ABSTRACT

With a unique — commercially not available (1) — computer program (“SOLARCALCS”), the performance of any solar photovoltaic or solar thermal energy installation can be simulated from [theoretical] first principles (2). The program calculates the amount of solar energy collected in 30-minute intervals, month by month, and integrates the results over an entire year, taking all relevant system parameters, weather, and site conditions into account. Using the SOLARCALCS software, it is extremely easy to analyze the effect of changing any one system parameter for design optimization purposes.

SOLARCALCS is a macro-based Excel spreadsheet and runs on a laptop computer. It can be used for any solar photovoltaic system, including single or dual heliostatic tracking, as well as for solar thermal installations, such as for solar swimming pool, spa, or domestic water heating systems. It lends itself for generating performance tables for generic systems for specific geographic locations, climates, and collector azimuth and tilt, which can then be quantified for specific collector sizes and efficiency characteristics, .

We present two generic result tables, obtained with the SOLARCALCS program, for two specific locations in California: The Sea Ranch (on the central coast), and Sunnyvale (San Francisco Bay Area). Similar tables for other locations can easily be established by users. These tables can be used as design tool for essentially any solar PV system in Northern California, without actually having to run the simulation with detailed user-specific parameters.

We then corroborated our theoretical results with detailed measured performance data obtained for two solar installations and found them to be so accurate that they enable valuable insights into the effect of panel orientation and shading, which cannot otherwise be quantitatively assessed.

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1. I developed the SOLARCALCS program in my activities as consultant and entrepreneur in solar engineering. The program can be made available to private solar enthusiasts who want to optimize and/or analyze the design of their private solar installation. An acquaintance with Excel spreadsheets is desirable to better enjoy the intricacies of this program. Alternately, we may offer to perform specific simulation runs on request. For such requests, we need the following information: location, number of panels, size and efficiency of the selected panel type, and roof tilt and orientation.

2. The calculations literally start from the solar constant.

INTRODUCTION

There is a common skepticism that a person’s home or business may not be suitable for a solar PV or thermal collector system if the roof is not perfectly oriented by tilt and azimuth, or if there is partial shading of the collectors. With the tools presented in this paper we demonstrate that this skepticism is largely unfounded.

I originally developed this software as a design tool for solar thermal domestic and commercial water and space heating applications, running in the meanwhile long forgotten “BASIC” language on a desktop computer. When the solar thermal market was surpassed by solar photovoltaic technology, I adapted the program to include PV systems, which are actually easier to simulate, because the PV solar energy collection is less affected by the ambient temperature and the temperature of a thermal mass of an object being heated, such as a swimming pool or domestic water heater or other heat storage device.

The increasing speed of today’s laptops rendered the computing time required for a one-year simulation from originally several minutes to a fraction of a second, which enabled me to incorporate further refinements into the calculations, such as going from one-hour to half-hour simulation increments, and including options for single-tracking and helio-static tracking of the collector arrays. This program is now running as a macro-operated Excel spreadsheet.

In this paper, we present user-friendly generic applications for
— solar PV installations in Sea Ranch and in Sunnyvale, CA, and
— solar thermal installations in the same two locations, with particular emphasis on swimming pools and spas; and
— we then compare computed predictions with actual performance measurements, and address shading situations.

PART A: SOLAR PV INSTALLATIONS

We discuss generic photovoltaic system installations, the results for which can be easily extrapolated to any actual installation, following simple steps explained below. We do this for a generic 3.28 kW installation in two different locations, The Sea Ranch, CA, (Table 1) and Sunnyvale, CA (Tab. 2). These two location have substantially different weather patterns, warrantying separate treatment. In principle,the SOLARCALCS program can handle any installation at any geographical latitude and elevation above sea level in the world, as long as basic weather data are known for that location (average mean temperature at solar noon and sunshine probability for each month of the year).

