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Dynamical Performance Investigation of Dynamical
Model Based Maximum Power Point Tracking
Controller in Solar Photovoltaic System
C.Vennila1, M. Vijayaraj2 1Assistant Professor, Dept. of EEE, Alagappa Chettiar Government College of
Engineering and Technology, Karaikudi, Tamilnadu, India
2 Professor, Dept. of ECE, Government College of Engineering, Tirunelveli, Tamilnadu,
India [email protected], [email protected]
Abstract
In solar photovoltaic systems, a maximum power point tracking (MPPT) controller is
used to tract the dynamically varying maximum power point to extract maximum power
from solar array to the load connected. In this paper a novel maximum power point
tracking controller based on dynamic model of solar photovoltaic array is proposed for
Luo converter based solar photovoltaic system in resistive load applications. The
proposed MPPT system is modeled and evaluated in MATLAB/Simulink software. The
dynamic model MPPT receives solar irradiance and temperature as input and predicts
optimum reference voltage and current for maximum power point operation. Evaluations
are done under static and dynamic climatical conditions. Results of proposed analytical
model MPPT controller are compared with the results of conventional incremental
conductance MPPT controller. Comparative results show that the proposed dynamic
model based MPPT is well situated for low cost, low complexity and moderate response
in tracking. Based the comparative results the proposed MPPT is suggested for
photovoltaic applications in temperate zone geological locations.
Keywords: Dynamic model MPPT, Dynamic response, Luo converter, Solar PV
system.
1. Introduction
Solar energy is the ultimate sources of energy. It is naturally replenished the depletion
of fossil fuels in a short period of time. But the main drawback of this solar energy
harvesting is the efficiency of solar cells. It is mainly depending on couple of factors
such as temperature and insolation. In addressing the poor efficiency of photovoltaic
systems, many methods have been proposed. Maximum power point tracking is one of
them. Confusion is always there for the proper selection of maximum power point
tracking technique among the available one century techniques. There is no evidence to
decide which one is the best of all. In evaluation of maximum power point tracking
based on European Standard EN 50530[1] has a scope in photovoltaic applications. The
overall efficiency of a PV system is depending on the efficiency of the individual
photovoltaic array, power converter and the implemented maximum power point
algorithm. The efficiencies of the PV panel and the converter are not easily improved
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because they depend on the type of hardware technology. But efficiency of maximum
power point tracking can be increased easily by introducing a new maximum power
point tracking algorithm. In this paper a novel cost-effective maximum power point
tracking for temperate zone geological locals is proposed and evaluated in simulation.
2. Proposed Dynamic Model based MPPT Tracker
Maximum power point tracker is an analog or a digital device, implemented with
maximum power point tracking algorithm along with a converter. During load variation
or the solar input variation there is only one point at which the photovoltaic module
exhibits maximum power point operation. Under different loaded conditions, the duty
cycle of the DC-DC converter is adjusted to change panel resistance (Rpv) to match
optimum solar panel resistance (Rpvopt), which is optimum for current atmospheric
conditions such as solar irradiation and panel temperature. The DC-DC converter in the
proposed system to do impedance matching is Luo converter, which is a higher order
switching mode buck/boost converter. It includes the advantages of high gain with
relatively lesser number of components and lower ripples in output voltage. The general
block diagram of proposed system is shown in Figure1.Block Diagram of the Proposed
Dynamic Model based Solar Photovoltaic System.
Figure 1. Block Diagram of the Proposed Dynamic Model based Solar Photovoltaic System
Modelling and simulation of the proposed dynamic model maximum power point
tracker in solar photovoltaic system for resistive load application is done simulation
software.
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3. Modeling of Photovoltaic Array in MATLAB/Simscape Environment
3.1. Solar Array Modeling
Modelling of solar panel is essential to analyze the output current, output voltage,
output power of a solar array with respect to associated temperature and irradiation. It is
also used to predict the maximum power point. A solar cell equivalent circuit shown in
Figure 2. Equivalent Circuit Diagram of a Solar Cell.
Figure 1. Equivalent Circuit Diagram of a Solar Cell
The basic equations of solar cell equations from (1) to (6) are derived from the theory
of semiconductors. These equations mathematically explain the current and voltage
characteristics of the ideal solar photovoltaic cell [2],
(1)
(2)
(3)
(4)
I=Np*Ipv−Np*Is [exp (q (V+Rse I(NsNp)) Ns K a T) −1] −V+Rs I(NsNp)Rp (NsNp) (5)
(6)
In this paper an 80W solar array is used for solar power generation. Two numbers of
ELDORA 40W solar modules are connected in parallel to form 80W solar array. This
module is made of 36 multi-crystalline silicon solar cells in series with 40 W maximum
power at STC. Table 1. Electrical Specifications of Solar Panel illustrates the datasheet
of this module at STC.
