IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008 2629
Optimized Maximum Power Point Tracker for
Fast-Changing Environmental Conditions
Dezso Sera, Student Member, IEEE, Remus Teodorescu, Senior Member, IEEE, Jochen Hantschel, and Michael Knoll
Abstract—This paper presents a high-performance maximum
power point tracker (MPPT) optimized for fast cloudy conditions,
e.g., rapidly changing irradiation on the photovoltaic panels. The
rapidly changing conditions are tracked by an optimized hill–
climbing MPPT method called dP -P&O. This algorithm sepa-
rates the effects of the irradiation change from the effect of the
tracker’s perturbation and uses this information to optimize the
tracking according to the irradiation change. The knowledge of
the direction of the irradiation change enables the MPPT to use
different optimized tracking schemes for the different cases of
increasing, decreasing, or steady irradiance. When the irradiance
is changing rapidly this strategy leads to faster and better track-
ing, while in steady-state conditions it leads to lower oscillations
around the MPP. The simulations and experimental results show
that the proposed dP -P&O MPPT provides a quick and accurate
tracking even in very fast changing environmental conditions.
Index Terms—Fast-changing irradiation, maximum power
point tracking, photovoltaic, solar.
I. INTRODUCTION
T
HE worldwide-installed photovoltaic (PV) power capac-
ity today shows a nearly exponential increase, which is
mostly dominated by grid-connected applications [1]. In these
applications, the typical goal is to extract the maximum possible
power from the PV plant during the entire time of operation;
thereby, these systems need a maximum power point tracker
(MPPT), which sets the system working point to the optimum,
following the weather (i.e., solar irradiance and temperature)
conditions. There are many MPPT strategies that are available
[2]–[10] for different converter topologies, which provide high
performance tracking during “nice” weather conditions, i.e., at
strong and stable solar irradiation and no partial shadowing.
These trackers are satisfactory if the PV system is installed at a
place where the possibility of clouds and partial shading is very
low. However, in many cases, when the PV system is installed in
an urban area, partial shadowing by the neighboring buildings
is sometimes inevitable [11]. Similarly, on places where the
Manuscript received October 31, 2007; revised March 27, 2008.
D. Sera is with the Institute of Energy Technology, Aalborg University, 9220
Aalborg East, Denmark (e-mail: des@iet.aau.dk).
R. Teodorescu is with the Power Electronics Section, Green Power Labora-
tory, Institute of Energy Technology, Aalborg University, 9220 Aalborg East,
Denmark (e-mail: ret@iet.aau.dk).
J. Hantschel is with the REFU-Elektronik GmbH, 72555 Metzingen,
Germany (e-mail: jochen.hantschel@refu-elektronik.de).
M. Knoll was with the REFU-Elektonik GmbH, 72555 Metzingen, Germany.
He is now with Daimler AG, 70546 Stuttgart, Germany (e-mail: ferchau.
knoll@daimler.com).
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/TIE.2008.924036
moving clouds are very often present on the sky, for example,
Northern Europe, the irradiation can show fast changes even
though the average value is fairly high. In these cases, if the
MPPT is not able to detect the partial shadowing and if is not
able to react quickly to the fast irradiation changes, the PV
system capacity will not be optimally used.
II. MPPT
SINRAPIDLY CHANGING CONDITIONS
As it was mentioned in Section I, an MPPT algorithm that
provides high-performance tracking in steady-state conditions
can easily be found. A very popular hill-climbing method is
the perturb and observe (P&O) [2], [12], [13] tracker, which
has some important advantages as simplicity, applicability to
almost any PV system configuration, and good performance
in steady-state operation. However, as with most of the hill-
climbing methods, there is a tradeoff between the accuracy and
speed of the tracking.
A. dP -P&O Method
The dP -P&O MPPT method [14] is an improvement of
the classical P&O in the sense that it can prevent itself from
tracking in the wrong direction during rapidly changing irra-
diance, which is a well-known drawback of the classical P&O
algorithm.
The dP -P&O determines the correct tracking direction by
performing an additional measurement in the middle of the
MPPT sampling period, as shown in Fig. 2. As it can be seen
in the figure, the change in power between P
x
and P
k+1
only
reflects the change in power due to the environmental changes,
as no action has been made by the MPPT. The difference
between P
x
and P
k
contains the change in power caused by the
perturbation of the MPPT plus the irradiation change. Thereby,
assuming that the rate of change in the irradiation is constant
over one sampling period of the MPPT, the dP that is purely
caused by the MPPT command can be calculated as follows:
dP = dP
1
− dP
2
=(P
x
− P
k
) − (P
k+1
− P
x
)
=2P
x
− P
k+1
− P
k
. (1)
The resulting dP reflects the changes due to the perturbation
of the MPPT method. The flowchart of the dP -P&O can be seen
in Fig. 1. Equation (1) represents a small extra computational
load compared to the classical P&O method, where, in order
to determine the next perturbation direction, a difference be-
tween two consecutive measurements of power is used (Fig. 2).
