Annual electricity production from a P/V station

The calculation of the electricity production from a photovoltaic station begins with the collection of the available solar radiation data. Since the geographical variation of the available solar radiation is not very intensive (compared, for example, to the wind potential), solar radiation data can be gathered from meteorological stations or academic and research institutes and be used with adequate reliability. Characteristic solar radiation data are presented in table 1 for the town of Heraklion, Crete, Greece. These data can be used for a broader geographical territory around the measurements station’s location.

 

A graphical representation of the solar radiation data presented in table 1 is provided in figure 1.

 

Figure 1: Total monthly solar irradiation and ambient temperature annual variation for the town of Heraklion, Crete, Greece.

 

Given the monthly available solar radiation data, the power production calculation procedure will be presented below on a monthly calculation step. Obviously, the same methodology can be respectively applied with different calculation time steps, in case the solar radiation data are available with higher time discrimination.

The power production from a photovoltaic station is given by the following relationship:

where:

• P_P/V the final power production from the photovoltaic station
• c_P/V the photovoltaic station power coefficient
• P_P/Vnom the photovoltaic station nominal station.

From the above relationship it is revealed that the calculation of the photovoltaic station power production is subject to the calculation of photovoltaic station’s power coefficient c_P/V.

The photovoltaic station’s power coefficient is given by the following relationship:

where:

• G_t the averaged daily solar irradiance calculated for the whole 24 hour period (in W/m²)
• G_STC the solar irradiance for standard operating conditions, equal to 1kW/m²
• PR_t the photovoltaic station’s overall efficiency.

The solar irradiance is given by the following relationship:

where:

• Η_t the total daily solar irradiation (in kWh/m²)
• t_m the total monthly time duration (in h).

 The overall efficiency of the photovoltaic station is given by the following product:

where

• PR_OPT the efficiency expressing any optical losses (reflections, shading from neighboring obstacles, dust etc)
• PR_ΝΙΤ the efficiency expressing the non-coincidence of the photovoltaic cells’ operating point with the  maximum power point
• n_trans the efficiency expressing any electricity transportation losses through cables, switches, diodes etc
• PR_Τ the efficiency expressing any losses arisen when the photovoltaic cell’s temperature becomes higher than the cell’s standard operation conditions temperature of 25^οC.

The efficiency PR_T is given by the following relationship:

where:

• γ_mp=-0.0045K^-1 the thermal efficiency coefficient of silicon
• θ_STC=25^οC the standard operation conditions temperature
• θ_c,wa the photovoltaic cell’s monthly averaged temperature, which is given by the following relationship:

where:

• θ_a,D: the ambient monthly averaged temperature
• F: an empirical parameter, which is given by the relationship:

where:

• G_t,D: the monthly averaged solar irradiance, calculated exclusively for the daytime duration, given by the following relationship:

where:

• t_d: the averaged daytime duration for each month
• a_d=t_d/24h the daytime time percentage over the 24 hours period
• κ(w_SD): the thermal resistance regarding the thermal energy transfer from the solar radiation to the photovoltaic cell (in (m²∙K)/W), given by the relationship:

where:

• Τ₁=19.6^οC, Τ₂=11.5^οC, Δθ=3^οC and Β=-0.223(m/s)^-1 are empirical constants, for photovoltaic panels of c-Si with consecutive constructive layers of glass protective plate, c-Si cells and insulation layer of Tedlar
• w_SD: monthly averaged wind velocity m/s.

Except from PR_T, characteristic values for the rest efficiencies of a photovoltaic station are present below:

• PR_OPT = 0.96
• PR_NIT = 0.95
• η_trans = 0.95.

The power production from a photovoltaic station is calculation following the relationships presented previously. A step-by-step analytical example is provided in the following tables 2 for a photovoltaic station of 10kW nominal power installed in Heraklion, Crete, Greece.

 

 

 

The annual electricity production calculation is integrated with the presentation of the following diagrams:

Figure 2: Annual variation of the available solar irradiance.

 

Figure 3: Annual variation of the photovoltaic station’s efficiencies.

 

Figure 4: Annual variation of electricity and power production from the photovoltaic station.

 

In figure 3 it is observed that the photovoltaic station’s efficiency is maximized during the winter period. This is because the photovoltaic cell’s temperature approaches the standard operating conditions temperature of 25^οC, hence the efficiency PR_T increases.

Nevertheless, in figure 4 that the electricity and power production from the photovoltaic station are maximized during summer period, obviously due to the higher available solar radiation.