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Table 1. Electrical Specifications of Solar Panel
Datasheet of the test
module at STC
Voc
(V)
Isc
(A)
Vmpp
(V)
Impp
(A)
Ns Kv
(V/oK )
Ki
(A/oK)
ELDORA-40W
21.9
2.45
17.4
2.3
36
-0.123
0.0032
A physical modelling and simulation are done in MATLAB/Simscape [3]. In order to
model a panel in simscape the values of series resistance (Rse), parallel resistance (Rsh)
and ideality factor(a) are required. Unfortunately, Manufacturer data sheet doesn’t have
the values. So, it is necessary to find these values. In this paper Newton Raphson
iterative technique is used for finding five unknown parameters. Five parameters require
five transcended equations to solve. The first three equations are derived from equation
(6) by applying short circuit, open circuit, and MPP conditions. The remaining two
equations are derived by differentiating the values of power and current with respect to
voltage [4]. Under the short circuit condition
(7)
After some approximation, the light generated current Iph can be described as follows,
(8)
Under the open circuit condition,
(9)
Equation (9) is rearranged and the reverse saturation current can be expressed as
follows,
(10)
Equation (8) is inserted into equation (10) and then the saturation current can be
derived from the following equation,
(11)
The MPP condition is applied in equation (6) and Impp can be described as follows,
(12)
Equations (8) and (11) are inserted into equation (12) and rearranged, by which Impp is
expressed as follows,
= -( (13)
Derivative of power with respect to voltage is zero at MPP and the same is expressed
as
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Substituting P=VI in equation (13),
(14)
From equation (14) and (13), can be expressed as follows,
(15)
Equation (15) can be derived using I - V characteristics of the PV module. The derivative
of the current with respect to voltage at the short circuit condition is mainly determined
by the shunt resistance Rsh [].
=
From equation (15), dI/dV can be expressed as
= = (16)
Improper selection of the initial values RSe and Rsh of the PV module may fail to
converge. So, it is necessary to select proper initial values. Initial values are given in
equations (17) and (18) are considered.
Rse_initial = - (17)
Rsh_initial = (18)
Equations (8), (11), and (16) are rearranged to determine the values of Vt , Rse , and Rsh ,
which are given by equations (19), (20), and (21), respectively.
(19)
(20)
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(21)
First, the transcendental equations (8), (11), and (16) are solved by the N-R method
and the values of a, Rse, and Rsh are obtained. Newton’s method is used for solving the
non-linear system of equations. Because of its time performance and convergence speed
N-R method is chosen. The flowchart for evaluation of parameters of the PV module is
shown in Figure 3.
Figure 3. Flow Chart for Evaluation of Solar PV Parameters
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MATLAB/m-file coding was done for the N - R method and executed successfully.
The estimated values of Rse, Rsh and a are 0.010 ohm,188.02ohm and 1.743 respectively.
Then a MATLAB/Simscape simulation model is developed by connecting 36 solar cells
blocks in series to form 40W panel. Then two 40W panels are connected in parallel to
form 80W solar array. The MATLAB/Simscape model shown in Figure 4.
MATLAB/Simscape Model of 80W Solar Array is simulated for 2 sec and its V-I and P-
V characteristics are obtained for various climatic conditions. The dependency to
insolation is shown in Figures 5a. V-I characteristics for Various Irradiation Levels and
Figure 5b. P-I Characteristics for Various Irradiation Levels. The dependency to
temperature is shown in Figure 6a. P-V Characteristics for Various Temperature Levels
and Figure 6b. V-I Characteristics for Various Temperature.
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Figure 5a. V-I characteristics for Various Irradiation Levels
Figure 5b. P-I Characteristics for Various Irradiation Levels
In order to validate the developed model, experiments have been done on real solar
array which is shown in Figure 7. Hardware Setups for Obtaining V-I and P-V
Characteristics with resistive load. In order to keep the temperature constant experiment
is performed at lower values of irradiance. The experimental results exhibited a good
agreement with the simulation ones. Thus, it can lay the foundation for in the following
research of the maximum power point tracking (MPPT). Rising temperature from 25oC
to 45oC the PV module, open circuit voltage (Voc) got down same time short circuit
current (Isc) slightly rises because of silicon bad gap energy. Maximum power (Pm) drops
with rise in panel temperature from 25oC to 45oC. Rise in solar irradiance from 200W/m2
to 1000 W/m2, voltage produced at open circuit and current produced at short circuit are
rises.
