3.4 Analysis of the MPPT Performances in a Noisy Environment
3.4.3 ADC Quantization Error in the P&O Algorithm:
In order to show the way in which (3.94) is used, the contribution of the measure- ment errors uv, ui in the increase of the step amplitude of a digitally implemented
P&O MPPT algorithm is described. Table 3.2 gives the parameters of the PV field and of the boost converter used for evaluating the P&O step perturbation.
For an ideal noise-free system (uvo =ui=uv=uE=0), the use of (3.94) gives
Δx ≥ 0.0059 (3.95)
The uncertainty components are added one at the time so that the con- tribution of each one of them to the increase of Δx is shown. In the mea- surement stage the uncertainty due to the quantization errors introduced by the ADCs is accounted for. According to [35], some additional error sources should be accounted for, but the modeling of such terms is out of the scope
TAbLe 3.2
Parameters of the PV Field and of the Boost Converter
PV Array Values at 300 W/m2 and T = 35°C
MPP voltage VMPP 356 V
MPP current IMPP 2.22 A
MPP resistance RMPP 161 Ω
HMPP 1.157·10−4 A/V2
Coefficient of the photo-induced current Kph 83 mA·m2/W
PV Measurable Parameters Maximum Values
PV field current IPV,max 10 A
PV field voltage VPV,max 600 V
MPPT Design Parameters Nominal Values
Irradiance variation
G
100 W/m2/s
P&O time interval Tp 2 ms
Boost output voltage Vo= Go 600 V
135
MPPT Efficiency: Noise Sources and Methods for Reducing Their Effects
of this book. It is assumed that the uncertainty is directly related to the last significant bit (LSB) and to ADC voltage resolution, so that
= = 1 =
2
1 2 2
ui uv LSB VFSN (3.96)
where VFS is the full-scale input voltage and N is the number of bits of the
ADCs. Moreover, in order to map the PV voltage and current in the VFS
range, the Hv and Hi scaling factors must be chosen according to the follow-
ing equations: , , H V V H V I v FS PV max i FS PV max = = (3.97)
If N = 10 bits and VFS = 5 V are adopted, which are typical values for the
ADC parameters from Table 3.2, it results that 1 2 2 2.4 5 600 0.0083 5 10 0.5 ui uv V mV H H V A FS N v i = = = = = (3.98)
Such values are put in (3.94), so that the new value for Δx must fulfill the following constraint:
Δx ≥ 0.0157 (3.99)
which is almost three times greater than the value in noiseless conditions given in (3.95).
Of course this is the condition in which the quantization errors, intro- duced in the measurement process, produce a wrong decision in the MPPT algorithm with a probability almost zero. If a lower level of confidence in the P&O decision is accepted, Δx can be reduced progressively.
Alternatively, in order to improve the MPPT performances as much as possible, the optimal Δx can be reduced by using different ADCs. Table 3.3 shows the results for three ADCs characterized by different numbers of bits but with the same VFS. Based on (3.88), it is also possible to evaluate sepa-
rately the effect of uv and ui on the PV power estimation; this can be useful
for identifying the channel that is more sensible to quantization error. Table 3.3 shows clearly which is the minimum number of bits in the ADC that makes the quantization error negligible. It is worth noting that the uncertainty coming from the two measurement channels can be signifi- cantly different. Indeed, in Table 3.3, such a difference has been highlighted by showing the values of the power uncertainty due to the two channels
136 Power Electronics and Control Techniques for Maximum Energy Harvesting
separately. In particular, ΔPUiis the increase in the power variation due
to uncertainty on the measurement of the PV current (ui), and ΔPUvis the
increase in the power variation due to uncertainty on the measurement of the PV voltage (uv). The sensibility of the MPPT performances with respect to
quantization error is such a critical aspect that some manufacturers produce ADC with high resolution specifically designed for power monitoring in PV application [36]. Alternatively, digital processing combined with multiple sampling of PV variables can be used for increasing fictitiously the equiva- lent number of the ADC bit [37]. In conclusion, it is possible to state that the action concerning the minimization of uncertainty must be focused on the noise sources that influence more heavily the decision process of the MPPT. Equation (3.94) shows clearly this dependency for the P&O algorithm.
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