-
Establishment and Study of a Photovoltaic System with the MPPT
Function
Establishment and Study of a Photovoltaic System with the MPPT
Function
Ting-Chung Yu Yu-Cheng Lin Department of Electrical
Engineering
Lunghwa University of Science and Technology
Abstract
The main purpose of this paper is to develop a photovoltaic
simulation system with maximum power point tracking (MPPT) function
using Matlab/Simulink software in order to simulate and evaluate
the behaviors of the real photovoltaic systems. A model of the most
important component in the photovoltaic system, the solar module,
is the first to have been established. The characteristics of the
established solar module model were simulated and compared with
those of the original field test data under different weather
conditions. After that, a model of a photovoltaic system with
maximum power point tracker, which was developed by DC-DC
buck-boost converter with two different MPPT algorithms
respectively, was then established and simulated. According to the
comparisons of the simulation results, the I-V curves of the
established solar module model could closely match those of the
original field test data, and the model of the photovoltaic system
that was built in this paper can track the maximum power point of
the system successfully and accurately using two different MPPT
algorithms respectively under arbitrary temperature and irradiance
conditions. The accuracy and practicability of the proposed
photovoltaic simulation system are, therefore, validated. Keywords:
Photovoltaic simulation system, solar module, maximum power point
tracking
(MPPT), DC-DC buck-boost converter.
1. Introduction As reported in the literature, the
amount of traditional energy such as petroleum and coal has been
gradually becoming insufficient to meet demands. The problem of a
looming energy crisis has stimulated rapid development of the
renewable energy to accommodate requirements worldwide as economies
continue to grow and develop. In all kinds of renewable energy
technologies, photovoltaic technology is one of the best renewable
energy technologies because it wont produce noise, air pollution or
greenhouse gases.
Most of the photovoltaic simulation systems proposed in
literature [1][4] were established using hardware and software to
perform and simulate the operation of
equipment in the system such as solar modules, maximum power
point trackers, PWM controllers, DC-DC converters, and so on. Y.
Yusof, S. Sayuti and M. Wanik [1] proposed a solar cell model that
simulated the maximum power and I-V curve diagram of the proposed
model using C language. However, it is hard to connect the proposed
solar cell model to the other equipment in the photovoltaic system
model. C. Hua, J. Lin and C. Shen [3] used DSP to implement their
proposed MPPT controller, which controls the DC/DC converter in the
photovoltaic system. K.H. Hussein, I. Muta, T. Hoshino and M.
Osakada [4] also used hardware to implement an incremental
conductance algorithm to track the maximum power. The main
distinguishing feature of this
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,2011.12 paper is to establish a model for the photovoltaic
system with maximum power point tracking function that solely uses
software simulation. This simulation system could predict and
evaluate the behaviors of a real photovoltaic system without using
any hardware equipment. Two commonly used algorithms are used to
implement the MPPT function of the system, and are discussed
later.
This paper includes 6 sections. The rest of this paper is
organized as follows. Section 2 introduces the characteristics of
solar modules and shows the relationship of current and voltage for
the solar modules along with the variations of irradiance and
temperature. Section 3 interprets the modeling of the DC-DC
buck-boost converter. Sections 4 introduces and explains two MPPT
algorithms used in the paper, section 5 shows the simulation
results of the proposed photovoltaic simulation system, and the
last section is the conclusion of this paper.
2. Characteristics of a Solar
Module The basic structure of solar cells is to
use a p-type semiconductor with a small quantity of boron atoms
as the substrate. Phosphorous atoms are then added to the substrate
using high-temperature diffusion method in order to form the p-n
junction. In the p-n junction, holes and electrons will be
rearranged to form a potential barrier in order to prevent the
motion of electrical charges.
When the p-n structure is irradiated by sunlight, the energy
supplied by photons will excite the electrons in the structure to
produce mobile hole-electron pairs. These electrical charges are
separated by the potential barrier at the p-n junction. The
electrons will move towards the n-type semiconductor and the holes
will move towards the p-type semiconductor at the same time. If the
n-type and p-type semiconductors of a solar cell are connected with
an external circuit at this moment, the electrons in the n-type
semiconductor will move to the other side
through the external circuit to recombine with the holes in the
p-type semiconductor. The above phenomenon shows how currents of
the external circuit generate.
Because the output voltage of a solar cell is extremely low
(about 0.50.7V), solar cells have to be connected in series and in
parallel in practical applications first in order to obtain a
higher terminal voltage. After connection, solar cells have to be
strengthened by a supported substrate and covered by tempered glass
to comprise the solar module (Fig. 1). After this, solar modules
can be connected in series and in parallel to create a solar array
according to capacity demands. At present solar modules are
combined with architecture, such as walls and rooftops, in order to
achieve the broadest development.
