MOSFET-Based Modeling and Simulation of Photovoltaics Module
1
Rakeshkumar Mahto1, Payman Zarkesh-Ha1 and Olga Lavrova2
Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131,
USA
2
Sandia National Laboratories, Albuquerque, NM, 87114, USA
Abstract — Commonly, single-diode, double-diode or three-diode
models are used for modeling of PV cells. Since all of them have
an exponential term due to the presence of a diode, the
computing of output power and performance of PV module
becomes power intensive and hard to implement on an embedded
system. Also, due to the presence of the exponential term, there is
no closed form solution for IPV vs VPV (output current of PV cell
vs output voltage of a PV cell). We are presenting a PV module
modeling using N-channel MOSFET transistor that doesn’t have
an exponential term. Moreover, a quadratic equation based
solution is obtained that can be solved for calculating the load
current. Using the same technique PV module can be also be
modeled for various configuration.
Index Terms — diode, MOSFET, photovoltaic cells, threshold
voltage.
I. INTRODUCTION
With increasing demand for utilizing Photovoltaic (PV)
cells in various applications, reliable and accurate modeling
and characterization of PV modules is very important. The
modeling techniques come in very handy for designing and
modeling the maximum power point tracking (MPPT)
algorithms [1]-[2]. Additionally, the simulation and modeling
methods can also be used for studying the effects of partial
shading, mismatch, and for finding out the faults in the
performance of the entire PV module[3], [4]. Additionally,
PV cell modeling techniques are very useful in the field to
check the performance of PV module by comparing the
measured result and the computed result [5], [6]. Commonly,
single-diode, double-diode or three-diode models are used for
modeling of PV cells [9]–[12]. Since all of them have an
exponential term due to the presence of a diode, the
computing of output power and performance of PV module
becomes very power intensive and hard to implement on an
embedded system. Also, due to the presence of the
exponential term, there is no closed form solution for I PV
(output current of a PV cell) vs VPV (output voltage of a PV
cell).
In this paper, we are presenting a PV module modeling
using N-channel MOSFET transistor that doesn’t have an
exponential term. Hence, implementation of this model is
simpler and also consumes less power on an embedded system
for comparative analysis between measured and computed
result. Similar modeling of PV module using N-channel MOS
transistor was presented in [11]. However, such a modeling
technique is not suitable when the load is continuously
changing or configuration of PV module is changing on the
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field based on the load requirement [5]. To address this issue,
a bottom-up approach for building PV module from a single
PV cell modeling using MOSFET is desirable.
II. PV MODULE MODELING AND CHARACTERIZATION
For building the model of a PV module, we start from
building the model from a single PV cell. For making it
simpler, a single diode PV cell model is being used as shown
in Fig. 11a. The diode can be replaced by the N-channel
MOSFET such that gate terminal is shorted with the drain
terminal as shown in Fig. 11b. In this paper, we are using a
MOSFET transistor of 0.5µm ON-Semi technology node.
The current across the load, IPV is given by (1)
(1)
 V  I PV  RS 
I PV  I Ph  I D   PV

RP


 VPV AIPVV RS

t
ID  IS  e
 1




I ph 
G
GSTC
(2)
 Id
(3)
a)
b)
Fig. 1. PV cell modeling a) using 1-diode PV cell model b) Nchannel MOSFET based PV cell model
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The symbols used in (1), (2) and (3) are summarized as
follows: Iph is the photon current; ID is current across the diode
and is given by (2): Vpv voltage across the load; Rs is the
internal series resistance of PV cell; Rp is the internal shunt
resistance of an PV cell; Is is the diode saturation current; Vt
is the thermal voltage which is equal to 26mV, A is diode
quality factor, G is solar irradiation; GSTC is solar irradiation
at standard testing condition which is equal to 1000 W/m2, Id
is the dark current.
Once the diode is replaced by an N-channel MOSFET
operating in the saturation region, the current across the load
is given by:
 VPV  I PV  RS 

