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Power Generation from
Renewable Energy Sources
Fall 2012
Instructor: Xiaodong Chu
Email：[email protected]
Office Tel.: 81696127
Flashbacks of Last Lecture
• The output of a PV module can be reduced dramatically when
even a small portion of it is shaded
• External diodes can help preserve the performance of PV
modules
– The main purpose for such diodes is to mitigate the impacts of shading
on PV I –V curves
– Such diodes are usually added in parallel with modules or blocks of
cells within a module
Flashbacks of Last Lecture
• Consider the case when the bottom n − 1 cells still have full
sun and still carry their original current I so they will still
produce their original voltage Vn−1
• The output voltage of the entire module VSH with one cell
shaded will drop to
VSH  Vn1  I ( RP  RS )
• The voltage of the bottom n − 1 cells will be
 n 1 
Vn 1  
V
n


• Then
 n 1 
VSH  
 V  I ( RP  RS )
n


Flashbacks of Last Lecture
•
•
•
•
Crystalline silicon technologies
Thin-film technologies
Multiple junction technologies
Concentrated photovoltaic (CPV) technologies
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Three most commonly configurations of PV systems
– Systems that feed power directly into the utility grid
– Stand-alone systems that charge batteries
– Applications in which the load is directly connected to the PVs
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The photovoltaics in a grid-connected system deliver dc
power to a power conditioning unit (PCU) that converts dc to
ac and sends power to the building
– If the PVs supply less than the immediate demand of the building, the
PCU draws supplementary power from the utility grid, so demand is
always satisfied
– If the PVs supply more power than is needed, the excess is sent back
onto the grid
– The power-conditioning unit also helps keep the PVs operating at the
most efficient point on their I –V curves as conditions change
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Grid-connected PV systems have a number of desirable
attributes
– Their relative simplicity can result in high reliability
– Their maximum-power-tracking unit assures high PV efficiency
– Their potential to be integrated into the structure of the building
means that there are no additional costs for land
– Their ability to deliver power during the middle of the day, when utility
rates are highest, increases the economic value of their kilowatt-hours
Photovoltaic Systems–Current–
Voltage Curves for Loads
• In the stand-alone system, an inverter converts battery dc
voltages into ac for conventional household electricity, but in
very simple systems everything may be run on dc and no
inverter may be necessary
• The charging function of the inverter allows the generator to
top up the batteries when solar is insufficient
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Stand-alone PV systems can be very cost effective in remote
locations where the only alternatives may be highmaintenance generators burning relatively expensive fuel, or
extending the existing utility grid to the site, which can cost
much more
• These systems suffer from several inefficiencies including
battery losses and the fact that the PVs usually operate well
off of the their most efficient operating point
• Inefficiencies are often increased by mounting the array at a
steep tilt angle to supply relatively uniform amounts of energy
through the seasons, rather than picking an angle that results
in the maximum possible annual energy delivery
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The third system type has photovoltaics directly coupled to
their loads, without any batteries or major power
conditioning equipment
• The most common example is PV water pumping in which the
wires from the array are connected directly to the motor
running a pump and when the sun shines, water is pumped
• There is no electric energy storage, but potential energy may
be stored in a tank of water up the hill for use whenever it is
needed
• These systems need to be carefully designed to be efficient
Photovoltaic Systems–Current–
Voltage Curves for Loads
• While the I –V curve for a photovoltaic cell, module, or array
defines the combinations of voltage and current that are
permissible under the existing ambient conditions, it does not
tell us anything about where on that curve the system will
actually be operating
• This determination is a function of the load into which the PVs
deliver their power
• Just as PVs have an I –V curve, so do loads
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The same voltage is across both the PVs and load, and the
same current runs through the PVs and load
• When the I –V curve for the load is plotted onto the same
graph that has the I –V curve for the PVs, the intersection
point is the one spot at which both the PVs and load are
satisfied, which is called the operating point
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Consider a simple resistive load
V  IR
or
1
I   V
R
which, when plotted on current versus voltage axes, is a
straight line with slope 1/R
• As R increases, the operating point where the PV and
resistance I –V curves intersect moves along the PV I –V curve
from left to right
Photovoltaic Systems–Current–
Voltage Curves for Loads
• By using a variable resistance, called a potentiometer, or pot,
as the load, and then varying its resistance, pairs of current
and voltage can be obtained, which can be plotted to give the
module I –V curve
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Since power delivered to any load is the product of current
and voltage, there will be one particular value of resistance
that will result in maximum power
Rm 
Vm
Im
where Vm and Im are the voltage and current at the maximum
power point (MPP)
• Under the special conditions at which modules are tested, the
MPP corresponds to the rated voltage VR and current IR of the
module
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The dc motors, such as those often used in PV-water-pumping
systems, exhibit a current–voltage relationship that is quite
similar to that of a resistor
• Most are permanent-magnet dc motors
• As the motor spins, it develops a back electromotive force e,
