chapter 5 fibonacci serach method for maximum...
Post on 22-Jun-2018
215 Views
Preview:
TRANSCRIPT
86
CHAPTER 5
FIBONACCI SERACH METHOD FOR MAXIMUM POWER
POINT TRACKING
5.1 INTRODUCTION
It has been shown in previous chapters that partial shading of
SPVA is one of the main causes for reduced energy yield of many SPV
arrays. Use of anti parallel diodes with series connected modules may produce
multiple power peaks in the P-V characteristics. For instance, partial shading
on a SPVA will result in different irradiance on the array’s individual
modules. This again will result in different optimal operating voltages and
currents for the individual modules. There are in principle two approaches to
handle this issue:
One solution is to cascade each module with a separate power
converter (Lindergen 1999). This allows the modules to
operate at different voltage and current while maintaining the
same current output after the power converter. This technique
is known as “module-converter approach”.
If the PV array is to be connected to one single power
converter, multiple MPPs on the power-voltage curve will
occur. Conventional MPPTs tend to lock to a local MPP,
which may not be the global optimum. One solution to ensure
the operating point corresponds to the global optimum is to
87
periodically scan the entire operating range and search for the
global MPP (Patel and Agarwal 2008 b).This is known as
“scanning MPP approach”.
If we assume lossless power converters, the module-converter
approach is able to harness more power. This is because the scanning MPP
approach can only set one operating point for the entire SPV array; therefore,
all modules connected in parallel must have the same voltage, whereas all
modules connected in series must carry the same current. Individual modules
may therefore not operate at their own optimum, although the SPV array as
such is at its optimum operating point. However, in reality lossless power
converters do not exist and from the point of view of converter efficiency, a
larger power rating is beneficial. Due to relatively large power loss in smaller
converters, the power loss under normal and shaded operating conditions is
higher than that by using a central or string inverter. This shortcoming is
particularly pronounced when partial shading conditions are rare. However, in
situations where partial shading would be the norm, such as the building
integrated systems, the module converter approach may be beneficial. When
the module converter approach is used, a scanning MPP algorithm is needed
at the module level, since an individual module may also have multiple
maxima in case of partial shading. To avoid such scanning, each bypass diode
in the module would have to be paired with one power converter. Such an
approach is feasible in principle, but would suffer even more from the
relatively large power loss resulting from small power rating of individual
converters. Therefore, in practice, a scanning MPP algorithm is necessary
whether string or module-converter approaches are used.
A very little attention has been drawn in the literature on assessing
the performance of MPPT under partial shaded conditions (scanning MPP
approach) due to the complexity and extensive measurement equipments
88
required for this purpose. Against this background, different MPPT schemes
proposed in the literature under non uniform irradiance conditions have been
reviewed and an improved MPP approach has been presented.
V/I ratio for the load is decided on other considerations. However
V/I ratio for the SPVA is governed by MPP of the array. To match these
different requirements, a dc-dc converter is interposed between SPVA and the
load. V/I ratio on the input and output sides of the dc-dc converter will be the
same whereas V and I values observed on the two sides may be different. The
situation is a kin to a transformer used in AC to match the impedances.
5.2 MPPT SCHEMES
Several MPPT schemes are available in the literature. A few
popular schemes are:
Perturb and observe (P&O) or Hill climbing methods (Hua et
al 1998, Fernia et al 2005).
Incremental conductance method (Hussein and Muta 1995)
Short circuit current method (Noguchi et al 2002)
Open-circuit voltage method (Dorofte et al 2005)
Ripple correlation method (Esram et al 2006)
Modified techniques to minimize hardware and to improve the
performance (Kasa et al 2000, Veerachary et al 2001, Dorofte
et al 2005, Sera et al 2006, Kasa et al 2005).
The tracking schemes mentioned above are effective and time
tested under uniform solar irradiance, where the P-V curve of SPV module
exhibits only one MPP for a given temperature and irradiance. But partial
shading results in a deformation of the overall P-V curve. That is P-V curves
89
often exhibit multiple local maxima at different locations, which may also
result in quite odd ratios between global MPP (GMPP) voltage and open-
circuit voltage. These factors can present a considerable hindrance to the
accurate operation of a MPPT. Some of the popular literatures which present
the methods to address this issue are presented here:
Solodovnik et al (2004) have suggested a state space- based
approach to search the GMPP. This method is fast and
accurate but is system specific, is complex, and requires more
sensors.
