B43 A6ce B11ac62ae3ae [612502]

Maximum Power Point Tracking Algorithm

Abstract— This paper present s the importance of increasing
the efficiency of the MPPT – Maximum Po wer Point Tracking –
algorithm in photovoltaic systems, being the principal low cost
method used in increasing the efficiency of the system. To achieve
the goal are presented two of the main algorithms: Perturb and
Observe and I ncremen tal Conductanc e.
Keywords—MPPT algortihm , efficiency, PV systems.
I. INTRODUCTION

The International Renewable Energy Agency (IRENA)
says the cost of generating power from onshore wind has fallen
by around 23 % since 2010 while the cost of solar photovoltaic
(PV) electricity h as fallen by 73% in that time. With further
price falls expected for these and other green energy options,
IRENA says all renewable energy technologies should be
competitive on price with fossil fuels by 20 20 [2].

Figure 1. Total renewable energy and solar energy produced from 2007 to
2016

From this statistic from Figure 1 we can observe an
exponential incre ase of the renewable energy and a large
increase of the power generated from solar systems begging
with 2014.
There are t hree main factors which determine the efficiency
of the photovoltaic systems:
– The efficiency of the solar panel (< 20%);
– The inverter efficiency (95-98%);
– The efficiency of the MPPT a lgorithm (> 98%).
Research has been focusing on conventional various MPP T
control algorithms to draw the maximum power from the
photovoltaic panel such as: Perturb and Observe(P&O),
Incremental Conductance, Fractional open circuit voltage and
the Fraction al open circuit current. The most popular algorithm is the Perturb & Obs erve
(P&O) a lgorithm. The P&O algorithm perturbs the duty cycle
or the voltage reference which controls the power converter, in
this way it takes steps over the P -V characteristic to find the
MPP. Another used algorithm is Incremental Conductance
which is based on the derivative of the power with respect to
the voltage which must be 0 when we reach the MPP.
Traditional maximum power point tracking algorithms are
based on search algor ithms to find the maximum output in
different external conditions, usually under uniform irradiation.
Due to that fact they have errors during partial shading on the
PV panel. They have poor convergence, slow tracking speed
and oscillation in steady -state.
In order to overcome the drawbacks and to have a better
performance the tendency nowadays is to combine those
conventional MPPT and set up a hybrid maximum power point
tracking.
II. THEORETICAL FUNDAMENTALS
A. Photovoltaic panels principal

Solar Photovoltaic (PV) is a technology that converts
sunlight into direct current electricity by using
semiconductors. When the sun hits the semiconductor within
the P V cell, electrons are freed and form an electric current.
The working principle of solar cells is based on the
photovoltaic effect, the effect due to which light energy is
converted to electric energy in certain semiconductor
materials.
A photovoltaic ce ll converts only a part of the solar
radiation in electrical energy due to some losses and efficiency
limits when conversion take place such as:
 The thermodynamic limit;
 The spectral mismatch (when the photons have lower
energy than the band gap energy of the
semiconductor);
 Loss due to conversion efficiency;
 Loss due to recombination;
 Loss due to the total reflection;
 Loss due to voltage factor;
 Loss due to fill factor.
Due to those losses the maximum efficiency is around
25%.
The efficiency of a solar cell is characterized by three
main factors: peak power, short -circuit current and open –
circuit voltage. The I-V characteristic of a solar cell behaves
as a diode and the behavior is i llustrated by a equivalent
circuit in Figure 2.

DCI
IdRs
RpDCI
VId+
–
Figure 2.The equivalent circuit of an ideal solar cell and a solar cell with
a series resistance Rs and a shunt resistance Rp

The solar cell is limited as a s ize and it delivers a limited
power under fixed current -voltage condition, due to that fact
they are not used stand -alone for most of the applications.
Several solar cells must be connected to form a solar panel in
order to use this energy for practi cal devices. This connection
is also called a PV module . The energetic efficiency of a solar
cell is the ratio between the maximum electric power and the
incident power:

 = P M / S * E (1)

where:
 E – irradiation[W/m2];
 S – active sur face of the panels[m2];
 PM – maximum power in Standard Test
Condition(STD), at a temperature of 25°C and
irradiation of 1000W/m2.

