1

Abstract—Photovoltaic modules have a single operating point

where the output of the voltage and current results in the

maximum power output. In most photovoltaic power systems, a

particular control algorithm, namely, maximum power point

tracking (MPPT) is utilized to take full advantage of the available

solar energy. The operation of maximum power point tracking is

to adjust the power interfaces so that the operating

characteristics of the load and the photovoltaic array match at

the maximum power points. This study reviews the latest

techniques and provides background knowledge about the recent

development in MPPT techniques. The paper can be used as a

reference for future research related to optimizing the solar

power generation.

Index Terms— Photovoltaic power systems, control systems,

digital control, and maximum power point tracking.

I. INTRODUCTION

HOTOVOLTAIC power is an established technology and

has recently experienced rapid growth over the last twenty

years. The maximum power point tracking (MPPT) is the

automatic control algorithm to adjust the power interfaces and

achieve the greatest possible power harvest, during moment to

moment variations of light level, shading, temperature, and

photovoltaic module characteristics. It has become an essential

component to evaluate the design performance of photovoltaic

power systems.

In recent years, many publications give various solutions to

the problem of maximum power point tracking for

photovoltaic power systems. In 2006, the review study has

summarized various MPPT techniques and has presented

valuable comparisons between them [1-2]. To continue the

literal chronology, this paper focuses more on the

implementation topology and the latest MPPT techniques with

a brief discussion and classification, which can be useful as a

reference for future research.

W. Xiao, A Elnosh, V. Khadkikar and H. Zeineldin are with the Electric

Power Engineering Program, Masdar Institute, Abu Dhabi, P O Box 54224,

UAE (E-mails: mwxiao@masdar.ac.ae, aelnosh@masdar.ac.ae,

vkhadkikar@masdar.ac.ae, hzainaldin@masdar.ac.ae).

This work is supported by Masdar Institute under MIT-Masdar Institute

joint research project grant.

II. IMPLEMENTATION TOPOLOGY OVERVIEW

A typical operation of MPPT is demonstrated in the block

diagram of Fig. 1, where the controller senses and assesses the

output power of the photovoltaic array and adjusts the power

interface to follow the optimal operating condition. The power

conditioner can be either a DC/DC converter or a DC/AC

inverter. The load can be typical DC and/or AC electrical load.

In grid-tied (or utility-connected) systems, the load includes

the electrical utility grid.

Fig. 1 Block diagram of the topology of maximum power point tracking in a

photovoltaic power system.

For MPPT systems, the control objective is to maximize the

power output and improve the solar energy harvest. One

implementation is based on a hill-shape curve representing the

relationship of the array output power and the switching duty

cycle because it is the control action for most switching

converters and inverters [3-7]. Study [8] shows another MPPT

algorithm by using the output parameters of the power

interface. In this application, the controller senses and

evaluates the output parameters, instead of the input power,

and regulates the control action to achieve MPPT. The reason

of this application lies in that the characteristics of output

parameters are usually not as nonlinear as the photovoltaic

output. Utility grid or battery can be estimated as constant

voltage loads, or the electrical feature of a resistive load is

linear. As a result, the measurement and algorithm can be

simplified.

However, both the output parameters and the switching duty

cycle are indirect factors to represent the photovoltaic power.

The photovoltaic power is the product of the photovoltaic

voltage and current, which are direct variables. The current-

voltage characteristics, as shown in Fig. 2 and Fig. 3,

demonstrate that either the photovoltaic voltage or the

photovoltaic current can represent the maximum power point

(MPP). For a particular operating condition, the control of

MPP tracking normally regulates either the voltage or current

Load/GridPower

ConditionerPhotovoltaic

Array

MPP Tracker

Power Delivery

Measured PV voltage

and current

Control

command

Overview of Maximum Power Point Tracking

Technologies for Photovoltaic Power Systems

Weidong Xiao, Member, IEEE, Ammar Elnosh, Student Member, IEEE, Vinod Khadkikar, Member,

IEEE and Hatem Zeineldin, Member, IEEE

P

978-1-61284-972-0/11/$26.00 ©2011 IEEE 3900

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to a value that represents the local MPP. Therefore, many

MPPT topologies are based on a regulation of either the

photovoltaic voltage or the photovoltaic current.

