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190 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

In Eq. (5.43) the sets J and T may also be empty. Eq. (5.43) represents the core of
FEMPV algorithm suited for buck-based LSCPVUs.

3.2.2 Distributed Maximum Power Point Tracking and Central Maximum
Power Point Tracking Based on Fast Estimate of Maximum Power
Voltages
In this section, it will be explained how the DMPPT control technique and the
CMPPT control technique can be jointly used and optimized by means of the knowl-
edge of the approximate PeV characteristic of the string of LSCPVUs. Without any
loss of generality, the discussion will refer to the case of boost-based LSCPVUs. The
extension to the case of buckeboost and buck-based LSCPVUs is straightforward.
As discussed in the previous section, once I SCk (k ¼ 1, 2, ., N) is known, the
approximate PeV characteristic of the string of LSCPVUs is easily obtained. So
that, I SCk (k ¼ 1, 2, ., N) needs to be measured. In the following, it will be assumed
that the measurement of I SCk (k ¼ 1, 2, ., N) takes place synchronously for all the
N LSCPVUs. Such a measurement is periodic, with period T m . The duration of the
measurement process will be indicated with Dt (measurement interval). Of course, it
is T m > Dt. During Dt, all the LSCPVUs are forced to work at a duty-cycle nearly
equal to one, because in boost converters this corresponds to short circuit conditions
at the input. The value of Dt must be high enough to allow the k-th LSCPVU (k ¼ 1,
2, ., N) to reach the steady-state corresponding to a nearly unit duty-cycle. Never-
theless, the value of Dt must not be higher than strictly necessary, because of course,
during the measurement interval, the MPP is not tracked. During Dt, because all the
LSCPVUs are forced to work at a duty-cycle nearly equal to one, the currents I pank
are nearly equal to I SCk (k ¼ 1, 2, ., N). Therefore, if the input currents of the
LSCPVUs are measured, it is possible to evaluate the approximate PeV equivalent
characteristic of the string of LSCPVUs and hence the corresponding R b can be
easily estimated in closed form. Each evaluation interval must be followed by a
period of time, indicated with T t :T m ¼ Dt þ T t . During T t , the controller of the
inverter (the CMPPT controller of Fig. 5.2) initially sets the reference voltage for
v b equal to V h (which is the mid-point of R b ) and then refines the operating value
of v b by means of a proper hill-climbing technique. During T t , also every LSCPVU
controller (the DMPPT controllers in Fig. 5.1) initially sets the reference signal v pan
refk for its input operating voltage equal to the nearly optimal value v pk , which can be
evaluated as explained in the following, and successively refines such a voltage by
means of a proper hill-climbing technique. The hill-climbingebased refinement
phases for v b and v pank are adopted to compensate for the small, unavoidable errors
associated to both the numerical and the theoretical approximations, which have
been adopted (e.g., the approximations of the IeV and PeV characteristics, the
assumption of lossless DC/DC power stages, the assumption of a unit MPPT accu-
racy etc.). The choice of T m must be made on the basis of a reasonable compromise
between speed of tracking and energetic efficiency. In fact, the lower T m , the higher
the rate of change of irradiance variation which can be tracked [1] and, at the same
time, the higher the amount of available energy that is wasted because of the