IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
21
Assessment of Perturb and Observe MPPT
Algorithm Implementation Techniques
for PV Pumping Applications
Mohammed A. Elgendy, Bashar Zahawi, Senior Member, IEEE, and David J. Atkinson
Abstract—The energy utilization efficiency of commercial photovoltaic (PV) pumping systems can be significantly improved by employing simple perturb and observe (P&O) maximum power point
tracking algorithms. Two such P&O implementation techniques,
reference voltage perturbation and direct duty ratio perturbation,
are commonly utilized in the literature but no clear criteria for
the suitable choice of method or algorithm parameters have been
presented. This paper presents a detailed theoretical and experimental comparison of the two P&O implementation techniques on
the basis of system stability, performance characteristics, and energy utilization for standalone PV pumping systems. The influence
of algorithm parameters on system behavior is investigated and the
various advantages and drawbacks of each technique are identified
for different weather conditions. Practical results obtained using
a 1080-Wp PV array connected to a 1-kW permanent magnet dc
motor-centrifugal pump set show very good agreement with the
theoretical analysis and numerical simulations.
Index Terms—DC–DC power conversion, maximum power
point tracking (MPPT), photovoltaic (PV) power systems, photovoltaic (PV) pumping, stability.
I. INTRODUCTION
S
TANDALONE photovoltaic (PV) pumping systems have
become a favorable solution for water supply, gaining more
acceptance and market share, particularly in rural areas that have
a substantial amount of insolation and have no access to an electric grid. The maximization of energy utilization of these systems via maximum power point tracking (MPPT) has not been
sufficiently exploited in the literature. As a result, most commercial PV pumping systems either utilize inefficient MPPT control
or do not utilize MPPT control at all. Directly connected systems for example operate at the intersection of current–voltage
curves of the PV array and the motor-pump set. This operating
point may be far from the maximum power point (MPP) of the
generator wasting a significant proportion of the available solar
power. A simple dc–dc converter controlled by an MPPT algorithm can be used as a pump controller to match the PV generator to the motor-pump set. A number of different MPPT algorithms have been proposed [1]–[3]. The simplest is to operate
Manuscript received September 30, 2010; revised June 24, 2011; accepted
September 01, 2011. Date of current version December 16, 2011.
The authors are with the School of Electrical, Electronic, and Computer Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, England,
U.K. (e-mail: mohammed.elgendy@ncl.ac.uk; bashar.zahawi@ncl.ac.uk; dave.
atkinson@ncl.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSTE.2011.2168245
the PV array at constant voltage equal to the MPP voltage of
the array at the standard test conditions (STCs) provided by the
manufacturer (ignoring the effects of insolation and temperature
variations on the MPP voltage). This value is used as a reference
for a feedback control loop that usually employs a PI controller
to adjust the duty ratio of the MPPT converter. The authors have
previously investigated this approach and found that it offered
significantly better energy utilization efficiencies (up to about
91%) compared to directly connected systems [4].
The utilization efficiency, however, can be further improved
(at the cost of a small increase in implementation cost) by employing a hill-climbing MPPT technique such as the perturb and
observe (P&O) algorithm. This is a simple algorithm that does
not require previous knowledge of the PV generator characteristics or the measurement of solar intensity and cell temperature
and is easy to implement with analogue and digital circuits. The
algorithm perturbs the operating point of the PV generator by
increasing or decreasing a control parameter by a small amount
(step size) and measures the PV array output power before and
after the perturbation. If the power increases, the algorithm continues to perturb the system in the same direction; otherwise the
system is perturbed in the opposite direction. The number of perturbations made by the MPPT algorithm per second is known as
.
the perturbation frequency or the MPPT frequency
Three techniques have been proposed in the literature for
implementing the P&O algorithm: reference voltage perturbation [5]–[11], reference current perturbation [12], [13], and direct duty ratio perturbation [6], [10], [14]–[16]. Fig. 1 shows a
block diagram for reference voltage perturbation in which the
PV array output voltage reference is used as the control parameter in conjunction with a controller (usually a PI controller) to
adjust the duty ratio of the MPPT power converter. The PI controller gains are tuned while operating the system at a constant
voltage equal to the STC value of the MPP voltage. These gains
are kept constant while the reference voltage is controlled by
the MPPT algorithm. Similarly, the reference current perturbation approach uses the PV array output current reference as the
control parameter. Due to its slow transient response to irradiance changes and high susceptibility to noise and PI controller
oscillation, reference current control will not be considered in
this paper. For direct duty ratio perturbation, the duty ratio of
the MPPT converter is used directly as the control parameter
(Fig. 2).
To date, there has been no publication which includes a clear
criteria for the choice of algorithm parameters and the impact
of these parameters on system performance under practical
1949-3029/$26.00 © 2011 IEEE
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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
Fig. 1. Block diagram of MPPT with reference voltage control.
Fig. 2. Block diagram of MPPT with direct duty ratio control.
Fig. 3. Circuit diagram of experimental PV setup.
operating conditions. The P&O algorithm implementation approaches have so far been utilized individually in the literature
and the choice as to which method to employ continues to be
an open question. This paper presents a detailed theoretical
and experimental evaluation of the reference voltage perturbation and direct duty ratio perturbation P&O implementation
techniques, operating under different weather conditions, in
terms of overall energy utilization and the local stability of the
system. The effects of different perturbation rates and step sizes
are investigated and criteria for the choice of these parameters
presented.