Detailed explanation of these tables

These tables can be used for any typical installation at a Sea Ranch or a Sunnyvale/Mid-Peninsula home.
For application to your specific home perform these five steps:

Step (1): From past PG&E bills determine how many kilowatt-hours you used in total last year. Add or subtract if you plan substantial changes in the future. Say, you end up with 9000 kWh. Then make a ballpark decision what percentage of that you want to cover with your solar installation. I recommend to use not more than about 80%. (I will address the reasoning for this recommendation later). This means, you would want to design for 7200kWh in this example.

Step (2): Determine where you can mount your collectors in a shade-free, architecturally pleasing location. Say, this is on a roof that faces in SW direction and has the typical “4-foot in 12-foot” tilt (18.4 degrees).

Step (3): Find (from the table above) that a typical 3.28 kW system in Sea Ranch will produce 4972 kWh per year for solar panels thus oriented. Since you want 7200 kWh, you want a bigger, nominally 7200/4972*3.28 = 4.75 kW system.

Step (4): Google for a collector type and manufacturer you like, e.g., a “Canadian Solar” or SunPower” or “Tesla” panel or something like that. Choose something that looks uniformly black and has a dark anodized frame - the Sea Ranch Design Committee prefers that. Find out the “rating” and physical dimensions of those panels. Say, the rating is 340 Watts. You determined that you want a 4.75kW=4750W system, so you need 4750/340 = 14 of those panels.

Step (5): Go back to Step (2) and determine if 14 of the panels you selected will actually fit on your roof. If not, go to step 4 and see if you can find panels working at higher efficiency, i.e., that are therefore smaller and might fit better, while costing a bit more in aggregate.

Now you have all you need to evaluate the quote you receive from your solar contractor. You might get a good deal for $200 per panel, or $2800 for the 14 you need. That would be $2800/4750W = $0.59 per Watt. This sounds like an OK deal. Compare this with what your contractor proposes. Then figure that you want micro-inverters, to limit the shading losses and simplify the electrical installation. Those cost somewhere around $150 each, or $2100 in total. Generously add another $500 for the controller, and another $1600 for mounting hardware, conduits, wiring, and misc. other hardware you need, and you come up with $7000 plus tax for the total hardware. Compare this with your quote. The installation should not take more than one day for two people, plus time for pulling the permit. Figure a reasonable pricing for that, add a reasonable margin for the contractor, and assess your quote.

Visitors to this website can use/extrapolate the data presented above to come up with surprisingly precise performance predictions for kWhs produced per month and per year with their as-designed or as-installed solar PV system.

PART B: SOLAR THERMAL INSTALLATIONS

Introductory remarks: complexity in solar pool heating systems compared to Solar PV systems.

The performance prediction for solar thermal collector systems is more intricate than it is for solar photo-voltaic systems. The ambient temperature, which is essentially irrelevant for PV, as well as the temperature of the water being heated to begin with, and even wind wind over the collectors, all have a major effect that must be considered in the solar thermal calculations. The SOLARCALCS program takes this into account.

If the temperature of the water to be heated is higher than the ambient temperature at the inlet into the collector bank, conductive, convective and radiative heat/energy losses must be considered that do not apply to PV systems. Additionally, conductive heat losses in the piping to and from the collectors play a significant role. These losses increase dramatically with increasing temperature differential between the water and ambient.

Therefore, solar thermal heating is generally more effective in warmer climates, and it is more effective for swimming pool heating, when the body of the water being heated is at relative low temperatures to begin with (we have assumed 85 degrees F for our calculations for swimming pool heating), than it is for spa heating (100 degrees) or domestic water heating (130 degrees).

It is for these reasons that unglazed and uninsulated collectors are typically only used for swimming pool heating, while more expensive glazed and (on the back side) insulated collectors are more likely specified for spa or domestic water heating applications. While the SOLARCALCS program can deal with the heat losses of glazed collector systems, we are using it in this web page only for swimming pool or spa heating applications with unglaced, uninsulated collectors.

