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8/12/2019 10.1049-cp.2011.0109
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Novel Maximum Power Point Tracking with Classical Cascaded
Voltage and Current Loops for Photovoltaic Systems
M.Fazeli, P.Igic, P.Holland, R.P.Lewis, Z.Zhou
College of Engineering, Swansea University,Swansea SA2 8PP, UK, Email:[email protected]
Keywords: Maximum Power Point, Photovoltaic.
Abstract
Almost all of the Maximum Power Point Tracking (MPPT)
methods for photovoltaic (PV) systems are based on
searching algorithms. Searching algorithms require relativelycomplex control schemes and reduce the speed and accuracy
of the MPPT method. This paper proposes a novel MPPTmethod which aims to circumvent traditional searching
algorithms thus increasing the speed and accuracy of the
response to varying irradiation levels. The method will be
validated through MATLAB-SIMULINK simulations.
1 Introduction
The global environmental, financial and political issues
necessitate the use of renewable resources to meet the fast
growth in energy demand. Among renewable resources, PVsystems have received considerable attentions and it is
expected that the penetration of PV energy generation will
increase steadily to become a significant proportion of totalenergy generation. One major issue with PV systems is that
its current-voltage (iPV-vPV) characteristics and hence its
maximum power vary according to the irradiation level (S).For a given S, there is only one maximum power:Pmax=ioptvoptwhere, iopt and vopt are the unique optimum PV current andvoltage for a given S. In order to increase the efficiency of thePV systems it is necessary to track the maximum power point
(MPP) as quickly and accurately as possible for varying S. Totrack the MPP either iPVor vPVshould be controlled to ioptorvopt, respectively. However, the voltage control is preferredsince the voltage at MPP is approximately constant for
different S while the current variation is much wider [1].
There are many MPPT methods introduced in papers. Themost common methods are briefly reviewed in the next
subsection:
1.1Review of MPPT methods
ThePerturb and Observe (P&O) andHill Climbing methods,which are probably the most common methods, are twodifferent ways to apply the same fundamental principal [2]. In
Hill Climbing a perturbation is applied on the duty cycle of
the PV converter while in P&O the perturbation is directly
applied on the operating voltage of the PV array. In both
methods, if the perturbation causes an increase of the output
power, the perturbation will continue in the same directionand if the output power decreases, the next perturbation will
be in the opposite direction. This will continue until the MPP
is reached then the system will oscillate around the MPP. It is
possible to reduce the perturbation size as approaching the
MPP in order to reduce the system oscillation [3].
The incremental conductance (IncCond) method utilizes thefact that dP/dVof a PV array is zero at the MPP, positive onthe left of the MPP and negative on the right. Thus, it can be
shown that I/-I/V I/-I/Von the left of
I/-I/V on the right [2]. Therefore, thereference PV voltage Vdc
*can be adjusted towards vopt.
The main disadvantage of P&O, Hill Climbing and IncCond
is their relatively slow responses due to the fact that they arebased on some sort of searching algorithm.
The Fractional Open Circuit Voltage uses the approximation
of voptk1VOCwhere VOCis the open circuit voltage of the PVarray. The Fractional Short Circuit Current is based on theapproximation of iopt2ISC where ISC is the short circuitcurrent of the PV array. The fact that there will be
periodically interruption on power supply in order to measure
VOC and ISC is the main disadvantage of these two methods.Moreover, the approximations are not quite accurate [2, 4].
There are also some other methods using, for example, fuzzy
logic or neural network method, which are relatively complexand expensive to apply.
This paper proposes a new and simple MPPT method using a
lookup table. Although lookup tables can be considered as a
searching algorithm, the method is much faster and simpler
than P&O, Hill Climbing and IncCond. Moreover, the method
uses a simple DC/DC boost converter with classical cascaded
voltage and current loops which is relatively simple and
cheap. This method does not address the issue of partial
shading and the paper assumes a uniform irradiance.