B. Maximum Power Point Tracking Algori thm

The PV pan el can produce the maximum power at the load
at a single point known as Ma ximum Power Point – MPP.
The behavior of a solar cell can be characterized by an I -V
curve because for every connection the shape of this curve
does not change. This curve can be ob served in Figure 3.
As it can be observed if the irradiance or temperatur e
changes, the I -V characteristics will change as well and the
position of the MPP will shift.

Figure 3. (I-V) characteristic curves of a solar panel, with different
irradiance levels and 25°C

Therefore, changes in the I -V curv e must be tracked
continuously such that the operating point can be adjusted to
always be on the MPP indicated in Figure 4. This function
must have done by a controller using a Maximum Power Point
Tracking algorithm.

Figure 4. A generic I -V curve and the associated P -V curve

Increasing the efficiency of the MPPT algorithm is the
principal low costs method for increasing the efficiency of the
PV system . The most known direct algorithms are Perturb and
Observe and Incremental Con ductance.

1) MPPT implementation using P&O algorithm

The Perturb and Ob serve algorithm is frequently used one
due to its easy implementation. The algorithm perturbs the
voltage reference which controls the converter, in this way it
takes steps over the P -V characteristic to find the MPP. In case
this output power is larger than the previous output power, this
point is set as the new operating point since ours is at a lower
voltage than the MPP.
In case it is lower, further perturbation towards lower
voltag es is required to achieve the maximum power point,
depending on the previous step direction. The steps of the
algorithm is described i n the flowchart from Figure 5.

Figure 5. Flow -chart of P&O algorithm

The waveforms oscillate around their MPP due to the
continuous perturbation even if the system is in steady -state
and t he irradiance and cell temperature are constant. Even if
P&O is easy to implement it has some drawbacks. As
mentioned earlier, one of them is the oscillating mod e around
the MPP in steady -state which leads to extra filters to absorb
the harmonic generated. However, if very small perturbation
steps are used this oscillation around the MPPT can be
significantly reduced.
The second drawback is that it cannot always operate at
the power point when we have suddenly change in irradiation
due to the slow trial an d error process.

2) MPPT implementation using Incremental Conductanc e
algorithm

Incremental conductance is another algorithm frequently
used in MPPT systems. It f ollows the change in time of the
power. The current and the output voltage of the PV panel
determine the conductance and the incremental conductance.
The principal of operation is presented in Figure 6.

Figure 6. Flowchart of I ncremental algorithm
When a chan ge appears in the value of the operating point
the instantaneous and the incremental conductance values are
compared. If the incremental conductance is greater than the
negative of the instantaneous conductance the referenc e
voltage, Vref, has to be increm ented.
On the other hand, if the incremental conductance is lower
than the negative of the instantaneous conductance, the current
operating point is to the left of the MPP, the reference voltage
is decremented. This proces s is repeated until the increment al
conductance is the same as the negative instantaneous
conductance.
The incremental conductance algorithm has a tracking
efficiency above 98% in steady -state conditions because is not
oscillating around the MPP. Despite t hat, when weather
conditions are varying quickly this method may become less
efficient. Moreover, a significant drawback is the complexity
of the hardware implementation and the additional software
steps.

C. Single phase full -bridge inverter

An inverter all ows conversion from direct current to
alternative current (DC to AC). In this case we can distinguish
two main types: inverter with natural commutation and
inverters with forced commutation. The inverter with natural
commutation is fully rea lized with thyristors and is directly
connected to the grid.
The switching part of the inverters with forced
commutation is done using power transistors with fast
antiparallel diodes, named feedback diodes, which provide a
path for the peak inductive loa d current when t he switch is
turned off.
Vd CdT1
T2T3
T4D1
D2D3
D4L
0R (-) (+)VAB
A B
VA0VB0+
-Id

Figure 7.Singl e phase full -bridge inverter topology

The inverter is one of the main parts in photovoltaic
systems. The full bridge PWM inverter is usually used in this
type of applications and its topology can be observed in Figure
7. The inverte r is built of two branches A and B. T1, T2, T3,
T4 are the power transistors (MOSFET, BJT, IGBT). Between
the output of those two branches is connected a R -L AC load.
The structure is po wered by a DC source Vd. The capacitor
Cd is picked such as it can quic kly take over the discharging
currents after the transistors are blocked .

