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A review of maximum power-pointtracking techniques for photovoltaicsystemsAnup Anuraga, Satarupa Balb, Suman Souravc & MrutyunjayaNandad

a Department of Electrical Engineering and InformationTechnology, ETH Zurich, Zurich, Switzerlandb Department of Electrical and Computer Engineering, NationalUniversity of Singapore, Singaporec School of Computing, National University of Singapore, Singapored Department of Electrical and Electronics Engineering,International Institute of Information Technology, Bhubaneswar,IndiaPublished online: 19 May 2014.

To cite this article: Anup Anurag, Satarupa Bal, Suman Sourav & Mrutyunjaya Nanda (2014): Areview of maximum power-point tracking techniques for photovoltaic systems, International Journalof Sustainable Energy, DOI: 10.1080/14786451.2014.918979

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International Journal of Sustainable Energy, 2014http://dx.doi.org/10.1080/14786451.2014.918979

A review of maximum power-point tracking techniques forphotovoltaic systems

Anup Anuraga∗, Satarupa Balb, Suman Souravc and Mrutyunjaya Nandad

aDepartment of Electrical Engineering and Information Technology, ETH Zurich, Zurich, Switzerland;bDepartment of Electrical and Computer Engineering, National University of Singapore, Singapore;cSchool of Computing, National University of Singapore, Singapore; dDepartment of Electrical and

Electronics Engineering, International Institute of Information Technology, Bhubaneswar, India

(Received 26 October 2013; final version received 23 April 2014)

This paper provides a detailed review of the maximum power-point tracking (MPPT) techniques used inphotovoltaic (PV) systems. The MPPT technique proves to be an essential part of the PV system, andhence the most appropriate method should be chosen in order to optimise the efficiency of the system,keeping in consideration the economic point of view. A small description of various MPPT techniques hasbeen provided and comparison based on features, such as convergence speed, implementation complexity,accuracy, the relative cost of implementing the set-up and their commercial availability has been done.This paper aims at choosing the most appropriate technique for any particular PV application taking intoaccount all the above-mentioned factors, especially the cost, complexity and accuracy, so as to maximisethe effectiveness of the system by optimising all the parameters. It aims to serve as a useful guide for bothusers and manufacturers.

Keywords: maximum power-point tracking techniques; PV array; renewable energy; power electronics

1. Introduction

Electrical energy from photovoltaic (PV) is currently regarded as the prerequisite sustainableresource for both stand-alone as well as grid-connected applications, since it is abundant, clean,offers zero input fuel cost and is distributed throughout the earth, as pointed out by De Britoet al. (2011). However, currently, the overall share of solar power generation among renewablepower still remains low at 8.9% (2012) (‘Solar Energy’ 2014). The major obstacle for widecommercialisation is the initial investment (Chen and Smedley 2004). Also, low efficiency (about15–27%) is observed in the commercially viable PV systems accounting for the fact that it dependson parameters such as external temperature and irradiation (Salas et al. 2006; Lawrence 2013).In power generation from PV, optimal utilisation of the available solar energy is imperativedue to the high costs of PV modules. As the PV systems are generally integrated with specificcontrol algorithms in order to extract the maximum possible power, it is highly imperative thatthe maximum power point (MPP) is achieved effectively. Due to the highly intermittent nature ofthe irradiation and temperature, in order to maximise the effectiveness an efficient MPP tracking(MPPT) technique is necessary to track the MPP at all atmospheric conditions.

∗Corresponding author. Emails: anuraga@student.ethz.ch, anup.rana123@gmail.com

© 2014 Taylor & Francis

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Several MPPT methods are proposed and implemented, as reported in the literature. In fact,the large number of methods developed creates confusion about which method to use for aparticular PV system application. Review analysis has been done in Salas et al. (2006), Esramand Chapman (2007), Hohm and Ropp (2000), Subudhi and Pradhan (2013), Tse et al. (2004) andCalavia et al. (2010), but a comprehensive analysis especially taking into account all the economicconsiderations has not been provided. This paper does not revisit in details all the MPPT techniquesbut provides a brief description on them. The major focus has been on the analysis and citing theadvantages and disadvantages of the various techniques under certain conditions.

This paper attempts to review the various MPPT techniques available in the literature andcompares them on the basis of features such as convergence speed, implementation complexity,accuracy, and most importantly the cost of implementing the whole set-up. Dependency on thePV array, the circuitry, type of MPP seeking, and also the use in commercial applications hasalso been considered. This aims at choosing the most appropriate technique for any particular PVapplication taking into account all the above-mentioned factors so as to maximise the effectivenessof the system by optimising all the parameters. Here, the focus has been put on the economicviability of implementing the MPP technique in one particular application with relevance toa particular application. Furthermore, the availability of commercial products based on someMPPT techniques has also been provided. Three important parameters are compared: the cost, thecomplexity and the accuracy. A trade-off has to be made between these so as to find the optimaltechnique suiting the needs of where it is going to be used.

The paper is organised as follows. The second section provides a general overview of theproblem statement. The third section deals with some brief ideas regarding the available MPPTtechniques. Factors affecting the choice of selection of a particular technique have been providedin the fourth section. The fifth section gives the detailed analysis and some discussions regardingthe various techniques and the sixth section concludes the paper followed by the references.

