Data predictions

   Predicting the amount of solar energy that can be collected is useful. Steps can be taken to prepare for low or high energy days.
   There are several publicly available databases of historical weather data as well as at least one that publishes data based on a mathematical model.
   Days that are statistically more likely to be cloudy or overcast can be anticipated with a measured level of reliability The likelihood of a likelihood.
   A comparison of the historical data and real time current data can be interesting.

   My first attempt to describe the data I collected using a graphic curve were based on best-fit-polynomial equations. In my case, I used spreadsheet software for this. The best curve to be had was with a two term polynomial. There was no benefit to increasing the number of terms.

   The results were not satisfactory. I began looking for an improved method. I was familiar with several websites that make solar cell/panel/array information available. PVEducation.org is a site that has more information any other I examined, which not to say there isn't one with more. I began perusing the site. I discovered mathamatical equations for several Sun and cell related phenomenon.

   I used the formulas for solar radiation orthogonal to, and incident to, a cell. That equation was incorporated into the equation for the effective solar radiation at a given tilt and angle and included the effects of air mass, refraction, and the curvature of the Earth's surface.

   The difference between the suggested curve and the curve of prediction in the above image, is due to limitations on charging current for the battery bank, by the MPPT controller's designers. A limit of about 2.5 amperes is placed on charging the batteries. This results in a loss of efficiency in terms of the amount of energy available. Where 585 watts is available, only 260 watts is typically used, maximum.

   The battery type I use is the deep cycle, flooded lead-acid type.The suggested charging current is 2.5 amperes:

10%-13% of the C20 rating which is, in this case, 108Ahr.
10% of 108Ahr = 10.8 amperes
13% of 108Ahr is 14.04 amperes
2.3% of 108Ahr is 2.5 amperes, the esuggested rate used by the controller's designers.

   A low charge rate is said to correlate with a longer battery life while a higher charge rate correlates with a shorter battery life. There is a trade-off for the lifetime of the battery and the convenience of energy availability. More batteries must be added for a low charge rate to achieve the availability goals. The cost of more batteries may cancel out the shorter lifetime caused by higher charge rates.
   The issue seems to become one of pay now or pay later, the end cost will not be much different. This is presumptuous. I do not have enough data about the effects of charge rates on deep cycle lead-acid batteries. The choice is open.