However, as far as the authors are aware, there is no MPPT
method that can track the real maximum power in partial
shading situations without an additional algorithm. The
method proposed in this paper can be augmented with all the
methods explained in literature to address the partial shading
issue. Furthermore, due to the relatively simpler and cheaper
equipments required in this method, the method seems to be a
proper option for parallel-connected PV system which is a
good structure to minimise the effects of partial shading [5,
6].
2 Control scheme
The PV system studied in this paper and the proposed control
structure is shown in Figure 1. The PV array consists of NPparallel connected strings ofNSseries connected cells.
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Vout-VFWLookup Table
NS ~
Grid
vPV*
vPV
VFW
Vout
L RiPV iL
iC
NP
T
-PI
-
iPV
PI
iL* -
iL
-/ PWM
1
0 Diopt
vopt
iPV
DC/DC boost converter
DC/AC
C
1
2
3
4
PVV
Figure 1. Proposed control structure for the PV system
A MOSFET-based DC/DC boost converter is used to control
the DC-link voltage of the PV array vPV to vopt as S and/ortemperature T changes. The lookup provides the referencevoltage for the DC-link of the PV array. The output voltage ofthe DC/DC converter is kept constant by the DC/AC
converter which transfers the generated solar energy to the
grid. This section consists of three subsections. The first
briefly explains the PV model used in the paper, the second
discusses the lookup table and the last subsection explains thecontrol loops of the DC/DC converter. The simulation results
are provided in section 3.
2.1 PV module model
The mathematical model of PV array is described by (1) [7]:
1exp
S
dcrsPphPPV
kTAN
qvININi
(1)
where Irs is the reverse saturation current of a p-n junction(1.2 10
-7A), qis the unit electric charge (1.60210
-19C), kis
-23 J/K), T is the p-n junctiontemperature (Kelvin), A is the ideally factor (1.92) and Iph ,
which is the short circuit current of one string of the PV
panel, is a function of Tand S [7]:
rTscrph TTkIS
I
100
(2)
where Tr is the cell reference temperature (300 K), KT is
temperature coefficient (0.0017 A/K), Iscr is the short circuitcurrent of one PV cell at the reference temperature (8.03 A)
and Sis the solar irradiation level normalised to 1 kW/m2[7].
2.2 Choosing the reference DC-link voltage
Considering a PV array composing of NP=1500 and NS=176cells [7], the PPV-iPVcharacteristics of the PV array is shownin Figure 2. Figure 2 shows thatPmax790.77iopt, which means
that vopt an accurate enoughapproximation, especially for lower S, as shown in Figure 2.
y = 790.77x
0
2000
4000
6000
8000
10000
0 2 4 6 8 10 12 14
PV current (A)
PVpower(W)
S=0.1 kW/m^2
S=0.25 kW/m^2
S=0.5 kW/m^2
S=0.75 kW/m^2
S=1 kW/m^2
Figure 2.PPV-iPVcharacteristics for differentSand T=25
C
Figure 3 illustrates the vPV-iPVcharacteristics of the PV arrayand shows that:
dcibiaiv op top top top t 23
(3)
y = 0.1488x3- 4.3249x
2+ 47.163x + 600.89
0
100
200
300
400
500
600
700
800
900
1000
0 2 4 6 8 10 12 14PV current (A)
PVvoltage(V
S=0.1 S=0.25 S=0.5 S=0.75 S=1 kW/m^2
Figure 3. vPV-iPVcharacteristics for differentSand T=25
C
Assuming that the DC/DC converter controls vPV to voptveryquickly, ipv=ioptand hence, (3) can be rewritten as:
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dcibiaiv PVPVPVPV 23*
(4)
For a given solar array, the coefficients a,b,canddare also afunction of Tas shown in Figure 4.
