rewrite functions in pv_model #689
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@@ -115,6 +115,7 @@ final case class PvModel private ( | |
| lat, | ||
| gammaE, | ||
| alphaE, | ||
| duration, | ||
| ) | ||
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| // === Diffuse Radiation Parameters ===// | ||
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@@ -337,7 +338,7 @@ final case class PvModel private ( | |
| val e0 = 1.000110 + | ||
| 0.034221 * cos(jInRad) + | ||
| 0.001280 * sin(jInRad) + | ||
| 0.00719 * cos(2d * jInRad) + | ||
| 0.000077 * sin(2d * jInRad) | ||
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| // solar constant in W/m2 | ||
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@@ -409,32 +410,27 @@ final case class PvModel private ( | |
| omegaSS: Angle, | ||
| omegaSR: Angle, | ||
| ): Option[(Angle, Angle)] = { | ||
| val omegaSSInRad = omegaSS.toRadians | ||
| val omegaSRInRad = omegaSR.toRadians | ||
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| val omegaOneHour = toRadians(15d) | ||
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| val omega1InRad = omega.toRadians // requested hour | ||
| val omega2InRad = omega1InRad + omegaOneHour // requested hour plus 1 hour | ||
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| if ( | ||
| // requested time is between sunrise and sunset (+/- one hour) | ||
| omega1InRad > omegaSRInRad - omegaOneHour | ||
| && omega1InRad < omegaSSInRad | ||
| ) { | ||
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| val (finalOmega1, finalOmega2) = | ||
| if (omega1InRad < omegaSRInRad) { | ||
| // requested time earlier than sunrise | ||
| (omegaSRInRad, omega2InRad) | ||
| } else if (omega1InRad > omegaSSInRad - omegaOneHour) { | ||
| // requested time is less than one hour before sunset | ||
| (omega1InRad, omegaSSInRad) | ||
| } else { | ||
| (omega1InRad, omega2InRad) | ||
| } | ||
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@@ -464,13 +460,23 @@ final case class PvModel private ( | |
| * @return | ||
| * the beam radiation on the sloped surface | ||
| */ | ||
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| def calculateTimeFrame(omegas: Option[(Angle, Angle)]): Double = { | ||
| omegas match { | ||
| case Some((omega1, omega2)) => | ||
| (omega2 - omega1).toDegrees / 15 | ||
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| case None => 0d | ||
| } | ||
| } | ||
| private def calcBeamRadiationOnSlopedSurface( | ||
| eBeamH: Irradiation, | ||
| omegas: Option[(Angle, Angle)], | ||
| delta: Angle, | ||
| latitude: Angle, | ||
| gammaE: Angle, | ||
| alphaE: Angle, | ||
| duration: Time, | ||
| ): Irradiation = { | ||
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| omegas match { | ||
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@@ -482,6 +488,9 @@ final case class PvModel private ( | |
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| val omega1InRad = omega1.toRadians | ||
| val omega2InRad = omega2.toRadians | ||
| // variable that accounts for cases when the integration interval is shorter than 15° (1 hour equivalent), when the time is close to sunrise or sunset | ||
| val timeFrame = | ||
| (omega2 - omega1).toDegrees / 15d / duration.toHours // original term: (omega2 - omega1).toRadians * 180 / Math.PI / 15, since a one hour difference equals 15° | ||
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| val a = ((sin(deltaInRad) * sin(latInRad) * cos(gammaEInRad) | ||
| - sin(deltaInRad) * cos(latInRad) * sin(gammaEInRad) * cos( | ||
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@@ -503,7 +512,7 @@ final case class PvModel private ( | |
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| // in rare cases (close to sunrise) r can become negative (although very small) | ||
| val r = max(a / b, 0d) | ||
| eBeamH * r * timeFrame | ||
| case None => WattHoursPerSquareMeter(0d) | ||
| } | ||
| } | ||
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@@ -533,6 +542,41 @@ final case class PvModel private ( | |
| * @return | ||
| * the diffuse radiation on the sloped surface | ||
| */ | ||
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| private def calcEpsilon( | ||
| eDifH: Irradiation, | ||
| eBeamH: Irradiation, | ||
| thetaZ: Angle, | ||
| ): Double = { | ||
| val thetaZInRad = thetaZ.toRadians | ||
