Proceedings of 2014 RAECS UIET Panjab University Chandigarh, 06 - 08 March, 2014

978-1-4799-2291-8/14/$31.00 ©2014 IEEE

Real Time Simulation and Analysis of Maximum Power Point Tracking (MPPT) Techniques for Solar

Photo-Voltaic System D. S. Karanjkar, S. Chatterji and Shimi S. L.

National Institute of Technical Teachers Training and Research, Chandigarh, India

Amod Kumar Central Scientific Instruments Organization,

Chandigarh, India

Abstract— Solar energy is abundant and renewable in nature. The maximum power point tracking (MPPT) system controls the voltage and the current output of the PV system to deliver maximum power to the load. Present work deals with real time simulation and comparative analysis of perturb and observe, incremental conductance, fuzzy logic, neural network and adaptive neuro-fuzzy inference system (ANFIS) based MPPT techniques. Five MPPT algorithms have been implemented using voltage, current, radiation and temperature sensors on laboratory prototype. Real time simulations have been carried out on MATLABTM/dSPACETM platform for solar photo-voltaic system with buck converter. Performance of MPPT methods have been compared based on tracking efficiency, steady state and dynamic behaviour. Experimental results of various MPPT techniques have been presented for tracking maximum power point under rapidly varying solar radiations.

Keywords— Maximum power point tracking; comparison of MPPT techniques; solar PV system

I. INTRODUCTION Solar energy is free to use and the most abundant form of

renewable form of energy available on our planet. Solar photo-voltaic (PV) system uses photo-voltaic modules composed of several PV cells to convert solar radiant energy directly in to an electrical energy. Several solar cells are connected together in either series or parallel configuration (to form a solar PV module or PV panel) to increase output voltage or current respectively. Individual PV modules are connected in array called solar PV array to further enhance the output. The major components of solar PV system are PV array, power converter, battery, AC / DC load etc. (figure 1).

Figure 1 Components of solar photo-voltaic system In solar power system the power delivered to the load is highly dependent on solar radiation and PV array temperature. I-V and P-V curves of a solar cell with constant module temperature and solar radiation have been shown in figure 2.

At the intersection of Imp and Vmp, array generates maximum electrical power [1].

Figure 2 Current-voltage and power-voltage characteristics of a solar cell

As per maximum power transfer theorem, the circuit delivers maximum power to the load when source impedance matches the load impedance. In case of stand-alone solar system dc-dc converter is connected in between PV array and the dc load. Maximum power point tracking (MPPT) system varies the duty cycle of the dc-dc converter in order to match source and load impedance and to deliver maximum power to the load. Various MPPT methods have been reported in the literature. These methods can be classified as: i) methods based on load line adjustment of I-V curve and ii) method based on artificial intelligence (fuzzy logic or neural network based MPPT methods). The MPPT methods viz. perturb and observe (P & O), incremental conductance (INC), voltage feedback (VF) are based on load line adjustment of I-V curve. These methods have been found less suitable under uncertainties due to varying atmospheric and load conditions. The MPPT system based on artificial intelligence (fuzzy logic or neural network) has robust capabilities in regard to uncertainties [2, 3].

Real time simulation and comparative analysis of five mostly referred MPPT techniques viz. perturb and observe, incremental conductance, fuzzy logic, neural network and adaptive neuro-fuzzy inference system (ANFIS) based MPPT techniques have been presented in this paper. The paper is organized as follows. In section two a brief introduction of various MPPT techniques has been presented. Section three describes the modeling of solar PV system. Modeling and real-time simulation of MPPT algorithms has been given in section four. In section five, comparative analysis of five MPPT techniques and experimentation results have been presented, followed by conclusions.