2. Problem overview

The characteristic P–V curve of a PV array is shown in Figure 1. The MPPT techniques aimat tracking the MPP by automatically finding the voltage at MPP (VMPP) or the current at MPP(IMPP). In real time, various conditions are taken into effect when a MPP tracker is used. Variousreal-time problems include ageing, intermittent irradiance, temperature, etc. This also includespartial shading conditions, where there are various MPPs but one true MPP. Most of the techniquesadjust themselves to varying temperature and irradiance. In various techniques, periodic tuningis essential for proper tracking of the MPP.

3. MPPT techniques for PV systems

Various MPPT techniques are proposed and implemented throughout the globe. However, lighthas been thrown on some of the widely used tracking techniques here and they have been discussedin brevity. An arbitrary order has been maintained.

3.1. Perturb and observe method

A PV panel requires a tracker to track the MPP at all times irrespective of the alterations in tem-perature and irradiation, and the corresponding flow-chart for implementing perturb and observe(P and O) method is shown in Figure 2. The P and O method periodically increments or decrementsthe panel voltage and compares the PV output power with that of the previous cycle. If the

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Figure 1. Characteristic P–V curve of a PV array.

Figure 2. Flow chart for the P and O method.

perturbation leads to an increase/decrease in module power, the subsequent perturbation occursin the same/opposite direction. However, it has two parameters: the step size and the time betweenalgorithm iteration. Hence, for faster tracking with accuracy, a trade-off is made between the twoparameters, as found out from the literature (Hua and Shen 1998; Hsiao and Chen 2002; Junget al. 2002; Femia et al. 2005; Liu et al. 2008; Chaitanya, Saibabu, and Surya Kumari 2011; Baland Babu 2012).

3.2. Modified P and O method

The P and O method encounters some limitations during rapidly varying environment as pointedout by Yafaoui, Wu, and Cheung (2007), which may lead to incorrect or slow tracking of the

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Figure 3. Flow chart for the MP and O method.

MPP. The modified P and O (MP and O) method isolates the perturbation-caused fluctuationsfrom those caused by the change in irradiance. Here, an irradiance changing estimate processis added to every perturb process to measure the amount of power change caused by changesin atmospheric condition. The tracking speed is however half that of the conventional P and Omethod. Figure 3 shows the flow chart of the algorithm used (Femia et al. 2007; Yafaoui, Wu,and Cheung 2007; Piegari and Rizzo 2010).

3.3. Estimated P and O method

This technique is basically an extension of the P and O method. The algorithm uses one estimationmode for every two perturbation modes. The perturbation process searches for the MPP over thecharacteristics PV curve, whereas the estimation process compensates the perturbation processfor conditions like rapid changes in irradiance, as given by Femia et al. (2007) and Piegari andRizzo (2010). It is a complex yet more accurate and faster method than the conventional P and Omethod.

3.4. Incremental conductance method

The incremental conductance (IncCond) method provides to be an alternative to the P & O method.It is derived by differentiating the PV power with respect to voltage and setting the result equal

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International Journal of Sustainable Energy 5

to zero.dP

dV= d(VI)

dV= I + V

dI

dV= 0 at the MPP. (1)

Rearranging Equation (1) gives

− I

V= dI

dV. (2)

The right-hand side of Equation (2) represents the IncCond and the left-hand side representsthe array’s instantaneous conductance. Based on the operating point, a set of inequalities can bederived on the fact that, that derivative is zero at the MPP, positive in the left and negative to theright of the MPP.

− I

V= dI

dV

(dP

dV= 0

),

− I

V>

dI

dV

(dP

dV< 0

), (3)

− I

V<

dI

dV

(dP

dV> 0

).

Equation (3) is used to decide the direction in which the perturbation should occur to achieveMPP. The PV array is forced to operate at a reference voltage (VREF), which equals VMPP. Withthe MPP achieved, the operation is maintained till �I remains constant. With any change in �I ,maybe due to change in atmospheric conditions, the tracking algorithm manipulates VREF to thenew MPP. Similar to the P & O method, this technique employs a trade-off between the step sizeand the time between algorithm iteration, for faster tracking with accuracy (Hussein and Mota1995; Hohm and Ropp 2000; Irisawa et al. 2000; Kim et al. 2001; Kobayashi, Takano, and Sawada2003; Enrique, Andujar, and Bohorquez 2010). The flow chart for the IncCond method has beenshown in Figure 4.

3.5. Current compensation method

The current compensation method produces a continuously varying reference current for eachswitching cycle during one sampling period (Lee et al. 2003; Zhou et al. 2008; Zheng, Shu-min,and Xing-peng 2010; Bal and Babu 2012). The continuously changed reference current is producedby the voltage control loop. Since, the output current of the PV module follows this continuouslychanged reference current in the current control loop, the MPPT is achieved. This method hasthus less error power. The integrator used in the current controller is reset during each switchingcycle to compensate the continuously changing current reference.

3.6. Constant voltage and current method

The constant voltage and current method uses the fact from the PV curve as in Figure 1 that theratio of VMPP to the open-circuit voltage, VOC, is approximately constant (K), which depends ontemperature.

VMPP

VOC

∼= K . (4)

The open-circuit voltage is measured by isolating the solar array from the MPPT. The algorithmcalculates the value of VMPP, using Equation (1) and the array voltage is adjusted accordingly

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Figure 4. Flow chart for the IncCond method.

Figure 5. Flow chart for the constant voltage method.

(Masoum, Dehbonei, and Fuchs 2002; Tse et al. 2004). Figure 5 gives the corresponding flow-chartfor the constant voltage technique.

A constant current method can also be implemented where the ratio of the current at MPP (IMPP)to the short circuit current (ISC) is taken to be constant. However, the constant voltage method ispreferred, because of the ease of measuring the voltages (Masoum, Dehbonei, and Fuchs 2002).