We can define V B0 and V A0 as the output of the two
branches regarding the ground. The instantaneous voltage V AB
will be equal with:

VAB = VA0 – VB0 (2)

The switches T1, T2, T3, T4 can be switched in three
different sequences:
 When T1 and T4 are turned on +VAB is obtained at
the output;
 When T2 and T3 are turned on –VAB is obtained at
the output;
 When T1 and T2 or T3 and T4 are turned on together
zero voltage is obtained at the output.

1) PWM command with bipolar voltage modulation

The PWM command with bipolar voltage switching
implies that the transistors on the bridge diagonals are
switched simultaneously. Thus, when the (T1, T4) pair is
open, the (T2, T3) pair is blocked and vice -versa. Therefore,
the four power transistors need t wo complementary pulse with
modulated (PWM) command signals each having a dead -time.
In the case of the si nusoidal modulation for implementing
the PWM command with bipolar voltage switching technique,
the PWM signal it’s obtained by comparing the tria ngular
carrier wave with a Vcontrol modulating sinusoidal signal.
For:
 Vcontrol >Vtr => (T1, T4) open, (T2, T3) closed and
VAB=+Vd
 Vcontrol <Vtr => (T1, T4) closed, (T2, T3) open and
VAB= -Vd.

Figure 8.Waveforms for Bipolar Modulation

D. Clark and Park Transforms

Clarke and Park transformation are used in high
performance architectures in three phase power system
analysis. Current and voltage are represented in terms of space
vector which is represented in a stationary reference frame. A general rotating reference frame has then been introduced.
This frame is described by d and q axes Clark e, Park and
Inverse Park transformations have been described. Through
the use of the Clarke transformati on, the real and imaginary
currents can be identified. The Park transformation is used to
realize the transformation of those real and imaginary current s
from the stationary to the rotating reference frame .
This computation simplifies the controls and the analysis
of the AC systems. The transformation can be separated in two
main steps:
 From (a, b, c) to (α, β), known as Clark
transformation, which output s a two co -ordinate time
invariant system;
 From (α, β) to(d, q), Park transformation, which
outputs a two co -ordinate time invariant system.

E. Synchronizing the inverter with the grid

A Phase Locked Loop (PLL) is an electronic circuit with a
voltage or cur rent driven oscillator that is constantly adjusted
to match in ph ase with the frequency of an input signal.
The block diagram of a phase locked loop is described in
Figure 9.

Figure 9.Block diagram of a PLL

The main idea of ph ase locking is to evaluate th e
difference between phase angle of the input signal and
generated output signal. A phase detector (comparator or
multiplier), a Voltage -Controlled Oscillator (VCO) and a loop
controller or a Loop Pass Filter (LPF) are used to estimate the
phase difference .
The phase angle difference between of the input signal and
output signal is measured by the phase detector and it also
provides at the output an error signal. To generate the output
signal, the LPF output signal drives the V oltage -Controlled
Oscillator. The VCO provides a measure of variations of the
phase and generates a signal whose frequency is equal to the
input signal.

III. SIMULINK IMPLEMENTATA TION

In order to implement and simulate the photovoltaic system
Matlab/Simulink was used due to the possibility to use Model –
Based Design .