II. EXPERIMENTAL SETUP AND METHODOLOGY
An experimental PV pumping system prototype was constructed comprised of six 180 Wp SANYO HIP-J54BE2 solar
modules (divided into two parallel branches of three series
connected modules), a step-down dc–dc converter, and a SunPumps SCB 10–185 motor-pump set consisting of a ten-stage
centrifugal surface pump driven by a PM brushed dc motor,
as detailed in a previous publication [4]. A simplified circuit
diagram of this setup is illustrated in Fig. 3. The PV array
was installed facing south at a fixed tilt angle of 54 with
respect to the horizontal. This angle was chosen at the time of
panel installation to obtain the maximum possible annual light
incidence without the need for sun tracking equipment. The
PV array current and voltage were measured with Hall Effect
sensors: LTS15-NP and LV25-P, respectively. For experimental
flexibility and ease of programming, a Texas Instruments
TMS320F2812 DSP-based eZdsp kit was used for control
and data acquisition. In a commercial product, a lower cost
microcontroller would be more than adequate to implement
the control algorithms under investigation. Meteorological
parameters were recorded at a 1-s sampling rate utilizing a
Vaisala MAWS201 weather station installed on the same roof
on which the PV array is installed. Motor armature resistance
and inductance were measured at 1.25 and 3.5 mH, receptively. A 470- F link capacitance was used together with a
PWM frequency of 10 kHz, ensuring converter operation in
continuous current mode throughout the full range of duty ratio
variations.
To study the effects of the algorithm parameters on system
performance, the experimental system was initially run at constant solar intensity and cell temperature for 30 s, ignoring variations in solar irradiance within 1%. System parameters were
recorded with a sampling rate of 2 K samples/s. Transient behavior was examined by disconnecting one of the two branches
of the PV array while the system is running, emulating a step
decrease in solar irradiance to 50% of its value. A longer experimental test duration of 20 min was chosen to study the effects
of solar irradiance and cell temperature variations on system
behavior and to calculate the energy utilization for different
weather conditions. In this test, parameters were recorded with
a low acquisition rate of 10 samples/s to limit the host computer buffer size and the storage memory required for the acquisition files. This 20-min test was repeated many times at different weather conditions and results are shown to demonstrate
the performance of the MPPT algorithm during periods of slow,
smooth changes in irradiance conditions as well as faster irradiance changes that occur over a period of a few seconds. Such
irradiance changes are common place in the U.K. where these
tests were carried out.
In this study, the energy utilization efficiency of the MPPT
algorithm was calculated by dividing the integral of the measured PV generator output power by that of the maximum possible power output calculated at the same solar irradiance and
cell temperature values. These calculated values are obtained
from the PV generator numerical model based on the measured
output characteristics of the PV array at different weather conditions. Further details of this approach are described in a recent publication by the authors [4]. A recent European standard EN50530 [17] has suggested a procedure for calculating
the transient and steady-state energy utilization efficiency of
an MPPT algorithm. However, the suggested approach requires
measurements at specific, controlled irradiance values and rates
of change. This makes it unsuitable for calculating the MPPT
efficiency of a site PV installation such as the one used in this
investigation, where the irradiance levels cannot be controlled
as would be the case in a laboratory investigation.
III. STABILITY ANALYSIS
A system employing P&O MPP tracking is continually subjected to two excitation sources, one originating from variations
in solar irradiance/cell temperature and the other from the perturbation of the tracking algorithm. When the system is operating under steady-state solar irradiance and temperature conditions, it is still subjected to continuous step changes in the control parameter at the selected perturbation rate. Although numerical simulations can predict the response to these step changes,
they do not give a clear understanding of the transient response
and the local stability of the system. An analytical solution is
ELGENDY et al.: ASSESSMENT OF P&O MPPT ALGORITHM IMPLEMENTATION TECHNIQUES FOR PV PUMPING APPLICATIONS
needed which is very difficult to develop for such a nonlinear
time-varying system.
Under constant and uniform irradiance and cell temperature
levels, the system operates around the MPP and it is possible
to develop a linearized analytical model to characterize system
behavior around this equilibrium point. This can be accomplished by taking an average over a switching cycle assuming
low output ripple. The averaged circuit is then linearized about
the equilibrium point by expanding any nonlinear function into
a Taylor series and retaining only the linear terms. The Taylor
series of a nonlinear function
in a neighborhood of an
operating point
is given by
23
Fig. 4. Averaged circuit model of PV system with a motor-pump load.
(1)
This can be applied to the torque equation of the motor-pump
set (2) which includes a nonlinear term representing the pump
load torque
[4]
Fig. 5. Array voltage to duty ratio small signal block diagram.
(2)
and
are
where is the torque constant of the motor and
constants that can be calculated from the Taylor series approximation of the summation of load and friction torques about the
equilibrium point.
At maximum power transfer, the PV generator can be replaced by a voltage or a current source whose internal resistance equals the resistance of its load. A current source with
parallel resistance
representation is chosen here since the
PV generator current is proportional to the solar irradiance. The
resultant averaged circuit model is shown in Fig. 4. This circuit
can be modeled by the equations
(3)
(4)
Neglecting second-order perturbation terms, removing the
steady-state quantities and transforming the equations to the
-domain, we obtain
(9)
(10)
(11)
where upper-case symbols represent the quantities as functions
of . From the above equations, the small signal block diagram
(Fig. 5) can be constructed.
