ELEC5564 POWER GENERATION BY RENEWABLE SOURCES
SECTION 1
SOLAR ELECTRIC POWER GENERATION
INTRODUCTION
Solar radiation can be converted to electrical energy directly without any intermediate
process by the solar photovoltaic cells. These cells are usually fabricated as flat discs, a
few inches in diameter. Advantages of photovoltaic generation include:
(1)There is no moving part so that little maintenance is required,
(2)They utilize an infinitely renewable and pollution free power source,
(3)The cells are reliable and long lasting with no harmful waste products,
(4)The cells are usually made of silicon which is one of earth’s most abundant and cheap
materials, and
(5) They have high power-to-weight ratio which is required in aerospace applications.
Despite all the above advantages they are still far too expensive for mass use but are
viable for specialised applications such as spacecraft, isolated communication stations
and certain defence needs. However with world wide concerns about fuel shortages and
environmental issue the profile of using solar PV and other forms of renewable power
generation systems has been raised significantly. Large financial investment is
forthcoming, so mass consumption of electricity generated using PV panels will soon
become reality.
In considering the cost of solar cells a terminology “peak watt” of power is used. This
means that the cell is required to generate 1 watt of power when the solar insulation is
1000 W/m2. . With a typical efficiency of 10 % 1 m2 of cell array area would generate
100 peak watts.
The quoted cost of electricity generated from solar cells varies widely, but the recent
report quoted costs in the range $.0.25 /kWh to over 1.0 /kWh (2002) for a domestically
managed system. Installed commercial systems, especially when retrofitted to existing
buildings, are much more expensive. This price is not competitive with the conventional
generation which is about $0.07 per kWh in the USA and £0.07 per kWh in UK.
1. SOLAR PHOTOVOLTAIC CELLS
1.2 Electronic structure and doping [1]
Materials commonly used as semiconductors, such as Silicon, lies in the fourth column of
the Periodic table of elements. The silicon crystal forms the so-called diamond lattice
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where each atom has four electrons at its outer layer, also called valence shell, which
enables a pure crystal of material to form tight covalent bonds, Fig 1.
Fig. 1 The diamond lattice
According to quantum theory, the energy of an electron in the crystal must fall within
well-defined bands. The energies of valence orbital which form bond between atoms
represent just such a band of states, the valence band. The next higher band is the
conduction band which is separate from valence band by energy gap, or bandgap. The
width of band gap is Eg=Ec-Ev . This is the most important characteristic of the
semiconductor. For silicon Eg=1.08 -1.12 eV, amorphous 1.75eV and GaAs 1.42eV.
A pure silicon crystal contains the right number of electrons to fill the valence band, and
the conduction gap is empty, so cannot conduct electricity. It can only conduct if carriers
are introduced into the conduction band or removed from the valence band. One way of
doing this is by alloying the semiconductor with an impurity. This process is called
doping. If some group 5 impurity atoms (say, phosphorus) are added to the silicon melt
from which the crystal is grown, Four of the five outer electrons are used to fill the
valence band and the one extra electron from each impurity atom is therefore promoted
to the conduction band. We call these impurity donors. The crystal becomes conductor
and the electrons in the conduction band are mobile. This type of semiconductor is called
n-type. The majority carriers are electrons.
The p-type is made by doping group 3 impurity atoms which is called acceptor. They
cause electron deficiency in this valence band. The missing electrons are called holesbehaving as positively charged particles, which are mobile and carry current. The
majority carriers are holes.
P-N junction: The operation of solar cells is based on the formation of a p-n junction –
formed by two different types of semiconductors. The important feature of the junction is
they form a strong electric field due to diffusion. This electric field pulls the electrons and
holes in opposite directions (for details read ref 1).
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Fig. 2 Band diagram and electron-hole distribution in semiconductors [1]
A semiconductor p-n device can be switched on by irradiating the p-n junction with light
rays and this is the basis of solar photovoltaic cell. The incident solar radiation passes
through the p-type material into the junction. We perceive this as a flux of particlesphotons-which carry the energy. Some of these photons-with energy excess of the
bandgap collide with the valence electrons of the silicon and are absorbed, releasing
electrons to the conduction band and holes left behind in the valence band, the absorption
process generates electron-hole pairs. If the silicon cell is electrically isolated on open
circuit a direct emf or voltage will appear across the terminals. If the cell has an external
electrical circuit connected to its terminal then a direct current will flow.
A p-n junction photovoltaic cell performs two functions simultaneously: it harvests
sunlight by converting photons to electric charges and it also conducts the charge carriers
from where the charges can be collected as electrical current.
Light absorbed
Reflected Light
Light gone through
Top electric grid
N layer
Load
PN junction
P layer
Fig 3 a solar P-N junction
Metal
contact
1.3. Physical Property
The energy content of the incoming radiation is in discrete packets that depend on its
frequency, according to the relation
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W  hf
(1)
Where f is the frequency in Hz and h is the Planck constant (6.626X10-34Js)
The velocity of light is f  c and c  2.998  10 6 m / s )
Thus the radiation energy in terms of wavelength. is
hc 1.974 10 25
(2)
W



Alternatively if the Planck constant is expressed in electron volt seconds, (eVs),
W
hc


