Modeling and Simulation of Photovoltaic Components of a
Solar Power System
Ajith Gopi
Parsons Brinckerhoff
• Parson Brinckerhoff
– >14,000 people
– 150 offices
– six continents
• PB Power Asia
– 500 people
– Most major Asian
cities
– Asia-Pacific region
since early 1990s
– Engineering Support
for solar and wind
power development
Recent Solar PV Modeling
Experiences
• LE’s Technical Advisor for
Multiple Solar PV Projects
in China (25.5MW)
• Technical Due Diligence
of PV Projects (20MW) in
Portugal for a client in
Korea
• LE for 25 MW Solar PV
project in Gujarat in India
Contents
PV Cell Model
The output current from the PV cell can be
found using the equation:
I=Isc-Id
(Where Isc is the short-circuit current that is
equal to the photon generated current, and Id is the
current shunted through the diode)
The diode current is given by the
Schottky diode equation:
Id= I0* (eq*Vd/(k*T) -1)
(Where Isc is the reverse saturation current of the
diode (A),
q is the electron charge (1.602 x 10-19C), Vd is the
voltage across the diode (V), k is the Boltzmann’s
constant (1.381x10-23 J/K) and T is the junction
temperature in Kelvin (K))
PV Cell Model (…continued)
Combining the diode current equation with the equation for the output
current of the PV cell creates:
I= Isc- I0* (eq*V/(k*T) -1)
(Where V is the voltage across the PV cell, and I is the output
current)
We can solve for the reverse saturation current (I0) by setting I=0 (no
output current).
I0=
Isc
(eq*Vd/(k*T) -1)
More accurate model of a PV Cell
Taking into account the series Resistance, Shunt Resistance and
Recombinations, the equation becomes:
I= Isc – I01 * (eq*V+I*Rs /(k*T) -1) – I02* (eq*V+I*Rs /(2*k*T) -1)- (V+I*Rs)/Rp
The two diodes can be combined to simplify the equation to:
I= Isc – I0 * (eq*V+I*Rs /(n* k*T) -1) - (V+I*Rs)/Rp
(Where n is known as the “ideality factor” and takes a value
between one and two)
Model of a PV Cell
The effect of the shunt resistance is minimal for a small number of
modules.
Therefore, we can assume Rp=∞
∞, simplifying the photon-generated
current equation to:
I= Isc – I0 * (eq*(V+I*Rs /(n*k*T)-1)
Simulink - PV Cell Model
PV Cell Model
I-V and Power Characteristics
Simulink Implementation of PV Module
PV Modules are implemented as Masked Subsystems in
Simulink in two Input modes
•
Current Input PV
Module
•
Voltage Input PV
Module
Model parameters for the Simulink
Model
Model parameters, in both cases, are
the standard PV module data-sheet
parameters:
• Short-circuit current Isc
• Open-circuit voltage Voc
• Rated current Ir at maximum power
point (MPP)
• Rated voltage Vr at MPP
(Under standard test conditions of
1kW/m2, 1.5 AM, 25oC).
Simulink Implementation of a Current
Input PV Module
Inputs:
• PV current Ipv [A]
• Insolation [W/m2]
Outputs:
• PV voltage Vpv [V]
• PV output power Ppv [W]
This model is well suited for the case
when modules are connected in series
and share the same current
Simulink PV Module Model
Simulink PV Module Model Sub System
with Current Input (Ipv)
Simulink Implementation of a Current
Input PV Module
Inputs:
• PV voltage Vpv [V]
• Insolation [W/m2]
Outputs:
• PV current Ipv [A]
• PV output power Ppv [W]
This model is well suited for the case when
modules are connected in parallel and share
the same voltage
PV Module Sub System with Voltage
Input (Vpv) (Suitable for Parallel Connections)
Simulink PV Module Model as a Software
Tool for Performance Analysis
PV Module Model – I-V and Power
Characteristics
Performance Comparison two PV
Modules
Data Sheet Parameters of
Module A
Data Sheet Parameters of
Module B
Isc
2.5 A
Isc
2.5 A
Voc
21.8 V
Voc
21 V
Imp
2.3 A
Imp
2.18 A
Vmp
17.3 V
Vmp
17 V
Power at S.T.C
40 W
Power at S.T.C 40 W
I V Characteristics comparison and
validating with PV Syst values
Fill Factor is
more for
Module A
since the
squareness of
the curves is
more for
Module A.
Hence
Module A is
more efficient
than Module B
Power Characteristics Comparison odf
Module A & B
Fill Factor is directly
proportional to the
Power output of the PV
Module
Hence it is evident that
output power of Module
A more compared to
Module B
Simulink – PV Array Model
(WITH SOLAR MODULE MODEL SUBSYSTEM BLOCK WITH CURRENT (Ipv) INPUT)
Conclusions
•
Photovoltaic components of a Solar Power System are
mathematically modelled and then simulated in Matlab/Simulink.
•
Simulink models are implemented for:
Solar Cell, PV Module (Current Input Model and Voltage Input Model)
& a typical Solar Array
•
Development of a Software tool for the PV Module Performance
Evaluation from the Module Data Sheet Parameters.
Any Questions?
Thank you for your attention!
Further information please contact:
Ajith Gopi
Principal Engineer
[email protected]