A. Direct Duty Ratio Control
The array voltage to duty ratio small signal transfer function
corresponding to Fig. 5 is given by
(5)
(12)
where lower-case symbols represent the quantities as a function of time. Replacing each quantity by a dc component (represented by an upper case symbol) plus a small perturbation component (represented by a lower case symbol with a circumflex)
we get
where
(6)
and
(7)
(8)
The coefficients of the transfer function can be calculated by
substituting the system parameter values given in Table I. These
parameters were obtained by a combination of measurement,
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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
TABLE I
SYSTEM PARAMETERS AT NOMINAL OPERATING CONDITIONS; SOLAR
IRRADIANCE OF 800 W/m AND 25 C CELL TEMPERATURE
Fig. 8. Root locus for reference voltage control utilizing a
1) Proportional Control: When using a
small signal control equation is given by
controller.
controller, the
(13)
In this case, the open loop transfer function is given by
while the closed loop transfer function is
Fig. 6. Array voltage response to a step increase in duty ratio.
Fig. 7. Block diagram of a PV system with reference voltage control.
design choice, and simulation as detailed in [18]. This transfer
function has a negative real pole at
and two complex conjugate poles at
. It has two zeros at
and
. The response for a step increase
in duty ratio is illustrated in Fig. 6. The signal has a negative
steady-state gain
of about 198, the rise time is about
2.2 ms, the settling time is about 23 ms, and the peak overshoot
is about 29%. This system can be approximated to an under
damped second order system by eliminating the real pole with
the zero at
. For this system, the damping ratio and
the natural frequency will be 0.34 and 635 rad/s, respectively.
B. Reference Voltage Control
For reference voltage control, an output voltage reference is
used in conjunction with the controller to adjust the duty ratio
(Fig. 7). Both proportional (P) and proportional-integral (PI)
control strategies are examined below. It is accepted that other
approaches such as PID control may enhance the transient response of the system to the MPPT perturbations, but will result
in a more fluctuating steady-state response in the presence of
noise [19]. Nonlinear controllers such as fuzzy logic [20], [21]
can also be utilized to adjust the MPPT converter duty ratio.
However, the implementation of such controllers requires the
use of Microcontrollers/DSPs with high processing abilities and
large memory sizes resulting in increased system cost.
(14)
, the open loop transfer
With unity feedback gain
function has the same poles and zeros as those stated above for
. From each of the three open loop poles, a root locus branch
starts; two of these end at the two real zeros and the third at an
infinite zero as shown in Fig. 8. The branches do not cross the
imaginary axis and the system is always stable. The steady-state
error
in the step response when using a controller can
be calculated by applying the final-value theorem to the error
signal as follows:
(15)
This steady-state error can be reduced by using a higher value
. However, any noise superimposed on the PV generator
of
voltage will be amplified by
, changing the duty ratio and
causing fluctuations in the array voltage. These fluctuations misguide the maximum power point tracker, when an MPPT algorithm is used to adjust the reference voltage.
To reduce the effect of noise on the MPPT algorithm, a lowpass filter is required for the PV generator voltage feedback
signal. Let us assume a 200-Hz cutoff frequency, first-order software filter is used. The small signal transfer function of the filter
is given by
(16)
Using a first-order low-pass filter adds a pole to the open loop
transfer function pulling the root locus to the right as shown in
Fig. 8. This tends to lower system relative stability and slows
down the settling time of the response. The system is stable for
low values of
and unstable for high values. The value of
that makes the system marginally stable
so that sustained
oscillation occurs is about 0.015 and the period of that oscillation
is about 0.0056 s. Because
is low for the stable
ELGENDY et al.: ASSESSMENT OF P&O MPPT ALGORITHM IMPLEMENTATION TECHNIQUES FOR PV PUMPING APPLICATIONS
25
Fig. 10. Array voltage response to a step increase in reference voltage.
Fig. 9. Bode diagram of PV system with reference voltage control.
range, the steady-state error is very high. According to (15), the
minimum steady-state error in the stable range (corresponding
to
) is about 25% of the steady-state output. Using
a higher order filter or one with a lower cutoff frequency will
result in a lower value of
and a higher steady-state error.
2) Proportional Integral Controller: The addition of an integral part to the controller eliminates the steady-state error and
makes the system less susceptible to noise. However, it adds
a pole at the origin to the open loop transfer function making
the system less stable and requiring proper consideration to be
given to the design of the controller gains. The small signal control equation of the PI controller is
(17)
The open loop transfer function will be
(18)
resonant peak, the closed loop transfer function is expected to
have a pair of complex conjugate poles with a damping ratio of
about 0.2. The system bandwidth is about 220 Hz.
The small signal closed loop transfer function is obtained by
substituting
with unity in (19) which is solved numerically
showing that the system has two real poles at
and
and a pair of complex conjugate poles at
. The real pole at
is eliminated by
a real zero reducing the system order to three. The damped natural frequency is close to the resonant frequency obtained from
the frequency response analysis. However, the damping ratio of
the complex conjugate poles (0.128) differs from that expected
from the frequency response analysis due to the effect of the
real pole at
which cannot be neglected since its relative distance from the -axis is not so high. The step response
of the closed loop system is shown in Fig. 10. The rise time is
1.5 ms, and the settling time is 25.8 ms. The peak overshoot is
29.7% of the steady-state output.
