(4)Expressions of PV I-V
( )
1
1
1
1 1, 1,
31 1
1( )/
1
( )
1 / ( ) ( )( )
( )
1
1
g
c c
OC c s
c
S
c
ac c sc c nom sc c nom
a nom
qVn
nk T Tsc c cqV T N
cnkT
q V IRnkT S
SH
GI T T I T I TG
I T T eT
e
V IReR
+
= +
+
(4)
The model of the PV module was implemented using a
Matlab/Simulink Level 2 s-function. The model parameters are
evaluated during execution using the equations (1) ~ (4). There are
24 input parameters in the model. The model considers the series
resistance and shunt resistance, by set the input parameter TestRp
greater than 1, the influence of RSH is calculated. Because
equation (4) is non-linear, so it only can be solved using
numerical methods, the Newton-Raphson method was used in this paper
model. Symbols in equations refer to [6].
The I-V, P-V curves under various irradiance and constant
temperature calculated by Matlab/Simulink model show good
correspondence to the manufacturers published curves [6].
Figure 2. Equivalent circuit diagram of the PV model
III. MPPT METHODS SIMULATION USING PV MODEL IN
MATLAB/SIMULINK
A. IMPP/ISC Constant Method (CI Method) Like VMPP/VOCconstant at
MPP, IMPP/ISC at maximum
power point is also nearly constant; the curve shape is almost
smooth along with whole scope irradiation, the ratio of VMPP/VOC is
affected mainly by solar cell temperature (Fig. 3).
In this algorithm, if the ratio of IMPP/ISC is calculated or
tested at different temperature first, then the MPPT controller
need a temperature sensor to detect solar cell temperature to
realize a simple, speed and accurate MPPT.
In fact, temperature sensor is not necessary, the MPPT
controller periodically close a short-circuit switch to allow a
measurement of the PVs short circuit current, and considers the
ratio of IMPP/ISC is nearly constant. A problem with this algorithm
is that the available energy is wasted when the short-circuit
switch turns on, and at the same time power supply is
interrupted.
100 200 300 400 500 600 700 800 900 1000
IMPP
/ISC@
MPP
.90
.92
.94
.96
.98
1.00
1.02
2( / )Irradiation W m
20cT C=
5cT C=
25cT C= 10cT C=
40cT C=
Figure 3. IMPP/ISC at MPP versus irradiation curve calculated by
model
B. dP/dV Versus I Control Method The P&O method measures the
increment of power (P)
and the increment of voltage (V) to judge the momentary
operating region, it has some limitations.
The present study indicts that the PV generators derivative of
power versus voltage (dP/dV) in relation to V and in relation to I.
dP/dV versus V is found to be nonlinear, so that the change of
reference voltage is difficult to compute. On the other hand, dP/dV
versus I can be proved theoretically to be nearly linear, so that
the change of current is easy to compute.
If does not consider the influence of series resistance RS and
shunt resistance RSH, equation (4) can be simplified as:
1CqV
nkTPH satI I I e
= (5)
Isat is the diode saturation current in PV model (Fig. 2). From
equation (5), V can be written as:
lnC PH satsat
nkT I I IVq I
+ = (6)
The output power of PV generator is expressed as:
1CqV
nkTPH satP V I V I I e
= = (7)
From equation (6), the differential of I to V can be expressed
as:
( )PH satC
dI q I I IdV nkT
= + (8)
From equation (7), the differential of P to V can be written
as:
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( )
( )
( )
1
PH satC
PH satC C
dP d VI dII VdV dV dV
qI V I I InkT
q qV I I I VnkT nkT
= = +
= + +
= + + (9) If defined C1 as:
1 1C
qC VnkT
= + (10)
C2 as:
( )2 PH satC
qC I I VnkT
= + (11)
Then Equation (9) can be simplified as:
1 2dP C I CdV
= (12)
In the process of MPPT, to avoid the system operating in the
collapse region, the PV generator is always operated in the
negative slope region of the characteristic P versus V curve [8].
In this region, the PV generator voltage variation is small (see
right region in Fig. 1), and can almost be considered as constant.
So C1 is only affected by solar cell temperature, C2 is mainly
affected by irradiation (Isat usually is very small compared to
IPH). If TC is constant, dP/dV versus I is nearly linear, and the
curve of dP/dV versus I is affected by irradiation.
Fig. 4 is the curve of dP/dV versus current calculated by model.
From this figure, the relation of dP/dV versus I is nearly linear,
just like equation (12).
Thus, because of the relation of dP/dV versus I is nearly
linear, so that the reference current command Iref is easily
acquired by computing the relative variation of dP/dV versus I.