Fig. 2 Simulated I-V curves of a specific solar module, BP350, which is

influenced by insolation when the cell temperature is constant at 25ºC.

Fig. 3 Simulated I–V curves of a specific solar module, BP350, which is

influenced by cell temperature when the insolation is constant at 1000 W/m2.

Study presented topologies by regulating the photovoltaic

current to follow the current of maximum power point [9-10].

The control block diagram is illustrated in Fig. 4. A discussion

has been presented in [11-12] to compare the photovoltaic

current regulation and the voltage regulation. However, the

majority of work [12-16] shows that the photovoltaic voltage

regulation is preferable because of the following advantages:

a) a good-quality measurement of the voltage signal is cheaper

and easier than that of current detection; b) the voltage of MPP

is within a certain range, about 70%–82% of the open-circuit

voltage; c) the changing irradiation slightly affects the voltage

of MPP; d) the cell temperature is the major factor that

significantly shifts the voltage of MPP, however, it has slow

dynamics and is always within a certain range. Fig. 5

demonstrates the control scheme for MPPT by regulating the

photovoltaic voltage.

III. REVIEW OF MPP TRACKING ALGORITHMS

A comparison study, presented in [1-2], has illustrated

various MPPT techniques developed before 2006. The

techniques include:

• Heuristic search (including hill climbing & P&O);

• Extreme Value Searching (Incremental Conductance);

• Linear Approximation Methods (Fractional Voc or Isc,

and Linear reoriented coordinates);

• Intelligent control (Fuzzy logic and neural network);

• Linear control techniques (dP/dV or dP/dI feedback

control);

• Other techniques (array reconfiguration, linear current,

and sliding control etc.).

Fig. 4 Block diagram of MPPT with a control loop for regulating photovoltaic

current.

Fig. 5 Block diagram of MPPT with a control loop for regulating photovoltaic

voltage.

Among these techniques, the Heuristic search is one of the

most straightforward and popular algorithms due to its

simplicity. Fig. 6 shows the normalized output characteristics

of photovoltaic module and illustrates the application of hill

climbing for maximum power point tracking. From the open-

circuit position, (v0, 0), the controller makes an adjustment of

operating point to point (v1, p1). The direction of movement is

decided by the corresponding change of power level. The

value of v1 is updated according to (1), where ∆v is a constant

step.

1k kv v v+

= ± ∆ (1)

Since the new operating point (v1, p1) makes the

photovoltaic modules output more power than that of former

condition, the relocation to (v2, p2). is made. This continues

until the movement from (v4, p4) to (v5, p5), where the

controller realizes the reduction of output power and moves

the operating point back to (v4, p4) then (v3, p3). This process

continues until the operating point moves backward and

forward around the maximum power point (v4, p4). The

continuous perturbation and observation guarantees that the

controller can always find the new maximum power point

regarding the variation of solar insolation and cell

temperature.

Continuous oscillation around the optimal operating point is

an intrinsic problem of the heuristic algorithms as shown in

Fig. 7, which illustrates the measured signals of the

photovoltaic voltage, VPV, the photovoltaic current, IPV, and the

output power PPV. In the steady state, the continuous

oscillation of the operating point around the Vmpp make the

averaged power level deviated from the maximum power

point.

0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

Voltage (V)

Curr

ent

(A)

MPP at Ga=1000W/m

2

MPP at Ga=800W/m

2

MPP at Ga=600W/m

2

MPP at Ga=400W/m

2

MPP at Ga=200W/m

2

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

Voltage (V)

Curr

ent

(A)

MPP when temperature=-25oC

MPP when temperature=0oC

MPP when temperature=25oC

MPP when temperature=50oC

ControllerPower

Conditioner

Load / Grid

Photovoltaic Array

MPP

Tracker

IMPP

Measured PV current

Control

command

+

-

Measured PV voltage and

current (Vpv and Ipv)

Power delivery

IPV

Limiter

ControllerPower

Conditioner

Load / Grid

Photovoltaic Array

MPP

Tracker

VMPP

Measured PV voltage

Control

command

+

-

Measured PV voltage and

current (Vpv and Ipv)

Power delivery

VPV

Limiter

3901

3

Fig. 6 Conceptual operation of hill climbing for MPPT.