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Figure 6a. P-V Characteristics for Various Temperature Levels
Figure 6b. V-I Characteristics for Various Temperature Levels
Figure 7. Hardware Setups for Obtaining V-I and P-V Characteristics
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4. DC-DC Impedance Matching Positive Output Voltage Lift Luo
Converter
The circuit diagram of a positive output voltage-lift Luo converter is shown in Figure
8. Circuit Diagram of Voltage lift Luo Converter. When switch S is on, the source
current iin = iL1 + iL2. Inductor L1 absorbs energy from the source.
Figure 8. Circuit Diagram of Voltage lift Luo Converter
At the same time inductor absorbs energy from source and capacitor C; both currents
iL1 and iL2 increase. When switch S is OFF source current iin = 0. Current iL1 flows
through the freewheeling diode D to charge capacitor C1. At the same time current iL2
flows through Co - R circuit and freewheeling through diode D to keep itself continuous
conduction. Hence both currents iL1 and iL2 are decreased. The change in magnitude of
currents iL1 and iL2 are small so that, iL1≈IL1 and iL2 ≈IL2, where IL1 and IL2 are mean
values of inductor current L1and L2[5].
Table 2. Circuit Components of Luo converter
The output voltage is 48V at 80W power. Hence, the range of duty cycle is considered
between 0.83 and 0.72. But the duty cycle is not fixed due to the tracking process of
MPP. The value of inductors is selected based on the ripple value, assumed as 10% of its
maximum input current at minimum input voltage i.e., 0.16667A. The peak-to-peak
ripple value of capacitor voltage is considered as 4% of the output voltage i.e.,1.92V.
The components specification of the positive output voltage lift Luo converter is
tabulated in Table 2. Circuit Components of Luo converter.
5. A Modelling of Proposed Dynamic Model Based Maximum Power
Point Tracking Technique
A Design and implementation of a cost-effective Dynamic Model based MPPT
technique has been proposed for static and rapidly changing climatically parameters
associated with 80W soar array. The efficiency of this technique found to be higher
Component Specification
Inductor L1 2mH
Inductor L2 5mH
Coupling Capacitor 100µF
Output Capacitor 10µF
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than that of other techniques at all levels of irradiance. The experimental results
show that the proposed technique is able to achieve substantial reduction in power
oscillations, thereby improving the efficiency of the system. Ortiz photovoltaic
model [] describes analytical equations, relate the PV current with PV voltage for a
given temperature and irradiance on single PV cell. The equations are as follows,
(23)
where Vx and Ix are the open circuit voltage and short circuit current with
dynamic values for solar irradiance and temperature [6], which are defined by
equations (42) and (43); b is the characteristic constant, it does not have units and is
the unique parameter that has to be calculated.
(24)
(25)
(26)
The electrical parameters of the 80 W PV module are illustrated in Table 3.2. is
used for parameter b calculation. Generally, the value of b is lies in the range of
0.01 to 0.08 [].
(27)
Through MATLAB m-file program on Fixed Point Algorithm, the value of
Characteristic constant b was found 0.0839 with error tolerance 10 -7. Then using
equation (1.15) and (1.16) Vx and Ix are found, further Vop is found by using
equation 19.
(28)
at MPPT equation (1.18) dP/dV=0, by solving equation (6) Vop is obtained [7].
(29)
6. Performance Evaluation of Proposed Dynamic Model based
Maximum Power Point Tracking Technique
Cost effective manner, indirectly the irradiance is measured from the MAX44009
ambient light sensor. DHT11 temperature sensor is used for measurement of
temperature. PV module are located at the roof top and readings were taken using mobile
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phone using IoT technology. The simulation block diagram of the proposed system is
shown in Figure 9. The dynamic MPPT simulated values are listed in Table 4. Dynamic
Model based MPPT Test Data Points.
Figure 9. Simulink model of proposed Dynamic Model based MPPT
Arduino Uno microcontroller board is used for PWM pulse generation. The variable
duty cycle change D is declared and initially assigned to 127 and it is increased or
decreased depends on the power value. The amount of change of the duty cycle, the step
size taken is 5% i.e., corresponding to 12.7 in Arduino code. The PWM pulse generated
from Arduino is shown in Figure 10. PWM Signal.
