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
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 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 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
Performance Comparison two PV Modules
Data Sheet Parameters of Module A
Isc 2.5 A
Voc 21.8 V
Imp 2.3 A
Vmp 17.3 V
Power at S.T.C 40 W
Data Sheet Parameters of
Module B
Isc 2.5 A
Voc 21 V
Imp 2.18 A
Vmp 17 V
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
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 GopiPrincipal Engineer