IV. P&O ALGORITHM PARAMETERS
While the closed loop transfer function is given by
(19)
and
obThe PI controller gains are calculated from
tained from the root locus, utilizing the second Ziegler–Nichols
method [19]. The obtained values using this method are
and
. At these values, the system has a gain
margin of 3.25 dB and a phase margin of 11.9 as given by the
Bode plot shown in Fig. 9. Although the system is analytically
stable, the stability of the practical system can not be guaranteed
due to the low stability margins. There will always be high oscillation and noise present in a practical system even if further
tuning trails are attempted.
To solve this problem, the low-pass filter is removed from
the feedback loop accepting higher noise levels as the cost of
better system stability. In this case, at the design values of the PI
controller gains (
and
), the system has
an infinite gain margin and a 21.5 phase margin (Fig. 9). These
margins are high enough to ensure stability against variations in
component values of the system and variations in the reference
voltage around the equilibrium point.
The magnitude curve of the closed-loop Bode plot (Fig. 9)
has a resonant peak of 8.6 dB at 158 Hz. Corresponding to this
The P&O algorithm continuously perturbs the operating point
of the system causing the PV array terminal voltage to fluctuate around the MPP voltage even if the solar irradiance and
the cell temperature are constants. Consequently, similar current and power fluctuations occur. These usually fluctuate between three levels provided that the perturbation frequency is
low enough so that the system can reach a steady state before
the next perturbation. The step size must also be high enough so
that control is not affected by noise (and the oscillation resulting
from the use of a PI controller in case of reference voltage perturbation) and to allow the perturbation to cause a measurable
change in array output power. Noise has considerable effect on
the MPPT algorithm performance, especially at low step sizes
where the system response to noise is comparable to that of the
MPPT perturbations.
With reference voltage control, the noise superimposed on the
array current and voltage feedback signals cannot be rejected
using low-pass filters since using such filters would result in
system instability as discussed in the above section. With direct duty ratio perturbation, the stability of the system is not affected by using such filters as they are placed outside the duty
ratio-array voltage control loop. However, the signal delay resulting from using these filters may influence the decisions of
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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
Fig. 13. Armature current and motor speed waveforms with three-level operation; P&O MPPT algorithm with reference voltage perturbation.
Fig. 11. Experimental verification of three-level operation of PV pumping
system employing P&O MPPT algorithm with reference voltage perturbation.
Fig. 12. Behavior of P&O MPPT algorithm with reference voltage perturbation
in thee-level operation.
the algorithm. A second-order low-pass filter with cutoff frequency of 200 Hz was chosen to ensure good noise rejection
with an acceptable signal delay of about 1.5 ms.
A. Three-Level Operation of the P&O Algorithm
Fig. 11 shows the three-level operation of the experimental
PV pumping system employing a P&O MPPT algorithm with
reference voltage perturbation when the system was started and
run at 857.1-W/m solar irradiance and 27.9 C cell temperature
with a low perturbation frequency of 1 Hz and a high step size of
10 V. System operation can be better explained with reference
to the array power–voltage curve at the same irradiance and cell
temperature levels (Fig. 12).
Array power was measured at about 900 W with the system
operating at the initial reference voltage (162 V) represented by
point A. The initial perturbation direction is to increase the reference voltage, so the reference voltage is increased by 10 V
(the step size) to 172 V moving the operating point to point
B. Array power is then measured after a perturbation period of
1 s has passed. Because power is decreased at point B (about
778 W), the P&O algorithm reverses the perturbation direction
decreasing the reference voltage to 162 V and moving the operating point back to point A. Due to the power increase at point
A, the algorithm continues to decrease the reference voltage to
152 V (point C) passing through the MPP (926 W at point O)
located at 155.82 V. Because the power at point C (915 W) is
higher than that at A, the P&O algorithm continues to decrease
the reference voltage to 142 V (point D) where output power
falls to 883.4 W. Consequently, the P&O algorithm reverses the
perturbation direction increasing the reference voltage to 152 V
(point C), then 162 V (point A) and the sequence is repeated
until there is a change in solar irradiance/cell temperature.
The dc motor draws a high starting current of about 35 A and
reaches a steady-state value equal to the array current divided
by the duty ratio of the power converter after about 50 ms, as
shown in Fig. 13. The motor current oscillates for about 20 ms
after each MPPT perturbation. The motor speed takes longer to
settle due to the higher mechanical time constant of the motorpump set. Transients and high frequency motor current ripple
are damped by the motor inertia, thus have less effect on motor
speed (Fig. 13). The flow rate is proportional to motor speed
while the load torque is a square function of motor speed.
Similarly, when employing direct duty ratio perturbation the
waveforms of the system fluctuate between three levels at a low
perturbation frequency and a high step size (Fig. 14). For an irradiance level of 946.3 W/m and a cell temperature of 43 C,
the initial operating point at 50% duty ratio is to the right hand
side of the MPP. The initial perturbation direction is to increase
the duty ratio (thus moving the operating point to the left along
the arrays power–voltage curve) with a chosen step size of 5%.
A higher array power was then measured after every perturbation period (1 s) and the algorithm increases the duty ratio until
the operating point crosses the MPP and the array power starts to
decrease (at a duty ratio of 90%). The algorithm reverses the perturbation direction decreasing the duty ratio and the operating
point then fluctuates between three levels in the same manner
described above for reference voltage perturbation.