Generally use solar thermal systems, not solar PV, for water heating

There are fundamental differences in the thermal and photo-voltaic solar energy utilization technologies. Solar water heating occurs at high efficiencies. When unglazed collectors are applied under low “delta-T” conditions, such as for swimming pool heating, they can operate in the 90 percent efficiency range, i.e., the sun’s energy impinging onto the collectors is converted directly to thermal energy, at this high efficiency ratio. This contrasts to solar PV energy collection which operates at much lower efficiency, typically only around 20% for panels currently on the market, peaking at about 25% for the most expensive panels (Sunpower markets a 22.7% efficient panel).

While the PV efficiency will eventually further increase, even the theoretical limit is not very much higher than where we are now. But it makes no sense to wait for more efficient PV panels, because there is, in most cases, no compelling reason to insist on super-high efficiency. If you get lesser efficient panels, you simply make up the difference by adding panels or panel area, if you have space on the roof. All that matters is the per-Watt cost you are paying. If you want a 4000-Watt system, and have enough space on the roof, it makes no difference if you use ten expensive 400-Watt panels or 20 very cheap 200-Watt panels. Price per Watt is all that matters.

Given that solar PV panels generate electricity, not heat, and inherently have lower efficiency than solar thermal panels, it is important to consider what you are using them for. Solar thermal systems are good for heating water directly. It generally makes little sense to install solar PV panels, which generate electricity, to then use this electricity to heat water.

This cardinal mistake is committed, however, over and over. Let us look at a practical example for a hot tub. Hot tubs are typically heated with a 5000-Watt resistance heater. Our hot tub in Sea Ranch uses about 5280 kWh per year on average (see https://www.healingguidance.net/home-energy-analysis). This happens to be about equal to — within a reasonable error margin — the performance of my entire relatively expensive 3.28 kW, 10-panel solar PV system (see Table 1 above), taking up 175 sq.ft. panel area on my roof. This same amount of energy, converted at 1kWh = 3413 equivalence between electricity and thermal energy, is collected by a very basic 72 sq.ft. Fafco-type plastic unglazed thermal collector system (see Table 4, which is for a 48 sq.ft. system). For this I paid about $1000 for the panels plus another $800 for incidental hardware at Amazon, and had it installed in a day by my handyman. It compares to the above described solar PV system costing about $10,000. Clearly, this is not such a clear-cut comparison for every situation, but in principle it demonstrates the point that solar thermal should be used for water heating whenever feasible.

Specific considerations for solar swimming pool heating

The situation for swimming pool and spa installations is often different in that the preference is often to get more solar auxiliary heating during the fall and spring, rather than the summer months. Therefore, steeper collector tilt may be required. We therefore focus here on such situations.

Tables 3 and 4 are for the very same generic pool heating system, both assuming 85 degrees pool water temperature, except that the tilt angle was increased from 18 to 45 degrees. The larger tilt angle provides a minor improvement in the total annual collection (3575 vs. 3409 kWh), but it spreads out the collection much more evenly over the entire year.

Increasing the tilt further, such as to 60 degrees (Table 5), further shifts the monthly solar yield toward the winter months, but the total annual solar yield drops off more significantly (3201 kWh for 60 deg vs. 3575 kWh at 45 degrees tilt. More extreme collector tilt, such as mounted flat on a vertical house wall), reduces the yield to 1783 kWh per year, which is only about 50% of the yield for 45 degrees tilt and, hence, for all practical purposes unacceptable.

Results for Mid-Peninsula locations

We had earlier established that for an otherwise identical solar photo-voltaic system, the annual collection in Sunnyvale was more than ten percent better than in Se Ranch. That pertains to a photo-voltaic system, where the ambient temperature has no notable influence. But when we ran the same calculations for solar thermal collection for swimming pool heating, this effect was reversed. During the winter season, the average temperatures in Sunnyvale are colder than in Sea Ranch, and for thermal collectors heat losses during solar collection are detrimental. Therefore, the annual energy yields from thermal collectors are better in Sea Ranch than in Sunnyvale. This effect is particularly pronounced during overcast periods: there is significant insolation also occurring during overcast periods, and a much higher percdentage of that is collected with PV panels than with thermal collectors, where the ambient temperature related heat losses usually equal or exceed the insolation during overcast periods.This means that, for all practical purposes, thermal solar energy collection only occurs when the sun is shining, while PV collection also benefits from diffuse insolation.