Solar radiation

PV array

Energy conditioning &

inversion

Energy distribution

Energy storage Utility grid

Energy use AC/DC load

Cur

rent

I-V curve

P-V curve

PmaxIsc

Imp

VocVmp Voltage

Power

II. INTRODUCTION TO MPPT TECHNIQUES

A. Perturb and Observe (P & O) Method In P & O method PV voltage and PV current are measured

using voltage and current sensors and resulting power P1 is calculated. Then introducing small perturbation of voltage ΔV or perturbation of duty cycle of dc-dc converter Δd in one direction, corresponding power P2 is calculated. Power P2 is then compared with power P1. If is more than P1, then the perturbation is in correct direction, otherwise direction of the perturbation need to be reversed [3]. With this approach, the maximum power point is reached. After that the system will oscillate around the maximum power point under steady state condition. These oscillations are responsible for energy loss and hence reduced efficiency. Flowchart of this method is shown in figure 3.

Figure 3 Flowchart of perturb and observe MPPT method

B. Incremental conductance (INC) MPPT method The incremental conductance method (figure 4) is based on

fact that the slope of power-voltage curve is zero at maximum power point (dP/dV=0). It is positive in the left and negative in right as shown in figure 2. According to this condition, the MPP can be found in terms of increment of PV array conductance. Equation for the slope dP/dV at MPP is given by: dP/dV = d(V*I)/dV = I +V (dI/dV) = 0 (1) ΔI/ΔV = -I/V (at MPP) ΔI/ΔV � I/V (in the left of MPP) (2) ΔI/ΔV � I/V (in the right of MPP) For practical implementation of this method voltage and current sensors are needed however, power calculation is not essential as in the case of P & O method. In literature we find the modified INC MPPT method with proportional integral (PI) regulator (figure 5) in order to improve response of the MPPT, minimizing the error between the actual conductance and incremental conductance [4].

C. Fuzzy logic based MPPT MPPT methods based on artificial intelligence have

become prevalent in recent years as compared to conventional methods because of good and fast response under rapid variations in temperature and solar radiation. The fuzzy logic based MPPT method does not require the exact model of PV system for its design [5]. In most of the literature, fuzzy logic based MPPT has been proposed with two inputs and one output. The two input variables are error E(k) and change in error ΔE(k), given by: E(k) = ΔI/ΔV + I/V (3)

ΔE(k) = E(k) – E(k-1) (4) Where, I is output current from PV array, ΔI is I(k)-I(k-1); V is output voltage from array, ΔV is V(k)-V(k-1).The fuzzy inference can be carried out by one of the various available methods (Mamdani’s method has been mostly used) and the defuzzification can be done using centre of gravity method to compute the output (duty cycle). The scheme of such MPPT method has been shown in figure 6.

Figure 4 Flowchart of incremental conductance MPPT method

Figure 5 Incremental conductance MPPT with PI regulator

Figure 6 Fuzzy logic based scheme for MPP tracking

D. Neural network based MPPT method: Neural network based MPPT technique operates like black

box model and do not require detail information about the PV system [6]. Block diagram of neural network based MPPT method is shown in figure 7. The inputs can be PV voltage, PV current and/or environmental data like solar radiation and temperature or combination of all/ any of these. Output of the neural network is the duty cycle used to operate the dc-dc converter at MPP. The input data to train the network can be obtained from experimental measurement or model based simulation results. Neural network can track the MPP after training it with the input data [7].

Figure 7 Neural network based MPPT technique

V(k+1)=V(k)-ΔV V(k+1)=V(k)+ΔV V(k+1)=V(k)-ΔV V(k+1)=V(k)+Δ

No

Measure V(k), I(k) Calculate P(k)

Start

No No Yes Yes

Yes P(k)-P(k-1)�0

V(k)-V(k-1)�0 V(k)-V(k-1)�0

V(k+1)=V(k)-ΔV V(k+1)=V(k)+ΔV V(k+1)=V(k)-ΔV

V(k+1)=V(k)+ΔV

Measure V(k), I(k)

Start

No

Ye

Yes

Yes

V(k)-V(k-1)=0

dI/dV�(-I/V) I(k)-I(k-1)�0

dI/dV=(-I/V) I(k)-I(k-1)=0

No No YesYesNo No

-

PI regulator

Divisor

Sum dV/dt Divisor

dI/dt zero

Vpv(t)

Ipv(t)dI/dV

error

d(t)

