At the beginning of simulation procedure, there are daily meteorological data (solar irradiance G and ambient temperature Ta) and load profiles (AC power PL) obtained by proper models. For each month an average day, characterised by the functions G(t), Ta(t) and PL(t), is defined.

The expression of global irradiance G (W/m2), derived for clear days, involves the parameters: daily irradiation as monthly mean value Hd (kWh/m2), daylight hours hi, peak value Gmax and shape factor cg. It is the normalised ratio between the peak value Gmax and the mean value Gmean = Hd/hl. The value of cG, for the same Gmean, determines the shape of the waveform: if cG=1, the waveform is sinusoidal; if cG>1, i. e. Gmax is higher than the sinusoidal peak value, the waveform is sharp. Different values of cG, for the same Gmean, determine different values of cell temperature TPV and PV energy. Then, the module over-temperature ATPV(t) with respect to the ambient temperature Ta(t) is evaluated by a linear function of irradiance, where the proportionality factor is the thermal resistance Rth between PV modules and ambient.

Proper mathematical models are used for each component: the equivalent circuits of the PV modules, of the batteries depending on the SOC and of the inverter depending on the losses at open circuit and load conditions. The main output is the reliability index.

The I-U characteristics of a PV module are determined by a typical equivalent circuit of the solar cell. The parameters of the one-diode model are: ideal PV current generator Iph; reverse saturation current of the junction I0; quality factor of the junction m; shunt resistance Rsh and series resistance Rs. In this model, only the PV current and the reverse saturation current depend on G(t) and TPV(t):

where IscIstc and IoIstc are determined at Standard Test Conditions STC (G = 1000W/m2 with AM = 1.5, TpV=298K) and aT is the temperature coefficient of Isc, besides the band-gap Eg and the Boltzmann constant k. The parameters of the solar cell equivalent circuit are obtained at STC by the manufacturer l(U) characteristic of one module: in table 2 the open circuit voltage Uoc is reported rather than l0 which can be calculated in this condition by Uoc.

Concerning the battery model, already presented, it is necessary to note that SOC is determined by the actual current of battery lb, taking into account a charge-discharge efficiency ^b = 0.88 which decreases the charge storage. In presence of a voltage generator (battery), the operating point at DC frame is determined by the PV current during daylight and by the lamp load during the night: it is easy to compute PV energy EPV, load energy El and SOC, besides number of charge-discharge cycles Nc and corresponding LOLH. To achieve a good accuracy about the SOC evaluation, a time step of five minutes has been chosen.

This procedure has been applied to the previous PV system, oriented in South direction with a tilt angle of 45° as prescribed by manufacturer, at latitude of 45° N in northern Italy (yearly irradiation of 1500 kWh/m2). The main results are presented in table 3 for some months, clarifying that LOLH occur in January and December, but an important waste of PV energy occurs in summer because SOC rises many times up to unity. Fig. 5 shows daily simulation results and fig. 6 reports the monthly variation of SOC in December.

1. Conclusions

The application of the simulation to a commercial road lighting PV system highlights that: in December and January it is not able to supply the load for all the night; the LOLH is higher than 200 h with a corresponding reliability index of 95% through the year; moreover a waste of PV energy in summer is too remarkable.

A greater tilt angle (60° — 65°), by increasing the PV energy in winter and reducing the same in summer, would enhance the reliability index and decrease the waste of PV energy; a theoretic study towards this goal is in developing phase.

Therefore this simulation is a useful tool in order to verify the sizing choice of PV power and battery capacity, usually based on an energy balance in a mean month.

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