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Solar Day
The "Solar Day" and "Solar Year" windows calculate energy characteristics of the same collector system of the latest active 3D View window. They display warnings if there are no 3D scenes (if the last 3D View window was closed), or if the latest active scene does not contain solar collectors.
The "Solar Day" window shows how the energy characteristics of your solar collectors (including the self- and full-shading) vary during a given day, and calculates their daily sums or daily average values.
All the calculations are implemented according to the climate model of the scene. To specify the climate model of the scene, read the next section and use the "Climate & Irradiance" window. Note also that the "Solar Day" window is an additional way to verify your climate model if you have the detailed hourly statistic for the average days of the months.
Create the climate model for the scene and transfer the climate data
If you did not specify the climate model of the scene, the default climate model is applied. Note that the default climate model uses the plain 50% probability of clear sky for all 12 months of the year. So to have a more realistic results, you need to adjust at least this setting according to the actual solar radiation statistic of your particular site.
The climatic information is a part of the scene record like any other scene parameters. The structure of this information is same as the structure of the input data of the "Climate" window. When the scene is firstly created, this structure is filled by the same default climate settings that appear in the firstly opened "Climate" window. You can change these default settings in two ways: either creating and adjusting the climatic model of your site in the "Climate" window and then transferring data from the "Climate" window into your scene, or retrieving the climatic model from another scene into the "Climate" window and then also transferring data from the "Climate" window into your scene. See details of your work with the climate model in the topic "Climate & Irradiance" of this chapter.
You can transfer the climatic parameters of the "Climate" window into the latest active 3D scene in two ways. If the "Climate" window is active, use the key "T" (export To the scene). If a 3D view is active, use the key "C" (import the Climate). Note that in both cases the parameter "Latitude" is not copied from the "Climate" window to the 3D scene. The climatic parameters are updated in the dynamic memory of the scene immediately after the transfer. Later, when you save the scene, the climatic information will be saved in the scene file too.
To retrieve the climatic parameters from the latest active 3D scene into the "Climate" window, use the key "F" (retrieve From the scene) when the "Climate" window is active. Note that in this case the parameter "Latitude" is copied from the 3D scene into the "Climate" window.
So you can use the "Climate" window as an intermediate data storage for the exchange of the climatic data between scenes. Use the key "L" in this case to lock the "Climate" window, and to prevent it from the occasional changing of the transferring data.
The "Solar Day" window
The name of the associated latest active scene is written in the title bar of the "Solar Day" window.
Pages:
1. Irradiance, kW/m2
2. Shading
3. System output, kW
To switch pages, use the keyboard keys "1", "2", "3", or the right mouse click, when the window is active.
The argument of functions of all pages is the same: time (hours) from true solar noon.
See "Set Geography..." for details about true solar time and local time.
To see the numerical values of the calculated function curves, use the "Solar Table" window.
There are no specific control elements or input data for the "Solar Day" window. It reacts on the changes provided in the latest active scene displayed in the latest active 3D View window. So to change the day in the "Solar Day" window, activate the associated 3D view, and use the control elements of the "3D View" toolbar or the keyboard keys as it is described in the sections "A typical session", "Use the toolbar 3D View", and "Use the keyboard modes" of the topic "Visualize Shadows".
Switch window modes with keys "M", "V"
Both the switches have same meaning as ones of the "Climate & Irradiance" window. However the "Climate" window does not have the "random clouds" mode. The switches of the "Solar Day" window work independently from the corresponding switches of the "Climate" window.
In the "constant month" mode (when "M" shows "const month"), all the monthly input parameters of the climate model stay the same within the corresponding months. The "constant month" mode is useful when you need to interpret experimental data of a particular day.
In the "month spline" mode (when "M" shows "month spline"), all the monthly input parameters of the climate model are parabolically splined. To see the parameter value of a particular day, transfer the climate model from the scene to the "Climate" window, open the corresponding input page of the "Climate" window (where the parameter is displayed graphically), and then open the "Solar Table" window.