630
680
730
780
830
880
0 2 4 6 8 10 12 14
PV optimum current (A)
PVoptimumvoltage(
T=15
T=30
T=45
T=60
Figure 4. vopt-ioptcharacteristics of PV array for different T(Celsius)
Figure 4 illustrates that as Tvaries, equation (4) also changes.However, as it can be seen, the variation of (4) is not
significant compared to that of the T. Therefore, it seems
accurate enough to store the coefficients of (4) for each 5-
10C. Obviously, interpolation can also be used to further
reduce the error. Knowing the vPV-iPVcharacteristics of a PVarray (which is usually provided by manufacturer), it is
possible to form (4) for different Tand sore it in the lookup
table. If the characteristics of the PV module is not provided
by the manufacturer, paper [8] proposes some adjustments in
order to match the mathematical model of PV array with thatof the practical one. The current paper assumes that the vPV-iPV characteristics of the PV module is available and uses
for a given T. The coefficients a,b,canddalso change asNSand/or NP change. It can be shown that NP has almost noeffect on voptand neither doesNSon iopt. Therefore, equations(5) and (6) can be used to adjust the lookup table for a new
number of parallel 'PN and series
'SN connected solar cells:
P
Pop top t
N
Nii
''
(5)
S
Sop top t
N
Nvv
''
(6)
Therefore, assuming that lookup table of the PV module
(NPNS) is available, there are two approaches to apply themethod for the PV array ofNP
NS
solar cells:
1. Is to make the new vPV-iPVcharacteristics in order toform the new lookup table.
2. Is to use the available lookup table and adjust the
measured current and voltage according to (5) and
(6), respectively.
In this paper the second approach will be used and validated
through MATLAB/SIMULINK simulation. Obviously, this
will also validate the first approach as well.
2.3 Control of DC/DC converter
The control scheme of the DC/DC converter consists of an
inner current control loop and an outer voltage loop as shown
in Figure 5.
Inner Current Loop
PI Controller Plant
-
PlantPI Controller
-
vPV* vPV
iPV
-
s
ask vv iL*
s
ask cc
iPV
iL-
ic
sC
1
RsL
1
Figure 5. Control diagram of the DC/DC boost converter
Inner current loop
The current loop controls the inductance current iL byregulating the duty cycle D of the MOSFET. Over oneswitching period of the converter, one can write (see Figure
1) [9]:
)(1234 FWou t VVDDVV
(7)
where VFWis the forward voltage of the diode and Voutis theoutput voltage of the DC/DC converter which is kept constant
by the DC/AC converter.Using and considering (7), one can write the
control plant as:
sLRsLR
VVDVI
VVDdt
diLRiv
FWou tPVL
FWou tL
LPV
0
(8)
Thus, as shown in Figure 1,Dwould be:
FWou t
PV
VV
VD
(9)
The duty cycle is then used to generate the PWM signal for
the MOSFET. As discussed in section 2.2, vPV is almostconstant around MPP. Therefore, in (9) an approximation of
vPV( PVV see Figure 1) will be quite sufficient. It is noted that
(9) is a compensation term and is used to reduce the transient
error, in fact the system can work without that.
Outer voltage loop
The voltage loop controls the voltage across the PV array.
The control plant is:
sCI
V
dt
dvCi
C
PV
PV
C
1
(10)
The voltage loop also provides the reference inductance
current for the current loop using :
LCPV iii (11)
It is noted that the bandwidth of the outer voltage loop must
be 5-10 times slower than that of the inner current loop.
