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 1c.vennila@yahoo.com, 2m_vijayaraj@yahoo.co.in

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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