Page 113 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

100 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
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Although the InC and P&O MPPT methods are based on the same operating principle, the
former is implemented by using the individual measurements of the PV array output voltage and
current, thus not requiring the computation of the corresponding output power. A variation of the
InC algorithm, employing a dynamic adaptation of the step size during the tracking process, is
proposed in [32].
In [33], it is demonstrated through experimental testing that the P&O and InC MPPT methods
exhibit similar performance under both static and dynamic conditions.

5.3.4 Model-Based MPPT

The operation of model-based MPPT methods is based on measuring the PV module/array output
voltage and current at multiple operating points [34]. Using the resulting measurements, the
parameters I ph , I s , V T , and R s , respectively, of the single-diode model of the PV source, which has
been described in Section 5.2, are initially estimated (the shunt resistance R p is neglected). Then,
(5.1) is used to calculate the voltage and current of the PV source at the operating point, where the
derivative of power with respect to the voltage is equal to zero (i.e., MPP) by applying numerical
techniques (e.g., Newton–Raphson method). A similar approach has also been employed in [35],
where successive measurements of the PV module output voltage are iteratively applied in a sim-
plified empirical mathematical model of the PV module, until a convergence to the MPP has been
achieved.
In [36], analytical equations are derived, which enable to calculate the PV module current and
voltage at the MPP, as follows:

I m = I m − V m1 (5.7)
1
R p

V m = V m − I R s (5.8)
m
1
where

  I ph ⋅exp 1 ()  
V m1 = α T    − 1 (5.9)
nV W 

   I s   

and I m = I pv is the PV module current at the MPP, V m = V pv is the PV module voltage at the
MPP MPP
MPP, n is the number of PV cells connected in series within the PV module, α is the quality factor,
and W ⋅ () is the Lambert function.
In order to apply this method, the value of I ph is estimated from (5.1) using measurements of the
PV module output current and voltage at an operating point away from the open-circuit voltage.
When using this technique, the accuracy of predicting the MPP voltage and current is highly
affected by the accuracy of estimating the PV module temperature, which affects the values of V T
and I s applied in (5.1) and (5.9). Also, due to the complexity of the computations required for calcu-
lating the MPP voltage or current, a microcontroller or DSP unit is required for the implementation
of such an MPPT scheme, while additionally, the response speed of the MPP control algorithm is
relatively low. However, due to the elimination of oscillations around the MPP, the MPPT units of
this type achieve a better steady-state response and are mostly attractive in cases of continuously
changing solar irradiation conditions (e.g., solar-powered electric vehicles). Instead of solving a
set of equations in real time, a lookup table, which has been formed off-line, may also be used for
calculating the MPP voltage [37], but this method is also characterized by computational complexity
and requires knowledge of the operational characteristics of the PV source. In [38], the output of an