The switch "V" between "100% clear sky", "mean cloudiness", and "random clouds" modes affects both the daily dynamics and the daily sums of solar radiation. The "random clouds" mode have an additional numerical switch with the "Y" key, which simulates 30 different random sequences of "sunny" and "cloudy" 10-minutes time intervals during a particular day for 30 different years. See the next section for details.
Basic formulas for calculations
To specify which a surface we are speaking about, we use the following suffixes:
"_N" -- for the direct solar radiation Dir_N measured on the "normal" surface,
"_H" -- for the components of solar radiation measured on the horizontal surface,
"_S" -- for the components of solar radiation measured on the arbitrary oriented surface S.
The main assumption that we use in the calculations of the "Solar Day" and "Solar Year" windows is that the diffuse radiation on an arbitrary oriented surface S is approximately equal to the diffuse radiation on the horizontal surface. So the value of Dif_S is substituted by the value of Dif_H. See "Comments" in the topic "Bird Clear Sky Model".
So we express the total solar radiation on an arbitrary oriented surface S as follows
Dir_S = Dir_N * cos(i);
Tot_S = Dir_N * cos(i) + Dif_H; (instead of Tot_S = Dir_N * cos(i) + Dif_S),
where "i" means the incidence angle (for a horizontal surface i = Z, and suffix "_S" becomes "_H").
In the "Climate & Irradiance" window, we introduced two variables:
Prob -- the probability of clear sky in % (or in dimensionless units from 0 to 1),
Dcs -- the correction coefficient for the diffuse solar radiation.
For the "100% clear sky" conditions, we apply the same formula as shown above:
Tot_S = Dir_N * cos(i) + Dif_H.
For the "mean cloudiness" conditions, we modify the formula as follows:
Tot_S = Prob * Dir_N * cos(i) + Dcs * Dif_H.
For the "random clouds" conditions, we modify the formula in two ways:
Tot_S = Dcs * Dif_H; (within "cloudy" time intervals),
Tot_S = Dir_N * cos(i) + Dcs * Dif_H; (within "sunny" time intervals),
and the parameter Prob determines the fraction of "sunny" time intervals within the entire light day.
The case of "random clouds" explains the sense of the correction coefficient Dcs for the diffuse solar radiation in the case of "mean cloudiness" conditions.
The "random clouds" mode simulates the variable cloudiness within one particular day by a random sequence of "cloudy" and "sunny" 10-minutes time intervals. The total duration of all "sunny" intervals divided by the duration of the light day is approximately equal to the parameter Prob (the probability of clear sky) of the "mean cloudiness" mode. However, "sunny" does not mean that the sky is totally free of clouds, as well as "cloudy" does not mean that the sky is totally covered by clouds. Clouds are moving over the sky, and "sunny" means that we see the solar disc clearly between clouds, while "cloudy" means that the solar disc is temporarily obscured by a cloud.
Under such conditions, the diffuse radiation can decline from the Bird model calculations (increasing due to the additional reflection from rare clouds, or decreasing due to the relatively dark sky, when it is almost totally covered by clouds). But what is more important, we should apply the same diffuse radiation to both cases of "sunny" and "cloudy" intervals, because the average brightness or "darkness" of the sky stays approximately the same independently of the fact is the relatively small solid angle around the solar disc temporarily obscured by an occasional cloud or not.
Summarizing both the formulas for "sunny" and "cloudy" time intervals of the "random clouds" mode, and taking into account their statistical weights, we can write the following:
Average_Tot_S = Prob * Tot_S_sunny + ( 1 - Prob ) * Tot_S_cloudy =
= Prob * ( Dir_N * cos(i) + Dcs * Dif_H ) + ( 1 - Prob ) * ( Dcs * Dif_H ) =
= Prob * Dir_N * cos(i) + Dcs * Dif_H;
that is just the same formula, which we use in the case of "mean cloudiness" conditions.
This approach is motivated also by the fact that the parameter Prob (the probability of clear sky) actually means the probability of the clear solar disc, because it is usually calculated as the ratio of the total monthly duration of available direct solar radiation to the total monthly duration of the light days.