Although the tests presented in Figs. 11 and 14 were not
carried out under the same solar irradiance and cell temperature conditions (they were in fact carried out on different days),
ELGENDY et al.: ASSESSMENT OF P&O MPPT ALGORITHM IMPLEMENTATION TECHNIQUES FOR PV PUMPING APPLICATIONS
27
Fig. 16. Experimental results showing the effect of algorithm parameters on
the array voltage; P&O MPPT algorithm with direct duty ratio perturbation.
Fig. 14. Experimental verification of three-level operation of PV pumping
system utilizing P&O MPPT algorithm direct duty ratio perturbation.
Fig. 17. Experimental results showing the effect of algorithm parameters on
the array voltage; P&O MPPT algorithm with reference voltage perturbation.
Fig. 15. Armature current and motor speed waveforms with three-level operation; P&O MPPT algorithm with direct duty ratio perturbation.
they nevertheless give an indication of the different starting behaviors of the two implementation techniques. Unlike the MPP
voltage which varies in a narrow range around its standard test
conditions value, the optimum duty ratio can vary from 0% to
100% depending on the irradiance level. As a result, a system
employing a P&O algorithm with direct duty ratio control has a
slower transient response compared with reference voltage perturbation. For instance, if the optimum duty ratio is 90% and the
system is started with 50% duty ratio, the system takes 40 perturbation cycles to reach the MPP with a step size of 1%. Armature
current and motor speed waveforms are shown in Fig. 15. Compared with Fig. 13, the slower response of the system is evident
together with the smaller oscillations in armature current due to
the absence of a PI controller.
B. Effect of Perturbation Rate and Step Size
A lower step size results in lower steady-state oscillations but
slows down the system response to radiation and temperature
changes, and vice versa. For example, at 946.3-W/m solar irradiance and 43 C cell temperature (Fig. 14), 5 s are enough
for the P&O algorithm to shift array voltage to fluctuate around
the MPP, with a 5% step size and 1-Hz perturbation frequency.
However, at similar weather conditions (Fig. 16), 15 s were required with a 2% step size at the same perturbation frequency.
The slow response at low step sizes can be resolved using a
higher perturbation rate (Fig. 16). The transient time was less
than 2 s when using a 10-Hz perturbation frequency with a 2%
step size at an irradiance level of 860.1 W/m and a cell temperature of 31.8 C. With direct duty ratio perturbation, higher
perturbation rates up to the PWM rate (or the ADC rate if lower)
can be used. However, if the perturbation period becomes lower
than the settling time of the system response, the system is never
allowed to reach a steady state and its response at a particular
time is affected by previous perturbations resulting in chaos-like
behavior.
With reference voltage perturbation, a practical system with
a low step size is more susceptible to any noise superimposed
on the array current/voltage waveforms. This is because the response to noise in such a system is comparable to the effect
of algorithm perturbations. The array output voltage fluctuates
between many levels around the MPP as shown in Fig. 17. A
higher perturbation frequency results in faster deviation from
the MPP, faster recovery, and a faster response to irradiance and
temperature changes. If the perturbation period becomes lower
than the settling time of the system, the system is never allowed
28
Fig. 18. Experimental results showing the system responses to a PV array
%,
Hz).
branch disconnection (
to reach a steady state and the array output voltage fluctuates
in a random-like pattern. Further increases in perturbation rate
may cause the PI controller to lose its stability.
An additional experimental test showing the effect of algorithm parameters on the transient response of the system was
carried out by disconnecting one of the two branches of the PV
array while the system is running. This mimics a step decrease in
solar irradiance to 50% of its value but without the slight change
in MPP voltage that occurs with real changes in solar irradiance.
The MPP duty ratio changes significantly by a branch disconnection as well as by a step irradiance change and the algorithm
parameter values have considerable effects on the system response, as shown in Figs. 18–20. However, because the MPP
voltage remains unchanged, the P&O algorithm with reference
voltage perturbation may be confused only for a single perturbation period (regardless of the algorithm parameter values) due
to the power change resulting from the branch disconnection.
For this reason such a test was not considered for the reference
voltage perturbation.
When one of the two PV array branches is disconnected at
an irradiance level of 889.1 W/m and a cell temperature of
41.3 C (Fig. 18), the algorithm takes eight perturbation cycles to adjust the duty ratio for the new maximum power level
(2 s at a 4-Hz perturbation frequency) including four cycles resulting from two algorithm confusions. The algorithm attributes
the power decrease due to branch disconnection to the preceding
perturbation which was to decrease duty ratio (at
s), accordingly, it reverses the direction of perturbation increasing the
duty ratio at
s and moving the operating point away
from the MPP. At
s, the measured power decreases and
the algorithm corrects the perturbation direction. However, less
power is measured at
s confusing the algorithm once
more and requiring another perturbation cycle to recover.
When the array branch is disconnected at a similar irradiance
level with a lower step size of 2% (Fig. 19), the P&O algorithm
takes 4.25 s to adjust the duty ratio to the new maximum power
level, including 1 s resulting from algorithm confusion due to
system dynamics. The algorithm is not confused by branch disconnection because the perturbation preceding that disconnec-
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
Fig. 19. Experimental results showing the system responses to a PV array
%,
Hz).
branch disconnection (
Fig. 20. Experimental results showing the system responses to a PV array
%,
Hz).
branch disconnection (
tion was to increase the duty ratio and the algorithm reverses the
perturbation to the correct direction.