Each solar cell can be represented as a structure consisting of
a photocurrent source, diode and resistors. Therefore, the
equivalent circuit of a solar module [5], [6] can be shown in Fig.
2.
From the equivalent circuit shown in Fig. 2, the relationship
between output voltage and output current of the solar module is as
follows [5], [6]:
PM
SMPVBPVBkTnNRIVq
oPphPVB RRIVeINII S
SMPVBPVB
)1()(
(1) with IPVB: output current of the solar module
(A). VPVB: output voltage of the solar module
(V). Iph: current source of the solar module by
solar irradiance (A). Io: reverse saturation current of a diode
(A). NP: parallel connection number of the solar
module. NS: series connection number of the solar
module. n: ideality factor of the diode (n = 1~2). q: electric
charge of an electron
( 19106.1 C). k: Boltzmann's constant ( J/K1038.1 23 ). T:
absolute temperature of the solar cell
(K). RSM and RPM are the internal series
resistance and parallel resistance,
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Establishment and Study of a Photovoltaic System with the MPPT
Function
respectively, of the solar module. Since the value of RSM is
usually small and the value of RPM is usually very large, RSM and
RPM are negligible under ideal conditions. In order to make the
simulation results more realistic in this paper, RSM and RPM are
considered to be included in an equivalent circuit. The equation of
the photocurrent source can be expressed as
PM
SMSCMkTnNRqI
oPSCMph RRIeINII S
SMSCM
)1( (2)
With ISCM being the short-circuit current of a solar module.
Fig. 1. Diagram of a solar module
Fig. 2. The equivalent circuit of a solar module
Since the open-circuit voltage and short-circuit current of the
solar module are dependent on the variation of irradiance and
temperature, the equation of open-circuit voltage and short-circuit
current of the solar module can be derived from the following
expressions:
)(1000 refC
SCBSCM TT
ISI (3)
)( refCOCBOCM TTVV (4) with ISCM: short-circuit current of the
solar
module ISCB: short-circuit current of the solar
module under the conditions of reference temperature and
1000W/m2.
VOCM: open-circuit voltage of the solar module.
VOCB: open-circuit voltage of the solar module under the
conditions of reference temperature and 1000W/m2.
S: solar irradiance (W/m2). Tref: reference temperature of the
solar
module (25oC). TC: temperature of the solar module. :
temperature coefficient of the
short-circuit current for the solar module (mA/ oC).
: temperature coefficient of the open-circuit current for the
solar module (V/ oC).
The output power of the solar module can be expressed as
follows:
PM
SMPVBPVBPVBkTnNRIVq
oPVBPphPVBPVBPVBPVB RRIVVeIVNIVIVP S
SMPVBPVB )()1()(
(5) In the following section,
Matlab/Simulink is used to set up the solar module model as well
as to simulate the I-V curve and the output power of the solar
module according to the equations derived above. The test solar
module used in this paper is HIP-200NHE1 (Heterojunction with
Intrinsic Thin Layer), manufactured by Sanyo Electric Company. The
electrical parameters of the test solar module were measured by
Sanyo Electric Company under the reference conditions (AM1.5,
irradiance of 1000W/m2 and temperature of 25oC) as shown in Table
1.
Table 1 Electrical Parameters of the Sanyo HIP-200NHE1 Solar
Module
Parameter Value
Maximum power (Pmax) 200 (W)
Max. power voltage (Vmp) 40.0 (V)
Max. power current (Imp) 5.00 (A)
Open-circuit voltage (VOC) 49.6 (V)
Short-circuit current (ISC) 5.50 (A)
Temperature coefficient of ISC 1.65 (mA/oC)
Temperature coefficient of VOC -0.129 (V/ oC)
Fig. 3 shows the comparisons of I-V
curves for simulation results and original field test data of
the test solar module under fixed temperature of 25oC and the
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comparisons of I-V curves for simulation results and original field
test data of the test solar module under fixed irradiance of
1000W/m2 and a variety of temperatures. According to Fig. 3 and
Fig. 4, the simulated I-V curves of the proposed solar module model
in this paper match very closely the measured I-V curves of Sanyos
field test data under different irradiance and temperature
conditions. The proposed solar module is, therefore, validated to
be accurate and practicable.