Fig. 7 Measured signals of photovoltaic panel with the operation of P&O

MPPT.

Another popular algorithm is the Incremental Conductance

method (IncCond), which was developed to intently eliminate

the oscillations around the maximum power point (MPP) and

avoid the deviation problem. It is based on the equation (2)

and implemented as the same topology shown in Fig. 5.

However, the experiments showed that there were still

oscillations under stable environmental conditions because the

digitalized approximation of maximum power condition of

dI/dV = -I/V, which is equivalent to dP/dV = 0, only rarely

occurred. The problem is caused by the local truncation error

of numerical differentiation, which has been discussed in [17].

0dI I dP

dV V dV= − ⇔ = (2)

The MPPT techniques will be further discussed in the

following section to give a general update about the latest

development since 2006. Despite of the tremendous

publications, the latest algorithms of MPPT can be classified

in the following categories: the real-time identification

method, the extremum seeking control, the particle swarm

optimization, the DIRECT search algorithm, and adaptive

step-size method.

A. Real-time identification method

In MPPT systems, the ideal operation is to determine the

maximum power point (MPP) of the photovoltaic (PV) array

directly rather than to track it by using the active operation of

trial and error, which causes undesirable oscillation around the

MPP [18-19]. Since the output features of a PV cell vary with

environment changes in irradiance and temperature from time

to time, the real-time operation is required to trace the

variations of local MPPs in PV power systems. As shown in

Fig. 8, the method of real-time estimation proposed in [18]

uses polynomials (PCF) to demonstrate the power–voltage

relationship of PV panels and implements the recursive least-

squares method (RLS) and Newton Raphson method (NRM)

to identify the voltage of the optimal operating point. The

proposed modeling process is based on the relationship of the

power and voltage outputted by the PV panels. Considering a

panel made of thin film, the output power is represented by a

fourth-order polynomial equation, as illustrated in (3), where

the p(k) symbolized the sensed power, v(k) is the measured

voltage, b1-4(k) can be identified by the RLS. For a poly-

crystalline solar panel, the model was expanded to a sixth-

order equation. According to the study, the experimental test

shows that in steady state, the estimation error of the voltage

of optimal operating point is less than 0.14% from the true

value. 2 3 4

1 2 3 4( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )p k b k v k b k v k b k v k b k v k= + + + (3)

Fig. 8 Control structure of MPPT with the real-time identification.

B. Extremum Seeking Control

Extremum-seeking control (ESC) is an algorithm that is

applicable to control problems involving a nonlinear plant or

control objective, where the nonlinearity has a local minimum

or maximum. The algorithm discussed in [20] employs the

injection of a small sinusoidal perturbation signal with

sufficiently high frequency to estimate the optimal input, as

shown in Fig. 9. Therefore, the plant output contains a high

frequency component (perturbation) that can be extracted

through a high pass filter and then demodulated. The produced

signal has a positive sign indicating the left portion of the P-V

characteristics and a negative sign showing the right of the

MPP. This signal is then integrated to close the loop. It is

analytically shown in [21] that this method ensures global

stability as the input estimate always converges to the optimal.

The ESC is considered to be better than conventional adaptive

control methods in the sense that it is not model-based and

does not require knowledge about the uncertain system

parameters which makes the implementation simpler.