PART C: ABOUT THE INFLUENCE OF SHADING ON SOLAR PV COLLECTION

It is usually exceedingly difficult to quantitatively assess the influence of shading on solar collector performance, leading to an abundance of guessing. With Table 8 we are able to present one particular example for this endeavor, pertaining to our house in Sea Ranch. This case is particularly interesting, because there are no trees contributing to shading, and the clear-story behind the collector bank is a well-defined geometric structure.

Until we did the actual analysis, we had believed that these panels would produce energy entirely free of shading influences. We simply did not suspect that the clear-story of the building located entirely behind the collectors would end up presenting a significant shading problem. In fact, we would have never followed the advice of the Sea Ranch Design Office to place the collector bank this close to the clear-story for architectural reasons, had we been aware of the shading predicament.

Table 8 analyzes the shading from the clear-story behind the collector bank on a specific day, May 4th. Of course, the shading effect changes from month to month, becoming a bit more prominent in June and July, when the sun rises even further eastward, and becoming less significant in the winter months when the sun rises more southerly. Our date, May 4th, is a good average approximation.

Unlike for thermal solar collectors, where shading-caused collector performance reduction is essentially proportional to the fraction by which the collector is shaded, the impact of shading is much more severe for PV panels. Due to the construction of typical PV collectors, any shading will essentially cut to zero the entire energy production of the panel for as long as the shading persists. One can observe this at the third panel from the right in the top row. It receives a significantly smaller percentage of shading than the six panels to its left, which nonetheless persists for roughly the same duration in the day, and it did essentially perform as bad as the other six panels to its left during the entire day (1.6 rather than 1.95 kWh, as would have been expected for entirely unshaded panels).

The clear-story part of the building partially shades 7 panels in the upper row, reducing solar energy collection by as much as 20% (from approx. 1.95 to 1.6 kWh/d/panel) on that date. Four panels in the lower row are also affected by shading (by about 5% to 1.85 kWh). The bar-graph on the right shows the time-dependent system collection on that day, which was a full sunshine day from dawn to dusk. Sunshine conditions and solar collection performance happened to be identical on the prior day and on the same date of the prior year. The area between the red line and the shaded area marks the aggregate collection lost due to shading on that specific day (~7%; theoretical performance simulation with the SOLARCALCS program confirms 5% shading loss averaged of an entire year).

As mentioned, the system has micro-inverters. Had we used just one system size inverter, partial shading of just one panel in a series of panels would cut the entire collection of all panels in that series. Numerically, the production loss could have been as high as the entire area between the blue and the red lines in the graph (about 30%). This attests to the importance of using micro-inverters. The initial somewhat higher cost over using one system-sized inverter will be well worth the extra expense if there is any possibility of shading.

PART D: OTHER NOTEWORTHY RESULTS

Performance Degradation of PV Panels Over Time
The readings shown in Table 8 were identical to the same day of the previous year, both having been cloudless days. Some solar experts assume collector performance degradation of more than one percent per year. Although our evidence is not overly accurate, we do not see any measurable degradation in one year at all.

Shift of Collection Curve for Panel Banks not Facing South
We have already discussed the dependence of system performance on collector azimuth (deviation from due south) and tilt in Tables 1 and 2. In Table 8 we see that, due to the roof orientation facing 60 degrees west of south, the peak collection time shifted by as much as 2 1/2 hours from solar noon to ~2.30 PM. For the specific climate prevailing in Sea Ranch, where the fog often does not lift until later in the day, this shift of optimum panel performance to the early afternoon hours is opportune. For these reasons, we generally advise to mount panel banks in Sea Ranch more westerly than easterly, when possible.