Figure 10. PWM Signal
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Table 4. Dynamic Model based MPPT Test Data Points
Te
mp
erat
ure
(oC)
Irradia
nce
(W/m2)
Circuit Model DM MPPT Abso
lute
Pm
Erro
r
(Wat
ts)
Voc
(Volts)
Isc
(Amps)
Vm
(Volts)
Im
(Amps)
Pm
(Watts)
Voc
(Volts)
Isc
(Amps)
Vm
(Volts)
Im
(Amps)
Pm
(Watts)
25 1000 21.9 4.9 17.23 4.62 79.66 21.95 4.88 17.41 4.58 79.82 0.16
30.3 681 20.92 3.39 12.74 3.37 42.92 21.46 3.33 13.45 3.04 40.88 2.03
40.4 698 20.25 3.58 13.33 3.52 47.03 21.53 3.43 14.52 3.10 45.01 2.01
45.3 739 20.15 3.85 14.1 3.73 52.58 21.66 3.64 15.91 3.09 49.16 3.41
50.5 900 20.03 4.77 16.07 4.25 68.35 21.98 4.49 17.81 3.87 68.92 0.57
The performance evaluation of proposed Dynamic model based MPPT technique for
static and dynamically varying environmental conditions are done in
MATLAB/Simulink software. The simulated wave forms are shown inf figures 1.14,1.15
and 1.16. and observations are listed in Table 5. Simulation result for STC, Table 6.
Simulation results for gradual variation, Table 7. Simulation results for step variation and
Table 8. Simulation results for rapid variation.
Figure 1.14 Simulated PV Array Voltage for STC
Table 5. Simulation result for STC
MPPT PV Array
Output
Converter
Output
Voltage
Ripple
Current
Ripple
Settling
Time
Tracking
Efficiency
Vpv
(Volts)
Ipv
(Amps)
Ppv
(Watts)
Vo
(Volts)
Io
(Amps)
Po
(Watts)
Δ Vo
(Volts)
Δ Io
(Amps)
t
(Secs)
η
(%)
INC 19.22 3.931 75.56 47.53 1.584 75.36 1.35 0.045 0.05 94.21
DM 18.53 4.314 79.45 48.28 1.609 77.7 1.21 0.042 0.04 97.12
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Figure 11. Simulated PV Array voltage for gradual variation
Table 6. Simulation results for gradual variation
MPPT
Simulation Time
(Secs)
Convergence
Time
(Secs)
Tracking
Efficiency
(%) t=3 From t=4 to t=6 t=8
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
Volts)
Ppv
(Watts)
Vpv
(Volts)
INC 43.63 15.23 75.33 19.25 50.63 15.55 0.0726 94.48
DM 30.19 10.28 76.82 16.16 41.75 12.22 0.0712 96.35
Figure 12. Simulated PV Array Voltage for step variation
Table 7. Simulation Results of ANN MPPT for step variation
MPP
T
Simulation Time
(Secs)
Conver
gence
Time
(Secs)
Trackin
g
Efficie
ncy
(%)
0-1
1-2 2-3 3-4 4-5 5-6
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
INC 77.46 20.01 75.21 19.54 72.15 19.20 68.91 18.71 65.23 18.21 60.65 17.75 0.0461 94.46
DM 77.94 16.38 76.89 16.17 74.72 16.11 72.25 16.06 67.05 16.07 61.56 15.63 0.0463 96.57
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Figure 13. Simulated PV Array Voltage for rapid variation
Table 8. Simulation results for rapid variation
MPPT
Simulation Time
(Secs)
Convergence
Time
(Secs)
Tracking
Efficiency
(%)
t=0.7 t=2.3 t=5.1 t=7.6
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
Ppv
(Watts)
Vpv
(Volts)
INC 63.14 17.38 79.81 19.73 76.65 19.37 52.56 15.92 0.0963 84.24
DM 61.95 14.41 81.22 18.61 78.63 18.04 44.52 12.21 0.0754 86.41
Conclusion
The conventional incremental conductance maximum power point tracking technique
exhibited a very good static response but a deficient dynamic response. The peak power
tracking capability is doubtful under dynamic conditions. But its efficiency remains high
about 94%. Because of their slow response, the tracking time is around 0.096 Seconds.
Implementation of this technique is more complicated since it requires a fast controller
with high sampling accuracy. The proposed cost-effective dynamic model MPPT
efficiency has been found around 96.35% with no overshoot, lower settling-time, low
value of steady state and dynamic error. Hence it is proposed for temperate zone
geological locations.
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