The ESC method was applied by Bractu et al. in [21-22] to

a two-stage grid-connected PV system, where the algorithm

sets the optimal voltage/current as a set-point to its respective

control loop. A different version of extremum-seeking that

does not involve sinusoidal perturbation has been developed in

[23] and shows a proven global stability. The latter method

was also applied through a digital controller in [24]. In [25], a

modified version the ESC method is developed that does not

6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7

1

1.1

1.2

Norm

. V

pv (

V/V

)

P&O tracking

True Vmpp

6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7

0.20.40.60.8

1

Norm

. I p

v (A

/A)

P&O tracking

True Impp

6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7

0.2

0.40.6

0.81

Time (s)

Norm

. P

pv (

W/W

)

P&O tracking

True Pmpp

3902

4

require an external perturbation signal. Instead, it makes use of

the inherent ripple in the current or voltage in any switching

power converter. It also uses a high-pass filter to get a small

high frequency signal to demodulate the direction of solar

array power. This method is different from the Ripple

Correlation Control (RCC) method discussed in [26] where

the time derivative of the ripple current (or voltage) is

correlated with that of the power. By considering the P-I

curve, it can be concluded that the product of the current time

derivative and that of the power is positive to the left of the

MPP, and negative to the right of the MPP. By integrating this

product, the duty cycle can be obtained. The ESC method was

experimentally demonstrated to work under rapidly changing

irradiance and temperature [26]. It has also been shown

experimentally to work in the case of multiple maxima in the

P-V curve. The latter issue was also analyzed for the

generalized approach in [27] analytically under different

cases, but still does not guarantee finding the global extremum

under all conditions.

Fig. 9 Operation block diagram of Extremum Seeking Control.

C. Particle Swarm Optimization (PSO)

A Particle Swarm Optimization (PSO) algorithm was

utilized to track the MPP for arrays with multiple PV modules

[28-30]. In [28], the proposed scheme use a centralized MPPT

controller to control the voltage of individual solar module to

reach the global MPP. The optimization is treated as a

multivariable problem. The array power is defined as the

objective function, which is a function of the individual

module voltages. In this approach, the module voltages are

treated as agents that can share information with each other

and move in the multidimensional space that has a unique

global maximum. Each agent keeps an updating memory of its

own best position and the best position achieved among all

agents, and uses these pieces of information to update its next

position. The iterations continue until all agents converge to

positions corresponding to the global optimum. This algorithm

is able to track the global peak in the presence of multiple

maxima, but a vital condition for this is the proper and

accurate selection of the algorithm parameters. Another issue

with PSO is that it is designed to optimize systems that are

time-invariant which is clearly not the case in PV modules.

This issue is resolved in [28] by having an additional

constraint that checks for the variation in solar irradiance by

computing the incremental power, and reinitializes the process

if a large variation is detected. The same problem of PSO was

tackled in [29-30] where a modified version of the algorithm

is proposed with ability of dynamic tracking, namely

Biological Swarm Chasing or “Bio-MPPT”. It was

experimentally reported that the Bio-MPPT has an efficiency

improvement of about 12% over the conventional P&O

algorithm.

D. DIRECT Search Algorithm

A searching algorithm has been developed in [31], called

the Dividing Rectangles (DIRECT) algorithm. The origin was

developed in [32] to optimize a certain kind of functions

called “Lipschitz function”. It was proved that the P-V

characteristics of a solar cell belongs to this group of

functions, since its first derivative (∂P/∂V) is bounded by a

constant and is continuous over a certain interval [a, b], and

hence, the function peak lies within this interval. The interval

is typically between zero and the open-circuit voltage of the

array when considering the voltage as the control variable. By

starting from a point at the center of the initial interval, the

interval is then divided into three by taking the center of the

right and left portions of the initial point as depicted in Fig.

10. Then, the new sample corresponding to larger power is

chosen as the center of a new interval. By bi-sectioning

intervals in each iteration, the optimal point can be

approximated within a finite number of iterations. The case of

multiple maxima as a result of partial shading is thoroughly

investigated in [31], and it is shown that the DIRECT method

can find the global maxima except under rare conditions.

Fig. 10 Illustration of the Direct Searching Algorithm.

E. Adaptive Step size for the perturbation

Incremental Resistance (INR) method proposed in [33] and

based on current-mode control is quite similar to the variable

step Incremental Conductance (INC) method. However, it has

a faster response under rapidly changing conditions. In INR

method, the variable step size is correlated with the power

derivative with respect to current (∂P/∂I), similar to the

variable INC method where (∂P/∂V) is used instead. Also

similar to INC, the proposed method relies on the comparison

between the incremental resistance with the instantaneous

resistance. The improved performance was verified

experimentally in [33].