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Figure 6. Calculation of IncCond for the parasitic capacitance method.

3.7. Lookup table or best fixed voltage method

In this method, the array’s output voltage and current are measured and they are compared withthose stored in the system. Values are calculated for the probable climatological conditions. Theimplementation of the MPPT takes in a way that, a particular MPP is selected from the memorysystem, according to a particular climatic condition (Ibrahim et al. 1999; Chen et al. 2003).

3.8. Parasitic capacitance method

This method has been first proposed by Branbrilla et al. (1999). This is similar to the IncCondMethod except for the fact that the PV cell’s parasitic union capacitance CP, which denotes thecharge storage in the p–n junction of the PV cell, is included. The addition of the effect of thecapacitance to the lighted diode gives:

I = F(VP) + CPdVP

dt. (5)

There are two components of the current I , a function of voltage and the current due to theparasitic capacitance. Now, Equation (5) is multiplied by Vp in order to find the array power. Also,the MPP is the point where the derivative of power w.r.t. voltage is zero.

dF(Vp)

dVp+ CP

(V

V+ V

V

)+ F(Vp)

Vp= 0, (6)

where these terms represent the IncCond, the induced ripple due to the parasitic capacitance andthe instantaneous conductance. It can be seen that if Cp equals 0, the equation reduces down tothe IncCond algorithm. The AC ripple components, generated by the converter, are taken care ofby the first and second derivative (Holm and Ropp 2003).

The array conductance can be easily calculated by taking the ratio of the instantaneous arraycurrent to the instantaneous array voltage. The differential conductance is obtained by:

gP = PGP

V 2o

, (7)

where PGP is the average ripple power and Vo is the voltage ripple. From Equation (7), the ratio ofthe values is found and is used until the IncCond equals the instantaneous conductance. Figure 6shows how the IncCond is calculated.

3.9. dP/dV or dP/dI feedback control technique

The technique is similar to the constant voltage or current method, with the only difference beingthe variation of power with voltage. Here the slope (dP/dV or dP/dI) is calculated and fed back

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to the power converter with some control to drive it to zero. Various papers reflect this technique(Sugimoto and Dong 1997; Chiang, Chang, andYen 1998; Bleijs and Gow 2001; Hou et al. 2004).However, the method to calculate the same is reported differently. As given by Chiang, Chang,and Yen (1998), a linearisation-based method has been used. Also as shown by Bleijs and Gow(2001), a sampling and data conversion followed by a digital division of power and voltage isused to obtain the result.

3.10. Differentiation technique

The MPP is determined in this technique by the following equation:

dP

dt= d(IV)

dt= I

dV

dt+ V

dI

dt. (8)

However, this technique is very complex due to large complex eight different measurementsand calculations (Jain and Agarwal 2004). The array voltage and current are to be measuredfollowed by a measure in the change in voltage at a given operating point. It is accompanied bythe calculation of the change in current corresponding to that point. A calculation of the productsthen takes place followed by the addition and a comparison. For efficient and quick tracking, astrong and expensive processor is required.

3.11. Sliding mode control MPPT technique

The sliding mode control (SMC) technique uses a sliding surface in order to generate the pulsesfor the converter. According to Zhang, Wu, and Zhao (2004), the PV array output power is givenby

Ppv = Vpv · Ipv. (9)

From the solar curve, as shown in Figure 1, a switch function is selected.

S = dPPV

dVPV= dIPV

dVPVVPV + IPV. (10)

Based on the slope of the V array curve, as shown in Figure 1, the switch control signal can beselected as

u ={

0 S ≥ 0

1 S < 0, (11)

where u determines whether the switch is opened or closed. In this way, the converter works atthe MPP (Chu and Chen 2009).

3.12. One-cycle control technique

One-cycle control (OCC) technique is a nonlinear MPPT technique, which involves the use of asingle-stage inverter. According to Yu et al. (2010), the real output power is given by

Po = Vo · Io = V 2o

Rs

(K − Vm

Vg

), (12)

where K is an introduced constant that determines the up bound for the output current, Vo is thegrid AC voltage, Vg is the voltage across the capacitor and Vm is a constant across each line cycle.

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Figure 7. MPPT controller with OCC method.

With some modifications in Equation (12), the OCC is realised. Here, a single power conversionstage is present, which works both as MPPT and DC/AC inversion. Figure 7 shows the MPPTcontroller with the OCC method (Chen and Smedley 2002; Yu et al. 2010).

3.13. Curve-fitting method

The nonlinear characteristic of PV generator can be modelled from a conventional single-diodemodel or a two-diode model and using mathematical equations or numerical approximations.However, to achieve an accurate fitting of the P–V curve, a polynomial function of the fourthdegree is used by Takashima et al. (2000) and it is given by:

Ppv = P1V 4pv + P2V 3

pv + P3V 2pv + P4V 1

pv + P5. (13)

The PV module’s voltage depends on the cell temperature in which it varies with the sun’sradiation; it is considered that the PV power is also a function of the temperature. Hence, thecoefficient functions of the P–V curve are determined in terms of the cell temperature.To determinean optimum PV voltage at which the PV power is equal to its maximum value from the fourth-order polynomial function, the condition dPpv/dVpv = 0 is considered. The PV module’s voltagethat is sensed by the controller is used to determine dPpv/dVpv value. If it is equal to zero, thePV generator is operating at optimum, whereas if it is greater than zero, the optimum voltage isrepeated by incrementing or decrementing the PV voltage (Takashima et al. 2000; Khatib et al.2010).