Fig. 20 shows that the algorithm takes a shorter transient time
of 1.1 s (including 0.6 s resulting from confusions due to branch
disconnection and system dynamics) when the branch is disconnected at an 888.9-W/m solar irradiance and a 40.5 C cell
temperature with a 10-Hz perturbation frequency. Although the
algorithm is confused three times, the transient response is still
faster than that shown previously in Fig. 18 with a 4-Hz perturbation frequency.
C. Choice of Perturbation Rate and Step Size
Different values of energy utilization efficiency have been reported in the literature for systems employing a P&O MPPT algorithm ranging from 68% [22] to 81.5% [23] and 97.8% [1].
In this project, a higher energy utilization efficiency of up to
99% was calculated for the experimental system used in this investigation system. The main reason for this variation in energy
ELGENDY et al.: ASSESSMENT OF P&O MPPT ALGORITHM IMPLEMENTATION TECHNIQUES FOR PV PUMPING APPLICATIONS
utilization efficiency values is the choice of the P&O algorithm
parameters, i.e., the step size and the perturbation frequency.
There is no published general procedure for the optimum choice
of P&O algorithm parameters and trial and error is often used
when making this choice.
Some attempts have been made to calculate the optimum
values of P&O algorithm parameters. Femia et al. calculated the
parameters of the P&O algorithm for a system with direct duty
ratio perturbation [16] and for a system with reference voltage
perturbation [6] in relation to the dynamic behavior of the specific systems used in those investigations. A perturbation period
higher than the settling time of the system response was chosen
considering a 10% steady-state error. With 10% steady-state
error, three-level operation occurs only with high step sizes increasing the amplitude of the steady-state oscillation, reducing
the energy utilization efficiency. Regarding step size calculations, Femia assumed that the optimum step size is the one at
which the algorithm will not be confused by solar irradiance
changes. This can be ensured if the magnitude of power change
due to perturbation during the perturbation period is higher than
that resulting from the irradiance change during the same period.
Based on this assumption, Femia derived a formula to calculate
the step size depending on some intrinsic parameters of the utilized solar cell such as the series resistance, the reverse saturation current, and the ideality factor as well as the rate of change
of solar irradiance. These cell parameters need to be calculated
initially as they are usually not given by the manufacturer. The
rate of change of solar irradiance varies significantly from time
to time for the same installation site and from one installation
site to another. For example, Fig. 27 (cf. Section VI) shows that
a rate of irradiance change of about 550 W/m per second was
reached during a 20-min period of measurement, while the average irradiance change during the day on which these measurements were taken was less than 10 W/m per second. If the maximum rate is considered for step size calculations, it will result in
very high steady-state oscillations and poor energy utilization.
If the average rate is used in calculations instead, the algorithm
is more likely to be confused during rapid irradiance changes.
A simpler general procedure for the choice of the parameters
of the P&O MPPT algorithm is described in this section. This
approach does not require complex mathematical calculations
or prior knowledge of site and/or array dependent parameters.
Figs. 21 and 22 show flowcharts of the proposed procedure for
direct duty ratio perturbation and reference voltage perturbation,
respectively. For three-level operation, the perturbation period
(for both perturbation techniques) must be chosen higher than
the settling time of the system response to a single MPPT perturbation, as calculated in the above stability analysis, considering
a 2% steady-state error. For commercial systems, this settling
time can simply be measured using an oscilloscope by running
the system at a high irradiance level with a low perturbation
frequency (say 1 Hz) and a high step size (say 10%) to ensure
three-level operation. If more than three levels are observed, the
perturbation frequency is reduced to allow the system to settle
to a steady state after each MPPT perturbation. A system with a
low settling time, allows the use of a lower perturbation period
and vice versa. The link capacitance should not be over-sized
unless this is necessary to ensure certain current ripple and ef-
29
Fig. 21. Choice of the parameters of the P&O algorithm with direct duty ratio
perturbation.
Fig. 22. Choice of the parameters of the P&O algorithm with reference voltage
perturbation.
fective series resistance of the capacitor as this will slow down
the system response and increase the sampling time.
The optimum step size should be calculated to give a low
steady-state error at an acceptable speed of system response. For
the system under consideration, the sizes of the PV array and the
motor-pump set were chosen so that the motor voltage did not
exceed 135 V at the STC irradiance. Taking into consideration
that the MPP voltage at the STC is 162 V, the duty ratio should
not normally exceed 90%
% . It is also assumed
that the system would not pump water when the duty ratio is
less than 10%, hence a value of
%. With direct duty
ratio perturbation, we recommend to set the initial duty ratio
of the converter to a central value of 50% to shorten the time
required by the P&O algorithm to change the duty ratio from
the initial value to the steady-state value, unless it is essential
to limit the motor starting current for motor-based loads. This
30
time is referred to as the starting transient time of the P&O algorithm
. With the above initial value and operating range of
the duty ratio, the algorithm needs to increase/decrease the duty
ratio by a maximum value
of 40% during starting.
Now, the question is how long should it take the P&O algorithm
to change the duty ratio by this amount? A shorter algorithm
transient time means better energy utilization during the transient stage but this is associated with a higher step size, higher
steady-state oscillations and lower steady-state energy utilization. As a compromise, we suggest a maximum transient time
of 2 s for the P&O algorithm to change the converter duty ratio
from its initial value to the optimum value. This means that the
required rate of change of the duty ratio
can be obtained
by dividing
by the corresponding transient time of the
P&O algorithm (2 s in this case). The percentage step size is the
product of
and the perturbation period. For example, with
a 10-Hz perturbation rate, the duty ratio can be increased/decreased by 40% in 2 s by using a step size of 2%. A smaller
change in duty ratio (smaller than 40%) is expected even for
significant changes in irradiation producing an even faster response by the algorithm. For instance, the total change in duty
ratio is about 18% when the irradiance increases from 500 to
1000 W/m producing an algorithm response time of less than
1 s.