1.232 10 6

eV when the wavelength is in metre. The energy per photon at
various parts of the solar spectrum is different and only part of the incident solar radiation
can produce a PV effect.
In silicon the amount of input energy per photon needed to liberate electrons into the
crystal lattice (energy bandgap) is almost 1.08eV or 2.63  10 19 J. This means only
wavelength less than 1150nm can release electron in silicon and the top 23% of the solar
spectrum wavelength cannot contribute in this respect (deep infra-red 3μm- infer-red 1.5
μm). This 23% is depicted as the left portion of the bar chart below.
23
0
28
Junction loss
due to the
solar cell
maximum
voltage being
less than Egap
Maximum
theoretical
efficiency
77
44
Small loss
due to
electrical
characteristics
of the cell
Absorbed
Energy
converted to
heat
100
Long
wavelength
photons
not
absorbed
Fig. 4 Efficiency of a silicon solar cell [2]
Some rough estimate of the magnitude of electric power generated.
By interpreting the light-induced electron traffic across the band gap as electron current
and neglecting losses each photon contributes one electron charge to the generation
current. So the electric current is I l  qNA
Where N is the number of electrons, q is the magnitude of electron charge. A is the
surface area of the semiconductor exposed to light. Terrestrial spectrum is about
1.6 x 10-19 x 4.4x10-17 =70mA/cm2, a silicon cell can convert at most 44mA/cm2. The
terminal voltage for a solar cell depends on the bandgap of the semiconductor and its
E
upper limit is V  g .
q
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1.4 Photovoltaic Materials
Many different solar cells are now available, yet more are under development. The range
of solar cells spans different materials and structures in the quest to extract maximum
power from the device while keeping the cost to a minimum.
Devices with efficiencies exceeding 30% have been demonstrated in the laboratory. The
efficiency of commercial devices, however, is less than half this value.
(1)Crystalline silicon
This holds the largest part of the market.
Early forms of silicon photovoltaic cells were very expensive because of difficulties
in the industrial preparation of the high-grade silicon. Very pure single-crystals of silicon
need to be grown as cylindrical ingots, about 10 μm diameter, in order to maximum the
cell exposure area. This is known as “monocrystaline silicon”.
Processing and fabrication problem still exist in the preparation of single crystalline
silicon cells which remains very expensive. The wafers are typically 250-300 um thick
and need to be cut by diamond slitting discs of about the same thickness. Also preparing
pure crystals involves heat control within 0.1c of a melt at 1420c. After cutting, grinding
and polishing – all labour-intensive operations – the silicon wafers have to undergo a
gaseous diffusion process involving the bonding of another material. Recent development
in this has been to grow silicon crystal in the form of a ribbon rather than an ingot. The
process results in less pure silicon than the traditional method and the efficiency is of the
order 10-12%.
(2)Polycrystalline silicon
Many small silicon crystals are oriented randomly within thin layers of
polycrystalline material. This is much cheaper to produce than single-crystal forms and
uses much less silicon material. Reported efficiency are only 5-7%
(3) Amorphous (Uncrystalline) silicon
In this there is no regular crystal structure. The very expensive process involving pure
single-crystal forms are unnecessary. The absorption coefficient for amorphous silicon, in
the visible light range, is more than ten times the value for single-crystal silicon.
Amorphous silicon can be deposited onto backing material in very thin films of the order
1 μm thick. This greatly reduces the amount of silicon material used and consequently the
cost of mass production. Amorphous silicon solar cells are relatively cheap, but their
maximum efficiency is low, of the order 7-10%.
1.5 Electrical Output Properties
The electric current generated in the semiconductor is extracted by contacts to the front
and rear of the cell. The top contact structure which must allow light to pass through is
made in the form of widely-spaced thin metal strips (usually called fingers) that supply
current to a larger bus bar. The cell is covered with a thin layer of dielectric material- the
antireflection coating or ARC – to minimize light reflection from the top surface.
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Light generated electron-hole pairs on both sides of the junction. The minority carrierselectrons from the p side and holes from the n side, then diffuse to the junction and are
swept away by the electric field, thus producing electric current across the device.
The p-n junction separates the carriers with opposite charge, and transforms the generated
current Il between the band into an electric current across the p-n junction.
The external characteristics of a solar cell are the property of current versus voltage. An
ideal characteristic would be rectangular in shape.
As shown in Figure 4, each different level of incident radiation results in a different
characteristic. The intercept of a characteristic on the current axis represent zero voltage
drop across the cell terminals and is the short circuit current ISC, which is directly
proportional to the incidental light intensity. The intercept of a characteristic on the
voltage axis represents zero current and is the open-circuit voltage VOC . Most cells
operate with a working direct voltage level of less than 1 volt.
Current
(A)
ISC
Pm
Imp
Current (A)
Terminal Voltage
(Volt)
Vmp
Voltage (Volt)
VOC
Figure 5. I-V characteristic of a
typical solar cell
1.6 Maximum Power Delivery
For typical characteristic shown in Figure 4 the maximum power delivery point lies in the
region of the knee of the curve, namely the product IV is maximum so we have
Pm  I mpV mp
One usually defines the fill-factor FF by
Pm  I mpVmp  FFVOC I SC
(4)
The efficiency η of a solar cell is defined as the Power produced by the cell at the
maximum power point under standard test conditions, divided by the power of the
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radiation incident upon it. Most frequent conditions are: irradiance 100 mW/cm2,
standard AM 1.5 spectrum, and temperature 25°C
Most solar cell loads are resistive in nature. A load resistor RL can be represented in the IV plane by a straight line through the origin. Load resistance can vary from zero for short
circuit to infinity for open circuit operation. In order to deliver the maximum possible
power, for a specified level of insolation, RL must satisfy the relationship
RL  RMP  VMP / I MP
(5)
1.7 Equivalent circuit model of a solar cell
The electrical performance of a photovoltaic cell can be approximated by the equivalent
circuit shown in Figure 5
RS
_
_
Ish
RL
RP
IDD
ISC
I
V
Figure 6.(a) Equivalent circuit model
A current source which delivers its short circuit current ISC. There is a diode shunt
connected across the current source representing the diffusion current through the p-n
junction. Internal series and parallel resistances are represented by RS and RSh
respectively. The former is due to transmission of electric current produced by the solar
cell involves omic losses. It is seen that series resistance affects the cell operation mainly
by reducing the FF.
In practice a simplified equivalent circuit may be used (shown in Figure 6(b)where the
internal series resistor RS is much smaller than RL and the internal shunt resistor RSh is
much larger than RL. A nonlinear resistor Rj representing the variable junction resistance.
I
Ij
V
ISC
Rj
RL
Figure 6(b) A simplified equivalent circuit representing a PV cell
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Rj 
V