The schematic of the Simulink implementation of PV
system conne cted to the grid can be seen in Figure 10. The
input for the MPPT block is coming from the solar systems
and the output is going throw a PI controller. The PWM
signals are finally gen erated after some d -q and α -β
transformation.
Using this schematic, it can be analyzed the functionality
of the PV system described above. For a fi rst analysis the
value of the irradiance will be 1000W/m2 at the ideal
temperature of 25 C. At the output of the panel we will
measure the maximum current and the maximum voltage
then being calculated the maximum power computing the
product of them.
The ph otovoltaic system gives at the output the maximum
value of the voltage, 34.5 V, respectively the maximum
value of the current ,4.35A. Finally, the output maximum
power at 1000W/m2 will be 150W.
At the input of the inverter it can be observed the two
capacitances which will give a path to the ground for the
current and at the output is the RL load where it can b e
measured the voltage of the grid.
The MPPT controller has as an output the voltage
reference which is used for controlling the PWM generator
for the inverter. The MPPT algorithm has the responsibility
to find the right value of the voltage reference such as the
maximum power point is reached at the output of the
inverter. After that is the control loop implemented with the
PI controllers. The PI co ntrollers will give a uniform current
at the output and using the Clark and Park transformation
the power los s in switching devices is very small. The
output of those will be the input of the PWM generator and
after it, it can be observed the four signals which will
control the branches of the inverter.

IV. SIMULATION RESULTS

A. The charateristic s of the PV array

This curve characteristics are implemented to see the
influence of the irradiation and of the temperature on the PV
array using the system implemented in Figure 1 0.

Figure 11. The characteristic of the PV array under different irradia tion

Based on the analysis of the P -V characteristics presented
the in Figure 11 it can be observed the increasing of the
power with the irradiance and i t can be deduce the effect of
the temperature, the power decreasing same time as the
temperature incre ases. I -V characteristics presents
represents the standard behavior of the solar panel.
The inflection point in the middle of the feature provides
information about the maximum power being essential to be
able to perform the maximum power transfer. The ob jective
being to operate at maximum efficiency, the algorithms for
determining the inflection point are used.
Figure 10. Simu link implementation of the PV system

B. Maximum Power Point Tracking results
For a comparation between the two algorithms the system
was simulated under a temperature of 25 C with a ch ange of
irradiation from 200 W/m2 at 1000 W/ m2 with a 200 W/m2
step.
After the simulation the maximum power point reached
was compared with the one from the PV array simulation in
steady -state and an efficiency was calculated. For a better
comparison the o vershoot, the rise time and the settling tim e
were measured.

Figure 12. PV array power and inverter power – P&O

TABLE I. P&O BLOCKS ALGORITHM EFFICIENCY

Irradiance
[W/m2] 200 400 600 800 1000
Maximum
Power [W] 30.48 61.59 92.11 121.8 150.5
Output
Power [W] 30.24 60.53 89.85 119.2 145.3
Efficiency
(η) [%] 99.21 98.27 97.54 97.86 96.54

Figu re 13. Simulation result for Incremental algorithm

TABEL II. INCREMENTAL CONDUCTANCE ALGORITHM EFFICIECY

Irradiance
[W/m2] 200 400 600 800 1000
Maximum
Power [W] 30.48 61.59 92.11 121.8 150.5
Output
Power [W] 30.17 60.9 90.7 119.45 146.7
Efficiency
(η) [%] 98.98 98.87 98.46 98.07 97.47
As it can be seen in the simulation results from Figure 12
and 13 both, P&O and Incremental algorithms have a main
disadvantage.
Even they are simple to implem ent they have a constant
oscillation around the MPPT even in steady -state.
They are oscillating because they must check if the
environment conditions changed and the maximum power
point has changed and the s tep-size of the perturbation is
fixed causing th e scanning process to take a very long time.

V. CONCLUSION
The efficiency of the photovoltaic system depends on
three parameters: inverter efficiency, panel efficiency and
on the maximum power point algorithm. Since improving
the MPPT algorithm is one of the easiest and cheapest way
to improve the efficiency of the system, this field has been
researched more in the last years.
This paper presents the implementation of two main used
algorithms in maximum power point tracking for PV
system, Perturb and Observe and Incremental Conductance.
In order to compare this algorithms, a thorough analysis has
been done under the operation of a PV system.
The experimental part was implemented in
Matlab/Simulink using a graphic interface and the
realization of the algorithms has been done using block code
and Matlab code for a better understanding of how they
work.
The algorithm Perturb and Observe has been improved to
obtain no perturbation i n steady -state at a constant
temperature and irradiation.
Finally, both algorithms have proven an efficiency above
97% and they both can be implemented regarding the
requirements of the application.
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