Novel Adaptive P&O MPPT Algorithm forPhotovoltaic System Considering Sudden Changes

in Weather ConditionSathish Kumar Kollimalla Student Member, IEEE, Mahesh Kumar Mishra Senior Member, IEEE

Department of Electrical Engineering,

Indian Institute of Technology Madras, Chennai, India.

kollimallasathish@gmail.com

Abstract—The output power of the PV system continuouslyvaries with change in irradiance and temperature. At a specifiedirradiance and temperature, the output power of the PV systemcan be varied from zero to maximum depending on the operatingvoltage and current. There are number of maximum power pointtracking (MPPT) methods available in literature to operate thePV system at maximum power point (MPP). Among differentMPPT methods, perturb and observe (P&O) method is widelyused because of its low-cost and ease of implementation. Whenirradiance and temperature are constant or slowly varying, theP&O method tracks MPP steadily. However it fails to track MPPwith rapid speed, for rapidly varying irradiance and temperature.In order to consider rapidly varying atmospheric conditions anadaptive control algorithm is proposed, by estimating the shortcircuit current. In this proposed method, current perturbationis considered to improve the tracking speed. The effectivenessof proposed MPPT algorithm in terms of faster dynamics andreduced oscillations compared to conventional P&O algorithm isverified using digital simulations.

Index Terms—Adaptive control, fractional short circuit currentmethod, maximum power point tracking (MPPT), perturb andobserve (P&O) method, PV module.

I. INTRODUCTION

Alternate energy sources gained a lot of importance in

power generation due to their abundant availability and eco-

friendly nature. The increasing power demand along with

reduction in conventional fuel sources and growing concern

about carbon emissions has driven the world towards cleaner

power generation. Among the alternative sources, solar power

generation is currently considered as a natural energy source

that is more useful, as it is pollution free, maintenance free,

distributed over the earth, fast technological progress and

continuous cost reduction. A great advantage with solar power

generation is the reduction of carbon dioxide emissions. The

fundamental element in solar power generation system is the

solar cell or photovoltaic (PV) cell that converts sunlight into

direct current (DC) electricity. A photovoltaic (PV) module is

an interconnected collection of cells combined as one item.

Multiple modules can be wired together either in parallel or

in series or in both to form an array. In general, the larger

the area of a module or array, the more electricity that it can

produce. The structure of PV cell, PV module and PV array

are shown in Fig. 1.

Fig. 1. PV cell, module and array

The main hindrance to solar energy going widespread is

the cost of installing solar modules. The biggest disadvantage

of solar energy production revolve around the fact that power

generation is not constant throughout the day, it is always

changing with weather conditions, i.e., irradiation and temper-

ature. Furthermore, the efficiency of solar energy conversion

to electrical energy is very low which is only in the range of

9-17% [1], especially under low irradiation states, this means

that a fairly vast amount of surface area is required to produce

a lot of electricity. Therefore, maximum power point tracking

(MPPT) is an essential part of the photovoltaic system to

ensure that power converter circuits operate at the maximum

power point of the solar array. Various MPPT algorithms have

been developed [2] - [3]. These algorithms are differ from

each other in terms of number of sensors used, complexity

in algorithm and cost to implement the algorithm. The main

objective of all these MPPT algorithms is to achieve fast

and accurate tracking performance and minimize oscillations

due to varying weather conditions. Each algorithm can be

categorized based on the type of the control variable it uses: a)

voltage, b) current, or c) duty cycle. Among different MPPT

methods, much focus has been on perturb and observe (P&O)

[4] - [5] and hill climbing (HC) [6] - [7] methods. The P&O

method involves a perturbation in the operating voltage of solar

array and hill climbing involves a perturbation in the duty ratio

of power converter.

In P&O method the voltage is being increased or decreased

with fixed step size in the direction of reaching the maximum

power point (MPP). The process is repeated periodically until

653978-1-4673-4430-2/13/$31.00 ©2013 IEEE

the MPP is reached. At steady state, the operating point

oscillates around the MPP giving rise to the wastage of some

amount of available energy. These oscillations can be mini-

mized by reducing the fixed step size, but it takes relatively

more time to reach MPP. The solution to this conflicting

situation is to have a variable step size as suggested in [8] - [9].

Although, the implementation of these methods are simple,

but it is not very accurate and rapid, since the effects of

temperature and irradiation are not taken into consideration.

Several methods are proposed to address these issues by

considering adaptive perturbation [10] - [11].