Ij
V
V
IS 
RL
,
Rj 
VRL
IR L

I S RL  V I S  I
(6)
1.8 The load line in the I-V plane
The slope of a load resistance line is defined by Ohm’s law. With a load resistance of
10 Ω, for example, the load line passes through the co-ordinates 0.1 V and 10 mA , 5 Ω
0.2 V and 40 mA etc.
To estimate the value of load resistance at the maximum power point we need to solve
Equ.(6) which is nonlinear.
R3
R2
Current (mA)
60
Maximum
Power points
1000W/m2
50
40
R1
500W/m2
30
20
10
0
0.2
0.1
0.3
0.4
0.5
0.6
Terminal Voltage
(Volt)
Figure 7 Cell and load characteristic
Solar PV Modules
In order to deliver increased power to a load the appropriate number of solar cells has to
be connected in parallel and/or in series as shown in Figures 7(a) and (b). Clusters of
cells are often referred to as solar modules. The electrical output characteristics of simple
series and parallel combination of cells are expansion of that in figure 7 vertically or
horizontally.
RS
ID1
IS2
ISH
C2
IS1
C1
ID2
D
D
Rsh
V
Figure 8(a) Solar cells connected in parallel
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When connected in parallel we have output current I = IS1 +IS2 +…+ISn when junction
diffusion current is negligible, the voltage V is equivalent to that of a single cell.
When they are connected in series, the output voltage is the sum of individual cell voltage,
while the current equals that of a single cell.
You can now try to write an equation according Equ (6) for a solar array having np cells
connected in parallel and ns cell in series.
I
S
IS1
D1
V=V1 +V2 + …+Vn
IS2
D2
Figure 8 (b) Solar cells connected in series
ISn
D3
Example 1
The typical photocell with characteristics depicted in Figure 7 is delivering power to the
load resistance RL = 7.5 Ω with an input radiation of 1000 W/m2. What is the value of the
junction resistor, Rj in the equivalent circuit?
5Ω
7.5 Ω
Current (mA)
60
50
1000W/m2
P
Pm
50 Ω
40
30
500W/m2
Pm
20
Figure 9 Specimen photovoltaic cell
characteristics
10
0
0.1
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0.2
0.3
0.4
0.5
0.6
Terminal Voltage
(Volt)
9
2. COMPUTER SIMULATION OF PV POWER MODULES
2.1 Introduction of Computer Modelling of Physical Components
Computer simulations are now commonly used in research as well as in industry to
analyze the behaviour of a circuit/system, for improving understanding, to study the
influence of parameters in the circuit/system and importantly to design the control
schemes. The purpose of this part is to describe the methods and algorithms commonly
used to establish a computer simulation model for a PV system. The principles and
technique introduced here can be applied to develop computer models for any physical
systems.
2.1 Modelling methods and Simulation Techniques
In principle modelling a PV system, in fact any physical system, requires having as
accurate as possible mathematical expressions for all components in the system. For the
system shown in Fig 10(b), these include the PV module/panel, power electronic
converters and batteries. For a system connected to a utility grid a model of the power
system should also be considered. There are, however, various types of simulation
models used, each has its appropriate details to represent the components in a system.
[3,4]. These include
 Open-loop large signal model,
This is used to study the behaviour of the system. All input signals to the system are
predefined (Temperature, radiation, switching period and duty cycle). All component
models in the system are simplified ‘idealized’ and each switching state is represented.
The objective is to verify the system behaves properly as predicted by analytical
calculations. This step provides us with a choice of topology and component values.
 Small-signal linear model,
Following the first model, we can develop linear transfer function model at the
norminal operating conditions. This is valuable for stability evaluation and controller
design.
 Closed-loop large signal model
Once the controller has been designed, the system performance must be verified by
combining the controller and all components under a closed loop operation, in
response to large disturbances such as step changes in load and inputs.
 Device detail model
For detailed investigation of system behaviour due to nonlinearity of components,
such as PV panel mismatching, semiconductor switch losses, stray inductances etc.
This is necessary in the selection of devices and assessing the tolerance of cell missmatching.
In this module we only study the first as a tool to analyse the behaviour of PV systems.
For simulation techniques there are two basic choices;
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(1) Circuit oriented simulations
Over the years considerable effort has been put into developing software for circuit
oriented simulation, resulting in various software packages such as MATLAB Simulink, SPICE, EMPT. The user needs to supply the circuit topology and
component values. The simulator internally generates the circuit equations that are
totally transparent to the user. Depending on the package the user may be able to
select component values. This is an easier and hence popular choice.
(2) Equation solvers
This is to describe the system/circuit using differential and algebraic equations. Users
then develop high-level language programs to solve these equations. This method
enables the user to have full control of the simulation process. However it is timeconsuming and relies on the user’s full understanding of the system and computing
skills.
In the following we describe the second method to develop models for individual
components in a PV system. However both approaches will be practiced in this
module during laboratory sessions.
2.2. Mathematical model for a Solar Cell
According to the equivalent circuit model shown in Figure 5 (a), we can derive the
equations for the circuit operation as follows:
The current through the diode can be expressed by Shockley’s diode equation
q (V  IRS )
(21)
]  1)
AkTc
where IS is the reverse saturation current, V is the output voltage, q is the charge of one
electron, Tc is the solar cell temperature in Kelvin, and k is the Boltzmann constant, and
A is the junction perfection factor, which determines the diode deviation from the ideal pn junction .
I d  I S (exp[
Current ISC in Fig.5(a) denotes the photocurrent which is dependent upon the light
spectrum and the spectral response of the solar cell. The latter is according to the number
of electron-hole pairs collected per incident photon, and therefore depends on the optical
absorption coefficient and diffusion length of the charge carriers.
The dependence of the photocurrent on the irradiance and cell temperature can be
described by the following empirical equation
G
I SC  I SCR  ki (Tc  Tr )
(22)
100
where ISCR is the short-circuit current generated at Tr which is the reference temperature
in Kelvin, the factor ki is the temperature coefficient of the short-circuit current and G is
the irradiance in mW/cm2.
Reverse saturation current IS is related to temperature. Higher temperature increases the
concentration of the intrinsic charge carriers and consequently results in higher carrier
recombination. Therefore rising temperature increases the reverse saturation current:
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 qE g  1 1  
Tc 3
) exp 
(23)
  
