Rs and Rsh are the series and parallel resistances
The Iph mainly depends on the solar radiation and cells working temperature which is described
as Eq (6.2)
Iph = Isc + Ki (Tc ----------------------------------------------------------------- (6.2)
Where Isc is the short circuit current at 250C and solar radiation of 1kW/m2
Ki is the cell temperature coefficient of current
Tref is the reference temperature of the cell
2
The cells saturation current varies with the cell temperature which is described as Eq (6.3)
AkT
TT
qE
T
T
II c
cref
g
ref
c
RSs/
11
exp
3
---------------------------------------------------- (6.3)
Where Irs is the cells reverse saturation current at reference temperature and solar radiation and
Eg is the Band-gap energy of the semiconductor used in the cell.
The shunt resistance Rsh in inversely related with shunt leakage current to the ground. In
general, the PV efficiency is insensitive to variation in Rsh and this shunt- leakage resistance can
be assumed to approach infinity without leakage current to ground. On the other hand, a small
variation in Rs will significantly affect the PV output power. Eq. can be rewritten as
69
I = Iph ( Is exp ( q (V+ IRs) / kTcA) -1) ------------------------------------------------------- (6.4)
For an ideal PV cell the values of Rsh is infinity and Rs is equal to zero. The simulated PV
system is shown in Fig 6.2.
Fig.6.2. Simulated PV System
6.2 Maximum Power Point Tracking System-
The output power of the solar PV module changes with change in direction of the sun, change in
solar insolation level and change in temperature. Also there is a single maximum power point in
the PV characteristics of the PV module for a particular operating condition. It is desired that the
PV module operates close to this point, i.e., output of the PV module approaches near to MPP.
The process of operating PV module at this condition is called as maximum power point tracking
(MPPT). Maximization of PV power improves the utilization of the solar PV module. Maximum
power point tracking or MPPT, is the automatic adjustment of the load of a photovoltaic system
to achieve the maximum possible power power output. PV cells have a complex relationship
between current, voltage and output power, which produces a non linear output. This output is
expressed as the current-voltage characteristic of the PV cell.
70
Constant fluctuations in external variables such as temperature, irradiance and shading cause
constant shifts of the I-V curve upwards and downwards. A change in temperature will have an
inversely proportional affect on output current.
As seen here, an increase in temperature will decrease output voltage, while a decrease in
sunlight will decrease output current. This means that to maintain the MPP in instances of
varying irradiance, a voltage must be found must be found to complement the raised or lowered
output current from the panel, in order to produce the maximum amount of power.
For a given I-V characteristic, with temperature and irradiance held constant, there is a single
point at the knee of the curve with a current-voltage pair that produces maximum power output.
A corresponding Resistance, R=V/I, is the resistance required across the terminals of the PV cell
to achieve this maximum power point (MPP). The purpose of the MPPT system is to monitor the
power output of the PV system and adjust the resistance to achieve maximum power as the I-V
characteristic shifts with changing irradiance and temperature MPPT systems are connected
between the PV array and its load, and are comprised of a control structure which allows them to
search for the max power point, as well as a way of varying the resistance across the terminals,
for example by varying the duty cycle of a DC/DC converter.
6.2.1 Perturb & Observe
The method used in this work to implement maximum power point tracking function is the
perturbation and observation method, which is the most popular method. The advantages of the
perturbation and observation method include simple structure, less measured parameters and no
need of measurement in advance. Perturb & Observe (P&O) is the simplest method. In this we
use only one sensor, that is the voltage sensor, to sense the PV array voltage and so the cost of
implementation is less and hence easy to implement. The time complexity of this algorithm is
perturbing on both the directions. When this happens the algorithm has reached very close to the
71
MPP and we can set an appropriate error limit or can use a wait function which ends up
increasing the time complexity of the algorithm.
6.2.2 Perturb & Observe Algorithm
The Perturb & Observe algorithm states that when the operating voltage of the PV panel is
perturbed by a small increment, if the resulting change in power _P is positive, then we are going
in the direction of MPP and we keep on perturbing in the same direction. If P is negative, we are
going away from the direction of MPP and the sign of perturbation supplied has to be changed.