Miyatake et al (2004) have reported an MPPT scheme that
uses Fibonacci sequence to track the GMPP under partially
shaded conditions. However, the method does not guarantee
GMPP tracking under all conditions.
Testing of various commercially available inverters in
partially shaded conditions and power loss due to shading has
been presented by Bruendlinger et al (2006).
Intelligent PV modules have been proposed by Roman et al
(2006).
Two stage MPPT scheme for partially shaded SPVA has been
proposed by Kobayashi et al (2006).
Behaviour of SPVA under partial shaded conditions has been
presented by Xiao et al (2007).
An analytical model, based on Lambert function and its
properties, has been presented by Petrone et al (2007).
Patel and Agarwal (2008 b) has developed a GMPP tracking
scheme with P&O as a subroutine.
In this chapter the modifications are made in Fibonacci method so
as to track GMPP always. The results are checked against binary search
method. The results are compared and validated.
90
5.3 IMPORTANT OBSERVATIONS OF SPVA UNDER
PARTIAL SHADED CONDITIONS
The partial shade has more impact on series connected modules.
The multiple peaks are mainly introduced by series connection in any
configuration. The simulation of series connected SPVA array characteristics
under partial shaded condition is shown in Figure 5.1 using the generalized
program discussed in Chapter 4.
Figure 5.1 Characteristics of SPVA under three different shading
patterns A, B and C
It may be concluded from the simulation results that:
V-I curves under partially shaded conditions have multiple
steps, while the V-P curves have multiple peaks. Maximum
number of peaks equals to the number of shading patterns.
In addition to irradiance and temperature, the magnitude of
GMPP, and the voltage at which it occurs are also dependent
on the shading pattern and array configuration.
91
The GMPP may lie on the left side of the load line (Rmp) too.
That is Rmp > Ractual (Ractual = Vactual/Iactual). So, the two stage
technique will not be able to track this point.
5.4 MODIFIED FIBONACCI SEARCH ALGORITHM
The Fibonacci search technique is a method of searching a sorted
array using a divide and conquer algorithm that narrows down possible
locations with the help of Fibonacci numbers. It continuously narrows down
the range with the optimal point always lying within that range. The shifting
can be either to the left or to the right. The direction of shifting is based on the
values of that function at two check points, V1 and V2. It is a mathematical
search. The Fibonacci search is based on the sequence of Fibonacci numbers
defined by the Equations (5.1) to (5.2)
1F,0F 10 (5.1)
2n1nn FFF for n = 2,3, … (5.2)
Hence the Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21…
Consider the points x1, x2, x3 and x4 as shown in Figure 5.2. x3 and
x4 are the extremities. The range is given by Equation (5.3)
iiii Aaba (5.3)
The two check points are x1 and x2. Since the value of the function
at x2 is greater than that at x1, the range is shifted to the right. x1 now becomes
x3. x2 becomes x1. A new value of x2 is generated using the Fibonacci search
formula as given in Equation (5.4)
92
3432 xx)n(F
)1n(Fxx (5.4)
where F (n) is the nth
Fibonacci number. From Equation (5.5) and Figure 5.2,
it is seen that the range is narrowed.
Figure 5.2 Fibonacci Search algorithm
iiii1i1i1i aAbaaba (5.5)
Now in the new range the value of the function at x1 is greater than
that at x2. Hence the range shifts to the left. x2 becomes x4 , x1 becomes x2.
The new value of x1 is given by the formula as given by Equation (5.6).
3441 xx)n(F
)1n(Fxx (5.6)
Here xi and F (xi) represent voltage and power respectively.
Initially two voltage values are generated. The power values at these voltages
are measured. They are compared and accordingly the range is shifted either
to the left or to the right. Another voltage value is generated and the process is
continued till the MPP is reached. The number of iterations and the voltage
93
values are decided with the help of Fibonacci numbers. Hence the names
Fibonacci search. The flowchart for Fibonacci search based GMPP tracking is
shown in Figure 5.3.