Tr
kA
T
T
r
c




where Ior is the reverse saturation current at Tr , and Eg is the band gap.
NOCT  20
G (kW m 2 )
If NOCT is given Tc is defined as TC  Ta 
0.8
However a simplified form ca be used as
(24)
Tc  Ta  0.2  G
Taking into account the internal resistance RP and RS , we have the cell current expressed
as
q(V  IRS )
V  IRS
I  I SC  I S (exp[
]  1) 
AkTc
RP
(25)
I S  I or (
2.2 Model for a PV array
The above model can be extended to represent PV array with Np cells in parallel and Ns
cell in series so we have
V
q (  IR ST )
(26)
R
ns
V / ns
I (1  sT )  n p I SC  n p I S (exp[
]  1) 
RshT
AkTc
RshT
np
ns
here RshT   RP and RsT   Rs .
ns
np
The above model shows that an array of PV cells is a nonlinear device having its
characteristics depending on the solar irradiance and ambient temperature.
2.4 Numerical Algorithm for Computer simulation
As can be seen from above, the equation representing the I-V characteristics of a solar
panel is a nonlinear and implicit function, i.e, a value of V requires a definite value of I
but one cannot express the I-V relationship in a form I=f(V) because I appears on both
sides of the equation. We can however find I numerically, using Newton’s algorithm as
follows. First we re-write the equation (26) as:
V
 IR ST )
V
RsT
ns
ns
(27)
f ( I )  I (1 
)  n p I SC  n p I S (exp[
]  1) 
RshT
AkTc
RshT
Then, treating V as a given constant, the problem is to find a root of this equation, i.e. a
value of I which makes f(I) = 0.
q(
(1) Principle of Newton-Raphson approximation algorithm (optional)
Newton's method, also called the Newton-Raphson method, is a root-finding algorithm.
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It is based on the principle that if the initial guess of the root of f(x) = 0 is at x i, then if
one draws the tangent to the curve at f(xi), the point xi+1 where the tangent crosses the xaxis is an improved estimate of the root (Figure 18 ).
Using the definition of the slope of a function, at
which gives
…..(28)
Equation (28) is called the Newton-Raphson formula for solving nonlinear equations of
the form
. So starting with an initial guess, xi, one can find the next guess xi+1,
by using equation (28). One can repeat this process until one finds the root within a
desirable tolerance.
Algorithm
The steps to apply Newton-Raphson method to find the root of an equation f(x) = 0 are
1.
Evaluate
symbolically
2.
Use an initial guess of the root, xi, to estimate the new value of the root xi+1 as
3.
Find the absolute relative approximate error,
4.
Compare the absolute relative approximate error,
relative error tolerance,
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. If
>
as
with the pre-specified
, then go to step 2, else stop the
13
algorithm. Also check if the number of iterations has exceeded the maximum number
of iterations.
Figure 18. Geometrical illustration of the Newton-Raphson method
(2). Application of Newton’s method for PV cell simulation
Now applying this to the problem of the I-V characteristic, f(I)is given by equation (27)
from which we get its derivative as:
R
q R ST
f ( I )  1  sT  n p
I S (exp[
R shT
AkTc
q(
V
 IR ST )
ns
])
AkTc
(28)
Then we have:
I (n  1)  I (n) 
f ( I ( n)
f ( I (n))
(29)
This converges very rapidly when the initial guess is reasonably close to the root. The
process can be terminated when the differences between the estimates become negligibly
small, e.g. we can use the stop condition |I(n+1) – I(n)| < δ where δ is a very small
constant which we can choose according to the accuracy desired.
Assignment:
Draw the flowchart and then write the program (MATLAB code or C language) for
simulating the I-V characteristics of a PV module specified below.
A = (ideality factor) 1.72
q =1.6x10-19(coulomb), k = 1.380658x10-23JK-1
-6
Eg=1.1eV
Ior=19.9693x10 A,
Iscr=3.3A
ki=1.7mA/K
-5
5
ns=40
np=2
Rs=5x10 Ω
Rp=5x10 Ω
Tr=301.18K
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3. PV POWER GENERATION SYSTEMS
3.1 Structure of a PV System
A PV system consists of a number of devices/elements
 The PV generator with its mechanical support and possibly a sun-tracking system.
 Batteries (or other storage devices),
 Power conditioning and controlequipment
 Possibly back-up generator.
The general structure of a PV power system is shown in Fig 10.
Battery
PV
generator
Power
conditioner
Grid
Load
Figure 10(a). Block diagram of a typical PV power
system
There are two main types of PV power generation systems:
(1)
A stand-alone system
This type of system is used to supply load far away from utility network. Solar PV panel
becomes the sole source of electric power backed up by a battery of sufficient energy
storage capacity. At the terminals of the PV panel, a DC-DC power converter is used to
step-up/down the DC voltage. It is also used to regulate the PV terminal voltage for
obtaining maximum power output. Loads and Batteries are connected to the DC-bus. The
latter is through a bidirectional DC-DC converter and is charged when there is a surplus
of generated electricity and discharged during the periods of insufficient sunlight.
(2) Grid-connected PV power generation system
As shown in Figure 7, electric power generated by a PV panel is supplied to the utility
grid through a DC-AC inverter. Adequate control must be implemented to obtain MPPT
as well as convertering the variable DC voltage to constant frequency AC voltage on the
grid side.
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Diode
DC-DC
converter
for MPPT
DC-DC
Converters
DC-Bus
+
PV
Panel
load
DC Bus
Filter
load
_
battery
Figure 10(b) A stand-alone PV
system
DC-DC
Bi-Directional
Converter
Transformer
DC-AC Inverter
PV Panel
ia
C
Grid
Ea E b E c
Lf
ib
ic
RL
Driver Circuit
GND
Temperature
Radiation
V dc
PV
Model
*
Vdc
DSP-based
PWM
Controller
Template Wave form cos (wt)
Host Computer