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Figure 6. MPPT for step change solar irradiance: (a) PV output power depicted on PPV-iPVcharacteristics (b) PV output power vs time forS=0.1,0.25, 0.5, 0.75, 1kW/m2
3 Simulation results
Let consider a PV module consisting of NP=44 and NS=100solar cells. Assuming that the vPV-iPVcharacteristics of the PVmodule is known, equation (4) is formed for S=0.1, 0.3, 0.7and 1kW/m
2
336.40921.12747.4666.0 23* PVPVPVPV iiiv
(12)
Considering a PV array composing of 4 strings of parallelconnect PV module with each string has 15 series connected
PV modules, the total PV array has NP=176 and NS
=1500
solar cells. In order to adjust (12) for the PV array (using (5)
and (6)), the measured iPVis multiplied by 0.25(=44/176) andthe output vPV
*is multiplied by 15 (=1500/100). As discussed
in section 2.2, an alternative approach is to find the vPV-iPVcharacteristics of the total PV array (i.e.NS
NP
) and form (4)
for the new arrangement directly (i.e. Figure 3).
The system parameters are .The switching frequency of the boost converter is 50 kHz and
the bandwidth frequencies of the voltage and current loops
are 15Hz and 150Hz. In order to keep the system simpler, the
output capacitor, DC/AC converter and the grid is replaced bya DC voltage source (950v). This section considers two
scenarios: in the first scenario Svaries in step changes whilein the second a real measured Sis applied. The temperature isassumed constant at 30
C.
3.1 Step change in solar irradiance
Figure 6 illustrates the output power of the PV array when Sincreases in four steps from 0.1 to 1kW/m
2. Figure 6.a shows
that the PV output power follows the MPP quite precisely and
Figure 6.b illustrates that the PV output power follows the
MPP quite fast.
3.2 Real solar irradiance
In order to be able to simulate the system with real solar
irradiance for a long time (e.g. several hours), it is needed to
replace the DC/DC converter with its equivalent average
(non-switching) model to reduce the simulation time:
Average model of DC/DC converterIt can be shown that over one switching cycle, the average
current to the DC/AC converter isDiLand the average voltageacross the MOSFET from PV side is DVout (neglecting thediode forward voltage) [1, 9]:
Vout
vPV*
vPVVout
L RiPV iL
iC
-PI
-
iPV
PI
iL*
-iL
-/
1
0 D
C
1
2
3
4
PVV
DVout DiL
Figure 7. Large signal average model for DC/DC boost converter
Therefore, in Figure 7, which shows the average model for
the DC/DC boost converter, the MOSFET is replaced by a
variable DC voltage source of DVoutand the diode is replacedby a variable DC current source ofDiL(Dis the duty cycle ofthe converter)
hence its controllers are identical to the switching model.
Considering the same PV array as before, Figure 8 shows the
results with real solar irradiance variations. Figure 8-topshows the applied solar irradiance measured every second on
2/6/2011 at College of Engineering, Swansea University,Swansea, UK (at 51.6100 northern latitude and 3.9797
8/12/2019 10.1049-cp.2011.0109
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western longitude). The reading starts at 5:40AM and
continues for almost 6 hours.
Figure 8. MPPT for real solar irradiance. Top: Per second solar
irradiance measured on 2/6/2011 at College of Engineering, Swansea
University, reading starts at 5:40AM. Bottom: PV output power
depicted onPPV-iPVcharacteristics
Figure 8-bottom illustrates that the PV array output power
follows the MPP very precisely.
4 Discussions and Conclusions
The paper proposes a new, simple and yet robust MPPT
method for PV systems. The method is faster and itsapplication is cheaper than similar methods. It has been
shown that using the method, the PV output power will
follow the MPP for fast (step change) and normal (real
measured) variations of solar irradiance. The main drawback
of the method is its dependency on temperature measurement.
If the measured temperature is not accurate, it can cause someerror. However, it was discussed that the variation of vopt is
not significant (compared to that of temperature) and the error
can be reduced using interpolation techniques.
Although the method does not address the issue of partialshading, it can be augmented with all available methods to
mitigate the problem. Moreover, due to its simplicity, the
method is a proper choice for parallel connected PV arrayswhich minimise the effects of partial shading.
Applying the method experimentally will be investigated in
future publications.
Acknowledgment
The financial support of the EU Convergence Programme is
acknowledged for this project.
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