Environmental Engineering Reference
In-Depth Information
(4.51)
With this, all parameters of the simple equivalent circuit are estimated.
However, this model can only provide a very rough correspondence with
measured characteristics. A diode factor higher than 1 ( m > 1) is used for a
non-ideal diode. The two independent parameters m and I S could be found
relatively easy using mathematical software such as Mathematica for a given
solar cell characteristic in the generating region. The simple equivalent circuit
with a real diode already provides a very good correspondence between
simulations and measurements.
The determination of the additional parameters R S and R P of the extended
one-diode solar cell model is more difficult. With higher numbers of independent
parameters, even professional mathematical programs reach their limits and the
best fit has to be determined iteratively. The initial values must be chosen
carefully for a good iteration convergence of the parameter estimation. However,
the estimation of initial values for R P and R S is relatively simple.
The parallel resistance R P can be estimated by the negative slope of the I-V
characteristic under short circuit conditions. The slope of the I-V characteristic
around or beyond the open circuit voltage provides the series resistance R S :
(4.52)
(4.53)
The parameters V Br , b and n for the negative diode breakdown operation can
be found analogously to the other parameters, when measured values at the
point of negative diode breakdown are used for parameter estimation.
E LECTRICAL D ESCRIPTION OF P HOTOVOLTAIC
M ODULES
Series connection of solar cells
Solar cells are normally not operated individually due to their low voltage. In
photovoltaic modules, cells are mostly connected in series. A connection of
these modules in series, parallel or series-parallel combinations builds up the
photovoltaic system.
Many modules are designed for operation with 12-V lead-acid
rechargeable batteries where a series connection of 32-40 silicon cells is
optimal. Modules for grid connection can have many more cells connected in
series in order to obtain higher voltages.
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