That means, when I is varied, dP/dV is varied proportionally, so
that the tracking process with linearly increasing or decreasing
Iref is rapid and smooth. By using dP/dV as an index to control
output current of PV generator, the proposed MPPT controller allows
a PV energy conversion system to track maximum power points very
rapidly and smoothly.
C. P-V Curve Simulation and MPPT Methods under Partial Shaded
Conditions Shadows created by clouds, neighboring buildings,
trees,
aging cells, pollution areas on the surface of solar cell etc
change the shape of PV modules power-voltage curve. In order to
obtain the P-V curves under partial shading conditions, series
connection and parallel connection are stimulated (Fig. 5).
From Fig. 6, the shape of parallel P-V curve under partial
shading condition is very similar to the shape of P-V curve under
normal condition: the power has one maximum point along with full
range voltage. So the MPPT methods suitable under normal condition
are also suitable under partial shading condition.
Current(A)0 1 2 3 4 5 6 7 8 9
dP/d
V
-23
-18
-13
-8
-3
2
7
21000 /G W m=
2800 /G W m=
2600 /G W m=
2400 /G W m=
2200 /G W m=
25cT C=
Figure 4. dP/dV versus current curve calculated by model
Figure 5. Simulation circuit under partial shading
conditions
Voltage(V)0 5 10 15 20 25 30
Pow
er(W
)
0
60
120
180
240
300
360
2 21 1000 / (25 ) Parallel 1 1000 / (25 )W m C W m C 2 21 1000 /
(25 ) Parallel 1 500 / (10 )W m C W m C
2 21 500 / (10 ) Parallel 1 500 / (10 )W m C W m C
Figure 6. Parallel P-V curve under partial shading
conditions
calculated by model In Fig. 7, solar cell temperature is 25, one
solar cells
irradiation is 1000W/m2, and another solar cells irradiation is
200W/m2, the peak value of power in right side is smaller than the
left one, so conventional MPPT methods may not be suitable. If more
PV modules series and more complex
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shading conditions, multi-local maximum power points will appear
in the P-V curve. Because of the shading conditions are
uncontrollable, so conventional MPPT methods cant converge to the
real maximum power point normally under these conditions.
Voltage(V)0 10 20 30 40 50 60
Pow
er(W
)
0
60
120
180
240
300
360
2 21 1000 / (25 ) Series 1 1000 / (25 )W m C W m C 2 21 1000 /
(25 ) Series 1 200 / (25 )W m C W m C
2 21 200 / (25 ) Series 1 200 / (25 )W m C W m C
Figure 7. Two SPG1786T-02E PV modules with different
irradiation
series P-V curve calculated by model Some MPPT methods have been
developed to find MPP in
partially shaded conditions, and they may be divided into two
kinds of types: (1) Hardware methods [9]-[11]. In these types, each
PV panel in PV generator has a parallel power repair unit, when the
PV panel is shaded, the power repair unit can supply compensation
current, this makes the P-V curve of the PV generator has only one
peak value along with whole scope voltage, so conventional MPPT
methods can be used. (2) Software methods. In these types, the P-V
curve of PV generator has multi-local maximum points, soft control
method is used.
Software methods can be divided into following types: (1)Current
sweeping method [12]; (2)Short-circuit current pulse method [13];
(3)Fibonacci search method [14]. This method gives fast
response, and it is able to handle multi-local maximum points,
but it requires powerful digital microcontroller to calculate the
process;
(4)State-based space approach [15]; (5)Compound MPPT methods
combined with conventional
MPPT methods [16].
IV. CONCLUSIONS MPPT methods are very important for PV
generator, many
papers have been reported various MPPT control techniques, most
of them are brought forwards and verified by experiments. In this
paper, a versatile, accurate Matlab/Simulink PV model suitable for
use by power electronics specialists has been developed, and has
been designed for easy implementation on Matlab/Simulink platform.
By using the model, several MPPT methods are verified, the
simulations results show good correspondence to the results of
theoretic analysis.
Most of MPPT methods are based on hill-climbing algorithms, but
the method cant work correctly if some panels of PV generator are
partially shaded. This paper gives a simple
overview of MPPT methods suitable for partially shaded PV
generator, and the P-V characteristics of PV generator under
partial shading conditions are simulated by model, MPPT methods
under partial shading conditions will be examined in later
research.
ACKNOWLEDGMENT This research was partly supported by the
Ministry of
Education, Science, Sports and Culture of Japan, Private
University Scientific Study Advancement Promotion Work in 2006,
Social Cooperation Promotion Work, Development of New Electric
Power Supply System by Micro-grid Network.
Authors would like to greatly appreciate for this grant
program.
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