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| ((eDifH + eBeamH / cos(thetaZInRad)) / eDifH + (5.535d * 1.0e-6) * pow( | ||
| thetaZ.toDegrees, | ||
| 3, | ||
| )) / | ||
| (1d + (5.535d * 1.0e-6) * pow(thetaZ.toDegrees, 3)) | ||
| } | ||
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| private def calcEpsilonOld( | ||
| eDifH: Irradiation, | ||
| eBeamH: Irradiation, | ||
| thetaZ: Angle, | ||
| ): Double = { | ||
| val thetaZInRad = thetaZ.toRadians | ||
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| ((eDifH + eBeamH) / eDifH + (5.535d * 1.0e-6) * pow(thetaZ.toRadians, 3)) / | ||
| (1d + (5.535d * 1.0e-6) * pow(thetaZ.toRadians, 3)) | ||
| } | ||
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| private def firstFraction( | ||
| eDifH: Irradiation, | ||
| eBeamH: Irradiation, | ||
| thetaZ: Angle, | ||
| ): Double = { | ||
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| (eDifH + eBeamH) / eDifH | ||
| } | ||
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| private def calcDiffuseRadiationOnSlopedSurfacePerez( | ||
| eDifH: Irradiation, | ||
| eBeamH: Irradiation, | ||
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@@ -555,12 +599,12 @@ final case class PvModel private ( | |
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| if (eDifH.value.doubleValue > 0) { | ||
| // if we have diffuse radiation on horizontal surface we have to check if we have another epsilon due to clouds get the epsilon | ||
| var epsilon = ((eDifH + eBeamH / cos(thetaZInRad)) / eDifH + | ||
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There was a problem hiding this comment. Both Duffie and the original Perez use the formula as before. Where did you find the formula with cos thetaZ again? There was a problem hiding this comment. This is my reference (Duffie p. 95f). Note that "I_b,n" is not the beam radiation on a horizontal surface, but rather the beam radiation on a surface normal to the direction of the sun. This can be calculated by dividing the beam radiation on a horizontal surface "I_b" (=eBeamH in code) by cos(ThetaZ). This is also demonstrated in Duffie: example 2.16.2 There was a problem hiding this comment. I think we need some more investigation here, probably focused on the weather data specification. I_b,n is certainly the "normal beam incidence radiation", which means the radiation in direction of the beam, i.e. on a surface that is exactly facing the sun, as you explained. I_b is certainly the radiationon a horizontal plane (i.e. on earth's surface). The question now becomes which type of radiation the weather data sources provide. For ERA5, solar radiation always seems to be specified on a horizontal plane. I have not found the specs for ICON and COSMO yet. So it seems likely to me that you're right with your assumptions. What should be done now is adapting the formula in documentation (replace |
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| (5.535d * 1.0e-6) * pow( | ||
| thetaZ.toDegrees, | ||
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| 3, | ||
| )) / (1d + (5.535d * 1.0e-6) * pow( | ||
| thetaZ.toDegrees, | ||
| 3, | ||
| )) | ||
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According to Iqbal, this is 0.000719 with three zeroes. The primary source, Spencer, also states the same. Duffie and Zheng as well. Please check again.
Furthermore, could you add the missing sources I just mentioned to the list of sources in documentation as well?
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This is Duffie p. 9, where I noticed the 2 zeros only. Can you maybe send me the PDFs of the other books, so I can look it up aswell?
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Interestingly, the fifth edition of Duffie seems to differ from all earlier editions in this point. Given that the cited sources stayed the same and I didn't find any other explanation (and the layout seems broken in this edition for the first time), I assume that the change did not happen on purpose and the number with three zeros is still correct. There should be some more investigations here, though.
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It'd be great if we added commentary to the readthedocs documentation regarding this issue, i.e. why we're using the fourth edition and not the fifth. (Extraterrestrial Radiation)