Fig.6.3: Solar panel characteristics showing MPP and operating points A and B
Figure 6.3 shows the plot of module output power versus module voltage for a solar panel at a
given irradiation. The point marked as MPP is the Maximum Power Point, the theoretical
maximum output obtainable from the PV panel. Consider A and B as two operating points. As
shown in the figure above, the point A is on the left hand side of the MPP. Therefore, we can
move towards the MPP by providing a positive perturbation to the voltage. On the other hand,
point B is on the right hand side of the MPP. When we give a positive perturbation, the value of
72
P becomes negative, thus it is imperative to change the direction of perturbation to achieve MPP.
The flowchart for the P&O algorithm is shown in Figure 6.4.
Fig. 6.4: Flowchart of Perturb & Observe algorithm
6.3 Simulation of Overall PV System
6.3.1 PV system without MPPT
As per the model of PV cell shown in the previous section, a PV system has been developed in
order to obtain the voltage and current characteristics. The developed PV system is shown in Fig
73
6.5. In order to normalize the current, a current controlled source is connected in conjunction
with PV cell. The voltage and current characteristics are then obtained with the help of scope1
and scope2 respectively.
Fig.6.5 Overall PV system without MPPT
6.3.2 PV system with MPPT
Based on the models developed in the previous section an overall model of PV system section
with MPPT has been obtained. The previously developed PV system and MPPT has been
contained along with an inverter and load in order to simulate the system under study. The
overall developed system with MPPT has been shown in Figure 6.6.
74
Fig.6.6 Overall PV system with MPPT
The working of the system can be understood by analyzing the model shown in figure 6.6. The
maximum power has been tracked with the help of MPPT. The output of the MPPT has been
given to the IGBT gate in order to trigger the IGBT. This in the will allow the PV array to itself
at maximum power point. The output of PV array, through a current controlled source is fed to a
universal bridge which is acting as an inverter in this model. The inverted supply has been fed to
the load or to the grid of in excess.
6.4 Simulation Results
When the model shown in fig. 6.5 is run, the waveforms have been obtained. The waveform for
voltage and current are shown in figure 6.7 and 6.8 respectively.
75
Fig.6.7: Voltage waveform Fig.6.8: Current waveform
When the model shown in fig. 6.6 is run, the waveforms have been obtained. The waveform for
voltage and current are shown in figure. 6.9. The waveform for power is shown in figure 6.10.
Fig.6.9: Voltage and current waveform
76
Fig.6.10 Power waveform
The nature of waveform is in compliance with the actual behavior of the system. The distortion
present in the waveform are due to the presence of ripples/harmonic while conversion from DC
to AC.
6.5 Calculation of Energy Metrics Using Matlab
MATLAB is a useful tool for such energy analysis. Energy metrics, as discussed in chapter five,
has been evaluated using MATLAB. Generalized codes have been developed in MATLAB in
order to calculate the energy metrics for PV systems with and without MPPT. The data required
for the evaluation is the open circuit voltage, short circuit current, fills factor, insulation,
embodied energy and left term of the system. The data, as shown in observation table has been
given as input to the software and the codes are run. The results obtained from software are
presented in the table 6.1.
77
Table 6.1: Comparison of energy metrics with and without MPPT
ENERGY METRICS
WITHOUT MPPT
WITH MPPT
EPBT
8.18
7.92
EPF
0.122
0.126
LCCE
0.1746
0.178
As can be inferred from table, the EPBT of the system with MPPT is slightly more than that of
system without MPPT. This is justified as an embodied energy for the system with MPPT has
increased which in turn has increased the energy payback time of the system.
The EPF and LCCE for system with MPPT have also increased since the MPPT directs the PV
array towards the maximum power point. This increased the production factor and efficiency of
the system.