I/V

+

-

Rule base

Divisor

Sum dV/dt

Divisor

dI/dt zero

Vpv(t)

Ipv(t)

dI/dV

error

d(k)

I/V

+

Defuzzification Fuzzy inference

Z-1

+

E(k)

E(k-1)

-

Vpv

Ipv

Input layer

Hidden layer

Output layer

d

wij j

i

E. ANFIS based MPPT Adaptive neuro-fuzzy inference system (ANFIS) (figure 8)

integrates neural network and fuzzy logic. Fuzzy logic has capability to transform the linguistic terms into numerical values using fuzzy rules and membership functions. However finding correct fuzzy rules and membership functions which highly rely on the system behavior can become challenging task. ANFIS combines neural network and fuzzy logic to overcome drawbacks of the individual techniques [8] and Properly tuned ANFIS based MPPT system can track MPP with higher accuracy than that of P & O method [9].

Figure 8 ANFIS based MPPT scheme

III. MODELING OF PV SYSTEM Typically a solar cell can be modelled by a current source

with an inverted diode connected in parallel to it as shown in figure 8. Series resistance is due to the hindrance in the path of flow of electrons from n to p junction and parallel resistance is due to the leakage current.

Figure 8 Ideal and practical single diode model of a PV cell The mathematical expression of the output current of the

PV module can be expressed as:

s sp pv p 0

t p

V + R I V + R II = n I - n I exp - 1 -V a R

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦ (5)

where, I is the current, V is the voltage of the PV module, Ipv is the photo-current, I0 is the reverse saturation current, np is the number of cells connected in parallel, ns is the number of cells connected in series, q is the charge of an electron (1.6*10-

19C), k is Boltzmann’s constant (1.38*10-23J/K), a is p-n junction ideality factor, (1 < a < 2, a = 1 being the ideal value), and T is the PV module temperature [10]. Vt = NskT /q is the thermal voltage of the module with Ns cells connected in series. Rs and Rp are equivalent series and parallel resistances. The PV current depends on the solar irradiation and is influenced by the temperature according to the following equation:

pv pv,n I nn

SI = (I + K (T - T ))S

(6)

where Ipv,n is the PV current at the nominal condition (at 25 0C and 1000W/m2), T and Tn are the actual and nominal temperatures, S and Sn are actual and nominal radiation and the short-circuit current/temperature coefficient (KI ). The

short-circuit current can be determined by [11], α

sc sc,nn

SI = IS

⎛ ⎞⎜ ⎟⎝ ⎠

(7)

where Isc,n is the short-circuit current under the nominal irradiance Sn; while Isc is the short-circuit current of the PV module under the irradiance S; α is the exponent responsible for all the non-linear effects that the photocurrent depends on. Under different irradiance levels, short-circuit current is different, so that the parameter α can be determined by:

( )( )

sc,n sc,1

n 1

ln I / Iα=

ln S / S (8)

where Isc,n and Isc,1 are the short-circuit currents of the PV module under radiation Sn and S1. Another important characteristics of the PV module viz. open-circuit voltage Voc, fill factor FF and the maximum power output Pmax are function of radiation and panel temperature [11]. The open-circuit voltage at any given condition can be expressed by,

( ),

1 ln /oc n n

ocn

V TVS S T

γ

β⎛ ⎞= ⎜ ⎟+ ⎝ ⎠

(9)

where, Voc and Voc,n are the open-circuit voltage of the PV module under the normal radiation S and the nominal radiation Sn , β is a PV module technology specific coefficient [12] and γ is the exponent considering all the non-linar effects. The values of α, β and γ can be referred from the datasheet of the solar module. Fill factor is a dimentionless term and is a measure of the deviation of the actual I-V characterestic from the idal one. Expression for determination of the fill factor is [13],

s0

oc sc

RFF = FF 1 -V / I

⎛ ⎞⎜ ⎟⎝ ⎠

(10)

where, ( )oc oc

0oc

v - ln v +0.72FF =

1+ v (11)

with, FF0 is the fill factor of the ideal PV module without resistance effects, Rs is the series resistance, voc is the normalized value of the open-circuit voltage to the thermal voltage i.e.,

ococ

Vv =nkT / q

(12)

The maximum power output Pmax can be given by, max oc scP = FF ×V × I

( )( )

αγoc oc oc,ns n

max sc,noc oc sc n n

v - ln v +0.72 VR T SP = 1 - I1+ v V / I 1+ βln S / S T S

⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠ ⎝ ⎠

(13)

The configuration of the solar system with buck converter has been considered in the present work (figure 9).