Another method is fractional open circuit voltage (or frac-

tional short circuit current) based algorithm, the MPP voltage

VMPP (or MPP current IMPP ) with respect to the open

circuit voltage VOC (or short circuit current ISC) [12] -

[14] is monitored. Since this method approximates a constant

ratio, its accuracy cannot be guaranteed under varying weather

conditions.

In this paper, a novel adaptive P&O algorithm is designed

in order to overcome the above mentioned drawbacks. In this

proposed method, current perturbation is considered to speed

up the tracking performance. The current perturbation can be

realized by using sliding mode controller (SMC) as discussed

in [15]. In order to handle the rapidly varying atmospheric

conditions an adaptive control algorithm is used.

This paper is organized as follows. The mathematical mod-

eling of PV module is discussed in Section II. In Section

III the proposed MPPT algorithm is explained in detail. In

Section IV simulation studies are reported. Finally, in Section

V conclusions are summarized.

II. MATHEMATICAL MODELING OF PV MODULE

The photovoltaic (PV) cell is basically a p-n junction

fabricated in a thin wafer of semiconductor. The solar energy

is directly converted to electricity through photovoltaic effect.

PV cell exhibits a nonlinear I-V and P-V characteristics which

vary with solar irradiance (S) and cell temperature (T ).

A. Modeling of PV Cell

There are different equivalent circuits of PV cell [16] - [17],

where the single-diode and two-diode models could be most

widely used. A single-diode model is used in this paper as

shown in Fig. 2. The equivalent circuit consists of a photo

current source, diode, a series resistor, and a parallel resistor.

Rs

RshIrs

Iph

Ipv

Vpv

S

Fig. 2. Equivalent circuit of PV cell.

The nonlinear I-V characteristic equation of a PV cell is

given as [18],

Ipv = Iph − Irs

(e

q(Vpv+IpvRs)

AkT − 1)− Vpv + IpvRs

Rsh(1)

where,

Ipv Output current (A)Iph Light generated current or photo current (A)Irs Diode reverse saturation currentVpv Output voltage (V)q Electron charge (= 1.609 x 10−19 C )A Diode ideality constantk Boltzmann’s constant (= 1.38 x 10−23 J/K )T Cell absolute temperature (K)

and other parameters can be obtained from specifications given

in [18].

B. Modeling of PV ModuleDue to low power ratings of each individual PV cell, the

cells are connected in series-parallel configuration in order

to produce required power. The equivalent circuit is shown

in Fig. 3. The PV module is described by its nonlinear I-V

characteristic equation given as [19],

Ipv = NP Iph −NP Irs

(e

q(Vpv/NS+IpvRs/NP )

AkT − 1)

−NPVpv/NS + IpvRs

Rsh

(2)

where, NS is number of cells connected in series and NP is

number of cells connected in parallel as shown in Fig. 3.

NP Iph

Ipv

Vpv

Ss

P

NR

N

Ssh

P

NR

N

NP

NS

�

S

Fig. 3. Equivalent circuit of PV module.

C. Solution for Nonlinear EquationThe model is processed in a MATLAB script file. Newton

Raphson (NR) method is used to solve the nonlinear equations

as given [20],

xn+1 = xn − f(xn)

f ′(xn)(3)

where, xn is the value of x at nth instant, f ′ is the derivative

of f with respect to x and f can be derived from (2) as given,

f(x) = Ipv −NP Iph +NPVpv/NS + IpvRs

Rsh

+NP Irs

(e

q(Vpv/NS+IpvRs/NP )

AkT − 1) (4)

where, x can be either Ipv or Vpv . In this paper, Vpv is

considered as x.

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III. MAXIMUM POWER POINT TRACKING ALGORITHM

The MPPT algorithm tracks the voltage (VMPP ) and current

(IMPP ) of PV array, such that the PV system operates

at maximum output power (PMPP ). In this paper, a novel

adaptive P&O MPPT algorithm for photovoltaic system con-

sidering sudden changes in weather condition is proposed

using fractional short circuit current and conventional P&O

methods. These two methods are explained briefly.

A. Perturb and Observe (P&O) MethodIn conventional P&O algorithm the voltage is incremented

or decremented by ΔV . The change in power is calculated

corresponding to change in voltage. If the given change in

voltage leads to an increase in output power, then the sub-

sequent change in voltage is generated in the same direction

otherwise in the opposite direction as summarized in Table I.

This process repeats until MPP is reached. The performance

of P&O algorithm is depends on the tradeoff between tracking

speed and oscillations that occurs around MPP.