Figure 10© A grid-connected PV power
system
2.2 The PV generator
This consists of PV modules which are interconnected to form a DC power-producing
unit . The physical assembly of modules with support is usually called an array.
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Figure 11 The PV generator hierachy
A typical solar cell, a 4-inch diameter crystalline silicon solar cell or a 10cmX10cm
multicrystalline cell provide between 1 to 1.5 W power at 0.5 to 0.6 V under standard
conditions depending on the efficiency. This voltage is too low for most applications, so
in general cells are connected in series to form a module.
The number of cells in a module is governed by the voltage of the module. The nominal
operating voltage of the system usually has to match to the nominal voltage of the storage
system. Most manufacturers have standard configuration which work with 12 V batteries.
Usually a set of 33 to 36 cells in series is found. The power of silicon modules falls
between 40 and 60 W. The module parameters are specified by the manufacturer under
the following standard conditions :
Irradiance 1kW/m2
Spectral distribution AM1.5
Cell temperature 25°C
The nominal output is usually called the peak power and expressed in peak watts W .
The three most important electrical characteristics of a module are the short-circuit
current, open-circuit voltage and the maximum power point as functions of the
temperature and irradiance.
Temperature is an important parameter of a PV system operation. For an individual cell
the open circuit voltage is -2.3 mV/°C. For nc cells in series the variation of voltage with
respect to temperature is:
dVOC / dT  2.3  N c mV / C
Note T is the cell temperature not the ambient temperature.
The short-circuit current is proportional to light intensity as
I SC (G )  I SC (at 1kW 2 )  G (in kW m 2 )
m
The operation should lie as close as possible to the maximum power point..
The characterisation of the PV module is completed by measuring the Norminal
Operating Cell Temperature (NOCT) defined as the cell temperature when the module
operates under the following conditions at open circuit
ELEC5564 Handout 1
17
Irradiance 0.8kW/m2
Spectral distribution AM1.5
Cell temperature 20°C
NOCT (usually between 42-46°) is used to determine the solar cell temperature TC during
module operation, Knowing ambient temperature Ta and G, TC can be expressed as :
NOCT  20
TC  Ta 
G (kW m 2 )
0.8
Example 2
A certain make of commercial solar photovoltaic cell has Vmp = 0.48 V and Imp = 20
mA/cm2 under standard isolation conditions. What combination of cells would be
required to fully charge a nickel-cadmium battery requiring 4.2 V and 70 mA ?
Example 3:
Determine the parameters of a module formed by 34 solar cells in series, under the
operating conditions G=700 W/m, and Ta =34°C. The manufacturer’s values under
standard conditions are ISC =3A; VOC=20.4V; Pmax=45.9W; NOCT = 43°C.
Interconnection of PV modules
A schematic diagram of a PV generator consisting of several modules is shown in Fig
12. In addition to the PV modules, the generator contains by-pass diodes and blocking
diode.
Figure 12 Interconnected PV modules
.
The principle reasons for by-pass diode are
 The solar cells and modules vary in quality as a result of the manufacturing
process.
 Different operating conditions may exist in different part of the PV array.
EXAMPLE:
ELEC5564 Handout 1
18
A PV module with 36 cells, 35 of them are under uniform irradiation but one is shaded
with irradiance reduced by 75%. The current through all cells is the same.
The voltage of the fully irradiated cells and the shaded cells are
V  VS ( I )  35  VF ( I )
The module characteristic has to follow the short circuit current of the shaded cell,
leading to a small area as shown in Figure below. Increasing the current leads to the
shaded cell having negative voltage, so it become a load.
It is clear that cell shading reduce module performance significantly The maximum
module power decreses from P1=20.3 W to P2=6.3 W, by about 70%. Though only 2% of
module surface is shaded. The dissipated power of the shaded cell is 12.7 W and is
obtained when the module is short circuited. This dissipation can cause hot spots on cell
materials or the module encapsulation is damaged.
Bypass diodes are integrated in the solar modules in parallel to the cell. Normally 18-24
cells per diode due to economic requirement. The bypass diode switches as soon as a
small negative voltage of about -0.7 V is applied, depending on the type of diode. This
negative voltage occurs if the voltage of the shaded cell is equal to the sum of the voltage
of the irradiated cells plus the that of the bypass diode.
Figure 13 Construction of Module Characteristics with a 75% percent
shaded cell
ELEC5564 Handout 1
19
Figure 14 Simulation of Module
Characteristics with bypass diodes
across different number of cells
Figure 15 P-V Characteristics of a
module with 36 cells and two
bypass diodes is shaded to
different degree.
Parallel connection:
Blocking diode is used to prevent battery discharging through the PV modules. When the
voltage at the battery exceeds the voltage at the generator, the diode becomes biased and
blocks the discharging path. During daytime operation when PV generated current
terminal flowing through the diode, there is a voltage drop across the diode.
ELEC5564 Handout 1
20
3.4 Power Conditioning and Control
The purpose of control is to achieve the following
1). Protecting the PV cells
2). Achieving maximum power generation for varying weather conditions
3). Proper interfacing to the power supply network and satisfy load requirements.
There are different approaches used in control the PV generation systems. Below are the
three most commonly used ones :
(1)Connect to a battery with charge regulator