Figure 9 Configuration of buck converter in solar PV system

The ratio of output to input voltage of buck converter is given by [14], Vo/Vin=D, where, Vo and Vin are the output and input

Vpv

Ipv

Layor 1

d

A1

A2

B1

B2

N1 1

2

3

4

N2

N3

N4

П1

П2

П3

П4

�

Vp IpLayor 2 Layor 3 Layor 4 Layor 5

Layor 6

Rp

id Ipv

Practical Model

Ideal ModelRS

Vo

+

-

I

IL L

+

- -

Vo

D

+

C

Ipv

Load PV Array

voltages respectively and D is the duty-ratio defined as the ratio of the on time of the switch to the total switching period.

IV. REAL TIME IMPLEMENTATION OF MPPT TECHNIQUES

A. Hardware details A poly-crystalline solar PV module (Vikram Solar ELV37)

with buck converter (of specifications mentioned in Table I and II) has been used for experimental analysis of various MPPT techniques. MPPT algorithms have been designed in MATLABTM/SIMULINKTM and implemented using dSPACETM ds1104 controller board. Radiation and temperature sensors are needed for calculation of theoretical maximum power (Pmax, theoretical) while voltage and current sensors are necessary for operation of MPPT controllers. Voltage sensor is designed using voltage divider resistive network. Current measurement has been done using low value (0.01 Ohm) shunt resistor (Rsh) that will output a voltage proportional to the current flowing through it. A reference solar module is used for the measurement of the solar radiation. The average intensity of the solar radiation the striking on PV module was calculated by measuring the radiation level at various points on the PV panel. According to this value the output of the radiation sensor was calibrated. For measurement of module temperature LM35 temperature sensor is used. Block diagram of hardware interfacing of PV system is shown in figure 10. The photo snap of experimental setup is given in figure 11.

TABLE I PV module parameters Short circuit current Isc 2.40 A Open circuit voltage Voc 21.8 V

Current at maximum power point IMPP 2.25 A Voltage at maximum power point VMPP 17 V

Number of cells in series Ns 36 Temperature coefficient of Isc 0.04% /ºC Temperature coefficient of Voc -0.32%/ºC

Pmax 37W TABLE II. Buck Converter Parameters

Vin 20.8 volts Vout 16.7 volts Pmax 36.8 W Switching frequency 80 KHz Max. inductor current ripple 10 % Inductor 1 Mh RL 7,55 Ohm Cout 100 µF D 0.8

Figure 10 Hardware interfacing of using dSPACETM

Four channels of analogue data input and one channel of PWM output channel have been used to interface four sensors

one output signal (duty-ratio). The dSPACETM system samples and converts the sensor outputs to digital signals, processes them as per programme in MATLABTM and then outputs the pulse-width-modulated (PWM) signal to the driving circuit of the buck converter via PWM output channel.

Figure 11 Experimental setup

B. Modeling and real-time simulation of MPPT algorithms MATLABTM/SIMULINKTM models of various MPPT

algorithms have developed and laboratory based real time simulations have been carried out for comparing MPPT algorithms with reference to their responses for step change in the solar irradiation. Step change in the solar radiation of the two halogen lamps was introduced using toggle switches. The model of P&O MPPT is given in figure 12, with initial value of the duty-ratio of 0.8. The model for INC MPPT subsystem with discrete PI controller is shown in figure 13. Fuzzy based MPPT system has been designed (figure 14) using two input variables viz. dP/dV and rate of change of dP/dV given by,

( ) ( ) ( )( ) ( )

p k - p k - 1dP k = anddV V k -V k - 1

( ) ( ) ( )dP dP dPΔ k = k - k - 1dV dV dV

⎛ ⎞⎜ ⎟⎝ ⎠

(14)

and one output variable viz. change in duty-ratio ( ΔD). Seven triangular membership functions have been assigned for input and output variables. The rule base is given in Table III.