TABLE ISUMMARY OF P & O METHOD

Perturbation Change in Power Next PerturbationPositive Positive PositivePositive Negative NegativeNegative Positive NegativeNegative Negative Positive

B. Fractional Short-Circuit Current (FSCC) MethodThe fractional short circuit current method is the simplest

MPPT method. The short circuit current depends on the solar

irradiance and temperature. The output current of PV array is

almost constant in the range of 0 to VMPP . When the output

current of PV array is approximately 90% of the short circuit

current, then PV array operates at MPP. The relationship

between IMPP and ISC is given as [2]

IMPP ≈ kscISC (5)

where, ksc is a proportionality constant, and it lies in between

0.78 and 0.92.The output power of PV array is reduced because of

approximation between IMPP and ISC in (5). This method

fails to track MPP exactly under varying weather conditions.

The short circuit current ISC is measured by shorting the PV

array periodically. An additional switch is used to short the PV

array. The output power is further reduced during this period.

C. Novel Adaptive P&O MPPT AlgorithmThe novel adaptive P&O MPPT algorithm incorporates two

major modifications to conventional P&O method:

1) Considering current perturbation instead of voltage per-

turbation in conventional P&O method to speed up the

tracking performance as explained using flowchart Fig.

4.

2) Moving the operating point to left hand side (LHS) of

MPP to handle the sudden changes in weather condi-

tions.

Start

Sample Vpv(k) and Ipv(k)

Cal. Ppv(k) = Vpv(k)*Ipv(k)

Ipv(k+1) = Ipv(k) + �I

Cal. Vpv(k+1) &Ppv(k+1) = Vpv(k+1)*Ipv(k+1)

Cal. �Ppv = Ppv(k+1) - Ppv(k)

Ipv(k+2) = Ipv(k+1) + �I

Ipv(k+2) = Ipv(k+1) - �I

Ipv(k+2) = Ipv(k+1)

Ipv(k) = Ipv(k+1)Ppv(k) = Ppv(k+1)

Ipv(k+1) = Ipv(k+2)

Ipv(k+2) = Ipv(k+1) + �I

Ipv(k+2) = Ipv(k+1) - �I

�Ppv�Ppv < 0 �Ppv > 0

YesYesNo NoIpv(k+1) > Ipv(k)

Ipv(k+1) > Ipv(k)

Adaptive control algorithm

Fig. 4. Flowchart of the proposed MPPT algorithm

1) Consideration of current perturbation: Flowchart of the

proposed MPPT algorithm is shown in Fig. 4, where Ipv(k),Vpv(k) and Ppv(k) are output current, voltage and power

of PV array at kth iteration respectively and ΔI is current

perturbation size.

The generalized equation is derived for the proposed MPPT

algorithm as given,

Ipv(k + 2) = Ipv(k + 1) + sign(Ipv(k + 1)− Ipv(k))

∗sign(Ppv(k + 1)− Ppv(k)) ∗ΔI.(6)

where, the function sign(.) gives either +1 or -1 depending

on positive or negative value inside the function respectively.

RHS of MPPLHS of MPP

ISCIMPP

VOCVMPP

PMPP2IMPP - ISC

Fig. 5. Nonlinear characteristics of PV array

Fig. 5 shows the nonlinear characteristics of PV array. The

output current of PV array in the left hand side (LHS) of

MPP i.e. 0 to VMPP region is almost constant. On the other

hand the current is drastically changing in the right hand side

(RHS) of MPP i.e. VMPP to VOC region. Therefore, if the

operating point lies in the LHS of MPP, then the current

perturbation gives faster response than voltage perturbation in

reaching the MPP with reduced oscillations. On the other hand,

if the operating point lies in the RHS of MPP and operating

current Ipv(k) is less than [IMPP − (ISC − IMPP )] as shown

in Fig. 5, then current perturbation gives slower response. To

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avoid this situation an adaptive control algorithm is proposed.

The operating current range for which current perturbation (6)

gives satisfactory response is given as,

ISC ≤ Ipv(k) ≤ 2 IMPP − ISC . (7)

2) Set the Operating Point to Left Hand Side of MPP:If there is a significant change in weather conditions or the

operating current violates the current limit (7), then only the

adaptive control algorithm (dotted box) comes into action. It

always tries to keep the operating point within the limits.