In small applications (up to 100 W) a PV generator may be connected to a battery via the
blocking diode and a shunt regulator can be used to dissipate the unwanted power from
the generator as shown in Fig 17. A common method may be to use a solid state switch in
parallel with the PV generator which is to turn on and divert current from the battery at a
certain threshold voltage value.
PV
generator
IB
IC
load
Battery Fig 17. PV generator control with a
shunt regulator
Control
(2) DC-DC converters as power conditioners
As shown in Fig 10 (a), a DC-DC converter is connected at the terminals of the PV
generator. This performs two functions;
 to keep the PV generator operating on its maximum power point, and
 to convert the PV output voltage to the load required level.
The variability of the power output from the PV generator due to changes of weather and
/or load implies that the generator may not deliver the peak power as shown in Fig 7.
Using a DC-DC converter the effective load impedance can be adjusted such that the PV
delivered power can reach its maximum.
(3) DC-AC converter
Though this converter is not covered in this part of the module but will be discussed in
the next section when we describe wind power generation system.
The DC-AC converter converts the input DC power from the PV generator or battery to
AC power used by AC appliances or fed into the utility grid. For the latter the most
commonly used ones are the self-commutating fixed frequency inverters.
Thus the functions of the inverters are again to track the maximum power point and to
interface the PV generator with AC load and/or grid
ELEC5564 Handout 1
21
Details in control system design for different structure will be described in the final part
of this section.
Example 4
(1)The I/V characteristics of a solar module at a radiation level of 1000 W/m2 are shown
in Figure E4(a). Draw the load line passing through the maximum power point Pm and
evaluate the load resistance value.
Current (A)
6.
Maximum
Power points
1000W/m2
5.
4.
500W/m2
3.
2.
1.
Terminal Voltage (Volt)
0
4
8
12
16
20
24
Figure E4(a)
.
Section 1 Tutorial sheet 1 Questions
1. What are intrinsic, n-type and p-type semiconductors? (Mark 3)
2. What is the minimum energy of the incoming radiation that will cause electrons to
flow across energy gap in silicon? How is this energy relates to the frequency,
wavelength and velocity of the radiation? (mark 3)
3. Define the efficiency of a solar cell, under what conditions it is usually measured?
What is the effect of temperature on the efficiency of a photovoltaic cell operation?
ELEC5564 Handout 1
22
(Mark 4)
4. Sketch the I-V characteristic of an ideal solar cell and a diode. How does it differ
from the I-V characteristic of a diode? For the solar cell I-V curve identify the
open-circuit voltage, short circuit current and maximum power point. (marks 4)
5. For a module of solar cells has ISC=1.5A when the radiation is 1000W/m2, what
will be the value of ISC when the radiation is (1) 850W/m2 , (2) 300W/m2. (mark 2)
6. For the solar cell characteristics of Figure below, identify the operating voltage
and current values with load resistances of 8 and 20 Ω respectively, for radiation
levels of (1) 1000W/m2 and 500, 850W/m2. (mark 4)
Fig Q6 Specimen PV
characteristics
7. The temperature effects on a certain solar cell are specified as -0.0024V/°C. A
module of 30 cells generates Voc=19V at 20°C. What is the change of Voc for each
10°C rise of cell temperature? Estimate the percentage change in the value of
maximum power Pmax at the same insolation level, neglect the temperature effect
on short circuit current changes. (mark 4)
8. How many cells usually comprise a module? How are the cells connected and
why? (mark 2)
9. What are the roles of by-pass diode and blocking diode ? Are they always
necessary? (mark 2)
10. At a radiation 1000W/m2, with a load of 10Ω, 100 solar cells of type in Fig Q6 are
connected in series. Calculate the current, voltage and power at the load terminal.
11. A step-down dc converter is used to convert a 100V dc supply to 75V output. The
inductor is 200μH with a resistive load 2.2 Ω. If the transistor power switch has an ‘on’ time
of 50 μs. and conduction is continuous, calculate
(a) the switching frequency and switch ‘off’ time,
(b) the average input and output currents,
(c) the minimum and maximum values of the output current.
ELEC5564 Handout 1
23
12. A step-up dc converter is used to convert a 75V battery supply to 100V output. The
inductor is 200μH and the load resistor is 2.2 Ω. The power transistor switch has an ‘on’ time
of 50μs and the output is in continuous current mode
(a) Calculate the switching frequency and switch off-time
(b) Calculate the average values of the input and output currents
© Calculate the maximum and minimum values of the input current
(d) What would be the required capacitance of the output capacitor in order to limit the output
voltage ripple ∆VO to 10% of VO?
13. The step-up and step-down converters can be combined to form a bi-directional dc-dc
converter used to control the charging and discharging of a battery in a PV system. Draw the
circuit diagram of this converter and explain how it can operate to control the energy flow
to/out of the battery.
References
1. Solar Electricity
edited by Tomas Markvart John Wiley &Sons
2. Energy Studies
W. Shepherd and D.W. Shepherd
3. Power Electronics
Mohan Underland and Robbins
4. Principles of Power Electronics
John G Kassakian, Martin F Schlecht, George C. Verghese
ELEC5564 Handout 1
24
Example solutions
Example 1: With RL = 7.5 Ω the resistance line intersects the 1000 W/m2 characteristic
at a point, P, Figure 7, where the terminal voltage V = 0.364 V. If the simplified
equivalent circuit of Figure 3 (b) is used then the load current is
I
V 0.364