3.14. Current sweep technique

In the current sweep method, a sweep waveform for the PV array current is used such that theI–V characteristics are obtained and updated at fixed time intervals (Bodur and Ermis 1994;Noguchi and Matsumoto 2003). The VMPP can thus be computed. The function chosen for thesweep waveform is given by

f (t) = k1df (t)

dt. (14)

The PV array power can be given by

p(t) = v(t) · i(t) = v(t) · f (t). (15)

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The solution of Equation (14) is given by

f (t) = k2 et/k1 . (16)

k2 is chosen such that it equals the maximum PV array current and k1 is chosen to be a negativequantity in order to form a decreasing exponential function.

It is known at MPP

dp(t)

dt= v(t)

df (t)

dt+ f (t)

dv(t)

dt= 0. (17)

Substituting Equation (14) in Equation (17)

dp(t)

dt=

[v(t) + k1

dv(t)

dt

]df (t)

dt= 0. (18)

Now, as the derivative of Equation (16) is non-zero, Equation (18) can be divided by df (t)/d(t),we get

dp(t)

dt=

[v(t) + k1

dv(t)

dt

]= 0. (19)

The above equation is used to verify whether the MPP has been reached; after the VMPP is calculatedafter the sweep.

3.15. Ripple correlation control method

In the ripple correlation control (RCC) method, the voltage and current ripple produced due to theinterfacing of the PV array with the converter is utilised for MPPT, as given by Midya et al. (1996).Since the ripple is naturally available, no additional perturbation is required. RCC correlates thederivative of power w.r.t. time with the derivative of voltage or current w.r.t. time in order to drivethe power gradient to 0; and thus achieving MPPT. According to Figure 1, the relationship can begiven by

dv

dt> 0 or

di

dt> 0 and

dp

dt> 0 ⇒ V < VMPP or I < IMPP, (20)

dv

dt> 0 or

di

dt> 0 and

dp

dt< 0 ⇒ V > VMPP or I > IMPP. (21)

It is well established that the increase in duty cycle increases the inductor current (in this case thePV array output current (I)). The duty ratio control is hence given by

d(t) = −k3

∫pv dt (22)

or

d(t) = k3

∫pi dt. (23)

Controlling the duty ratio in this way makes sure that the MPPT is continuously and effectivelytracked (Midya et al. 1996; Esram et al. 2006).

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International Journal of Sustainable Energy 11

Figure 8. PV curve with the power ripple caused by voltage modulation.

3.16. Forced oscillation technique

In the forced oscillation technique, as mentioned in (Hohm and Ropp 2000; Tse et al. 2001),a small voltage is added to the operation voltage of the PV generator. This generates a ripplepower; the phase and amplitude of which are dependent on the relative location of the operatingpoint from the MPP. In the occurrence of the modulation in the left side of the MPP, as shown inFigure 8, the ripple voltage of the power will be perfectly in phase, else it is 180 ◦ out of phasew.r.t. voltage. In case, the operation point is exactly at the MPP, the curling of power output hastwice the frequency of the curling of the voltage, the magnitude being very small.

3.17. DC link capacitor droop control technique

This technique is implemented where PV panel is integrated with the AC load through inverterand is specifically designed to work with the PV system that is connected in parallel to an ACsystem line (Holm and Ropp 2003).The duty ratio of an ideal boost converter is given by:

D = 1 − VPV

VDClink. (24)

Since, the VDClink is kept constant, the increase in the input current to the inverter leads to theincrease in the power output from the PV panel. The current is increased as long as the powerrequired by the inverter does not exceed the maximum power that can be delivered from the PVpanel, else the DC link voltage starts drooping (Kitano, Matsui, and Xu 2001). Hence, the AC linecurrent is fed back to prevent the DC link voltage from drooping and the duty ratio is optimisedto keep the PV panel operate at the MPP point.

3.18. Load current/voltage maximisation method

This is especially used for stand-alone purpose where the PV source is connected to load througha switched mode power converter and a power controller. Depending on the type of load, either

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Figure 9. Fuzzy-logic algorithm.

the load current or load voltage is ensured to be the maximum so that the output power is themaximum (Sullivan and Powers 1993; Blavi et al. 2002; Arias et al. 2004; Shmilovitz 2005).

Usually since battery is used as the load for energy storage, only the output current is controlledsuch that maximum power is obtained at the output. The feedback is used as control signal forthe converter such that maximum current is obtained at the output and MPP is tracked.

However, since the converter is assumed to be powerless for study purpose, in practical life theMPP point can never be achieved perfectly.

3.19. Fuzzy-logic-based MPPT method

Fuzzy logic is known by multi-rules-based resolution and multi-variable’s consideration. Thefuzzy-logic algorithm is based on four factors: the knowledge base of the expert, the fuzzification,the inference diagram and the defuzzification, as shown in Figure 9.

The knowledge base is formed by defining various fuzzy partitions as deemed necessary. Thecontrol table is constructed with radiation (G) and temperature (T ) as the inputs and duty cycleαopt as the output.