RP


(4)
 Vth  (1  VDS )
(5)
I PV  I Ph  I M  
where,
IM 
Kn W
2 L
V
DS
2
VDS  VPV  I PV  RS  Vn
(6)
In (4), (5) and (6), IM is the current across the N-channel
MOSFET; Kn is the process transconductance parameter, W
is the width of the channel in µm; L is the length of the
channel in µm, Vds is voltage between drain and source
terminal of N-channel MOSFET; Vth is the threshold voltage
of the N-channel MOSFET, λ is channel length modulation
effect, Vn is the voltage source connected to source terminal
to lowering the Vth of N-channel MOSFET. For
characteristics of the PV cell model shown in Fig. 1a and 1b
to be equal, the (2) and (5) have to be equal. Equating and
solving for the W/L term we get,
 VPV AIPVV RS 
t
2  Kn  Is   e
 1


W



2
L
V
DS
(7)
 Vth  (1  VDS )
For calculating the value of Vn, the following equation can
be used:
Vth  VthO  

2 F  Vn 
2 F

(8)
where, Vtho is the threshold voltage when source and body
are at same potential, γ is the body-effect coefficient
parameter
that is dependent on the technology, ΦF is the Fermi
potential and Vn is the voltage between the source and body
terminal.
For obtaining IPV vs VPV curve, all the known values have
to be substituted in Eqn. 4
b  b  4ac
2
I pv 
2a
K W  2
a  n   Rs
2  L
Where,
R
W 
b  1  K n   RS (VPV  Vn  Vth )  S
RP
L
c   I ph 
Kn  W
Vp
2

  VPV  Vn  Vth  
2  L
RP
(9)
(10)
(11)
(12)
Eqn. 9 is only valid if Vds >Vth ,otherwise, output current ,
IPV, can be calculated by considering current IM =0 in equation
(4) which is given below
I R  VPV
I PV  Ph P
(13)
RP  RS
Fig. 2. Cell decomposition to form a simple model to predict output voltage and current of a PV module of configuration Ns x Np =3 x2
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The scheme for building the module level characteristics
from a single N-channel MOSFET based PV cell is shown in
Fig. 2. A PV cell model is such that if they are connected in
an array then mathematically they can be treated as a single
PV cell as shown in Fig. 2 for NS(number of cells in series) x
NP (number of cells in parallel). To illustrate the cell
decomposition we are assuming NS x NP = 3 x 2 cells. Firstly,
in row decomposition the series PV cells are converted into
equaivalent PV cells. Later, using column decomposition
paralle PV cells can be translated into equivalent circuit. The
current IPV across the NS x NP PV cell module is given by,
V
I  RS 

( PV  PV
)


NS
NP
I PV  N P  I Ph  I M 

(14)
RP




IM 
K n W  VPV


I PV RS

 Vn  Vth 

2
(15)


2 L  NS
NP
The channel length modulation effect, λ is ignored in (15).
In (14), (15) it is assumed that all PV cells are identical in the
module and are operating at same temperature and receiving
the same intensity of light. IPV can be calculated in the same
way as was done in (9), (10), (11), (12), and (13).
III. SIMULATION RESULT AND DISCUSSION
We compared the spice simulation of the PV module
containing 1-diode based PV cells, N-channel MOSFET
based PV cells, with the mathematical model presented in this
paper for different Ns x Np as shown in Fig. 3. In the IPV vs
VPV characteristic curve, the solar irradiance, G is assumed to
be of 1000 W/m2 when the temperature, T= 25 °C.
Compared to other PV cell modeling techniques such as
single-diode, double diode or three diode based PV cell, that
are widely being used by researchers, the technique described
in this paper gives a closed form solution.
Fig. 3. I-V curve comparison between spice simulation with Nchannel MOSFET vs single diode PV module vs hand calculation
978-1-5090-2724-8/16/$31.00 ©2016 IEEE
Unlike diode based PV-cell modeling, where an iteration
technique is used for the IPV vs VPV characterization, the
technique presented in this paper gives IPV= (VPV, T, G, Ns,
Np). Additionally, due to quadratic nature of the mathematical
model presented in this paper, it can be easily implemented on
an embedded system for a fault detection and mitigation
system. Furthermore, with recent advancements in PV
manufacturing, where a monolithic MOSFET is embedded
with a PV cell, such a modeling technique is very useful for
characterization.
IV. CONCLUSION
In this paper, we proposed an N-channel MOSFET based
PV module modeling using cell decomposition technique
from individual PV cells. We also presented an easier
calculated closed form solution for the IPV vs VPV curve which
was previously not possible with the single, double or three
diode PV cell models.
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