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Offline Photovoltaic Maximum Power Point Tracking
Fyali Jibji-Bukar1
, and Olimpo Anaya-Lara1
1University of Strathclyde, Department of Electrical and Electronics Engineering, 16 Richmond Street, G1 1XQ, Glasgow, United
Kingdom
Abstract. As more renewable energy sources are connected to the electrical grid, it has become important
that these sources participate in providing system support. It has become needful for grid-connected solar
photovoltaics to participate in support functions like frequency support. However, photovoltaic systems
need to implement a maximum power tracking algorithm to operate at maximum power and a method for
de-loading photovoltaic systems is necessary for participation in frequency support. Some conventional
maximum power tracking techniques are implemented in real time and will not adjust their output fast
enough to provide system support while other may respond fast but are not very efficient in tracking the
maximum power point of a photovoltaic system. This paper presents an offline method to estimate the
maximum power voltage and current based on the characteristics of the photovoltaics module available in
the datasheet and using the estimated values to operate the photovoltaics at maximum power. The
performance of this technique is compared to the conventional technique. This paper also describes how the
photovoltaic system can be de-loaded.
1 Introduction
Power in electrical systems is increasingly supplied from
diverse generation sources. As sources such as
photovoltaics gain a larger share of power generation
and replace conventional generators, the inertia of power
systems will be reduced. The could lead to a high rate of
change of frequency when there is a difference in
generation and demand [1]. This problem is exacerbated
in island systems where there are very few generators
and high renewable energy penetration because they
have reduced inertia and variability in power generation
which could lead to more frequency deviation events [2].
As a result of this, it has become important for different
kinds of generation sources to participate in frequency
support if more renewable generation is to be added to
electrical grids.
Wind turbines have been demonstrated to contribute
to frequency support by providing inertia support and
providing primary frequency support similar to the
support obtainable from conventional power plants in [3]
and [4]. Energy storage systems have also been shown to
provide frequency support. In [5], flywheel energy
storage system is shown to provide frequency support.
Battery storage systems can also be used to provide
frequency support as shown in [6]. This is because they
are fast-acting and can increase active power supply in
the time-scale of inertia response.
Like battery storage systems, PV systems can support
grid frequency with the appropriate control and
operation method. However, PV systems require a
maximum power point tracking method. Common
methods used for operating PV at maximum power
include perturb and observe, incremental conductance
and fractional open-circuit voltage [7]. These methods
are not suitable for systems required to provide
frequency support because they either require significant
computation which makes them slower or are fast but
lead to significant power losses.
Various methods for estimating PV power have been
proposed in [8] and [9]. [8] uses artificial neural network
but this will require historical information on the
performance of the PV system and the method used in
[9] will require some real-time calculation to estimate
maximum power. This paper proposes a method to
operate the PV systems at maximum power by obtaining
the maximum power voltage from the PV current-
voltage (I-V) curve for the entire operating range of the
PV module using the characteristics of the PV module
from the PV datasheet.
Section 2 describes the effect of temperature and
irradiance on the open-circuit voltage (VOC) and short-
circuit (ISC) and how VOC and ISC can be estimated for
any combination of temperature and irradiance. Section
3 describes how the maximum power voltage and current
can be calculated from the I-V curve and how the PV
system can be operated at the desired de-loading level.
Section 4 presents the operation of the proposed method
and compares the result with operation using incremental
conductance.
2 Estimating VOC and ISC
2.1 Effect of Changing Irradiance
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© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).
The ISC current varies directly with the irradiance up to
very high levels of irradiance [10]. This is because the
generated photocurrent is a direct result of the amount of
available sunlight. This implies that for any given
temperature, the ISC can be readily determined. The ISC
current at standard testing condition (STC) is available in
the datasheet. The VOC is also affected - to a lesser extent
-by changing irradiance. The VOC changes
logarithmically to the irradiance. Figure 1 shows the I-V
at different irradiances and constant temperature.
Fig. 1.Effect of Changing Irradiance on VOC and ISC
2.2 Effect of changing temperature
A change in temperature results in a change in both the
VOC and ISC. As temperature increases, the ISC increases
while the VOC reduces. This results in
an overall loss of efficiency with increasing
temperature. This is because the increase in temperature
leads to an increase in the bandgap of the semiconductor
which leads to an increase in the ISC [11]. VOC reduces
with an increase in temperature because of the increase
in the dark current density [11].