which is a voltage proportional to the speed of the motor (ω)
that opposes the voltage supplied by the photovoltaics
Photovoltaic Systems–Current–
Voltage Curves for Loads
• From the equivalent circuit, the voltage–current relationship
for the dc motor is
V  IRa  k
where back emf e = kω and Ra is the armature resistance
• A dc motor runs at nearly constant speed for any given
applied voltage even though the torque requirement of its
load may change
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Notice that at start-up, while ω = 0, the current rises rapidly
with increasing voltage until current is sufficient to create
enough starting torque to break the motor loose from static
friction
• Once the motor starts to spin, back emf drops the current and
thereafter I rises more slowly with increasing voltage
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The inefficiency of the simple PV–motor setup
Photovoltaic Systems–Current–
Voltage Curves for Loads
• There is a device, called a linear current booster (LCB), that is
designed to help overcome this loss of potentially usable
insolation when current delivered to the motor is insufficient
to overcome friction
• What an LCB does is to convert low-current, high-voltage
power into high-current, low-voltage power
• The lower voltage means that the motor will spin at a slower
rate
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Since PVs only provide power during the daylight hours and
many applications require energy when the sun is not shining,
some method of energy storage is often needed
– For a water pumping system, this might be the potential energy of
water stored in a tank
– For grid-connected systems, the utility lines themselves can be
thought of as the storage mechanism: PV energy is put onto the grid
during the day and taken back at night
– For most off-grid applications, energy is stored in batteries for use
whenever it is needed
Photovoltaic Systems–Current–
Voltage Curves for Loads
• An ideal battery is one in which the voltage remains constant
no matter how much current is drawn, which means that it
will have an I –V curve that is simply a straight up-and-down
line
Photovoltaic Systems–Current–
Voltage Curves for Loads
• A real battery has some internal resistance and is often
modeled with an equivalent circuit consisting of an ideal
battery of voltage VB in series with some internal resistance Ri
• During the charge cycle, with positive current flow into the
battery, we can write
V  VB  Ri I
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The simple equivalent circuit representation is complicated by
a number of factors, including the fact that the open-circuit
voltage (VB) depends not only on the state of charge but also
on battery temperature and how long it has been resting
without any current flowing
• Internal resistance is also a function of temperature and state
of charge, as well the age and condition of the battery
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Example 9.1 of the textbook: you should master it!
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Significant efficiency gains could be realized if the operating
points for resistive, dc motor, and battery loads could
somehow be kept near the knee of the PV I –V curves
throughout the ever-changing daily conditions
• Devices to do that, called maximum power trackers (MPPTs),
are available and are a standard part of many PV systems—
especially those that are grid-connected
• There are some very clever, quite simple circuits that are at
the heart of not only MPPTs but also linear current boosters
(LCBs) as well as a number of other important power devices
• The key is to be able to convert dc voltages from one level to
another
Photovoltaic Systems–Current–
Voltage Curves for Loads
• A boost converter is a commonly used circuit to step up the
voltage from a dc source, while a buck converter is often used
to step down voltage
• A buck-boost converter is capable of raising or lowering a dc
voltage from its source to whatever dc voltage is needed by
the load
• The transistor switch flips on and off at a rapid rate under
control of some sensing and logic circuitry
Photovoltaic Systems–Current–
Voltage Curves for Loads
• There are two situations to consider: the circuit with the
switch closed and the circuit with the switch open
• The duty cycle D (0 < D < 1) is the fraction of the time that the
switch is closed, which controls the relationship between the
input and output voltages of the converter
Photovoltaic Systems–Current–
Voltage Curves for Loads
• As a typical solar day progresses, ambient temperature and
available insolation are constantly changing, which means
that the I –V curve for a PV array is constantly shifting and the
operating point for any given load is constantly moving
around as well
• Manufacturers provide I –V curves for various temperatures
and solar intensity, but there are times when hour-by-hour
curves are helpful
Photovoltaic Systems–Current–
Voltage Curves for Loads
• Over most of a PV I –V curve, current at any voltage is directly
proportional to insolation, which suggests we can simply scale
the 1-sun (1000 W/m2) I –V curve by moving it up or down in
proportion to the anticipated insolation
• This generalization is completely true for short-circuit current
ISC (i.e., V = 0)
• Open-circuit voltage VOC decreases as insolation decreases, so
the simple assumption of current being proportional to
insolation breaks down near VOC
• Under most circumstances, however, the operating voltage of
a system is around the knee, or even lower, where current is
very close to being proportional to insolation
Photovoltaic Systems–Current–
Voltage Curves for Loads
Photovoltaic Systems–Current–
Voltage Curves for Loads
• The simple assumption that current is proportional to
insolation makes it easy to draw hour-by-hour I –V curves for
clear days
• We need to do is scale the 1-sun (1 kW/m2) I –V curve in
direct proportion to those estimated hourly solar intensities
• Since the 1-sun I –V curve itself depends on cell temperature,
and cell temperature depends on insolation and ambient
temperature, we could imagine adjusting the 1-sun reference
curve on an hour-by-hour basis
Photovoltaic Systems–Current–
Voltage Curves for Loads