With the reference voltage perturbation technique, the system
has better transient response as the MPP voltage varies in a
narrow range around its STC value equal to 81% of the STC
open circuit voltage and varies from 65% to 85% of that voltage
depending on irradiance and temperature levels, as discussed in
[4]. This means that at worst, when the system is started at the
STC value of the MPP voltage (also recommended to shorten
the transient time), the P&O needs to decrease the reference
voltage by 14% of the STC open circuit voltage (i.e., 28 V for
the considered system) during starting. Assuming a 2-s transient
time, this can be achieved with a step size of about 1.1 V. The
reference voltage step size should be chosen high enough so that
the algorithm is not confused by noise and oscillation resulting
from the PI controller.
V. ALGORITHM CONFUSION DUE TO IRRADIANCE CHANGES
During solar irradiance changes, the P&O algorithm may be
confused depending on the direction of the last perturbation.
For example, if the irradiance increases just after the algorithm
decreases the reference voltage, the power increase will be attributed to the perturbation and the algorithm will continue to
decrease the reference voltage moving the operating point away
from the maximum power point. For a step change in solar irradiance, the P&O algorithm recovers the correct direction after
a single perturbation period (Fig. 23). For a ramped change in
solar irradiance, the duration of the confusion period depends
on the relative effect of the irradiance change and the perturbation on the array output power. For example, if the irradiance
increases from 500 to 1000 W/m in 0.2 s with a step size of
2 V and a perturbation frequency of 10 Hz (Fig. 24), the confusion remains until the irradiance change stops (since the irradiance change is more significant). For a ramp decrease in solar
irradiance, the algorithm confusion has less effect on the array
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
Fig. 23. Simulation results showing the confusion of the P&O algorithm with
reference voltage perturbation by a step increase in solar irradiance.
Fig. 24. Simulation results showing the confusion of the P&O algorithm with
reference voltage perturbation by a ramp increase in solar irradiance.
output power as the algorithm reverses the perturbation direction after each sample. The recovery time depends on the distance between the operating point and the MPP, the step size,
and the perturbation rate.
With direct duty ratio control, the P&O algorithm may be
confused during solar irradiance changes in the same manner
discussed above for reference voltage control. For a step change
in solar irradiance, the P&O algorithm recovers the correct direction after a single perturbation period. For a ramp change, the
duration of the confusion period depends on the relative effect
of the perturbation and the irradiance change on the PV array
output power. For example, if the irradiance increases from 500
to 1000 W/m in 0.75 s with a step size of 1% and a perturbation frequency of 10 Hz (Fig. 25), the maximum array power
increases at about 73 W per perturbation cycle due to irradiance
increase while the maximum change in array power due to perturbation is about 24 W per cycle. As the irradiance change is
more significant, the confusion is supposed to remain until the
irradiance change stops. However, as the operating point moves
away from the MPP, the system response becomes slower resulting in confusion as a result of system dynamics at
s. The P&O algorithm then reverses the direction of perturbation to the correct direction, i.e., increasing the duty ratio. For
a ramp decrease in solar irradiance, the array output power is
ELGENDY et al.: ASSESSMENT OF P&O MPPT ALGORITHM IMPLEMENTATION TECHNIQUES FOR PV PUMPING APPLICATIONS
31
Fig. 25. Simulation results showing the confusion of the P&O algorithm with
direct duty ratio perturbation by a ramp increase in solar irradiance.
less affected by the confusion of the P&O algorithm since the
algorithm reverses the perturbation direction continually during
a period when array power is decreasing.
Fig. 26. Experimental system performance under slow changing irradiance;
P&O algorithm with reference voltage perturbation.
VI. ENERGY UTILIZATION
The energy utilization efficiency of the experimental
system was calculated for 20-min operation periods under slow
changing irradiance and rapidly changing irradiance conditions.
For the reference voltage perturbation, with slow changing solar
irradiance (Fig. 26), the calculated energy utilization efficiency
was 97.2% with a 2-V step size and a perturbation frequency
of 5 Hz. The utilization efficiency is relatively low due to
the effect of noise. In the presence of noise, the magnitude
of the array voltage ripple may not be decreased by using
lower step sizes. For example, no significant difference was
observed in array voltage ripple when a 2-V step size was used
(Fig. 26) compared to the steady irradiance periods in Fig. 27
where a 5-V step size is used. The calculated energy utilization
efficiency was marginally lower during rapidly changing irradiance due to the energy loss during the confusion and recovery
periods. For example, the energy utilization efficiency for the
solar irradiance shown in Fig. 27 was about 97% at a step size
of 5 V and a 5-Hz perturbation frequency.
Slightly higher energy utilization efficiency was achieved
with direct duty ratio control than that obtained with reference
voltage control due to the lower impact of noise and the absence
of the oscillation resulting from the PI controller. For instance,
the calculated energy utilization efficiency of the experimental
system for the 20-min operation periods under slow changing
irradiance was about 99% when using a 2% step size and
10-Hz perturbation frequency (Fig. 28). It is worth noting that
the peak–peak array voltage ripple with the chosen algorithm
parameters (Fig. 28) is about 6% of the MPP voltage compared
to about 12% in the corresponding case in [16] (see [16, Fig.