T o

T o

S 2

(a)

S 2

S 2

T o

(b)

Fig. 6. Simulated I-V and P-V characteristics of PV array, (a) at constantsolar irradiance 500W/m2 (b) at constant temperature 10oC

Let assume that, initially PV array is operating at point

A as shown in Fig. 6(a) and Fig. 6(b). The operating point

A corresponds to MPP indicated by E. If there is a sudden

increase in temperature or irradiance, then the operating point

changes from A to B i.e., left hand side (LHS) of new

MPP denoted by F as shown in Fig. 6(a) and Fig. 6(b)

respectively. The MPPT algorithm directs the PV array to

change the operating point from B to C. The operating point C

corresponds to new MPP as indicated by F. If there is a sudden

decrease in temperature or irradiance, then the operating point

changes from C to D i.e., right hand side (RHS) of new MPP

denoted by E as shown in Fig. 6(a) and Fig. 6(b) respectively.

Therefore, if the operating point violates the condition (7)

due to significant change in irradiance or temperature, then

the operating point is to be shifted to LHS of MPP. This

can be done by obtaining the short circuit current. Different

methods are available for obtaining the short circuit current as

mentioned in fractional short-circuit current method, but these

methods will give losses. A generalized expression is derived

in this paper to estimate the short circuit current for changes

in irradiance and temperature.

The variation of short circuit current with temperature and

irradiance is given by,

ISC = KSKT ISC(Snom, Tnom) (8)

where,

KS =S

Snom, (9)

KT = 1 +[ISC(T1)− ISC(T2)]

[T1 − T2]ISC(T2)[T − T2] , (10)

Tnom, Snom, and ISC(Snom, Tnom) are temperature, irradi-

ance, and short circuit current of PV array at STC respec-

tively. T is variable temperature and S is variable irradiance.

ISC(T1) and ISC(T2) are short circuit currents measured at

temperatures T1 and T2 respectively.

2

T o

T oISC

ISC

Fig. 7. Variation of short circuit current with irradiance and temperature

Fig. 7 shows the variation of short circuit current with

changes in irradiance and temperature. Currents calculated

using (2) and (8) are almost same. Therefore, the short circuit

current can be estimated using (8), instead of measuring,

hence saving the component cost. Variation of short circuit

current with temperature is very less as compared to irradiance.

Therefore, (10) can be approximated to unity. This approxima-

tion will save the memory, computation time and temperature

sensor cost.

Once the short circuit current ISC is estimated, then the new

operating point on LHS of MPP is calculated as explained in

fractional short circuit method [2]. In (5), ksc varies between

0.78 and 0.92 depending on weather conditions. In order

to avoid the operating point on RHS of MPP, consider the

maximum value of ksc. Therefore, the new operating point is

given as

Ipv(k) = 0.92 ISC . (11)

IV. SIMULATION STUDIES

To compare the proposed MPPT algorithm with conven-

tional MPPT algorithm Solarex MSX60 [20] PV module is

considered for simulation. A PV array is formed by connect-

ing 6 x 6 modules in series and parallel respectively. The

TABLE IISPECIFICATIONS OF PV ARRAY AT STC (S = 1000W/m2, T = 25oC)

Parameters Symbol ValueMaximum Power PMPP 2160 WVoltage at Maximum Power VMPP 102.6 VCurrent at Maximum Power IMPP 21 AOpen Circuit Voltage VOC 126.6 VShort Circuit Current ISC 22.8 A

specifications of PV array at Standard Temperature Condition

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(STC) is given in Table II. The perturbation sizes considered

in simulation are ΔI = 0.06A (for proposed MPPT) and

ΔV = 1.25V (for conventional MPPT).

A. Study of Proposed MPPT Algorithm for Sudden Change inIrradiance

PV array is simulated for sudden change in irradiance, as-

suming constant temperature of 25o C. Figs. 8(a)-(c) show the

output current, output voltage, and output power of PV array

against number of iterations. Fig. 8(d) shows tracking of MPP

for proposed and conventional MPPT algorithms for sudden

decrease in irradiance from 900W/m2 to 500W/m2. Fig. 8(e)

shows tracking of MPP for proposed and conventional MPPT

algorithms for sudden increase in irradiance from 500W/m2

to 900W/m2.

Initially, PV array is simulated at S = 900W/m2. For

proposed MPPT algorithm the operating point starts from point

A and reaches the maximum power point B as shown in

Fig. 8(d) and oscillates around B. For conventional MPPT

algorithm the operating point starts from point E and reaches

the maximum power point B as shown in Fig. 8(d) and

oscillates around B.

At 50th iteration the irradiance is decreased to 500W/m2.

For proposed MPPT algorithm the operating point follows the

path B-C-D to reach the new MPP denoted by D as shown

Proposed MPPT PV Curve Conventional MPPT

Fig. 8. Simulation results of sudden change in irradiance.

in Fig. 8(d). For conventional MPPT algorithm the operating

point follows the path B-F-D to reach new MPP D as shown

in Fig. 8(d).