TABLE III. Rule base for fuzzy-MPPT system dP/dV NB NM NS ZE PS PM PB

rate_dP/dV NB ZE ZE NS NM PM PM PB NM ZE ZE ZE NS PS PM PB NS ZE ZE ZE ZE PS PM PB ZE NB NM NS ZE PS PM PB PS NB NM NS ZE ZE ZE ZE PM NB NM NS PS ZE ZE ZE PB NB NM NS PM PS ZE ZE

Mamdani method of fuzzification and centroid method of defuzzification are used for real time implementation of the fuzzy MPPT algorithm. Neural network based MPPT controller is modeled as shown in figure 15. Two layer feed-forward neural network with ten sigmoid hidden neurons is designed with nntool of MATLABTM. The network has been trained with experimental set of input data using Levenberg-Marquardt back-propagation algorithm. A total of 7609 samples were collected from real time system out of which 5327 samples were used to train the network while remaining samples were used for validation and testing purpose. In the present work the ANFIS controller has been developed with two inputs and one output (figure 16). In this controller fuzzy rule base has been generated based on Sugeno inference model. The data used for training is similar to that of NN based MPPT design. The anfisedit tool of MATLAB has been used to design the ANFIS controller with two neurons in layer 1 and 14 neurons in the fuzzification layer. An algorithm for

Rsh

Load Rp

Rv

Vpv

+

- +

PV module Buck

converter

D

dSPACETM ds1104/CPL1104

Personal computer with MATLABTM

+

Ipv

- -

+

Temperature sensor

Radiation sensor

calculation of Pmax, theoretical has been modeled in MATLABTM/SIMULINKTM as shown in figure 17. The algorithm has been developed using equations 13. Values of α, β and γ are referred from the Vikram Solar PV module ELV37 datasheet.

Figure 12 Model of P&O MPPT algorithm

Figure 13 Model of INC-PI subsystem

Figure 14 Fuzzy MPPT subsystem

Figure 15 Model of neural network based MPPT system

Figure 16 Model of ANFIS based MPPT system

Figure 17 Model for determination of Pmax (theoretical)

V. RESULTS AND DISCUSSIONS

Response of various MPPT algorithms has been shown in figure 18 (a) to (g). Performance of P&O MPPT method was analyzed with three different fixed perturbation sizes (ΔD=0.1, 0.01 and 0.001). It can be seen from the responses that the steady state oscillations have been reduced and efficiency has

been increased with decrease in ΔD and satisfactory response can be achieved with ΔD=0.001, but overall MPPT efficiency is limited to around 85 %. Incremental conductance (with PI regulator) method of MPPT exhibits very little steady state oscillations but offers overshoot (3.35%) with response to abrupt change in the input radiation. The settling time in case of INC-PI is large than that of P&O MPPT. It can be seen that the dynamic response has been improved as compared to the P&O MPPT. Fuzzy logic based MPPT technique resulted in about 89 % of efficiency with lower settling time and the steady state error as compared to the INC-PI technique of MPPT. Other artificial intelligence based techniques offered higher efficiency as mentioned in Table IV. Good balance between overshoot, steady state error and settling time can be achieved with well trained neural network based MPPT. Although the ANFIS MPPT method resulted in higher efficiency it offered much higher overshoot and settling time.

TABLE IV. Comparison of MPPT algorithms MPPT method

Efficiency ( %)

Over-shoot ( %)

Settling time ( sec)

Delay in dynamic response

( sec)

Max. Steady

state error( %)

Sensors used

PO (ΔD=0.1)

77.60 to 79.39

No 0.48 0.06

15.14 Voltage, current

PO (ΔD=0.01)

81.00 to 81.60

No 0.41 0.039 12.77 Voltage, current

PO (ΔD=0.001)

81.23 to 84.37

No 0.40 0.04 12.03

Voltage, current

INC PI 86.32 to 87.25

3.35 1.78 0.001 7.35 Voltage, current

FUZZY

85.63 to 88.88

4.32 0.472 0.039 3.63

Voltage, current

NN

87.35 to 90.10

2.185 0.6439 0.038 3.88 Voltage, current

ANFIS

87.15 to 93.31

6.56 5.35 0 3.55 Voltage, current

Figure 18 (a) Response of PO MPPT with ΔD=0.1

Figure 18 (b) Response of PO MPPT with ΔD=0.01(contd.)

