Page 206 - Advances in Renewable Energies and Power Technologies

3. Necessity of Joint Adoption of Distributed Maximum Power Point 179

to move their input operating voltage in the direction from zero to V MPP ,to increase
their output power. As a worst case, it is possible to assume that the starting and ending
input voltages of the N d LSCPVUs, respectively, are just V MPP and 0, while the start-
ing and ending input voltages of the N i LSCPVUs, respectively, are just 0 and V MPP .
Of course, the corresponding times T 1 and T 2 represent the worst-case (longest)
possible times needed by the aforementioned LSCPVUs to reach the new steady-
state condition associated with v b ¼ v a þ Dv bref . Moreover, it is worth noting that
the inverter itself is characterized by its own dynamics so that it needs a time T 3 to
change its input voltage v b from v a to v a þ Dv bref . In conclusion, the whole process
associated to the change from the steady-state condition associated to v b ¼ v a to the
steady-state condition associated to v b ¼ v a þ Dv bref needs, in the worst-case, a
time T tot equal to: T tot ¼ T 1 þ T 2 þ T 3 . Times T 1 ,T 2 ,and T 3 can be estimated as
it follows:
V MPP
T 1 ¼ T 2 ¼ $T a (5.17)
Dv pan ref
Instead, T 3 can be estimated as the settling time of the step response of the
v b ðsÞ T cv ðsÞ
closed-loop transfer function W(s) between v b and v bref :WðsÞ¼ ¼ ,
v bref ðsÞ 1þT cv ðsÞ
where T cv (s) is the loop gain of the inverter outer voltage feedback loop [45,46,53]:
K V 2
T cv ðsÞ¼ G cv ðsÞ$ $ RMS (5.18)
R s V b $s$C b
where G cv (s) is the transfer function of the inverter bulk voltage compensation
network of Fig. 5.2,V RMS is the RMS value of the grid voltage, V b is the nominal
value of the DC inverter input voltage (V b min < V b < V b max ), R s is the value of the
gain of the sensor of the current injected into the grid by the PV system, K is the gain
of the multiplier belonging to the inverter control circuitry. Once the closed-form
expression of T cv (s) is known, then the estimate of time T 3 can be carried out in
numeric form in Matlab or PSIM environment. As a consequence of the above dis-
cussion, it is evident that, to correctly perform the scan of the whole PeV character-
istic by correctly evaluating the steady-state values of the power obtained from the
string of LSCPVUs, without making under- or overestimation errors, which could
lead to a more or less consistent waste of available energy of the PV system, it
must be

T b T tot (5.19)
The capability of the well-designed CMPPTS technique to not be deceived in the
presence of multimodal shape of the PeV characteristic of N LSCPVUs represents
its main advantage. The other side of the medal is represented by the quite low speed
of tracking of the MPP of the PV system (the whole scan takes a time equal to n$T tot )
and by the fact that, during the scanning process, a more or less large part of the PV
available energy is lost. Of course, the repetition period of the CMPPTS technique
(T r ) must be greater than n$T tot :T r > n$T tot . The choice of T r must be made on the