The effect of temperature on VOC and ISC is defined
by the temperature coefficient of the PV module and is
provided by the manufacturer in the module datasheet.
Figure 2 shows the effect of changing temperature on the
I-V curve of the PV module.
Fig. 2.Effect of Changing Temperature on VOC and ISC
2.3 Effect of series and shunt resistances
The series and shunt resistances of the PV module/cell
make up the parasitic resistances. They reduce the
efficiency of solar cells. The series resistance is as a
result of the resistance of the electrical contact of the cell
[12]. The series resistance does not affect the VOC except
at high values. The effect of the series resistance can be
discounted in estimating VOC.
The shunt or parallel resistance is as a result of
leakage current from the side of the cell which leads to
loss of power and should be as high as possible to reduce
losses [12]. The shunt resistance has no significant effect
in measuring VOC and ISC. The parasitic resistances result
in a shift in the maximum power point and must be
considered in obtaining the I-V curve.
Figure 3 below shows the I-V curve of a Trina Solar
TSM310PD14 cell with the series and shunt (parasitic)
resistances and without the series and shunt resistances.
The VOC and ISC changed very little but there is a
significant shift in the maximum power point. The
maximum power voltage dropped from 0.5536V without
the parasitic resistances to 0.5033V with the parasitic
resistances while the maximum power current dropped
from 8.4533A to 8.3256A. This presence of the parasitic
resistances resulted in a maximum power loss of
0.4895W which is about 10% of the power without the
parasitic resistances. The shunt and series resistances are
not given in the module datasheet but can be calculated
using the method described in [13].
Fig.3. I-V curve of TSM310PD14 at STC with and without
Parasitic Resistances
3 Obtaining the I-V curves
The first step in obtaining the I-V curves is to determine
the ISC and VOC for all values of temperature and
irradiance. This is done by extrapolation of the I-V curve
at standard testing condition (STC) using the effect of
changing irradiance and temperature on ISC and VOC.
Two tables are generated for the VOC and ISC. The
range of irradiance considered is from 0-1700w/m2 in
intervals of 50w/m2 while the range of temperature
considered is from -40qC to 85qC in intervals of one.
The PV module used is the Trina Solar TSM-310PD14.
3.1 Calculating VOC
The Effect of temperature on VOC is given by the
temperature coefficient which is given in the module
datasheet. At a given the irradiance, VOC is given by
equation 1.
VOC (t) = VOC (STC) +
D
(t-25) (1)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Voltage(V)
0
1
2
3
4
5
6
7
8
9
10
Current(A)
Without Resistances
With Resistances
Maximum Power Point
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Where D is the temperature coefficient of the open-
circuit voltage and t is temperature. To determine the
VOC for any irradiance (I) at a given temperature,
equation 2 is used.
=
ln
+1 (2)
Where m is the diode ideality factor, kB is the Boltzmann
constant, J0 is the diode saturation current and T is the
temperature in Kelvin. To obtain the VOC voltage for any
combination of irradiance and temperature, equation 1
and 2 are combined resulting in equation 3. Equation 3
gives the VOC for any temperature and irradiance
combination.
(,)=ln
(,)
+ 1 + ( − 25) (3)
3.2 Calculating ISC
The ISC should be calculated first because it is needed in
equation 3 to calculate the VOC. ISC varies linearly with
the irradiance for any given temperature. The ISC for a
given irradiance at any temperature is given in equation
4.
ISC (t) = ISC (STC) +
D
(t-25) (4)
Where D is the temperature coefficient of the short-
circuit current. To obtain the ISC for any combination of
temperature and irradiance, the ISC at STC have to first
be adjusted for the irradiance and then adjusted for the
difference in temperature from 25qC. Equation 5 can be
used to calculate the short-circuit current for any
temperature and irradiance.
(,)=
×
()+(−25) (5)
3.3 Calculating maximum power voltage/current
To determine the maximum power point at any
irradiance and temperature, the I-V and P-V curves need
to be obtained. PV cell can be modelled as a current
source connected in parallel to a diode and the shunt
resistance (RSH) and in series to the series resistance
(RS). The five parameter model of a PV cell is given in
figure 4.
Fig. 4. Five parameter model of a solar cell
The I-V curve can be obtained by solving for the
current in the terminal of the module. The current from
PV module is given by equation 6.
