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Overview of PV Maximum Power Point Tracking Techniques 103

is compensated by employing a suitable model of the power converter, but the complexity of the
control unit would also be increased in such case.

5.3.7 MPPT Methods Based on Numerical Optimization Algorithms

A simple approach for deriving the position of a PV source MPP is to apply an exhaustive search process,
where the entire power–voltage characteristic is sequentially scanned. By measuring and comparing the
power production levels at the individual operating points that the PV source is set to operate at during
the power–voltage curve scanning, the MPP position can be detected. Since this process requires a large
number of search steps to be executed, which results in power loss until the tracking process has been
accomplished, various MPPT algorithms based on numerical optimization techniques have been applied
in order to detect the position of the MPP on the power–voltage curve of the PV array with reduced
search steps.
A golden section search algorithm has been employed in [45], where the MPPT process is per-
formed by iteratively narrowing the range of the PV output voltage values where the MPP resides. For

each search range V min , V max  (initially it holds that V min = 0 and V max = V oc ), the output power of the PV


source is measured at two operating points of the PV source, where the values of the PV source output
voltage (i.e., parameter V pv in Figures 5.1, 5.2, and 5.5b), V pv,1 and V pv,2 , respectively, are given by
r V max −
V pv,1 = V max − ⋅( V min) (5.12)
r V max −
V pv,2 = V min + ⋅( V min) (5.13)


where r = 0 618 so that V pv,1 , V pv,2 are placed symmetrically within V min , V max  and, also, V pv,2 is
.


placed at a position where the ratio of its distances from V pv,1 and V max , respectively, is equal to the
ratio of distances of V pv,1 from V min and V max , respectively.
Then, the PV module/array output power is measured at V pv,1 and V pv,2 . If the output power at V pv,1
is higher than that at V pv,2 , then it is set that V max = V pv,2 , or else it is set that V min = V pv,1 . This process
is repeated until the distance between V min and V max is smaller than a predefined value.
In [46], a multistage MPPT process is presented, which comprises a combination of the P&O,
golden section search, and InC algorithms. A flowchart of this process, which is based on the
method proposed in [46], is depicted in Figure 5.9. Initially, the P&O algorithm is applied with
a large perturbation step in order to quickly converge close to the MPP. Then, the golden section
search algorithm is applied for accurately and quickly detecting the MPP, and finally, the InC
algorithm is executed for ensuring the operation at the MPP in steady state and for triggering the
initiation of a new search process in case that a large deviation from the MPP is detected (i.e.,
when ∂P pv / ∂V pv > ε, where ε is a preset threshold) due to changing environmental conditions.
An iterative approach, where the search window is progressively modified, is also performed in
the linear iteration algorithm presented in [47]. However, in that case, the new search range at each
iteration of the algorithm is calculated based on the power slope of the abscissa on the power–volt-
age characteristic of the point, which is defined as the intersection of the tangent lines at V min and
V max (i.e., point Q in Figure 5.10, which is based on the procedure proposed in [47]). If the gradient
at point Q is positive, then Q is set as the new lower limit of the search range, or else it will be the
upper limit.
In the parabolic prediction MPPT algorithm [48], the power–voltage curve of the PV source,
(
P pv( ), is approximated by a parabolic curve, Q V pv) (in Watt), which is given by
V pv
pv V )⋅(
(
V 0
2
1
V 2
V 1
Q V pv) = P pv ( ) ( V pv − )⋅( V pv − ) + P pv () ( V pv − )⋅( V ppv V− ) + P pv V ( ) ( V − 0 V pv V− )
2
V 0
V 1
∆ V ⋅∆ V 02 ∆ V ⋅∆ V 12 ∆ V ⋅∆ V 21
20
01
10
(5.14)