Fig. 3 Comparisons of the I-V curves of the test solar module
under fixed temperature and different irradiance conditions
Fig. 4. Comparisons of the I-V curves of the test solar module
under fixed irradiance and different temperature conditions
3. Modeling of the DC-DC Buck-
Boost Converter Generally speaking, the output voltage
of a typical photovoltaic system is usually
less than that of its load. Therefore, a DC-DC boost converter
is used as the maximum power point tracker in most photovoltaic
systems. In order to extend the applicability of the proposed
photovoltaic simulation system, a DC-DC buck-boost converter is
used as the maximum power point tracker in the proposed
photovoltaic system model.
A DC-DC buck-boost converter is a switched-mode device that
periodically cycles the operation of an electrical switch on and
off. The output voltage of this converter can be greater or less
than the input voltage of the converter. A DC-DC buck-boost
converter with a maximum power point tracking algorithm can adjust
the output voltage of the solar module in order to operate on
maximum power point in the photovoltaic system.
The circuit diagram of the DC-DC buck-boost converter is shown
in Fig. 5 [7], [8]. The rL and rC shown in Fig. 5 represent the
parasitic resistors of inductor L and capacitor C respectively. The
DC-DC buck-boost converter used in this paper is operated in
continuous current mode (CCM), and the parasitic components are
also included in the converter model to conform realistic circuit
operation.
The power switch Q is an electronic switch, usually a field
effect transistor (MOSFET) or, at higher power levels, an insulated
gate bipolar transistor (IGBT). This switch is able to switch on
and off at high speed, with low resistance when on and very high
resistance when off. The power switch operation can be divided into
two states: A. The power switch Q is turned on
When the power switch Q is turned on, the diode is cutoff due to
reverse-biased voltage. The equivalent circuit of the converter is
shown in Fig. 6.
The state-space equation of DC-DC buck-boost converter can be
derived in the following section. According to Kirchhoff's voltage
law, the voltage across the inductor L can be expressed as
LLinL riVv (6)
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Establishment and Study of a Photovoltaic System with the MPPT
Function
SincedtdiLv LL , (2) can be modified to
LLinL riVLdtdi
1 (7)
According to Kirchhoff's current law, the current of the
capacitor C can be expressed as
C
CRC rR
vii
(8)
Equation (8) can be modified to
C
CC
rRv
Cdtdv
1 (9)
The output voltage of the converter can be expressed as
CC
o vrRRV
(10)
Fig. 5. The circuit of the DC-DC buck-boost converter
Fig. 6. The equivalent circuit of the DC-DC buck-boost converter
when the power switch is closed
B. The power switch Q is turned off
When the power switch Q is turned off, the diode is conducted
due to forward-biased voltage. The equivalent circuit of the
converter is shown in Fig. 7. According to Kirchhoff's current law,
the current of the inductor L can be expressed as
R
rdt
dvCv
dtdvCiii
CC
CC
RCL
(11)
Equation (11) can be modified to
CC
LC
C vrR
irR
RCdt
dv 11 (12)
According to Kirchhoff's voltage law, the loop voltage of the
inductor L and capacitor C can be expressed as
0 CCCLLL rivdtdiLri (13)
Equation (13) can be rearranged to
C
CL
C
CLCLL vrR
RirR
RrrrRrLdt
di 1 (14)
The output voltage of the converter can be expressed as
CC
LC
Co vrR
RirR
RrV
(15)
Fig. 7. The equivalent circuit of the DC-DC buck-boost converter
when the power switch is opened
By mixing in switching control parameter u and rearranging (7),
(9), (12) and (14), the derivative of iL and vC can be expressed
as
CLLCC vuRiRi
rRCdtdv
1 (16)
]})([1{1 uRvRviRrrrRruiRrrR
uVLdt
diCCLCLCLLC
Ci
L
(17) When the DC-DC buck-boost
converter operates in steady-state, the net change of the
inductor current over one period should be zero; that is,
0 offLonL ii (18) 01)( L
TDVLDTV oin (19)
The output voltage of the converter can be derived from (19) and
is expressed as
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ino VDDV
1
(20)
withTt
tttD on
offon
on
; 10 D ; D is the
duty ratio. The Vin and Vo in (20) indicate
magnitudes of input and output voltage, respectively, of the
converter. According to Figs. 5 to 7, the output voltage Vo has
opposite polarity of the input voltage Vin. Output voltage
magnitude of the buck-boost converter could be greater or less than
the source voltage, depending on the duty ratio of the switch. If D
> 0.5, Vo is greater than Vin. If D < 0.5, Vo is less than
Vin.