The determined fuzzy partition leads to calculation of the membership functions for eachvariable. Considering the most common symmetric triangular type, membership function can bedefined as

μ(xi) = 1 − |x − xi|εxi

. (25)

By means of the obtained membership function, a rule base is established, using the general ruleformat

Rijk if (xi is Ck and yi is Bj) then zk is Ck . (26)

Using the Max–Min rule aggregation the membership function of an operating point of theαopt, fuzzy partition is found out. Since the rules are aggregated, the defuzzification consistsof calculating the real value, αopt using the centroid method.

z0k =∫ 1

0 zkμc dzk∫ 10 μc dzk

, (27)

where z0k is the defuzzified or real αopt. With the duty cycle obtained, the MPP can be trackedeasily (Salah and Ouali 2011; Messai, Mellit, and Guessoum 2012).

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Figure 10. The neural network architecture.

3.20. Artificial neural network-based MPPT method

The artificial neural network (ANN) technique uses a three-layered recursive feed forward networkto estimate the optimal duty cycle αopt, which corresponds to Pmax at any given solar radiation(G) and PV cell temperature (T ). The NN controller consists of three layers; input layer, hiddenlayer and output layer, as shown in Figure 10. The input layer is composed of two nodes, thatare the PV cell temperature and the solar radiation. The number of neurons in the hidden layerdetermines the training degree. This is calculated by the empirical formula

Nh = 12 (NI + NO) + √

NE, (28)

where NI is the number of input neurons, NO is the number of output neurons and NE is the sizeof training sample. The hidden layer uses sigmoid activation function and the output layer iscomposed of one node whose output is the optimum duty cycle αopt, which corresponds to thePmax whose function of activation is of linear type.

The connection weight values and the thresholds of the NN are selected randomly at the startingof the training process, and then during training they are fixed so as to make minimum squareerror between estimated and training data. The training data-set is chosen with a wide variation ofirradiation and temperature. The retro-propagation training technique is used, which ultimatelyminimises the mean square error (MSE).

MSE = 1

2

∑(On − tn)

2, (29)

where On is the nth measured output read by the network and tn is the nth target (the estimatedoutput). The retro-propagation algorithm calculates the error MSE and distributes it back fromoutput towards input neurons through the hidden neurons using following formula:

�wn = δ�wn−1 − η∂E

∂w, (30)

where w is the weight between any two neurons, �wn and �wn−1 are the changes of theseweights for n and n−1 iterations, δ is the speed term and η is the training rate. With the weightvalues optimised, the MSE is minimised and αopt is obtained thus ensuring MPPT (Hiyama andKitabayashi 1997; Veerachary and Yadaiah 2000).

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3.21. Particle-swarm-optimisation-based MPPT

PSO is a stochastic, population-based search method that is used to track the MPP in the multi-PV array structure under partial shaded conditions. A solution vector of duty cycles with Np dutycycles is determined, i.e.

xki = dg = [d1, d2, d3, . . . , dj] j = 1, 2, 3, . . . , Np. (31)

The objective function is defined by

P(dki ) > P(dk−1

i ), (32)

where P(s) is the fitness function.To start the optimisation process, the algorithm transmits a certain number of duty cycles to

the power converter in the first iteration. The duty cycle with the best fitness value is selected andthe process is repeated in subsequent iterations to find the overall best duty cycle. Under partialshaded conditions the global peak is easily determined corresponding to the best duty cycle.

3.22. Hybrid MPPT techniques

The hybrid technique is an existing technique made efficient by the use of artificial intelligence.Recently, a hybrid technique with both P and O and ANN has been proposed by Amrouche,Belhamel, and Guessoum (2007). In order to improve the search capability of the ANN-basedhybrid technique, a genetic algorithm by Larbes et al. (2009) has been used for tuning the weights.The membership function and control rules are optimised here.

3.23. Steepest descent technique

A mathematical model for MPP Tracking is the steepest descent, which is also called gradientdescent method (Xiao et al. 2006), which is originally an optimisation method in applied math-ematics. In this technique, the nearest local MPP can be tracked by computing the followingfunction:

vk+1 = vk + (dp/dv)|v=vk

kε

, (33)

where kε is the step-size corrector and dp/dv is the deviation. The value of kε decides how steepeach step takes in the gradient direction. The value of dp/dv can be calculated by

dp

dv= f (v, p), (34)

f (v(k), p(k)) = p(k + 1) − p(k − 1)

2�V+ O(�V)3, (35)

where O(�V)3 is the local truncation error for the centred differentiation and is of second-orderaccuracy.

3.24. Gauss–Newton technique

The Gauss–Newton technique, also known as Newton–Raphson method, is the fastest algorithm(Weisstein 2006; Xiao, Dunford, and Capel 2007), which uses a root-finding algorithm. In its

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algorithm, first and second derivatives of the change in power are used to estimate the directionand number of iterations of convergence while solving the following:

vk+1 = vk − dp/dv|v=vk

d2p/dv2|v=vk

. (36)

Hence, this algorithm needs to numerically perform both single and double differentiation, and isthus the fastest algorithm compared with the steepest descent method. Nevertheless, this procedurecan be unstable regarding the initial condition.

3.25. Analytic-based MPPT technique

This technique is based on observations and experimental results. From the experiments, the endvalues of the PV curve are determined, i.e. the short circuit current and the open-circuit voltage.Based on these observed values, a ball of small radius r is selected for each panel such that MPPis inside the ball. The MPP is obtained from that ball by using mean value theorem (Rodriguezand Amaratunga 2007). It is the point which satisfies the condition

f ′(vMPP, PMPP) = 0. (37)

3.26. MPPT control based on dual-carrier chaotic search

The dual-carrier chaotic search algorithm helps in increasing the adequacy of chaos search, therebyimproving the search efficiency. In the single-chaos mechanism, it is impossible to ensure thesufficiency of the search. Adoptive logistic mapping, as the chaos generators to produce thecarrier and taking the carrier as stochastic searching step, is implemented in the algorithm. Aftervarious steps from the two different chaoses, they are recorded together and used to disturb thesystem in order to search for the MPP.

