Environmental Engineering Reference
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the recombination term:
j s ( c s ) exp q ( V
jr s )
j = j ph ( c 0 ,c T )
j r ( c r ) exp q ( V
jr s )
jr s
2 kT
r p
To determine the fitted parameters, current-voltage curves ( I - V curves) at different
irradiance and temperature levels are required, which are not available for the majority
of modules on the market. Work has also been done on using nonlinear regressions
on dark I - V curve measurements at different temperature levels to determine all
parameters except the photocurrent, which has to be obtained from light measurements
(King et al. , 1996). Again the data is usually not available from the manufacturers.
If measured I - V curves are given at one or more irradiance and temperature levels,
INSEL provides a block for the determination of all parameters. The fitted algorithm
is based on linearizing the equation system for all measured current density-voltage
( j, V ) data point sets. This is achieved by setting the series resistance r s toafixed
value and then solve the overdetermined linear equation system with five unknowns.
A genetic algorithm is then used to vary the series resistance and solve the equation
system again, until the global minimum quadratic error between the measured and
simulated curve is obtained.
As an alternative, a new method was developed in Stuttgart to obtain analytically
six parameters for the one diode equation from the manufacturer's data sheet. In the
one-diode model, the diode factor α is now a free parameter, and there is only one
coefficient c s needed for the exponential term. To determine all six parameters, the
short-circuit current, the maximum power point (MPP) voltage and current, the open-
circuit voltage and the temperature coefficients for current and voltage are required.
The new feature in the implemented algebraic equations is the assumption that an
infinite shunt resistance is no longer required. INSEL now contains the one-diode
parameters for more than a thousand PV modules:
j ( c r ) exp q ( V
jr s )
jr s
j ph ( c 0 ,c T )
r p
The PV generator is operated with an MPP tracker, which varies the voltage on the
I - V curve until the product of current and voltage is maximized. The inverter is
modelled using the Schmidt-Sauer equation requiring only three partial load effi-
ciencies for the model parameter extraction (Schmidt and Sauer, 1996). The energy
dissipation is made up of the losses which are independent of input power (inter-
nal current supply and magnetization losses p own ), the losses in the semiconductor
switches v switch which are linearly dependent on the power output, and the ohm cable
losses r ohm which rise as the square of the AC performance. The inverter efficiency
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