In case of dP -P&O, an extra measurement needs to be taken;
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2630 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008
Fig. 1. Flowchart of the dP -P&O algorithm.
Fig. 2. Measurement of the power between two MPPT sampling instances.
however, this does not require a new sampling of the mea-
sured PV voltage and current, as they are sampled with high
frequency for the dc voltage controller and power feedforward
(see Fig. 4).
Determining the dP allows tracking in the correct direction
during irradiation changes. However, in order to track very fast
changes of irradiation, the voltage perturbation step has to be
increased. This would lead to oscillations around the MPP in
steady-state conditions, degrading the overall performance. To
overcome this drawback, the information regarding the change
of output power due to external conditions dP
2
is used. From
the value of dP
2
, it can be determined if the irradiation is
stable, increasing, or decreasing. This information allows the
use of an optimized tracking strategy for the different cases.
The flowchart of this method is shown in Fig. 3.
In Fig. 3, the symbols have the following meanings:
1) ThN—negative threshold for dP ;
2) ThP—positive threshold for dP .
In Fig. 3, if the change in power due to irradiation (|dP
2
|) is
smaller than the change of power due to the MPPT perturbation
(|dP |), it is considered to be a slowly changing condition and
the system will use the basic dP -P&O algorithm with small
increment values to reduce oscillations around the MPP.
B. Optimized dP -P&O During Rapidly Changing Irradiation
The inverter control system considered when examining the
optimized dP -P&O MPPT is shown in Fig. 4.
In Fig. 4, the MPPT gives the voltage reference to the dc
voltage controller, whose output will serve as the reference
for the grid current peak value. The dc voltage controller is a
proportional integrator, whereas the grid current controller is
considered ideal as well as the inverter.
If a fast rise of irradiation was detected by dP
2
in Fig. 3, it
means that the MPPT should increase the PV array reference
voltage in order to follow the irradiation change. Thereby, in
this situation, the MPPT switching strategy is in favor of in-
creasing the voltage reference. V
dc
ref in Fig. 4 is decreased only
when the voltage was increased in the previous MPPT sam-
pling instance, and it caused a reduction of power dP < ThN.
A negative threshold value ThN has been applied in order to
avoid unnecessary switching around the MPP. If—due to the
action of the MPPT in the last sampling period—dP becomes
negative, the MPPT holds the voltage reference at the same
level for one sampling period instead of decreasing it, unless
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SERA et al.: OPTIMIZED MAXIMUM POWER POINT TRACKER FOR CHANGING ENVIRONMENTAL CONDITIONS 2631
Fig. 3. Flowchart of the dP -P&O method with optimized tracking.
Fig. 4. Single phase MPPT and current control structure for green power inverter.
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2632 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008
Fig. 5. Movement of the operating point of the PV system on the P–V
characteristic (a) with the basic dP -P&O tracking method and (b) with the
optimized tracking.
the caused decrease of power became larger than the threshold
(|dP | > |ThN|). The flowchart in Fig. 3 assumes that the MPP
voltage increases with irradiance, which is valid in most of the
cases. However, in some cases, due to the panel series resistance
at high irradiation levels, the MPP voltage could decrease with
irradiation [15].
C. Determination of the Threshold Values
A theoretical analysis regarding the optimal choice of the
main parameters (sampling frequency and perturbation size) of
the P&O method, which is also valid for the dP -P&O, can be
found in [16].
The threshold ThP has been chosen to be zero. This is be-
cause if the last perturbation had a positive effect on the output
power, regardless of the size of the change, the MPPT should
continue the perturbation in the same direction. A nonzero ThP
would introduce a stationary error in the tracking by stopping
the perturbation when the working point is approaching the
MPP. On the other hand, when choosing the negative thresh-
old ThN, the goal is to avoid unnecessary switching when
the MPPT is closely following the changing MPP in varying
irradiation, as it is shown in Fig. 5. If |ThN| is chosen to be
too large, it would allow the working point to move away too
far from the MPP, decreasing the MPPT efficiency. On the
other hand, if |ThN| is too small, it will result in unnecessary
switching around the MPP, also causing additional losses. In
order to obtain the value of ThN, the change of power ∆P
I
due to one voltage increment in the vicinity of MPP should be
determined first, which requires a model of the used PV system.
For the present purpose, a simple model is sufficient.
The current–voltage relationship of a PV panel using an ideal
single-diode model can be described as follows:
I = I
sc
− I
0
e
V
n
s
V
t
− 1
(2)
where I
sc
is the panel short-circuit current, I
0
is the dark
saturation current, and V
t
is the cell’s thermal voltage. I
sc
is given in the panel data sheet, whereas I
0
and V
t
can be
calculated by using the data sheet values and the panel basic
equations or by measurements [17]–[19].