A modified P&O technique with variable step is presented

in [34] where different ranges of power are specified, and for

each range a different perturbation size is used. Other adaptive

methods [35-36] were proposed to vary the perturbation step.

In [35], an exponential adaptation method is proposed that

f(x)

HPFX∫+

+

αsin(ωt) sin(ωt)

K

yx

x* f*Plant

3903

5

accelerates the convergence. In [36], an adaptive P&O

algorithm is presented that utilizes the error signal between

two consecutive power measurements. This error signal is

minimized by making use of a PI controller that generates the

adaptive step.

The study in [17] concentrates on two critical aspects to

improve the performance of maximum power point tracking

(MPPT). One improvement is to accurately locate the position

of the maximum power point (MPP) by using the centered

differentiation. Another effort is to reduce the oscillation

around the MPP in steady state by controlling active

perturbations. This work also adopts the method of steepest

descent for MPPT, which shows faster dynamic response and

smoother steady state than the method of hill climbing.

IV. SUMMARY

This study summarizes the latest approaches to the problem

of maximum power point tracking and serves as a summary or

review for future research in photovoltaic power generation.

The latest algorithms of MPPT are classified into the

following categories: the real-time identification method, the

extremum seeking control, the particle swarm optimization,

the DIRECT search algorithm, and adaptive step-size method.

Generally, the advantage of the heuristic search methods

lies in its simplicity, especially for digital implementation. The

algorithm requires no mathematical information about the

shape of the hill curve. Both P&O and IncCond were

developed based on the extreme value theory. Ideally, they can

track the maximum power point accurately based on the

maximum value condition. However, both rely on the

numerical approximation of differentiation, of which the

stability and accuracy is difficult to be guaranteed in practical

applications considering noise and quantization error etc. The

continuous oscillation around the optimal operating point is an

intrinsic problem of the algorithms, which are based on either

heuristic search or extreme value theory. The method of

steepest descent is one way to optimize the operation of P&O

algorithm by introducing a step-size corrector. Latest studies

focus more on making the step size adaptive to improve the

transient and steady-state performance.

To avoid the drawbacks addressed in the above study, the

latest study shows that the maximum power point tracking can

be performed by the advanced control algorithms, i.e. adaptive

control techniques and recursive least square. This allows the

use of well-developed control theory to analyze the system

stability. However, the disadvantage of the advanced control

algorithms lies in their complication. Further, the recursive

least square method requires either intensive computation or

complicated hardware implementation. Due to the limited

resolution and computational power, the real-time

identification is difficult to be achieved by a 16-bit-fixed-point

microprocessor, which is widely used in industrial control. In

the future, the practical development relies on improved or

simplified mathematical model that represents the

characteristics of photovoltaic outputs, and thus ease the

computational hurdle in real-time.

The extremum seeking control is considered better than

conventional adaptive control methods in the sense that it is

not model-based and does not require knowledge about the

uncertain system parameters which can make the

implementation simpler. The maximum searching can utilize

the switching ripple of power interfaces to avoid intentional

perturbations. The advantages indicate a bright future for the

control application of maximum power point tracking.

A Particle Swarm Optimization (PSO) algorithm is a

computational method that can be adopted for the maximum

power point tracking. The DIRECT method tracks the global

peak in the presence of multiple local maxima, which can be

caused by the partial shading on the solar array. Partial

shading cannot be easily avoided for residential installations,

since the sunlight direction changes from sunrise to sunset in a

day period. The shading can be caused by obstacles, such as

trees, other constructions, or birds etc. This generally results in

irregular photovoltaic output when photovoltaic panel are

connected in series. This generally makes it difficult to

perform the maximum power tracking. Current tracking

techniques still have difficulty to eliminate the generation

degradation caused by partial shading. As a result, further

development is still desirable to find a simple and effective

control algorithm to operate solar power systems efficiently.

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