=
−
( )/! −1"−#
$ (6)
Where i is the current across the terminals of the PV, RSH
is the shunt/parallel resistance, RS is the series resistance,
V is the voltage and q is the electric charge.
The I-V curve can be obtained by solving the
equation 6. The voltage should be taken in small steps
from 0 to VOC and the current computed to obtain the I-V
curve. The step should be as small as possible as the
maximum power point is usually around the end of the
curve. This will increase the accuracy of the curve.
However, equation 6 is an implicit equation and have to
be solved numerically. For every voltage from 0-VOC,
the value of current which satisfies the equation is
determined numerically. This was done using the fzero
function in Matlab. Figure 5 shows the I-V curve at
different points using the described method.
Fig. 5.Calculated IV curves
The maximum power point can be determined by
plotting the graph of voltage against power. It is the
highest point in the PV graph. Table 1 shows the
maximum power voltage of one module of Trina Solar
TSM 310 PD14 at different temperature and irradiance
using the described process.
Table 1: Calculated maximum power voltages
Irradiance -20qC 25qC 45qC 65qC
500 42.12 36.4 33.72 31.13
1000 42.04 36.8 33.4 30.3
1500 41.41 36.2 33.15 30.61
1700 41.63 35.4 32.25 29.78
4 Operating PV system at maximum
power
To test the proposed method, a PV system was modelled
in Simulink. The maximum power points at different
operating conditions are calculated and stored in a
lookup table. Because of the number of possible
combinations of temperature and irradiance, it is
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Cell Voltage (V)
0
2
4
6
8
10
12
14
16
Current (A)
800w/m2, 25°C
500w/m2, 35°C
1500w/m 2, 5°C
1200w/m 2, 15°C
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important that only a manageable number of power
points are calculated for. For any irradiance and
temperature value not stored in the lookup table, the
closest approximation should be used.
For any combination of temperature and irradiance,
the lookup table will give the maximum power voltage
as the reference voltage. The reference voltage will then
be used to obtain the duty cycle which will be the input
of the DC-DC converter. The operation of the system is
shown in figure 6 below. Fig. 6.Offline MPPT Implementation
Fig. 7. Offline MPPT (1000w/m250°C)
Fig.8. Incremental conductance (1000w/m2, 50°C)
The performance of the offline method is compared
to the performance of the system using incremental
conductance. In figure 7, the PV system is using the
offline maximum power point tracking while in figure 8,
the PV system is using incremental conductance
maximum power point tracking technique. The time
taken to reach maximum power by the PV system using
the proposed offline method is about 100ms while the
time taken to reach maximum power using incremental
conductance is about 700ms.
The system can be de-loaded by storing a percentage
of the maximum power voltage in the lookup table as the
reference voltage. This implies that if the system is
required to operate with a 10% reserve the maximum
power voltage will be multiplied by 0.9 before being
stored in the look-up table. This is because the voltage is
approximately directly proportional to the power up to
the maximum power point. The system can also be de-
loaded by operating it higher than the maximum power
voltage but it is more difficult to get it to operate at the
desired percentage of maximum power because the
power drops steeply after the maximum power point.
This method depends on the behaviour of the PV
module and as a result, the accuracy of the system is
affected by degradation of the PV module. This can be
factored into the calculation of the maximum power
voltage.
5 Conclusion
This paper describes and tests a fast and accurate method
for operating PV systems at maximum power or at
maximum power with a predetermined reserve. The VOC
and ISC are first determined using the temperature
coefficients of the PV module and the effects of
changing irradiance on the PV. Then the maximum
power is determined by obtaining the I-V curve. The
points of the I-V curve are obtained by numerically
solving the diode equation. This maximum power
voltage is stored in a lookup table and is the reference
voltage for a given irradiance and temperature. The
implementation of the offline method shows that the
system reaches maximum power quickly and is faster
than when incremental conductance is used. This main
0 0.5 1 1.5
-0.4
-0.2
0
0.2
0.4
Power(KW)
0 0.5 1 1.5
Time(S)
0
20
40
Voltage(V)
0 0.5 1 1.5
-0.4
-0.2
0
0.2
0.4
Power (KW)
0 0.5 1 1.5
Time(S)
0
20
40
Voltage
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advantage of this method is the speed at which the
reference voltage is determined. The method presented
in this work will find application in the use of converter
connected sources such as PV and grid-scale batteries in
providing frequency support and thus will enable more
converter connected sources in electrical grids.
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