Algorithm
Step 1 : Initialize the variables.
Step 2 : Measure power.
Step 3 : If the power has changed from the previous settled
(previous MPP) and if the power difference is greater
than the power ripple, then sudden irradiance change
is said to have occurred and hence goto step 4 else
goto step 3.
Step 4 : Two voltage values V1 and V2 are generated.
Step 5 : The power values P1 and P2 are measured.
Step 6 : If (P1>P2) then shift left else shift right.
Step 7 : A voltage value either new V1 or new V2 is generated
accordingly.
Step 8 : Power value is accordingly measured. The other
voltage remains the same.
Step 9 : Go to step 6
The original method proposed in literature (Miyatake et al 2004)
does not guarantee the GMPPT tracking under all positions of the initial
operating point. The proposed method can find GMPPT by doing wide range
search irrespective of the initial position of operating point. That is,
irrespective of the Global peak's position in the P-V characteristics, the
Fibonacci search algorithm tracks the Global peak thus making the solar panel
94
to operate at the voltage where it delivers the maximum power. Figure 5.4
indicates the GMPP tracking of Fibonacci search algorithm when it occurs at
different locations. M-file code for Improved Fibonacci search method is
given in Appendix A3.1.
Figure 5.3 Flow chart for Fibonacci Search algorithm
95
Figure 5.4 P-V characteristics with tracked MPP for different cases
5.5 DESIGN AND IMPLEMENTATION OF MPPT WITH
PROPOSED ALGORITHM
MPPT can be realized using different converter topologies. In this
work, boost converter is used due to its high efficiency. The MPPT design is
explained below. The DC voltage transfer function is given by Equation (5.9)
D1
1
V
V
s
o (5.9)
where Vo = Output voltage, Vs = Source voltage, D = Duty cycle
96
The critical values of the inductance and capacitance can be
calculated using the Equation (5.10) and Equation (5.11).
f2
DRD1L
2
b (5.10)
fR2
DCmin (5.11)
f = frequency 10 kHz. The inductance and capacitance are calculated as
L=100uH, C=220uF. The value of resistance used is 100
Fibonacci search algorithm implementation is done in embedded
MATLAB function block available in MATLAB. Most of the cases the
requirement of load voltage is greater than source voltage, because long series
strings in SPVA may result in more power loss under partial shaded
conditions. Hence the boost converter is used to match the source impedance
with the load impedance thus delivering maximum power to the load. Figure
5.5 shows the block diagram for implementing the improved Fibonacci search
algorithm with boost converter. The embedded function block provides the
reference voltage, which is in turn compared with the actual voltage at which
the solar panel is operating. The error signal is fed to the PI controller block
and the resultant signal is finally compared with the triangular wave to
produce gating signal to the switch. MATLAB-SIMULINK model for the
system is shown in Appendix A3.2. PI controller is tuned using Zeigler-
Nichol first method. The value of Kp is 0.005 and Ki is 20.
97
Figure 5.5 Block diagram of Fibonacci algorithm based MPPT method
The simulation results shown in Figure 5.6 are obtained when both
the panels receive uniform irradiance of 1000 W/m2 up to a time of 0.3 sec.
After 0.3 sec the input to the second panel is suddenly changed to 500 W/m2
whereas the first panel receives the same irradiance of 1000 W/m2 thus
indicating partial shaded condition. Step input is applied to simulate the
sudden irradiance changes. The results shown in Figure 5.7 are obtained when
both the panels receive uniform irradiance of 200 W/m2 up to a time of 0.3
sec after that the input to the second panel is changed to 800 W/m2
whereas
the first panel receives the same irradiance of 200 W/m2 thus indicating
partial shaded condition.