There is a common point of possible misunderstanding of the graphical diagrams of "solar" windows. Some users might be confused being unable to find a particular function curve on a diagram. It might occur when one curve is overdrawn partly or completely by another curve. For example, if the collector system consists of sun-tracking collectors, for which permanently cos(i) = 1, then the curves of Dir_N and Dir_S are the same, and the curve of Dir_S (as one painted after Dir_N) completely covers the curve of Dir_N. The order of painting and colors of curves correspond to the order and colors of their names.
Note also that you can switch the width of the curve lines using the key "W" of your keyboard, or with the command "Increase Line's width" of the "Copy to Clipboard" section of the Edit menu.
Page 1: Irradiance
The page shows the direct, diffuse, and total irradiance on the collector surface (remember that we assume Dif_S = Dif_H).
If there are no active collectors in the associated scene, then the irradiance is calculated for a horizontal surface.
The first line of the legend shows the system type and objects that constitute the collector system.
The second line of the legend shows the geographical latitude and the date.
Curves:
The line below the title "Daily sum, kWh/m2, and …" shows the daily sum of components of solar radiation in kWh/m2, and the value of cos(i) averaged by time over the day. The values are shown in the following order: Dir_N, <cos(i)>, Dir_S, Dif_H, Tot_S. The symbol <…> means the averaging over the day.
For a scene without collectors, the corresponding values are calculated for the case of a horizontal surface, so the values of cos(i), Dir_S, Tot_S are substituted by cos(Z), Dir_H, and Tot_H.
On four screen shots above, you see one case of a scene without solar collectors, and three cases of the scene "s823 ..." with solar collectors for three variants of the "V"-switch.
Page 2: Shading
The page shows the shading of the collector system. We distinguish self-shading (only by elements of the system) and full shading (a combination of self-shading and the shading by other objects).
If there are no active collectors in the associated scene, the page shows the warning.
The first line of the legend shows the system type and objects that constitute the collector system.
The second line of the legend shows the geographical latitude and the date.
Curves:
Note that the shading is expressed as a dimensionless coefficient in range from 0 to 1, and means the part of the collector area that is shaded. We consider the shading in therms of the shaded area only, and do not consider more detailed electrical effects for PV panels, when one shaded cell in an electrical chain can interrupt PV generation of the entire panel. See some additional materials on this theme, for example, in http://www.solaroregon.org/learn/solar-site-analysis/siting-pv.
The line below the title "Daily losses of Dir_S as % of the Tot_S" shows the daily full shading and self-shading energy losses as the percentage of maximal possible value of the daily sum of total solar radiation on collectors.
On four screen shots above, you see one case of a scene without solar collectors (where the warning is displayed), and three cases of the scene "s823 ..." with solar collectors for three variants of the "V"-switch. Note that there is no self-shading in the scene "s823 ...", so the corresponding curve overdraws the bottom coordinate line.
Page 3: System output
The page shows the output of your collector system (the daily profile in kW, and the daily sum in kWh) for three cases: without shading, with full shading, and with self-shading.
If there are no active collectors in the associated scene, then the page shows the warning.
The first line of the legend shows the system type and objects that constitute the collector system.
The second line of the legend shows the geographical latitude and the date.
The fifth line of the legend shows the number of collector shields, their dimensions, and their total area, m2.
The sixth line of the legend shows the efficiency of the collector system.
Note that you can set the efficiency calling the "Efficiency" dialog with the key "E" of your keyboard. You call this dialog, when the "Solar Day" window (but not the 3D View window) is active, and the dialog will change uniformly the efficiency of all the collectors of the associated scene, which name is written in the title bar of the "Solar Day" window.
Curves:
The line below the title "Daily sum in kWh and %" shows the daily sum of the system output, calculated without any-, with full-, and with only self-shading respectively. The sum for the case without any shading is accepted as 100% for the calculation of the percentage values.
On four screen shots above, you see one case of a scene without solar collectors (where the warning is displayed), and three cases of the scene "s823 ..." with solar collectors for three variants of the "V"-switch. Note that there is no self-shading in the scene "s823 ...", so the corresponding curve for the "Self" shading overdraws the curve for "No shading".