The operation of the DC-DC buck-boost converter used in this
paper is in CCM, the minimum inductance and capacitance designed to
generate continuous current can be expressed as [8]
f
RDL2
1 2min
(21)
)/(min oo VVRfDC
(22)
witho
o
VV : output voltage ripple
In order to verify the correctness of the DC-DC buck-boost
converter model proposed in this paper, a test case is performed in
the following section. The input voltage of the test case is 40V,
and the output voltages are set to be 60V and 20V respectively. The
load resistance, switching frequency and output voltage ripple are
set to be 50, 25Hz and 1% respectively. The minimum value of
inductance and capacitance of the converter can be calculated by
(21) and (22).
The appropriate parameters chosen for the DC-DC buck-boost
converter in the test case are listed in Table 2. The converter
simulation results for voltage step-up and voltage step-down are
shown in Fig. 8. According to Fig. 8, it can be observed that the
buck-boost converter can transform the source voltage to 60V
(voltage step-up) and 20V (voltage step-down) successfully.
The correctness of the DC-DC buck-boost converter model is
therefore validated.
Table 2 Parameters of the DC-DC Buck-Boost Converter
Parameter Value Input voltage (Vin) 40.0 (V) Load resistance (R)
50 ()
Inductance (L) 0.16 (mH) Capacitance (C) 48 (F)
Switching frequency (f) 25 (kHz)
Fig. 8. Output voltage of the DC-DC buck-boost converter
4. The Algorithms of Maximum
Power Point Tracking Perturbation and observation (P&O)
and incremental conductance (INC) algorithms are used in this
paper respectively to implement the maximum power point tracking
function [3], [9], [10], [11]-[15]. The advantages of these two
power-feedback type MPPT algorithms include simple structure, less
measured parameters and no need of measurement in advance. A.
Perturbation and observation algorithm
By continuously perturbing the output power of the solar module,
the P&O algorithm could find the location of maximum power
point and send a control signal to the DC-DC buck-boost converter
through a PWM controller to modulate the operating point of the
solar modules. The basic theory of the P&O algorithm is to
periodically vary the duty ratio in order to adjust the voltage
across the solar module,
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Establishment and Study of a Photovoltaic System with the MPPT
Function
and hence the module current and power. The magnitudes of output
voltage and
power before and after the variations are observed and compared
in order to determine that the output voltage of the solar module
should be increased or decreased for the following perturbation
step. By using the procedures of perturbation, observation and
comparison again and again, the output power of the solar modules
can then reach its maximum working point gradually. The power
tracked by the P&O algorithm will oscillate and perturb up and
down near the maximum power point. The magnitude of oscillations is
determined by the magnitude of variations of the output voltage.
The flow chart of the P&O algorithm is shown in Fig. 9.
Fig. 9. Flow chart of the P&O algorithm B. Incremental
conductance algorithm
The theory of the incremental conductance method [11]-[14] is to
determine the variation direction of the terminal voltage for PV
modules by measuring and comparing the incremental conductance and
instantaneous conductance of PV modules. If the value of
incremental conductance is equal to that of instantaneous
conductance, it represents that the maximum power point is
found.
When the operating point of PV modules is exactly on the maximum
power point, the slope of the power curve is zero (dP/dV = 0) and
can be further expressed
as,
dVdIVI
dVdIV
dVdVI
dVVId
dVdP
)(
(23) By the relationship of dP/dV = 0, (23) can be rearranged as
follows,
VI
dVdI
(24)
dI and dV represent the current and voltage variations before
and after the increment respectively. The static conductance (Gs)
and the dynamic conductance (Gd, incremental conductance) of PV
modules are defined as follows,
VIGs (25)
dVdIGd (26)
The maximum power point (operating voltage is Vm) can be found
when
mm VVsVVdGG (27)
When the equation in (24) comes into existence, the maximum
power point is tracked by MPPT system. However, the following
situations will happen while the operating point is not on the
maximum power point:
)0 ,( ; dVdPGG
VI
dVdI
sd (28)
)0 ,( ; dVdPGG
VI
dVdI
sd (29)
Equations (28) and (29) are used to determine the direction of
voltage perturbation when the operating point moves toward to the
maximum power point. In the process of tracking, the terminal
voltage of PV modules will continuously perturb until the condition
of (24) comes into existence. Fig. 10 is the operating flow diagram
of the incremental conductance algorithm.
In theory, INC algorithm can calculate and find the exact
perturbation direction for the operating voltage of PV modules.
However, the perturbation phenomenon is still happened near the
maximum power point due to the less probability of meeting
condition dI/dV =I/V.