98
Figure 5.6 Input and output characteristics of the Boost converter
(Figure 5.5). Characteristics (a) – (f) show input current,
output current, input voltage, output voltage, input power
and output power of the converter when solar insolation
suddenly changes from 1000W/m2
to 500W/m2
after 0.3 sec
for the second panel only
99
Figure 5.7 Input and output characteristics of the Boost converter
(Figure 5.5). Characteristics (a) – (f) show input current,
output current, input voltage, output voltage, input power
and output power of the converter when solar insolation
suddenly changes from 200W/m2
to 800W/m2
after 0.3 sec
for the second panel only
100
5.6 HARDWARE IMPLEMENTATION OF PROPOSED
ALGORITHM FOR GMPP TRACKING
The schematic diagram of the proposed system is shown in Figure
5.8. In Direct Coupled system the solar panel is directly connected across the
load. The maximum power is not transferred to the load because the load and
the source resistances do not match. DC-DC converter (step up/step down)
serves the purpose of transferring maximum power from the SPV module to
the load. The DC-DC converter acts as an interface between the SPV module
and the load. n order to move the operating point of the solar panel to the
MPP, a closed loop system must be implemented to sense the voltage and
current. After sensing the two parameters, an algorithm must be implemented
to generate the error signal. The error signal in digital form is given to the
DAC (0808) which converts it to the corresponding analog signal. This signal
is then compared with a high frequency triangular wave of 10 kHz. The pulse
generated is given to the gate of the power semi conductor device (MOSFET-
IRF 460), thereby changing the duty cycle of the converter. This generated
pulse must be able to trigger the MOSFET of the power circuit. Thus the
source impedance is matched with the load impedance and maximum power
is transferred. The hardware set up of the proposed system is shown in Figure
5.9. The hardware results are shown in Figure 5.10 without shading, that is,
two panels in series receive same illumination. The same for shaded
conditions are shown in Figure 5.11. In Figure 5.10 and Figure 5.11, the
waveforms are traced using single phase clamp on power quality analyzer to
measure the input and output powers directly. In this display, the values in
watts and VA are the rounded-off values by the meter. Figure 5.12 shows the
pulses produced by PIC microcontroller before and after shading are
introduced.
101
Figure 5.8 Hardware Schematic of the proposed MPPT system
Figure 5.9 Hardware set-up of the MPPT system
SPV Panel boardStep down circuit for PIC controller
PIC controllerDAC,
Comparator,Op-amp, optocoupler Boost
Regulator
Power supplycircuit
103
Figure 5.11 I-V characteristics of two panels connected in series with
partial shading
Input
Output
104
Figure 5.12 CRO screens showing gate pulse and output voltage before
and after tracking
The results for other shading patterns are tabulated in Table 5.1.
The values in % indicate the % of ripple content. From the tabular column it
can observed that the ripple percentage in most of the cases lies below 1%
Table 5.1 Results for different shading patterns
G1
(W/m2)
G2
(W/m2)
VSPV
(V)
ISPV
(A)
PSPV
(W)
Vo
(V)
Io
(A)
Po
(W)
1000 80035
(0.8%)
1.76
(0.8%)
62.1
(0.7%)
77.5
(0.4%)
0.78
(0.8%)
60.1
(0.9%)
1000 50035
(0.9%)
1.12
(0.7%)
39.25
(0.5%)
61.6
(0.3%)
0.62
(0.6%)
38
(0.8%)
800 20017.48
(2.2%)
1.43
(0.9%)
24.92
(0.2%)
49.19
(0.4%)
0.49
(0.2%)
24.2
(0.8%)
500 50033.28
(0.9%)
1.03
(0.4%)
34.28
(0.4%)
57.58
(0.3%)
0.58
(0.3%)
33.15
(0.8%)
1000 30017.84
(2.8%)
1.72
(0.1%)
32.5
(0.3%)
54.98
(0.4%)
0.6
(0.1%)
30.12
(0.1%)
105
5.7 CONCLUSION
Since the efficiency of the solar panel is only 13%, it is necessary
to operate it at its maximum power point. If the solar panel operates at a point
other than the point where it delivers maximum power, the power transferred
to the load can be as low as 70% of the maximum value. Hence it is necessary
to the track the GMPP under partial shaded conditions. In this chapter, the
Fibonacci search algorithm has been discussed to track the GMPP under
partial shaded conditions. It is proved that the Fibonacci search algorithm
tracks the GMPP when multiple peaks exist in the P-V characteristics using
MATLAB software and hardware. The GMPP tracking algorithm can be
further improved by using intelligent optimization techniques. These
improvements are discussed in Chapter 6 and Chapter 7.
top related