In order to determine the battery parameters for the following simulation, experimental tests in laboratory have been performed on a scaled PV system constituted by: a PV module of the same manufacturer with 25 Wp peak power; one battery of the previous system (12 V — 110 Ah); a charge regulator of the same model but with nominal voltage of 12 V; an energy saving lamp (7 W). The experimental procedure can be summarised as in the following.

Firstly, starting from the receiving conditions of battery, a complete discharge has been carried out to verify the switch off by the charge regulator at 11.1 V threshold (p = 30%). Initially SOC is lower than 100% and in this case open circuit voltage Ub0 ~ 13 V. The battery voltage and the lamp current have been measured by a data logger supplied by the grid. Thus an extrapolation to 14 V has been calculated on the basis of mean values of AU variations in the first 7 h during discharge: this evaluation has provided more than 80 h before the start of discharge. Furthermore, a grid black-out has prevented to record the measurements for 30 hours and a linear interpolation has been calculated with 3 hourly mean values of AU variations before and after black-out. Finally, after more than 200 h, the charge regulator has switched off at the prescribed threshold: globally a discharge time of more than 300 h at 0.5 A corresponds to an assessed capacity of 156 Ah. Fig. 2 reports the discharge test with extrapolated and interpolated data.

The current-voltage I-U characteristics of the batteries can be obtained by the transient charge of a suitable capacitor, for battery as generator, and by the transient discharge of the same capacitor, for battery as load. In such a way, during these charge or discharge, the battery does not modify SOC. It is worth noting that the parasitic inductance of wires, at closing of switch, prevents step variation in the exponential waveform of capacitive current (fig. 3 for battery as generator); moreover, the selected value of capacitance (e. g. 6.8 mF) must prevent a L-C resonance and too much energy storage in the electric field. Hence, vanishing time variable, on DC frame it is possible to draw the corresponding I-U curves. Then, a complete charge has been performed up to equalisation and the corresponding I-U curve has been obtained by the capacitor method. These two characteristics (fig. 4 for battery as generator), determined in the limit conditions during a cycle of discharge-charge (e. g. from p = 30% to 100%), can be used for obtaining the battery parameters involved in the following simulation procedure.

Fig. 2. The waveforms for the battery discharge.

6 8 Current (A)

12

14

10

Time (s) Fig. 3. The transient charge of capacitor by battery.

SHAPE * MERGEFORMAT

Fig. 4. The I-U characteristics of battery as generator by the capacitor method.

Fig. 4 shows also the equations of the straight lines which interpolate the experimental I-U curves: in particular the measuring uncertainties of the open circuit voltage and the internal resistances are about 2% and 8%, respectively. Thus, by these data (voltage Ubo, resistances as generator Rbd and as load Rbc) it is possible to calculate the battery parameters according to the following formulas for a 2 V element:

• Ub0 = Ubmin + ap where Ubmin is the open circuit voltage at p = 0;

• Rbd =——- where In is the nominal current corresponding to the ratio of capacity to

1n

discharge time of 10 h for battery as generator (discharge phase);

• Rbc = ^ + yp with 0.3 < p < 0.75 and Rbc = ^with 0.75 < p < 1 for battery as

In In

load (charge phase).

Finally, in table 1 the values of battery parameters, which are used in the system simulation, are reported.

Table 1 Ubmin (V) « (V) є (V) Л (V) P (V) У (V) 6 (V) 1.703 0.458 1.938 1.586 0.25 1.00 1.375