Page 125 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

112 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
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the duty cycle of the power converter or the reference voltage of the PI regulator, which controls the
power converter DC input voltage.
The evolutionary MPPT algorithms exhibit algorithmic complexity, thus necessitating the use of
microcontrollers or DSP units for their implementation. Also, since random numbers are employed
during the execution of the evolutionary MPPT algorithms, it cannot be mathematically guaranteed
that they will converge to the global MPP under any partial shading conditions.

5.4.3 MPPT Methods Based on Numerical Optimization Algorithms
These algorithms are employing numerical methods, which are suitable for deriving the maxi-
mum of an objective function, without requiring the calculation of derivatives of the objec-
tive function. Thus, due to their inherent computational simplicity, they can effectively be
implemented into a microcontroller or DSP device within the control unit of the PV energy
management system.
In the dividing rectangles (DIRECT) algorithm [69], individual intervals within the output volt-
age range of the PV source are iteratively explored for detecting the position of the global MPP.
Each such interval is divided into three subintervals of equal range. Among them, the potentially

,
optimal interval is defined as the jth interval α j b  for which there exists a value K > 0 satisfying
j 

the following inequalities for each value of i (i = 1,..., 3):
b j − α b i − α
P pv() + K j ≥ P pv () + K i (5.18)
c j
c i
2 2
b j − α
P pv() + K j ≥ P pv,max + ⋅ P pv,max (5.19)
ε
c j
2
where
c j , c i are the midpoints of intervals j and i , respectively
α i , b i are the end points of the ith interval
ε> 0 is a constant
P pv,max is the power at the currently detected MPP

Only potentially optimal intervals are selected for reapplying the same dividing process until
the global MPP is detected [70]. The DIRECT MPPT algorithm has the drawback of not being able
to guarantee that it will be able to achieve convergence to the global MPP with a fewer number of
steps than an exhaustive search procedure, which sweeps the entire power–voltage curve of the PV
source, under any partial shading conditions.
In [71], a sequence of Fibonacci search numbers (i.e., F 0 − F n ≥ 0) is produced for performing
,
n
the MPPT process under partial shading conditions as follows:
F 0 = 0
F 1 = 1 (5.20)

F n = F n 2 + F n 1 ( n ≥ 2)
−
−
In the ith iteration of the search process, the control signal of a boost-type DC/DC converter, con-
(
i
i
i
nected to the PV source, is adjusted to the values c 1 and c 2 c 1 < c 2) , which lie within the search interval
i
cc ( i 3 , c 4) . The distance α i between c 1 , c 3 and c 2 , c 4 and the distance b i between c 1 and c 2 are given by
i
i
i
i
i
i
i
α i = n F +1 , i b = n F (5.21)
α i+1 = n F , i b +1 = n F −1