 0.0485 A
RL
7.5
(e.1)
 48.5 mA
The constant current delivered by the constant current generator is the short circuit value
of 50 mA, With 7.5 Ω load the junction resistor current is therefore, from (6)
I j  Is  I
 50  48.5
(e.2)
 1.5 mA
Junction resistor Rj therefore has the value
Rj 
V 0.364

1.5
Ij
1000
364

 242.7 
1.5
(e.3)
Example 2: Number of cells in series to supply the voltage
4 .2

 8 .7
(e.4)
0.48
Area of solar cell material to generate the required current
70

 2.4 cm 2
(e.5)
29
The number of parallel-connected cells to generate the required current will depend on
the individual cell areas. A standard size of cell is 1 cm2, which would require 2.4 cells in
parallel. This is obviously not possible and the choice might be 3 cells of standard size.
With 3 cells of 1 cm2 in parallel,
I mp  3  29  87 mA
(e.6)
Example 3
Short circuit current
I SC  (700W / m 2 )  3  0.7kw / m 2  2.1A
Solar cell temperature
Tc  34  0.7  (43  20) / 0.8  54.12C
ELEC5564 Handout 1
25
Open circuit voltage
Voc (54.12C )  20.4  0.0023  34  (54.12  25)  18.1V
The maximum power point can be determined using the simplifying assumption that FF
factor is independent of the temperature and irradiance
FF  45.9 /(3  20.4)  0.75
Pmax (G, T )  2.118.1 0.75  28.5W
Thus 62% of its nominal value.
Example 5
Boost converter (Connecting between a PV panel and, a DC bus-load)
(V1= input voltage)
(V2=output voltage)
When the converter operates in voltage step-up mode, switches S and D are active. In this
operation S is switched periodically according to the predetermined switching period, Ts and the
duty ratio, K 
t on
. The output voltage, i.e. the battery terminal voltage, is controlled by
Ts
varying K2 and at steady-state, we have V1  1  t on V2  off V2 . According to current variation

Ts 
Ts

equations for the inductor, L, and voltage equations for both the input and output capacitors, two
state-space formulae describing the converter at S2 turn-on and off states are derived[4]. Thus
when S is turned on, we have
t
L
di L (t )
 v1 (t )
dt
C1
dv1 (t )
 i PV (t )  i L (t )
dt
C2
dv2 (t )
v (t )
 2
dt
R
which can be expressed as
y  W1 y  U  P
… (1)
 y1   i L 
   
where output variables are y  y 2  v1 , input variables are P = i PV and
   
 y 3  v 2 
ELEC5564 Handout 1
26

 0

1
W1  
 C
 1
 0

For small Ts and ton =


0

1
0
0 , U   

 C1 
1 
 0 
0 
RC 2 
1
L
0
 ' 1 ,
y ( ' )  y ( 1 )
t on
Hence, we yield
y( ' )  (I  W1ton )y(1 )  Uton  P
y 
where
…
(2)
…
(3)
…
(4)
…
(5)
…
(6)
1 0 0 
I  0 1 0
0 0 1
When the switch S is turned off, we have
L
di L (t )
 v1 (t )  v2 (t )
dt
C1
dv1 (t )
 i PV (t )  i L (t )
dt
C2
dv2 (t )
v (t )
 i L (t )  2
dt
R
and the state equation becomes
y  W2 y  U  P
where

