As was seen in Section 9.1.3, the performance of the solar cell depends on the cell temperature. This temperature can be determined by an energy balance and considering that the absorbed solar energy that is not converted to electricity is converted to heat, which is dissipated to the environment. Generally, when operating solar cells at elevated temperatures, their efficiency is lowered. In cases where this heat dissipation is not possible, as in building integrated photovoltaics and concentrating PV systems (see Section 9.7), the heat must be removed by some mechanical means, such as forced air circulation, or by a water heat exchanger in contact with the back side of the PV. In this case, the heat can be used to an advantage, as explained in Section 9.8; these systems are called hybrid photovoltaic/thermal (PV/T) systems. Because these systems offer a number of advantages, even normal roof-mounted PVs can be converted into hybrid PV/Ts.
The energy balance on a unit area of a PV module that is cooled by heat dissipation to ambient air is given by
For the (Ta) product, a value of 0.9 can be used without serious error (Duffie and Beckman, 2006). The heat loss coefficient, UL, includes losses by convection and radiation from the front and back of the PV to the ambient temperature, Ta.
By operating the load at the nominal operating cell temperature (NOCT) conditions (see Table 9.1) with no load, i.e., r|e = 0, Eq. (9.32) becomes
which can be used to determine the ratio
By substituting Eq. (9.34) into Eq. (9.32) and performing the necessary manipulations, the following relation can be obtained:
TC (TNOCT Ta,NOCT'
An empirical formula that can be used for the calculation of PV module temperature of polycrystalline silicon solar cells was presented by Lasnier and Ang (1"0). This is a function of the ambient temperature, Ta, and the incoming solar radiation, Gt, given by
When the temperature coefficient of the PV module is given, the following equation can be used to estimate the efficiency according to the cell temperature:
(3 = temperature coefficient (KT1). % = reference efficiency.
If, for a PV module operating at NOCT conditions, the cell temperature is 42°C, determine the cell temperature when this module operates at a location where Gt = 683 W/m2, V = 1 m/s, and Ta = 41°C and the module is operating at its maximum power point with an efficiency of 9.5%.
TC (TNOCT Ta,NOCT)
Using empirical Eq. (9.36),
TC = 30 + 0.0175(683 - 300) + 1.14(41 - 25) = 54.9°C
As can be seen, the empirical method is not as accurate but is almost as accurate.
It should be noted that, in Example 9.7, the module efficiency was given. If it was not given, then a trial-and-error solution needs to be applied. In this procedure, a value of module efficiency is assumed and TC is estimated using Eq. (9.35), provided that Io and Isc are known. Then, the value of TC is used to find Vmax with Eq. (9.14). Subsequently, Pmax and r|max are estimated with Eqs. (9.17) and (9.18), respectively. The initial guess value of re is then compared with rmax, and if there is a difference, iteration is used. Because the efficiency is strongly related to cell temperature, fast convergence is achieved.
9.5.4 Sizing of PV Systems
Once the load and absorbed solar radiation are known, the design of the PV system can be carried out, including the estimation of the required PV panels area and the selection of the other equipment, such as controllers and inverters. Detailed simulations of PV systems can be carried with the TRNSYS program (see Chapter 11, Section 11.5.1); however, usually a simple procedure needs to be followed to perform a preliminary sizing of the system. The simplicity of this preliminary design depends on the type of the application. For example, a situation in which a vaccine refrigerator is powered by the PV system and a possible failure of the system to supply the required energy will destroy the vaccines is much different than a home system delivering electricity to a television and some lamps. The energy delivered by a PV array, EPV, is given by epv = anegt
Gt = monthly average value of Gt, obtained from Eq. (2.97) by setting all parameters as monthly average values. A = area of the PV array (m2).
The energy of the array available to the load and battery, EA, is obtained from Eq. (9.38) by accounting for the array losses, LPV, and other power conditioning losses, LC:
Therefore, the array efficiency is defined as
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