An output of low–high–low (P1 < P2 > P3), the two points (P1 and P3) are taken to be theendpoints and the searching zone thus becomes smaller. When the distance between the outputpower and the last is less than a predetermined threshold and also the distance between the outputpower and the next is less than the threshold, the searching stops, and thus the MPP is obtained(Zhou et al. 2011).

3.27. Other MPPT techniques

In distributed MPPT (DMPPT), each module uses a single MPPT (Tsao, Sarhan, and Jorio 2009).Various different DMPPT approaches are mentioned in (Tsao, Sarhan, and Jorio 2009; Paja et al.2010).

Another technique is the array reconfiguration technique. Here, the PV arrays are arranged invarious different series and parallel combinations. It is done due to the fact that the resulting MPPsshould meet specific load requirements (El-Shibini and Rakha 1989).

Some model-based MPPT techniques have also been used where the solar cell voltage andcurrent are calculated from the irradiation and temperature and the MPP voltage is calculateddirectly (Takashima et al. 2000).

Another MPPT technique has been proposed by Petrone, Spagnuolo, and Vitelli (2010), whichis based on the equalisation of the output operating points in correspondence of the forced dis-placement of the input operating points of two identical PV systems. It is known as TEODI. Inthis, each panel of the PV array has its own DC/DC converter. However, all the DC/DC convertersare controlled in a centralised fashion by a single control block.

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An approximate solution known as linear-reoriented coordinates method (LRCM) is found byPan et al. (1999) to find the solution of the PV array equation iteratively.

4. Factors affecting the choice of selection of MPPT techniques

A large number of MPPT techniques are now available and extensively studied in the literature.However, confusion always lies with the user in order to choose the best MPPT technique takinginto consideration all the factors. The MPPT techniques widely vary from each other startingfrom their operating principle and the cost of implementation to the amount of complexity andaccuracy offered by the same.

The best choice has to be made by the PV user, as to which technique that should be used,suiting his needs and economy. Many aspects should be taken into account for choosing the properMPPT. Several of them are listed here but major focus should be put on cost, complexity andaccuracy since these factors truly affect the efficiency of the product and the economy of thecompany.

4.1. Complexity and ease of implementation

The complexity of the circuit, the ease of implementing it in real time and hardware greatlydetermine the technique that a user should use. The implementation of the method here impliesthe nature of the method; it may be analogue or digital. This is basically a user-dependent choice.According to the ease of implementation, one might go for any analogue or digital MPPT method.The complexity basically implies the number of sensors used, the control variables taken and thecontrol strategies implemented.

The sensors play a significant role in determining the technique to be used. It is quite oftenseen that it is easier to measure the voltage rather than current, since current sensors are usuallyexpensive. It is therefore inadvisable where a large number of sensors are required and methodsthat require less number of sensors are preferred. Measuring irradiance level with the help ofsensors is also quite an expensive task and thus not preferred.

The number of control variables, in a way, determines the different types of sensors required.With techniques that require sensing of voltage, current, irradiation, temperature, etc., manydifferent kinds of sensors are required, which is not always feasible and practical. Basically, thelesser the number of control variables, the easier is its implementation and the less is its complexity.

Control strategies are basically divided into three categories, namely direct control (true-seekingcontrol), indirect control (quasi-seeking control), and probabilistic control (artificial intelligentmethods). According to the needs of the user, the control strategy has to be determined taking intofact that the direct control seeks MPP directly by taking into account the weather variations, andthat the indirect control is based on a database that includes information such as the characteristiccurve of the PV panel for different irradiations and temperature. In case of probabilistic controlmethods, information is present on the basis of probability. Rule-based sets are formed from wherethe MPPT is tracked.

4.2. Environmental conditions/multiple local maxima

The environmental conditions at a particular place also affect the choice of the MPPT technique tobe used. The occurrence of partial shading provides a real problem to the functioning of the MPPtracker. Due to this, there is a considerable power loss, which leads to the decrease in efficiencyof the same. In many cases, an initial stage is introduced to overcome the problem.

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In many other cases, due to intermittent sunlight and sudden changes in weather conditions, theMPP shifts and the tracker needs to track the point yet again. Some MPPT techniques effectivelytrack this and some are less efficient in this particular operation.

4.3. Cost of implementation

The cost constitutes one of the most important factors in the implementation of a particularMPPT technique. However, it is generally very difficult to find the monetary cost of every MPPTtechnique unless it is implemented.

However, an idea regarding the cost of each particular MPPT technique can be made by knowingwhether it has digital or analogue circuitry. In general, the analogue circuit is cheaper comparedwith a digital one. The number of sensors also determines the cost of the technique, with thecurrent sensors playing a major part in it.

A reduction in the number of current sensors used drastically reduces the implementation cost.A rough estimation of the cost has been provided, having set a cost-line of US$1000 and a

cost below this has been termed as cheap and a cost above this has been termed as expensive.Approximately, based on the factors and an average cost of the circuitry it involves, the costcomparison has been made, as given in Table 1.

4.4. Accuracy and efficiency

The accuracy of the tracker in tracking the MPPT and the efficiency of the technique also helpdetermining the method to be used by the user. Some techniques provide accurate results, whereassome are not able to track the MPPT efficiently thus decreasing the efficiency of the tracker. Theefficiency can be calculated by the following formula (Subudhi and Pradhan 2013)

ηMPPT = PPV

PMPPT× 100. (38)

The accuracy of the tracker to make PPV closer to PMPPT determines the efficiency of the system.The closer the PPV is to PMPPT, the more accurate is the technique.

