Simplified methods for calculating the performance of solar power plants<br/>1 Principle of methods<br/>In the study of solar thermal conversion, we are led to focus on phenomena of threshold (start, transition between operating modes etc.) and nonlinearity of efficiency as a function of radiation. The solar resource is therefore characterized by the cumulative frequency curve. For collectors of a given type characterized by their optical factor  and thermal conductance U (see Section 8.2.2), control being set (values of the differential, mass flow), the amount of heat that we can recover, at best, only depends on the fluid inlet temperature (Ti) Figure 1: Energy available in Ajaccio, on a horizontal plane in January and July in collectors. We call it &quot;Energy available at temperature Ti &quot; and we denote it Q(Ti). The easiest way to calculate it is to admit that during each hour, the steady state corresponding to the average hourly radiation and the outdoor temperature is established: stop, steady pulse or steady operation without pump stop. It is a linear function of the surface of the CFC below the threshold. We call usable energy the area between the curve itself and the operating threshold. It can also be determined analytically based on CFC formulations, to provide usability curves presented below.<br/><br/>2 Usability curves<br/>If the reduced threshold value of a solar system is ys, solar energy available is given by: 1 g(ys) =  f(t) dt  (11.10)<br/><br/>ys It is thus possible to express g as: g(y) = g0(y)+A1g1(y)+A2g2(y)+A3g3(y)+A4g4(y)+A5g5(y)+A6g6(y)+A7g7(y)+A8g8(y) with g0 = 0.5 (1-y)2 (1-y) g1 =(2 y + 1) (1-y)2 (5/6)0.5 g2 = y2 (1-y)2 (105/2)0.5 g3 =(1-y)2 (1 + 2 y - 42 y2 + 84 y3) (1/10)0.5 g4 = y2 (1-y)2 (1 - 4 y + 4 y2) (1155/2)0.5 g5 = (1-y)2 (1 + 2 y - 207 y2 + 1404 y3 - 2970 y4 + 1980 y5) (13/420)0.5 g6 = y2 (1-y)2 (18 - 176 y + 605 y2 - 858 y3 + 429 y4) (35/4)0.5<br/><br/>R. Gicquel<br/><br/>June 2008<br/><br/><br/>2 g7 = (1-y)2 (1+2 y -627 y2 +8404 y3 -41470 y4 +94380 y5 -100100 y6 +40040 y7) /210 (595)0.5 g8 = y2(1-y)2(30-520 y +3445 y2 -11154 y3 +18837 y4 -15912 y5 +5304 y6) (10.45)0.5 This curve, known as usability (Figure 1), reads very easily: the daily energy available H on a horizontal plane in Ajaccio above threshold 200 W/m2, is equal to 4,500 Wh/m2 in July and 600 Wh/m2 in January. These values fall to 1,010 Wh/m2 for threshold 500 W/m2 in July and 0 in January. It is thus possible for different thresholds, to determine energy available during the year (Figure 2). The calculation of the collector output is done by multiplying this energy by optical factor , and subtracting heat losses, equal to the product of the difference (Ti - Tout) by U and the number of hours of operation. The threshold varying according to Tout, we must first determine the threshold value for each month, taking as value of the average outdoor temperature Tout the daytime one, as solar collectors do not operate at night. Knowing usability curves, it is possible to determine the energy available at the desired temperature Ti. This energy is indeed equal to the sum of several terms: · usable energy as given by curves of Figure 1, multiplied by the optical factor  of solar collectors; energy threshold, multiplied by the number of hours above the threshold and ; heat losses, counted negatively, multiplied by the number of hours above the threshold.<br/><br/>·<br/><br/>·<br/><br/>The first two terms Figure 2: Monthly energy use in Ajaccio, 60 °, depending on the threshold correspond to the whole irradiation received by the collectors, reduced by the optical factor, and the third to heat loss. It turns out that the sum of the two latter is nil, so that only the first has to be taken into account. In a solar power plant, all the power produced by thermal collectors is not converted into electricity, because of: · the need to store that energy when it is available, until the stored heat is sufficient so that the power plant operates stabilized, which implies some storage losses; · storage capacity, which is necessarily limited, so that at certain periods in summer, solar heat can be a surplus, which induces additional specific losses during this period. We can consider a storage effectiveness constant for the first of these terms, and depending on the radiation received and the storage volume for the second. Simplified methods being unable to calculate the influence of these losses, they often include correction terms based on hourly simulation software which allow them to be estimated with reasonable accuracy.<br/><br/>References<br/>ADNOT, J., BOURGES, B., CAMPANA, D., et GICQUEL, R. Utilisation des courbes de fréquences cumulées de l'irradiation solaire pour le calcul des installations solaires. In : Climatologie solaire. Ed. CNRS, Paris, 1979.<br/><br/><br/>3<br/>BOURGES B., European simplified methods for active solar system design, ISBN: 0792317165, Kluwer academic publishers, Dordrecht, The Netherlands, 1991. KLEIN, BECKMAN et DUFFIE, &quot;A design procedure for solar heating systems&quot; Solar Energy, vol. 18, p. 113, 1976. SWANSON et BOEHM, &quot;Calculation of long term solar collector heating system performance&quot; Solar Energy, vol. 19, p.129, 1977.