78
Appendix
Relevant data for Solar based project
Solar Energy Corporation of India Limited, New Delhi has provided some relevant
data for Solar PV and Solar Thermal projects
Table 1: Data sheet
Perticulars
Value
Average cost of grid connected
rooftop solar systems
About Rs. 75 per watt or Rs. 7.5 crore per MWp capacity
Size of grid connected rooftop
solar system
The rooftop solar systems from 1 kWp upto 500 kWp or in
combination can be set up on the roofs.
Roof area required to set up the
grid connected rooftop solar
system
About 10sq.m area is required to set up 1 kWp grid connected
rooftop solar system
Potential available in India
According to a study conducted by NISE (2014-15), a potential
of 749 GWp SPV Rooftop plants has been estimated in the
country. This can be achieved through active supports from the
States
What is the present status
about sanctions under the grid
connected rooftop solar
programme
The Ministry has so far commissioned aggregate capacity of
4675.31 MWp grid connected rooftop solar systems in the
country (2015)
Cost of a 1 MW solar PV plant
In the year 2014-15, Central Electricity Regulatory
Commission has given the benchmark capital cost for solar PV
projects as 691 lakhs/ MW. Actual cost would depend on site
location, components selection, contractor hired etc.
Source: SECI, New Delhi
Cost of various solar appliances provided by Solar Energy Corporation of India
Limited, New Delhi (2013)
Table 2: Data sheet
SPV System
Capacity
Benchmark cost
(Rs./Wp)
Solar lighting System, home-lights,
lanterns, power packs(Multi use)
CFL
Up to 300 Wp
270
LED
Up to 300 Wp
450
Solar Water Pumping System
With DC motor
Up to 5kWp
190
With AC motor
Up to 5kWp
161.50
Solar Street light
Up to 100 kWp
300
Source: SECI, New Delhi
79
CENTRAL ELECTRICITY REGULATORY COMMISSION, NEW DELHI
CERC, New Delhi has release an order in the matter of determination of Benchmark Capital Cost
Norm for Solar PV power projects and Solar Thermal power projects and in response, written
comments/ suggestions/ objections are received from different stakeholders.
make a benchmark for capital cost norms for Solar PV power projects and Solar Thermal power
projects
On Date 23rd March 2016, commission released an order for Solar PV power projects and Solar
Thermal power projects applicable during FY 2016-17
Benchmark capital cost norm for Solar PV projects for FY 2016-17 shall be INR 530.02
lakhs/MW, with breakup as follows
Table 3: Data sheet
Perticulars
Capital cost norm proposed for FY 2016-17
(Rs. Lacks/MW), for Solar PV pojects
% of Total
Cost
PV Modules
328.39
61.96
Land Cost
25
4.7
Civil & General
Works
35
6.6
Mounting Structures
35
6.6
Power Conditioning
Unit
35
6.6
Evacuation Cost up to
inter-connection Point
(Cables and
Transformers)
44
8.3
Preliminary and Pre-
Operative Expenses
including IDC &
Contigency
27.63
5.21
Total Capital Cost
530.02
100
Source: CERC, New Delhi.
Table 4: Data sheet
Details
Solar PV
Solar Thermal
Useful life in years
25
25
Rate of depreciation for 12 years (%)
5.83
5.83
Rate of depreciation after 12 years (%)
1.54
1.54
Source: CERC, New Delhi.
Apart from that, the usual ball-park figures used in solar sector are:
Project Cost: Around 5.5-6.5 Cr./MW
Area required (Ground mounted): 4.5-5 Acres/MW
Area required (Roof-Top): 10-12sq.meters/MW
80
Lenders generally give loans depending on the credibility of the developers. And
for Indian lenders CERC ranges it at around 12-13%. International banks go as
low as 9-10%.
Payback period is around 6-8 years. Return on Investment is about 13%
(Source: SECI, New Delhi)
81
BIBLIOGRAPHY
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[3] Rajput S.K., Shukla C.K., Chatterji S. Energy Pay Back Analysis of Roof-Top Photovoltaic
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[4] Singal R.K. and Singal Saroj. A selective course in Non Conventional Energy Resources,S.K.
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[5] Singh Shobh Nath. Non-Conventional Energy Resources, Pearson, 2015
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