It is particularly difficult to estimate the exact accuracy of a technique without implementingof the same. However, in this paper, the accuracy of a technique has been classified into threecategories, as in Table 1, based on a thorough literature study. The classification cannot be gen-eralised, as the efficiency and accuracy of a particular technique depends on a huge number offactors, the most important of them, being the experimental skills of the user. Nevertheless, a roughapproximation regarding the accuracy has been provided, taking into account the MPPT methodand the complexity of the technique. This is expected to provide a rough estimate regarding thechoice of technique, where accuracy serves as the prime factor.

4.5. Commercial availability

The availability as a commercial product also serves as a factor for choosing a particular typeof MPPT technique. It is, however, hard to mention the direct commercial availability of everysingle MPPT technique. Companies such as SMA, Siemens, Steca, Refusol, Kaco, etc. hold alarge share in the market in regard to manufacture of PV inverters and solar charge controllersimplementing advanced MPPT techniques. It is particularly difficult to estimate the techniqueused by them, since, the details regarding the same are seldom provided by the manufacturers ontheir websites. However, the availability of some of the techniques, as commercial products, hasbeen provided in Table 1. However, many of the techniques need only similar components like the

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Table 1. Comparison of characteristics of various MPPT techniques.

MPPT Convergence Commercialtechniques Cost Complexity Accuracy speed Applications products

P and O method Expensive Low Medium Varies Stand-alone Outback-Mx60and FlexMx60

MP and O Expensive Low/medium Medium Varies Stand-aloneEP and O method Expensive Medium Medium Varies Stand-aloneIncCond method Expensive Medium Medium/high Varies Stand-aloneCurrent compensation

methodExpensive High High High Stand-alone

Constant voltagemethod

Cheap Low Medium Medium Stand-alone

Constant currentmethod

Cheap Medium Medium Medium Stand-alone

Lookup table method Cheap Low Varies NA Stand-aloneParasitic capacitance

methodExpensive Medium High Varies Stand-alone

dP/dV feedbackcontrol technique

Expensive Medium Low/medium Fast Stand-alone Triple LynxPV Inverter,Danfoss(Denmark)

dP/dI feedbackcontrol technique

Expensive Medium Low/medium Fast Stand-alone Triple LynxPV Inverter,Danfoss(Denmark)

Differentiationtechnique

Expensive Medium/high Medium/high Medium/fast Stand-alone Danfoss (Den-mark), UniLynx PV inveter

SMC MPPT technique Expensive High High Fast BothOCC technique Cheap Medium Medium Fast Grid connected Model Enphase,

Enphase EnergyCurve-fitting method Cheap Low Low/medium Medium Stand-alone FlexMx60 and

Outback-Mx60Current sweep

techniqueExpensive High High Slow Grid connected

RCC method Expensive Low Medium/high Fast Stand-aloneForced oscillation

techniqueExpensive High High Slow Stand-alone

DC link capacitordroop controltechnique

Expensive Low/medium Medium Medium Grid connected

Load currentmaximisationmethod

Cheap Low Low/medium Fast Stand-alone Aerl CoolmaxSR Maximizer(Australia)

Load voltagemaximisationmethod

Cheap Low Low/medium Fast Stand-alone Aerl CoolmaxSR Maximizer(Australia)

Fuzzy-logic-basedMPPT method

Expensive High Very high Fast Both Morningstar-TrackstarMPPT ChargeController,Solar ElectricSupply, USA

ANN-based MPPTmethod

Expensive High Very high Fast Both

PSO-based MPPT Expensive High High Fast BothHybrid MPPT

techniquesExpensive Medium/high High Fast Both

Steepest descenttechnique

Expensive Medium High Medium Stand-alone

(Continued)

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Table 1. Continued.

MPPT Convergence Commercialtechniques Cost Complexity Accuracy speed Applications products

Gauss–Newtontechnique

Expensive Low/medium Medium/high Fast Stand-alone

Analytic-based MPPTtechnique

Expensive Medium/high High Medium/fast Stand-alone

MPPT control basedon dual-carrierchaotic search

Expensive Medium/high High Fast Stand-alone

DMPPT technique Expensive Medium Medium/high NA Both Solar Magic, eIQEnergy (USA)

Array reconfigurationtechnique

Cheap High Depends Slow Both Maximizer ES andMaximizer EPPowerBox

TEODI technique Expensive Medium Depends NA Both Solar Magic,Xandex (USA),Tigo Energyand Sun Mizer

LRCM Expensive High NA NA Stand-alone

sensors and field programmable gate arrays. These can be purchased directly and programmedaccording to the needs.

4.6. Applications

The most important aspect of choosing a technique over another is its application. In high-endapplications, such as satellite power supply or in orbital power stations, complexity and cost arenot important. However, accuracy and the response time are of foremost importance here. Also,the tracker should be chosen such that it does not need any periodic tuning.

The choice also depends on whether our aim is for using the set-up in a grid-connected mode oronly in stand-alone mode. Generally, the technique is chosen accordingly since some techniquescan be used for either only stand-alone or only grid-connected applications.

Also, partial shading provides a hindrance in nearly all kinds of applications. Therefore, amethod to bypass the multiple maxima and to track the global maxima is imperative.

