Eclipse graph

   I posted I would present the graph for the day of the partial solar eclipse (northeast Tennessee) for interest. The data was collected on a clear day with a few short intrusions. The time was still Daylight Savings Time.

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.
 

Seasonal changes in the solar path.

   Previously, I posted the impracticality of sensing resistors in a solar arry. I've decided that such sensors are needed. I do not have any of the design details of the MPPT controller I'm using, but I suspect the device is not up to parr with the rest of the system. A sensing resistor in series with the mainline will let me verify the power transfers taking place in the system. A small ADC board will convert analog data into computer compatible, digital data. I have all the parts and software on hand.

   If knowing the details of the panel system were crucial, I could insert a series of relays into the circuitry and a digital switching system to isolate each component in turn. Doing the same for the battery system would make SoC data available. I could then implement any of a series of algorithms.

   I stated in the last post, I would publish a series of graphs illustrating the seasonal changes in the amount of sunlight available. I do that here. First, I'll preface that series with a discussion of the variables involved.

   Throughout the year, the Sun's path through the sky changes. On June 21st, the Sun is closest to the Earth and highest in the sky at noon. On December 21, the Sun is farthest from the Earth and lowest in the sky at noon. Visualize an arc in the sky. The arc sinks lower as the days pass, until the lowest point occurs in December, then begins to rise till June, when the highest point is reached. This arc represents the path of the Sun throughout the day.

   One of the results is the lengthening of shadows in Winter. Since the Sun is lower in the sky at noon, the shadows will be longer. In Summer, the Sun is highest in the sky and the shadows will be shortest. What this means to me, is that solar energy is least when needed most, and most abundant, when needed least. For this reason, a system needs to be designed for Winter, the low energy months.

Note, in particular, the difference between the first, June 3, and the last, October 31. The difference is the effect of a changing solar path and shadows. Also note that most of the images were constructed from data collected on a clear day.

Here are the graphs:

Timelapse shadow study

November 24, 2017

This is a cellphone (Apple iPhone 4) timelapse video of the area of my yard of interest. The region of least shadow, and therefore most sun, is easily determined. The iPhone phone 4 has a lower resolution imagery, but I'm not interested in details in this video and the file size and screen size are ideal for a blog like this.

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I include a couple of graphs of the before-and-after type as illustrations. I've included a graph for the day of the eclipse as an interesting example.

The above image is the 'before' shot. Half my solar day is lost due to obstructions. October 30, 2017.

This image is the 'after' shot. I've recovered a great deal of the lost energy. November 23, 2017.

I'll post a page on the changes in available sunlight throughout the year, next.

Mathematical equations and charting

Some things have happened since the last post.

   I found an equation for the irradiation on a solar panel. The equation takes into account air mass, refraction and the curvature of the earth's surface. I translated the math into the Python programming language I've been using and now collect that data along with the rest.
   By adding historical data in the form of averages, I can make a reasonable prediction of the amount of irradiation on a clear day.
   I located an extensive set of equations for determining the position of the sun. They are from the NOAA SPA set. I'm translating the Excel format of the equations into the Python format. I've been using a ephemeris programming library to do those calculations but decided to do them myself as an exersize.
   I used a cellphone to record shadow activity in the back yard. I studied the results and moved the array to a new location. Half of my solar day was lost to shading by trees on an adjacent lot. There's some shading in the new spot, but not quite as much. I will move the array to an area with the maximum exposure after adding some wire to the station. I need to add another fifteen to twenty feet to the line from my house to the array.
   I've redesigned the station and am going to add a linear actuator and PWM power supply. I'm going to split the array up. Three panels will be mounted on a steel pipe tilted at an optimum 45 degree angle. The actuator will rotate the array by rotating the pole on which they are mounted. I will double the amount of energy I collect using the shade-free site and one-dimensional tracking using the linear actuator.
   Two panels will be used as an adjunct. The manufacturer of the MPPT controller I've been using states the charger is limited to charging batteries unless in the float stage. Only then can excess be bled off into a real-time system, e.g. laptop, web router and modem, coffee grinder, pumps, etc.. The manufacturer of the MPPT controller has set the maximum charge rate for the bank at a level equal to the energy supplied by only three panels.
   I have an older Xantrex PWM charger/controller That will supply ongoing needs while the 36VDC system's primary function remains charging the 5KW battery bank. I'll add a couple of smaller (8AHr) batteries to stabilize the Xantrex output. Those batteries will act as capacitors to filter the PWM output of the Xantrex. The Xantrex takes a 24VDC input. That leaves one 12VDC panel which will be used to run12VDC devices such as the 12VDC battery charger for a 18VDC reciprocating saw battery.