 0

1
W2  
 C
 11

 C 2
1 

0
L 
1
0
0 , U   

 C1 

1 
 0 
0 
RC 2 
1
L

For small Ts and toff =  2   ' ,
y ( 2 )  y ( ' )
y 
t off
Hence, we yield
y ( 2 )  (I  W2toff )y ( ' )  Utoff  P
ELEC5564 Handout 1
27
Substituting (3) into (6) gives
y ( 2 )  (I  W2 t off )(I  W1 t on )y ( 1 )  (I  W2 t off )( U  P)t on  (U  P)t off
y( 2 )  W2  W1 t on t off y( 1 )  I  W1  t on  W2  t off y( 1 )  W2 U  P t on t off 
 I  U  P t on  U  P t off
(7)
For high frequency, the product of ton and toff is significantly less than the product of L and C
elements in the circuit and (7) can be expressed as

t off 
Ts
 1


L
L   y1 ( 1 )   0 
 y1 ( 2 )  

 y ( )    Ts
   Ts  P
1
0
y
(

)
2
2
2
1


  C
 C 
1
  y 3 ( 1 )   1 
 y 3 ( 2 )  
T
 0 
 t off
0 1 s 
 C 2

RC 2 
… (8)
Under high switching frequency, we derive an equivalent average model for (8) by replacing toff with
(1-k2)TS and hence, we have

Ts
(1  K )Ts 
1



L
L
 y1 ( 2 )  
  y1 ( 1 )   0 
 y ( )     Ts
  y ( )    Ts  P
1
0
2
2

 
 2 1  C 
C1
  y 3 ( 1 )   01 
 y 3 ( 2 )   (1  K )Ts
T
 


0
1 s
C2
RC 2 
… (9)

The derivatives for y can then be expressed as
y  2   y  1 
y 
Ts
… (10)
Subsequently, the state-space equations over a period become

1
(1  K ) 

 0

L
L   y1   0 
 y1  
 y     1
  y    1  P
0
0
 2 
  2   C1 
C1
 y 3  
 
(1  K )
1   y 3   0 


0

RC 2 
 C 2
… (11)
Expressing (10) in s-domain, we obtain the transfer functions as
1
V1 (s)  (1  K )  V2 (s)
Ls
1
I PV (s)  I L (s)
V1 ( s) 
C1  s
I L ( s) 
V2 ( s ) 
V ( s) 
1 
(1  K )  I L ( s)  2 

C2  s 
R 
…
(12)
…
(13)
…
(14)
Buck converter operation (Connected between a PV panel and a DC bus load)
(V1 = input voltage)
(V2 = output voltage)
ELEC5564 Handout 1
28
Switch on:
L
di L (t )
 v1 (t )  v2 (t )
dt
C1
dv1 (t )
 i PV (t )  i L (t )
dt
C2
dv2 (t )
v (t )
 i L (t )  2
dt
R
and the state equation becomes
y  A1 y  B  P
(15)
where

 0

1
A 1  
 C
 11

 C 2
1 

0
L 
1
0
0 , B   

 C1 

1 
 0 
0 
RC 2 
1
L
For small Ts and ton =

 ' 1 ,
y ( ' )  y ( 1 )
t on
Hence, we yield
y( ' )  (I  A1t on )y( 1 )  Bt on  P
y 
… (16)
… (17)
When the switch S is turned off, we have
L
diL (t )
 v2 (t )
dt
C1
dv1 (t )
 i PV (t )
dt
C2
dv2 (t )
v (t )
 i L (t )  2
dt
R
and the state equation becomes
y  A 2 y  B  P
…
ELEC5564 Handout 1
(18)
29
where

0
A2   0
1

 C 2
1 
0
L 
1
0
0 , B   
1 
 C1 

0 
 0 
RC 2 
0

For small Ts and toff =  2
y ( 2 )  y ( ' )
y 
 ' ,
t off
…
(19)
…
(20)
Hence, we yield
y ( 2 )  (I  A 2toff )y ( ' ) Btoff  P
Substituting (16) into (19) gives
y ( 2 )  (I  A 2 t off )(I  A 1 t on )y ( 1 )  (I  A 2 t off )(B  P)t on  (B  P)t off
y( 2 )  A 2  A 1 t on t off y( 1 )  I  A 1  t on  A 2  t off y( 1 )  A 2 B  P t on t off 
 I  B  P t on  B  P t off
(21)
is significantly less than the product of L and C elements
For high frequency, the product of ton and toff
in the circuit and (20) can be expressed as

t on
T 
 s 
 1
L
L   y1 ( 1 )   0 
 y1 ( 2 )  
t
 y ( )    on
(21)
  y ( )    Ts  P
1
0
2
2

  C
 2 1  C 
1
 y 3 ( 2 )  
  y 3 ( 1 )   01 
T
T
 
s
s


0 1
 C 2
RC 2 
Under high switching frequency, we derive an equivalent average model for (21) by replacing toff with
(1-k2)TS and hence, we have

KTs
T 
 s 
 1
L
L   y1 ( 1 )   0 
 y1 ( 2 )  
KT
 y ( )   
  y ( )    Ts  P
s
1
0
 2 2   C
 2 1  C 
1
 y 3 ( 2 )  
  y 3 ( 1 )   01 
T
T
 
s
s


0
1
 C 2
RC 2 
(22)
The derivatives for y can then be expressed as
y  2   y  1 
y 
Ts
(23)
(10)
Subsequently, the state-space equations over a period become
ELEC5564 Handout 1
30

 0
 y1  
 y    K
 2  C
1
 y 3  
1

 C 2
K
L
0
0
1 

L   y1   0 
 1 
0   y 2     P

C
   1
1   y 3   0 


RC 2 

(24)
Expressing (23) in s-domain, we obtain the transfer functions as
1
K  V1 ( s)  V2 ( s)
Ls
1
I PV ( s)  K  I L ( s)
V1 ( s ) 
C1  s
I L ( s) 
V2 ( s) 
ELEC5564 Handout 1
V ( s) 
1 
I L ( s)  2 

C2  s 
R 
…
(25)
…
(26)
…
(27)
31