Voltage

Saturation

RTI Data Product Power

Param

Enabled

V

I

DPandO

MPPT Control Param

MPPT Parameters

1.25

Gain3

10

Gain2

10

Gain1

10

Gain

EnableMPPT

PWM Channel 1

PWM Channel 2

PWM Channel 3

PWM Channel 4

DS1104SL_DSP_PWM

MUX ADC

DS1104MUX_ADC

ADC

DS1104ADC_C5

D

Current

0

Constant3

0

Constant2

butter

AnalogFilter Design1

butter

AnalogFilter Design

1

Delta_D

1/z

1/z

1

KiGain

K Ts

z-1

Discrete-TimeIntegrator

Dead Zone

1e-6

0

0

~= 0

3

ENABLE

2

I_PV

1

V_PV

V

dI/dV

I

dV

dI

I/V

errorDelta_D

D delta

dP/dV DELTA dP/dV

1

Delta_D

1/z

1/z

1/z

Product

Power

Fuzzy Logic Control ler

2

I_PV

1

V_PV

I

dV

P dP

Voltage

Saturation

RTI Data

Product Power

In1 Out1

Neural Control ler

1.25

Gain3

10

Gain2

10

Gain1

10

Gain

PWM Channel 1

PWM Channel 2

PWM Channel 3

PWM Channel 4

DS1104SL_DSP_PWM

MUX ADC

DS1104MUX_ADC

ADC

DS1104ADC_C5

D

Current

0

Constant3

0

Constant2

butter

AnalogFil ter Design1

butter

AnalogFi lter Design

Voltage

Saturation

RTI Data

Product Power

1.25

Gain3

10

Gain2

10

Gain1

10

Gain

PWM Channel 1

PWM Channel 2

PWM Channel 3

PWM Channel 4

DS1104SL_DSP_PWM

MUX ADC

DS1104MUX_ADC

ADC

DS1104ADC_C5

D

Current

0

Constant3

0

Constant2

butter

AnalogFil ter Design1

butter

AnalogFil ter Design ANFIS

Control ler

T

G

V oc

Temp

Pmax

Isc1

Voc1Radiation

P max

I sc

10

10

ADC

DS1104ADC_C7

ADC

DS1104ADC_C6

273In1 Out1

Calibration1

In1 Out1

Calibration

Add2

Delay in dynamic response

Max. steady state error

Initial offset

Delay in dynamic response

Max. steady state error

Figure 18 (c) Response of PO MPPT with ΔD=0.001

Figure 18 (d) Response of INC-PI MPPT

Figure 18 (e) Response of fuzzy MPPT

Figure 18 (f) Response of NN MPPT

Figure 18 (g) Response of ANFIS MPPT.

VI. CONCLUSIONS Comparative assessment of five MPPT techniques has been

presented in this paper. MATLAB/ SIMULINK models of various MPPT algorithms have been developed and real time simulations have been carried out on prototype of solar PV system with buck converter. Performance comparison of MPPT methods under rapid change in radiation have been presented based on tracking efficiency, steady state and dynamic behaviour.

VII. ACKNOWLEDGEMENTS Authors would like to acknowledge technical and financial

support of AICTE, Government of India, Director, NITTTR, Chandigarh and Principal, Institute of Petrochemical Engineering, Lonere, Maharashtra, India.

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Settling time

Max. steady state error

Peak overshoot Settling time

Max. steady state error

Peak overshoot

Settling time

Max. steady state error

Max. steady state errorPeak overshoot Settling time

Peak overshoot Settling time

Max. steady state error