S = Solar radiation available on a horizontal surface (in Watt per ft2 or m2) A = Angle of incidence, between the sun's radiation and the normal to the PV surface Efficiency

Published solar cell efficiencies depend on the materials and manufacturing processes used. There is a correlation between conversion efficiency and the operating temperature of a solar cell. In general, efficiency decreases by about 0.5% for every 1.8°F (1°C) rise. For example, a solar cell with a 15% conversion efficiency at 77°F (25°C) degrades to 10% efficiency when the operating temperature is 95°F (35°C). This is why solar cells typically perform better in cooler climates (assuming similar levels of available solar radiation) than in very hot ones. This de-rating factor should be based on the actual cell temperature, which may be slightly higher than ambient temperature. In addition, the efficiency can degrade over time. For example, the guaranteed efficiency of one solar cell manufacturer drops from 90% of rated efficiency to 80% of rated efficiency after 12 years. The conversion efficiency may also be lower under conditions of relatively low irradiance.

The published efficiency may show both dc and ac output. For ac output, inverter losses must be included in the efficiency term or added to the performance equation as an additional efficiency term as shown in Equation 14-6.

Available Solar Radiation

Quantification of available solar radiation begins with the extraterrestrial radiation from the sun (outside the atmosphere). This quantity, known as the Solar Constant (Gsc), has been established empirically to be 428 Btuh/ft2 (1,353 W/m2) per hour. This value varies somewhat with sunspot activity and earth-sun distance, but the variation is negligible. Before the solar radiation can be utilized by a PV cell, however, it is degraded by atmospheric diffusion and cloud cover, which are much more significant and must be accounted for. Values for actual horizontal radiation can be obtained for many locations in various formats, e.g., hourly values, daily means, monthly averages.

Databases containing solar irradiation and insolation values are compiled and published by the National Oceanic and Atmospheric Association (NOAA), the National Renewable Energy Laboratory (NREL), the World Meteorological Organization, and others. Irradiation is the instantaneous quantity of solar radiation received on a surface. This is expressed in Watt per unit area (e.g., W per ft2 or m2). Insolation refers to the aver age amount of solar radiation received on a surface during the entire day. This is expressed in W-h or kWh per unit area (e.g., kWh per ft2 or m2). It is essentially the summation of the irradiation on an object throughout a day. The overall worldwide daily average on an optimally sited collector is 0.465 kWh/ft2 (5.01 kWh/m2). The databases can be accessed directly from these organizations, as well as from their Web sites. Because weather patterns vary, database values will be better indicators of long-term performance than for a particular day or month or year. Monthly variation in solar radiation actually received may vary by 30%, while yearly variation may be 10%.

Incidence Angle

The angle of incidence varies with season and time of day. Maximum solar radiation is received when the sun is directly overhead, so that the incidence angle is closest to 0 degrees and "cos A" in Equation 14-5 is unity. At a given time of day, this happens when solar altitude angles are highest, which means that radiation is highest in the summer and lowest in the winter. Available radiation also peaks at noon and decreases at earlier or later times as the sun altitude angle decreases. The computation for angle incidence involves the use of a complex geometric equation that takes into account the sun's declination angle (for seasonal variation), the solar hour angle (for time of day), the latitude of the site where the solar cell is located, and the tilt and azimuth angles of the collector, which can also vary if a tracking device is used. Various nomographs and tables are available in solar literature to aid the calculation of this parameter. Some sources combine both horizontal radiation and incidence angle calculations into one look-up table for radiation available for common collector configurations.

As an example, at 10:00 am on June 21, at 40 degrees N latitude, there is 80 W/ft2 (861 W/m2) of direct solar irradiation available. The solar cell proposed for use is a high-density semi-crystal type with a published conversion efficiency of 15%. The solar panel is tilted at 45 degrees and the temperature is 77°F (25°C). Using Equation 14-5, the estimated output is:

15% x 80 W/ft2 x cos (45°) = 8.5 W/ft2 (91.5 W/m2)

Thus, the output of a 2 ft (0.6 m) wide by 4 ft (1.3 m) long (8 ft2 or 0.74 m2) PV module under these conditions would be approximately 68 Watt. A summation for each hour is required to calculate the total daily electric output of the solar cell.

As an additional step in calculating the useful output, other system losses may need to be applied. If an inverter is used to convert dc power to ac, or batteries are used to store solar energy for re-release during nighttime or cloudy periods, then the cell output must be multiplied by these conversion efficiencies to get net useful output:

Net UsefuKW/ft2 or W/m2) = px rjinverter x ristomge (14-6) Output


P = PV output calculated from Eqn. 14-5

ninverter = Inverter efficiency (energy output/energy input)

nstorage = Battery efficiency (energy output/energy input)

Other factors that will degrade system performance and, therefore, merit consideration are shading from obstacles (and even one PV module on another) and electrical losses due to wiring, module mismatches, and inverter performance below rated levels. Latitude-specific sun charts can be plotted to predict how buildings, trees, hills, and other obstacles will affect the amount of sunlight falling upon the PV system at a particular location at discrete time intervals throughout the year. These data can be entered into computer simulations programs to better refine insolation prediction.

Consider the example of a carefully monitored 60 kW grid-connected PCV system at an office building in southern Sweden situated at 56.6°N and 14.1°E. The system consists of two parts: the larger is a roof installation with four rows of multi-crystalline silicon modules and the smaller is an installation with facade integrated amorphous silicon thin-film modules. There are 58 SMA inverters, each with a rated output of 0.85 kW at 125-250 Vin dc, that connect the system to the grid. Table 14-3 provides a comparison of the accumulated energy from the 4,069 ft2 (378 m2), 49.5 kW rated roof plant between October 1997 and December 2000 with the measured annual solar insolation.

From this and the other monitoring data taken, the overall performance ratio (PR) was determined to be 76% for the roof-mounted system. This PR represents the amount of actual power output achieved as a percentage of the maximum possible power output if the solar cells produced their rated power for the given amount of measured annual solar insolation. A PR of 100% means that the system would operate the entire period at standard test

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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