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176 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

zero the DC value of such an error. The instants when the steps of v b ref occur will be
called sampling instants.Moreover, we will indicate with the symbols Dv b ref and T b ,
respectively, the amplitude and the duration of the steps of v b ref . The two parameters
Dv bref and T b need to be properly chosen to obtain the correct working of the
CMPPTS technique. Of course, the initial value V b min and the final value V b max
of v b ref must fall within the allowed inverter input voltage operating range. As
shown in Fig. 5.6, the waveform of v b ref is characterized by n different values:
v b max v b min
n ¼ 1 þ . After the occurrence of each step of v b ref , the control
Dv b ref
system waits for an interval of time equal to T b during which the PV system reaches
a new steady-state condition and, in particular, the voltage v b becomes nearly equal
to v b ref . As a consequence, before driving the new step of v b ref at the following sam-
pling instant, the CMPPTS controller is able to record the steady-state value of the
total power P extracted from the PV system: P ¼ v b $i b . In fact, the CMPPTS
controller has two inputs: v b and i b (see Fig. 5.2). In this way, the n steady-state
values of the powers extracted in correspondence of the n different levels assumed
by v b ref are recorded. After the whole scan from V b min to V b max , the CMPPTS
controller sets its output equal to V b opt , which is the level of v b ref in correspondence
of which the recorded value of P has assumed its maximum value. Of course, the
whole scan requires a total time T tot equal to n$T b . It is evident that only two param-
eters must be chosen to design the CMPPTS technique: the step amplitude Dv b ref
and the interval of time T b between two consecutive steps of v b ref . In the following,
the criteria for choosing two parameters are discussed. As concerns the value of Dv b
ref , it must be chosen on the basis of a reasonable compromise between two contrast-
ing requirements. The first requirement is strictly linked to the energy storage func-
tion carried out by the bulk capacitor C b placed at the interface between the string of
LSCPVUs and the inverter (see Fig. 5.2). It is well-known that the voltage v b across
C b undergoes an oscillation characterized by a frequency nearly equal to 2$f line ,
where f line is the grid frequency.
In fact, v b oscillates, that is, it increases or decreases, to allow the capacitor C b to
store or release the energy required for balancing the DC power extracted from the
LSCPVUs with the instantaneous power injected into the grid [45,53,54].As a
consequence of such an oscillation, at the end of the scan, the CMPPTS controller
may provide a wrong value of V b opt . In fact, during the scan, when v b ref is fixed
and assumes one among its n possible levels, said v a ¼ V b min þ k$Dv b ref (k ¼ 0,
1, .,n 1), the total steady-state power P extracted from the LSCPVUs is not nearly
constant in time but it is characterized by an oscillation at a frequency nearly equal
to 2$f line . Such a power oscillation acts as a sort of unavoidable and undesired, addi-
tional, local scan of the PeV characteristic, caused by the aforementioned oscilla-
tion of v b in a voltage region around v a . The peak to peak amplitude Dv b fline of
P
such an oscillation is equal to [45,53,55]: Dv b fline ¼ , where P is
C b $2p$f line $v a
the DC power injected into the grid. Therefore, to avoid errors of the CMPPTS
controller caused by the aforementioned oscillation of v b , errors which could