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Fig. 10 Flow chart of the INC algorithm
5. Simulations of the Photovoltaic Systems
In order to verify and compare the effects of the two MPPT
algorithms for the photovoltaic simulation system, some test cases
are implemented under different irradiance, temperature and load
conditions to observe whether the output power (load power) of the
photovoltaic simulation system can reach the maximum power of the
solar modules or not. The solar module used in the following test
cases is the same as that used in Section 2. The schematic diagram
of the photovoltaic simulation system is shown in Fig. 11.
Fig. 11 The schematic diagram of the photovoltaic simulation
system
The weather conditions and load resistances used in the test
cases are shown in Table 3. The simulation results of the test
cases are shown in Fig. 12-20. Table 3 Weather conditions and load
resistances of the test cases
Weather condition Case irradiance temperature Load
1 1000W/m2 25oC 10 2 700W/m2 30oC 15 3 400W/m2 20 oC 25
A. Perturbation and observation algorithm (a) Case 1
Fig. 12 Comparison of the output power with and without MPPT
Fig. 13 P-V curve of a solar module
(b) Case 2
Fig. 14 Comparison of the output power with and without MPPT
Fig. 15 P-V curve of a solar module
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Establishment and Study of a Photovoltaic System with the MPPT
Function
(c) Case 3
Fig. 16 Comparison of the output power with and without MPPT
Fig. 17 P-V curve of a solar module
B. Incremental conductance algorithm (a) Case 1
Fig. 18 Comparison of the output power with and without MPPT
(b) Case 2
Fig. 19 Comparison of the output power with and without MPPT
(c) Case 3
Fig. 20 Comparison of the output power with and without MPPT
Figs. 12, 14, 16 and 18-20 are comparison diagrams of output
powers for the PV system with the two MPPT algorithms under
different test conditions. Fig. 13, 15 and 17 are the P-V curve
diagram of PV modules under each test condition, which are used to
collate the tracking results simulated by the PV system. From Figs.
12, 14, 16 and 18-20, it can be observed that the output powers
with MPPT algorithms are obviously greater than those without MPPT
algorithms. After cross matching procedures, the output tracking
powers of two MPPT algorithms can all approach the ideal maximum
powers. They are very close to each other. It indirectly indicates
and validates that the two MPPT algorithms used in this paper have
considerable accuracy.
Figs. 21-23 illustrated the comparisons of output power of the
PV system with P&O and INC algorithms under different test
cases. Table 4 is the computer elapsed time when the PV simulation
system is executed with the two MPPT algorithms under three
different test conditions. According to the results of Figs. 21-23
and Table 4, it can be found that the tracking speed of the P&O
algorithm is faster than that of the INC algorithm under all test
cases. The tracking speed of the MPPT simulation systems is
dependent not only on computer specifications, but also on
perturbation sizes of MPPT algorithms. For P&O and INC
algorithms, since both algorithms use voltage perturbations of PV
modules to track the maximum power point, the tracking number will
be close to each
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,2011.12 other based on the condition of the same perturbations.
However, INC algorithm spends more time to track the maximum power
point because of its complicated judgment procedure.
Fig. 21 Comparison of P&O and INC algorithms under case
1
Fig. 22 Comparison of P&O and INC algorithms under case
2
Fig. 23 Comparison of P&O and INC algorithms under case
3
Table 4 Comparison of the elapsed time for different MPPT
systems
Computer elapsed time (s) Case 1 2 3
P & Q 0.0399 0.0396 0.0414 INC 0.0532 0.0528 0.0552
6. Conclusion The main purpose of this paper is to
establish a model for a photovoltaic system with maximum power
point tracking function completely through the use of software
techniques. A model of a solar module was first established and
then combined with an MPPT algorithm, as well as models of a PWM
controller and a DC-DC converter, in order to set up a complete
photovoltaic simulation system. In order to extend the operation
range of the photovoltaic simulation system, a DC-DC buck-boost
converter with P&O and INC algorithms is used in this paper to
implement the MPPT task.
The simulation results shown in the paper not only verify the
accuracy of the characteristics for the established solar module
model, but also prove that the photovoltaic simulation system can
accurately track the maximum power point rapidly and successfully
using two different MPPT algorithms respectively under different
test conditions. The correctness and practicability of the pure
software photovoltaic simulation system established in this paper
are then validated.
By comparing the simulation results of P&O and INC
algorithms, it can be found that P&O algorithm possesses faster
dynamic response than INC algorithm owing to its simple judgment
procedure in every perturbing period. However, INC algorithm has
advantages of exact perturbing (ideal) and tracking direction, it
is suitable for rapid changing weather conditions. References [1]
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