At 100th iteration the irradiance is increased to 900W/m2.

For proposed MPPT algorithm the operating point follows the

path D-B to reach the new MPP denoted by B as shown in Fig.

8(e). For conventional MPPT algorithm the operating point

follows the path D-X-Y-X-B to reach new MPP B as shown

in Fig. 8(e).

Figs. 8(a)-(c) show that, the proposed MPPT algorithm

comparatively takes less number of iterations to reach MPP.

The graphs are zoomed in the intervals of 20 - 40, 70 -

90 and 120 - 140 iterations to observe the oscillations and

perturbations. It is also observed that, for proposed MPPT

algorithm the oscillations around MPP are minimized when

compared to conventional MPPT algorithm.

B. Study of Proposed MPPT Algorithm for Sudden Change inTemperature

PV array is simulated for sudden change in temperature,

assuming constant irradiance of 1000W/m2. Figs. 9(a)-(c)

show the output current, output voltage, and output power of

PV array against number of iterations. Fig. 9(d) shows tracking

of MPP for proposed and conventional MPPT algorithms for

sudden decrease in temperature from 60o C to 30o C. Fig. 9(e)

Proposed MPPT PV Curve Conventional MPPT

0 50 100 15015

20

25

(a)

Cur

rent

(A)

0 50 100 15080

100

120

(b)

Vol

tage

(V)

0 50 100 150

2000

2500

(c)

Pow

er (W

)

20 4021

22

120 14021

22

70 9021.2

21.8

20 4092

96

70 90107

109

120 14092

96

20 402035

2045

70 902325

2330

120 1402035

2045

Iterations

Iterations

Iterations

(d)

0 40 80 1200

1000

2000

(e)

Pow

er (W

)

Voltage (V)

CBX

0 40 80 1200

1000

2000

Pow

er (W

) F

Voltage (V)D

EB C

A

Fig. 9. Simulation results of sudden change in temperature.

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shows tracking of MPP for proposed and conventional MPPT

algorithms for sudden increase in temperature from 30o C to

60o C.

Initially, PV array is simulated at T = 60o C. For proposed

MPPT algorithm the operating point starts from point A and

reaches the maximum power point B as shown in Fig. 9(d)

and oscillates around B. For conventional MPPT algorithm the

operating point starts from point D and reaches the maximum

power point B as shown in Fig. 9(d) and oscillates around B.

At 50th iteration the temperature is decreased to 30o C. For

proposed MPPT algorithm the operating point follows the path

B-C to reach the new MPP denoted by C as shown in Fig. 9(d).

For conventional MPPT algorithm the operating point follows

the path B-E-F-C to reach new MPP C as shown in Fig. 9(d).

At 100th iteration the temperature is increased to 60o C. For

proposed MPPT algorithm the operating point follows the path

C-B to reach the new MPP denoted by B as shown in Fig. 9(e).

For conventional MPPT algorithm the operating point follows

the path C-X-B to reach new MPP B as shown in Fig. 9(e).

Figs. 9(a)-(c) show that, the proposed MPPT algorithm

is relatively faster than conventional MPPT algorithm. The

graphs are zoomed in the intervals of 20 - 40, 70 - 90 and 120

- 140 iterations to observe the oscillations and perturbations.

It is observed that, the proposed MPPT algorithm has lesser

oscillations and consistent steady state output when compared

to conventional MPPT algorithm.

From the above simulation results, it is observed that the

proposed MPPT algorithm is relatively faster and has reduced

sustained oscillations compared to conventional MPPT algo-

rithm, irrespective of decrease or increase of irradiance and

temperatures.

V. ACKNOWLEDGEMENT

This work is supported by the Department of Sci-

ence and Technology, India, under the project grant

DST/TM/SERI/2k10/47(G). The authors would like to thank

the Department of Science and Technology, DST, India.

VI. CONCLUSION

A new MPPT algorithm for solar power extraction has

been presented in this paper. A simple algorithm to extract

maximum power is discussed and simulated using MATLAB

software. The algorithm is capable of maximizing output of

PV array under varying irradiance and temperature conditions.

The proposed MPPT algorithm consists of two parts. The

first part of the algorithm increases the tracking speed to

reach MPP by considering current perturbation under steady

weather conditions. The second part of the algorithm moves

the operating point to LHS of MPP to consider the sudden

changes in temperature and irradiance by estimating the short

circuit current. An equation relating short circuit current,

irradiance and temperature is derived to estimate the short

circuit current. The simulation results successfully demonstrate

that, the algorithm works well and shows good dynamic and

steady state performance.

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