Power calculations based on available test methodologies
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Collector instantaneous efficiency n is defined as a ratio between the useful heat Q delivered and the hemispherical irradiance Gcol on the collector aperture Aa, according to (Rabl, 1985):
The hemispherical radiation Gcol reaching the collector aperture plane, to which the collector instantaneous efficiency is referred to, is calculated by the summation of the different components of radiation, for a given beam radiation incident angle в, and the plane tilt angle P, according to (Rabl, 1985):
Gcol =Icos6 + D(1 + cose)/2 + Rg (1 - cosy?)/2 (2)
where the ground reflected component - Rg = pgG - depends both on the global radiation G reaching the horizontal (ground) plane and on the ground reflectivity (albedo) pg.
As known, in the steady-state efficiency test (EN 12975-2; section 6.1) the collector efficiency curve is described by four parameters (considering a glazed collector): the optical efficiency n0, a global heat loss coefficient ai and (in the second order approach) a temperature dependent coefficient for the
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global heat loss coefficient a2. The test includes also the measurement of incidence angle modifiers K(O) based on hemispherical irradiance, to be used in instantaneous power calculations.
In the quasi-dynamic efficiency test (EN 12975-2; section 6.3), the collector efficiency curve is described by five parameters (considering glazed collectors) and the incidence angle modifier values based on beam radiation. The five parameters are: the optical efficiency for beam radiation ц0Ь, the incidence angle modifier for diffuse radiation Kd, a global heat loss coefficient ci, a temperature dependent coefficient for the global heat loss coefficient c2 and a dynamic response coefficient c5 representing the effective heat capacity of the collector.
Besides the treatment of the dynamic response of the solar collector to temperature changes included in the quasi-dynamic test methodology, the major difference to the steady-state methodology lies in the decoupling of the radiation components, allowing the separation of effects affecting differently each of those components (e. g. optical effects, as referred by NEGST (2006) and Horta et al. (2008)).
According to EN 12975-2; section 6.1 the calculation of instantaneous collector power from steady - state efficiency curve parameters follows equation 3:
Qss = nAO PcoA - a, (f - Ta ) - a2 (Tf - Ta ) Aa
whereas the same calculation using dynamic test efficiency curve parameters follows equation 4 [EN 12975-2; section 6.3]:
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Horta et al. (2008) suggested a power correction methodology, applicable to power values determined after Eq.(3), accounting for the collector optical effects, affecting differently the radiation components which reach the absorber surface. According to this methodology, the power value is corrected using the following equation:
ss_______
1 - f (1 - KdfJ
where:
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is a diffuse radiation fraction to be suggested by the efficiency test laboratory after reference irradiation conditions for the collector test (Horta et al., 2008), and:
J Jні»,.в, )cos (O )sin (в )ів{ dOl
_п - л/
K = /2 /2_______________________
dif. h
J J cos(O )sin(O ')dOtdOl - П2 - П2
is a weighted average hemispherical incidence angle modifier (Carvalho et al, 2007), calculated after the longitudinal and transversal incident angle modifier (IAM) values measured in the steady state efficiency test. Since this correction applies to test results performed according to steady-state test method, the incidence angle modifier is based on hemispherical radiation.