In case of solar vehicles, where the PV array is used to charge a huge number of batteries, afast convergence to MPP is required.

In case of residential areas, economy is the major consideration for choosing the technique.The aim should be to reduce the payback time of the set-up. PV set-ups used for street lightningalso have the same demands as of cheap and less complex implementation.

In case of low-power applications, such as mobile charging applications, less complex andcheap methods are generally preferred.

5. Analysis and discussions

Due to the presence of the huge number of MPPT techniques, the best technique that should beused has to be analysed for its effectiveness and economy. With the different factors explained inthe previous section, an analysis has to be provided so as to choose the best technique.

In case of P and O and IncCond techniques, they are best suited for applications where wedo not require parameter tuning. Since, the cost of implementation lies on the more expensiveside, it is not generally preferred for small-scale applications where the economy is given prime

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importance. The estimated P and O (EP and O) technique and the MP and O method are usedover the P and O method when there is a rapid environmental variation, especially fast varyingirradiation. The IncCond technique uses a digital environment and is suitable for users proficientin digital techniques. The main advantage of this method is that it offers a better yield under fastvarying atmospheric conditions. Also, it achieves lower oscillation around the MPP. The majordisadvantage is that it requires a complex circuit, which is quite expensive. These methods aretherefore generally preferred for satellite applications.

The current compensation method being complex in nature is not widely used. However, itprovides the advantage of having considerably less error power. Thus, it provides high efficiency.

The constant voltage method is considerably cheaper to implement since it is done with ananalogue hardware. However, it has a pretty low MPP tracking efficiency as compared to othermethods. In case of the constant current method, current sensors are required, thus, making theset-up expensive. In the lookup table method, the efficiency is nearly same as that of the constantvoltage method. This belongs to the cheaper side of the various techniques and can be used forsmall-scale applications where the efficiency and accuracy do not play a big role. Since parametertuning is essential, these methods are not implemented where the set-up is inaccessible. Theseare used in some solar water pumping systems.

The parasitic capacitance method is used where a simple digital circuit is required. The majoradvantage of this method is that it offers high efficiency. However, it is expensive and sometimesthe complexity increases on account of the multiplications used.

The differentiation feedback control, the sliding mode, and the differentiation techniques haveall their advantages and disadvantages. The major advantage being that they are independent ofthe PV array and that they do not require a periodic tuning. Even with the efficiency remaining inthe higher side, the SMC technique is considered to be in the more expensive side, and also it hasa higher amount of complexity as compared with others. A very low convergence time is foundin the differentiation feedback control.

The OCC technique being inexpensive and less complex than others has the limitation ofbeing used only in grid-connected applications. This is suitable for providing power to residentialsystems, since inverters act as a load there. In comparison, the curve-fitting technique can onlybe used in stand-alone applications.

The curve-fitting technique has its advantage in being inexpensive and less complex, but asexpected it has lesser efficiency as compared with some other techniques. It is basically usedfor experimental purposes and also in some applications where complexity and economy areconsidered to be greater factors than efficiency or accuracy.

Similarly, the current sweep technique is limited to grid-connected applications. It requiresparameter tuning and the convergence to the MPP takes about 50 ms, which leads to some loss ofavailable power. It is shown by the work of Bodur and Ermis (1994) that this technique can onlybe used if the power consumption of the set-up is less than the increase it will be able to make tothe whole system.

The RCC method is generally used in satellite applications where the tracker should be able totrack the MPP quickly and periodic tuning is not required.

The forced oscillation technique is expensive and complex and is used in a few applicationsonly. It has an advantage of the analysis of the amplitude and phase, which provides information ofthe location of MPP, and thus there is no oscillation around the MPP. However, the convergence isslower. Also, greater complexity of the circuit and measurement of signals of very low amplitudelimit its application.

The DC-link capacitor droop control does not require computing the PV array power. The mainadvantage is its easy implementation with analogue amplifiers and logic gates. However, it is seenthat the response worsens compared with methods that detect power directly (Kitano, Matsui, andXu 2001).

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The load current or voltage maximisation technique is adequate to maximise either the loadcurrent or voltage. In most of the PV systems, battery is used as load (Arias et al. 2004), like insolar vehicles, and hence with the use of one sensor, the control mechanism can be done. However,the efficiency is low since true MPP is not achieved here.

The artificial intelligence methods, which include the fuzzy-logic-based MPPT method, ANN-based MPPT method, PSO-based MPPT and hybrid MPPT techniques, require high complexityand are generally expensive. Hence, the applications are generally limited to space programmesor solar vehicles where cost is not a constraint. They converge to the MPP at a very fast rate andprovide very high efficiency, which is of major interest to the users wanting a highly efficientsystem.

Other methods including the steepest descent technique, the Gauss–Newton technique, etc.have their own advantages and disadvantages. Accordingly, they are used in certain applicationswhich demand the advantages offered by them with the drawbacks being less important.

A concise tabulation has been given in Table 1 highlighting various aspects, such as cost,complexity, efficiency, convergence speed, applications and commercial products.

6. Conclusions

This paper provides an insight into various MPPT used along with the various advantages anddisadvantages. Since, for a particular application it is imperative to use the best available technique,prime focus has been put on three basic factors, namely cost, accuracy and complexity. Otherfactors have also been taken into consideration but they can be broadly put under the above threecategories. An effort has also been made to point out the drawbacks of a particular technique fora particular application. The table provides a comprehensive guide for the effective choice of aMPPT technique. This paper is intended to be a useful tool, serving the cause of both users andmanufacturers.

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