Up to few years ago no guidelines about the benchmarking of different MPPT techniques were available, but only some indication about the rea- sonable speed of variation of the irradiance to be used in testing an MPPT technique was given. For example, in [40], the slope 30 W/m2/s is considered
a reference value. More recently, a standard for testing DC/AC inverters’ efficiency, the EN 50530, has been introduced, and a part of it is devoted to fix the conditions the MPPT algorithm must be subjected to for testing its performances. Steady-state and time-varying irradiation values and slopes are given, and some authors have published the results of their experi- mental analyses aimed at comparing the most famous MPPT approaches. For instance, in [41], the author assesses that the performances that can be obtained by the two most used algorithms, the P&O and the INC, are approx- imately the same. The fundamental role of the MPPT efficiency has not been recognized as the conversion efficiency is. In fact, many efforts are usually done by power electronics designers in order to increase the conversion effi- ciency of the power processing system. In addition to the classical peak effi- ciency value, the European efficiency (ηev) has been proposed as a measure of
82 Power Electronics and Control Techniques for Maximum Energy Harvesting
the performances of the conversion system at different power levels, which means at different irradiation levels along the day. The European efficiency is defined in (2.62) in order to give a weight to the conversion efficiencies in the beginning of the day and approaching sunset, so that a power processing system having a flat and high-efficiency profile has a high ηEU.
EU 0.03· 5% 0.06· 10% 0.13· 20% 0.10· 30% 0.48· 50% 0.20· 100%
η = η + η + η + η + η + η (2.62)
A similar formula has been also proposed by the Californian Energy Commission: The weights are different but the idea is the same.
CEC 0.00· 0.04· 0.0.05· 0.12· 0.21· 0.53· 0.05· 5% 10% 20% 30% 50% 75% 100% η = η + η + η + η + η + η + η (2.63)
Nevertheless, the in-depth studies concerning the MPPT efficiency and the factors affecting its value are very few in literature, essentially because of the difficulty in understanding that the efficiency of the PV system is almost the product of the MPPT efficiency and the conversion efficiency.
The MPPT efficiency is defined as follows:
P t dt P t dt MPPT t t MPP t t ( ) ( ) 1 2 1 2
∫
∫
η = (2.64)so that its value is unitary if the operating point remains in the MPP during the whole time interval going from t1 to t2. An approximation of the MPPT
efficiency can be easily obtained by assuming that the P-V curve of the PV array behaves like a parabola across the MPP (see Figure 2.33). This analysis
2 PMPP ∆P 1 ∆VPV ∆VPV 3 4 96 94 92 90 88 86 84 13 14 15 16 PV Voltage [ V ] PV P ower [ W] 17 18 19 Figure 2.33
83
Maximum Power Point Tracking
allows us to show what is the best steady-state condition that can be obtained by any perturbative MPPT approach. The first analysis is performed by sup- posing that there are operating points, with the one in the middle placed in the MPP and the side ones at the same power level, because of the parabolic approximation, on the ascending and descending sides of the P-V curve, respectively.
If the MPPT controller leaves the system working in each one of these points for Tp seconds, then the waveform of the power looks as depicted in
Figure 2.34.
The period of this waveform is 4·Tp, and due to the piecewise constant
waveform of the PV power, it is easy to determine the numerator of (2.64), so that the MPPT efficiency is
P P MPPT MPP 1 2· η = − (2.65)
where ΔP depends on the amplitude of the perturbation applied to imple- ment the perturbative MPPT method and on the PV array parameters and operating conditions.
If the steady-state operation consists of four points, two on one side and two on the other side of the MPP, under the same assumption of a parabolic P-V curve with the vertex in the MPP, it results that
P t P P P P MPPT T MPP MPP p ( ) 1 2· 6· 1 2 η = < > = − + (2.66) where the condition under analysis is shown in Figures 2.35 and 2.36.
Equations (2.65) and (2.66) reveal that the best condition in terms of MPPT efficiency is achieved when the steady state consists of three points, one in the MPP and two on its sides. The condition consisting of four points, and of course of more than four points, leads to a reduction of the MPPT effi- ciency and must be avoided as much as possible. In Section 2.4.2 the value of
PMPP – ∆P PMPP PMPP PMPP PMPP – ∆P P( t) 4 1 Tp Tp 2 Tp 3 Tp 4 1 Tp t PMPP – ∆P Figure 2.34
84 Power Electronics and Control Techniques for Maximum Energy Harvesting
the power drops ΔP used in the expressions above has been calculated as a function of the amplitude of the perturbation signal used in the perturbative MPPT approach and of the PV array parameters.
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