14]). The energy utilization efficiency was lower in rapidly
changing irradiance due to the energy loss during the confusion
and the recovery periods, where the operating point is away
from the MPP. For example, the energy utilization efficiency
for the solar irradiance shown in Fig. 29 was calculated at
Fig. 27. Experimental system performance under rapidly changing irradiance;
P&O algorithm with reference voltage perturbation.
97.9%. Higher variations in the array voltage occur at lower
irradiance levels since the power–voltage curve of the array
becomes flatter so that the perturbation causes a tiny change
in the array power which becomes comparable to that caused
by noise and/or system dynamics, confusing the algorithm.
At higher irradiance levels, the energy utilization efficiency
is increased. This is due to the change in control parameter
producing a higher array power change magnitude and consequently lower algorithm confusion. In addition, higher energy
utilization is expected for systems with lower time constants
as the algorithm confusion resulting from system dynamics
is reduced. The change in average array voltage with solar
irradiance shown in Figs. 27–29 is unusually low. This is due
to the superior temperature characteristics of the HIT PV array
used in this investigation (open circuit voltage temperature
coefficient of 0.26% per C) and the significant cooling effect
of the high wind speeds at the installation site which frequently
exceeds 20 m/s.
32
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012
calculated at 97.2% for slow changing solar irradiance. The energy utilization efficiency is marginally lower at 97% for rapidly
changing irradiance due to the energy loss during the confusion
and recovery periods when irradiance changes.
Direct duty ratio control offers better energy utilization and
better stability characteristics at a slower transient response and
worse performance at rapidly changing irradiance. System stability is not affected by using low-pass feedback filters. Higher
energy utilization efficiency was achieved with direct duty ratio
control due to the lower impact of noise and the absence of the
oscillation resulting from the PI controller. The calculated energy utilization efficiency of the experimental system was about
99% and 97.9% for the slow and rapidly changing irradiance, respectively. In addition, direct duty ratio perturbation allows the
use of high perturbation rates up to the PWM rate without losing
the global stability of the system.
Fig. 28. Experimental system performance under slow changing irradiance;
direct duty ratio perturbation.
ACKNOWLEDGMENT
The authors would like to thank the staff at Narec and in particular Dr S. McDonald for the use of their PV arrays and for
their valuable support.
REFERENCES
Fig. 29. Experimental system performance under rapidly changing irradiance;
direct duty ratio perturbation.
VII. CONCLUSION
The paper presents a comprehensive analysis and experimental evaluation of the reference voltage perturbation and
direct duty ratio perturbation techniques for implementing the
P&O MPPT algorithm. The effects of the perturbation rate and
step size on system behavior were examined, the criteria for the
choice of these parameters presented, and the energy utilization
calculated at slow and rapidly changing weather conditions
using a 1080-Wp experimental setup.
With reference voltage perturbation, the system has a faster
response to irradiance and temperature transients. However, it
loses stability if operated at a high perturbation rate or if lowpass filters are used for noise rejection from the array current
and voltage feedback signals. This noise has significant impact
on the algorithm performance and consequently on the energy
utilization, especially with low step sizes where the system response to noise is comparable to that of MPPT perturbations.
The energy utilization efficiency of the experimental system was
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Mohammed A. Elgendy was born in Behera, Egypt,
in 1974. He received the B.Sc. degree in 1997 from
Menoufia University, Egypt, the M.Sc. degree in
2003 from Ain Shams University, Egypt, and the
Ph.D. degree from Newcastle University, England,
in 2010, all in electrical engineering.
From June 1998 to May 2006, he was a Research
Assistant at the New and Renewable Energy Department, Desert Research Centre, Cairo, Egypt.
He is currently a Research Associate at the School
of Electrical, Electronic & Computer Engineering,
Newcastle University, England. His research focus is on control of power
electronic converters for photovoltaic systems and other renewable generation
schemes.
33
Bashar Zahawi (M’96–SM’04) received the B.Sc.
and Ph.D. degrees in electrical and electronic engineering from Newcastle University, England, in 1983
and 1988.
From 1988 to 1993, he was a design engineer
with a U.K. manufacturer of large variable speed
drives and other power conversion equipment. In
1994, he was appointed as a Lecturer in Electrical
Engineering at the University of Manchester and in
2003 he joined the School of Electrical, Electronic
and Computer Engineering at the Newcastle University, England, as a Senior Lecturer. His research interests include small
scale generation, power conversion, and the application of nonlinear dynamical
methods to electrical circuits and systems.
Dr. Zahawi is a chartered electrical engineer.
David J. Atkinson received the B.Sc. degree in electrical and electronic engineering from Sunderland
Polytechnic, England, in 1978, and the Ph.D. degree
from Newcastle University, England, in 1991.
He is currently a Senior Lecturer in the Power
Electronics, Drives and Machines Research Group
at the School of Electrical, Electronic and Computer
Engineering, Newcastle University. He joined the
university in 1987 after 17 years in industry with
NEI Reyrolle Ltd. and British Gas Corporation. His
research interests are mainly focussed on control of
power electronics systems including electric drives and converters.
Dr. Atkinson is a chartered electrical engineer.