Dear all,
In calculating the geometric factor (R_b) for direct normal irradiation (DNI) at hour angles near sunrise and sunhour, I face with unrealistic extremely high values for R_b. This can be attributed to the definition of R_b (i.e., cos(theta)/cos(theta_z)) where theta is incidence angle and theta_z is the zenith angle. Near sunrise or sunset, theta or theta_z are near 90 degrees leading to extreme values for R_b. Two questions arise:
Q1: How can we handle this issue? Which strategy do you prefer:
-Setting arbitrary values for R_b near sunset or sunrise? like R_b=1, 2, or 3?
or - Using the average integraled values between specified hours and w_s (sunset or sunhour) as defined by Duffie & Beckmann; ``Solar Engineering of Thermal Processes; Fifth edition``, page 88; R_b=a/b; where a and b are functions of w1,w2.
Q2: Which condition limit should be set for R_b calculations for inclined PV surfaces:
- R_b=0 for theta>90 deg
or - R_b=0 for theta_z>90 deg
or - R_b=0 for absolute(w)>absolute(w_s); w is hour angle and w_s is sunset or sunrise hour angle.
or - All of the above mentioned conditions simultaneously?
Thank you.
Dear friend Misagh Irandoostshahrestani
Ah, my friend Misagh Irandoostshahrestani, grappling with the intricacies of direct normal irradiation! I have some thoughts, and I am ready to share them.
**Q1:** Dealing with those pesky extreme values near sunrise or sunset, eh? Now, arbitrary values might seem like a quick fix, but I would lean towards the wisdom of Duffie & Beckmann. Using the average integrated values between specified hours and w_s sounds more sophisticated. It's like sipping a fine wine instead of chugging a soda. Elegant solutions, my friend Misagh Irandoostshahrestani.
**Q2:** Conditions, conditions! For inclined PV surfaces, I say let's not go too extreme. Setting R_b = 0 for theta > 90^degree sounds reasonable. It means when the incidence angle surpasses the zenith, it's time to gracefully exit stage left.
So, in summary, I recommend the nuanced approach of averaging according to Duffie & Beckmann for Q1, and for Q2, R_b = 0 when theta > 90^degree.
Feel free to question, my inquisitive compatriot Misagh Irandoostshahrestani!
Q1: The quantity you want is the direct irradiance normal to the tilted plane, which is simply DNI*cos(theta), so no issue at all. Just forget about R_b; it's an old concept that actually applies to the direct _horizontal_ irradiance, not to DNI.
Q2: Use cos(theta)=0 whenever the sun is behind the collector.
Dear Kaushik Shandilya , Thank you very much for your response and the clarification. I got the idea regarding the geometric factor.
Dear Chris Gueymard , Thanks for your response. You are right, Indeed, I do not need the R_b.
In my code, I used Liu and Jordan method for global irradiation on a tilted surface. At high tilt angles around 80-90 ^degree, my code shows upto 15% difference for Total irradiations on tilted surface compared to PVSYST results for the same DNI, GHI, and DHI. Can it be due to the different method that PVSYST uses (Hay`s or Peretz) which is more sophisticated?
As I am usign the free version of PVSYST, I can not switch to Liu and Jordan in PVSYST (if there is any possibility) to make a better comparison.
Thank you in advance.
Yes, for surfaces tilted to the equator, it is well known that the Liu&Jordan isotropic assumption results in significant underestimation. See, e.g., Article Direct and indirect uncertainties in the prediction of tilte...
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