From (2), the panel voltage as a function of current can be
expressed as follows:
V = n
s
V
t
ln
I
sc
− I
I
0
. (3)
If the PV system current is perturbed by a small dI,from(3)
V
= n
s
V
t
ln
I
sc
− I − dI
I
0
. (4)
From (3) and (4), the change of voltage caused by the small
current perturbation can be calculated as follows:
dV
I
= V
− V
= n
s
V
t
ln
I
sc
− I − dI
I
0
− ln
I
sc
− I
I
0
(5)
dV
I
= n
s
V
t
ln
I
sc
− I − dI
I
sc
− I
. (6)
By solving (6) for dI, the effect of a small voltage perturbation
on the array current can be obtained as follows:
dI
V
=(I
sc
− I)
1 − e
dV
n
s
V
t
. (7)
The general expression of the power change due to a small
voltage perturbation has the form
dP
V
= dV I + dI
V
V + dI
V
dV. (8)
By inserting (7) into (8), the PV power change due to a
small voltage perturbation at an arbitrary point of the V –I
characteristic can be estimated.
If one replaces the term dV in the aforementioned equation
with Incr, it will result in the variation of power due to one
perturbation of the MPPT.
Obviously, (8) depends on the actual irradiation conditions
and the instantaneous working point of the system on the
V –I characteristic. It is well known that, at a given irradiation
intensity
∂P
∂V
MPP
=0. (9)
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SERA et al.: OPTIMIZED MAXIMUM POWER POINT TRACKER FOR CHANGING ENVIRONMENTAL CONDITIONS 2633
From (9), the change of power due to a small ∆V is the
minimum in the vicinity of the MPP
∆P
∆V
MPP
≤
∆P
∆V
V =V
MPP
I=I
MPP
. (10)
The calculation of the threshold values are based on (8),
where the actual working point on the I–V characteristic is
considered to be V = V
MPP
± Incr, with a perturbation that
moves the working point away from MPP.
III. S
IMULATION RESULTS
The inverter-control structure shown in Fig. 4 has been
implemented in Simulink in order to verify and compare the
behavior of the optimized dP -P&O to the basic dP -P&O. The
considered system parameters are described in the following.
The PV array consists of three parallel strings, each containing
16 series-connected BPMSX120 PV panels with the following
data sheet parameters:
1) I
sc
=3.87 A—short-circuit current in STC
1
;
2) V
OC
=42.1 V—open-circuit voltage in STC;
3) V
MPP
=33.7 V—voltage at the MPP in STC;
4) I
MPP
=3.56 A—current at the MPP in STC;
5) P
MPP
= 120 W—power at the MPP in STC.
Considering that each string contains 16 panels with the afore-
mentioned parameters, the rated MPP voltage of the system
results as V
rated
=16× 33.7 = 539 V. The maximum power
of the entire plant results as P
rated
=3× 16 × 120 = 5760 W.
The rated current of the system is I
rated
=3× 3.56 = 10.68 A.
The model of the PV plant is using the detailed single-diode
model, considering the full characteristic of the cells, where the
reverse characteristic equations were implemented according
to [20]. The inverter and the grid current controller are con-
sidered ideal; they are modeled by an ideal current source
and a two-sample delay, respectively. The LC filter and grid
impedance have been modeled by using the PLECS toolbox,
with values of L
f
=1.7 mH and C
f
=4.3 µF for the LC filter
and L
g
=50µH and R
g
=0.2Ωfor the grid impedance. The
minimum system voltage allowed is V
sys min
= 150 V.
In order to visualize and compare the behavior of the initial
and optimized dP -P&O algorithms, they have been simulated
in the following two different MPPT configurations: 1) when
the MPPT provides the dc current reference (Figs. 6 and 7) and
2) when the MPPT provides the dc voltage reference (Figs. 8
and 9). In the following, the simulation results for these two
cases will be presented.
A. Comparison of the MPPT Algorithms With Current
Reference as Output
In order to facilitate the comparison of the basic and opti-
mized dP -P&O, the same current increment values were used
1
Standard test conditions—The testing conditions to measure photovoltaic
cell or module nominal output power. Irradiance level is 1000 W/m
2
, with
the reference air mass of 1.5 solar spectral irradiance distribution and cell or
module junction temperature of 25
◦
C.
Fig. 6. Current references of the basic dP -P&O algorithm and the ideal MPP
current during rapidly changing irradiation. It can be seen that the tracker “turns
back” when it crosses the MPP current. The trapezoidal irradiation profile starts
at 2 s on the time axis, reaches the maximum at 6 s, and returns to the initial
level at 11 s.
Fig. 7. Current references of the optimized dP -P&O algorithm and the ideal
MPP current during rapidly changing irradiation. The tracker does not decrease
the current reference when it reaches the MPPT current but waits for one MPPT
period without perturbation instead.
Fig. 8. PV system voltage and ideal MPP voltage during a trapezoidal
irradiation profile. It can be seen that the dc voltage oscillates around the
optimum value during the irradiation slope. The ramp starts at 4 s on the time
axis from 250 W/m
2
, reaches its maximum (500 W/m
2
) at 12.5 s, and arrives
back at its initial value at 24 s.
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