Comparison of Field Results with Theoretical “SOLARCALCS” Performance Simulations

We apply Table 1 for these system parameters. For a 3.28 kW system at 18.4 deg tilt we expect 5205 kWh/y at due south orientation, 4972 kWh/y for SW and 4430 kWh/y for W orientation. For our 60-degree orientation we interpolate to expect 4800 kWh for an unshaded 3.28 kW system per year. (In fact, an exact calculation with the SOLARCALCS program for 60 deg azimuth confirms 4801 kWh/y). Our system has 20 panels of .305 kW each, or 6.1 kW in total. So the calculated full sunshine system performance must be 6.1 / 3.28 * 4800 = 8928 kWh/year. The actual performance, measured with the Enphase system controller and software, was 8500 kWh for that year (left in Table 9). This evidences a 5% reduction due to shading.

We confirm this situation with an identical installation at Sea Ranch (same collector type, same tilt, almost same orientation (35 deg west of south) but zero shading). SOLARCALCS predicts 5062 kWh/y for the nominal 3.28kW system at 35 deg azimuth. That system has only 14 panels, hence 4.27 kW in total, hence 4.27 / 3.28 * 4972 = 6590 kWh expected per year. Measurement with the same type Enphase controller comes up with 6400 kWh collected during that period. (right in Table 8). However, we experienced 6 days of documented system downtime in July, 2021 (due to a tripped circuit breaker while the house was unoccupied). This would have added another 180 kWh to the total count, which gives 6580 kWh, i.e., perfect agreement between theoretical prediction and actual measurement.

The above result of 5% annual shading reduction (about 400-450 kWh/y) due to the unassuming clear-story above/behind the solar panels is, therefore, quite realistic.

PART E: PV SYSTEM SIZING AND BATTERY BACK-UP RECOMMENDATIONS

Arguably the biggest problem for homeowners considering to invest in a solar PV system is the question of system sizing.
— How many panels should I install?
— How many kWh per year should my system produce?
— What panel brand should I select?
— What panel efficiency should I go for?

Even more critical are the questions:
— Should I get simply a solar panel array, feeding into the “Grid”?
— Or I should invest in an expensive, integrated battery back-up package?
— Or is there an alternative, lower cost solution to bridge me over brown-out periods?

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These are the questions where installers tend to have the least incentive and/or expertise to give the best advice, as they may, understandably, be biased to recommend the larger, more expensive alternative. Without prejudice, unbiased and from experience, we recommend here some answers to these questions. We are careful not to spend too many words in defense of our recommendations but rather ask the reader to contact me with specific requests for detail.

PLEASE NOTE THAT THESE RECOMMENDATIONS ARE BASED ON THE FOLLOWING PRIORITY OF CONCERNS:
(1) RETURN ON INVESTMENT (“I want to maximize my energy cost reduction for the minimum capital expense”)
(2) GHG FOOTPRINT REDUCTION (“yes, I also want to reduce my carbon footprint”)
(3) GENERAL CONVENIENCE (“I’m willing to adjust my lifestyle during brownout periods”)

(a) How many panels should I install? — How many kWh per year should my system produce?
Choose anything less than about 80% of the total kilowatt-hours evidenced in your annual electricity bills.
You may want to go to our paper titled “Home-Energy-Analysis for Carbon Footprint Reduction (https://www.healingguidance.net/home-energy-analysis) for assistance with getting to that number. Adjust for planned consumption increases (e.g., if you plan to get an EV; or if you plan to convert your gas- or propane-powered space heater to a heat pump), or for permanent decreases (e.g., reduction of the use pattern of your house; solarizing the heating of your hot tub, or alike).
Optimal financial payback is obtained when all kilowatt-hours produced by your PV system replace only your highest cost/tier energy usage.

(b) What collector brand should you choose? — What panel efficiency?
Grab the lowest cost panels on the market. Balance cost with efficiency.
Panel prices are highly competitive, and quality is similarly good through-out. If there is enough space on your roof, choose much lower-priced panels and a bit larger area to get to the same kWh/y production. However, consider that more panels also require more micro-inverters and more mounting hardware.

(c) Feeding into the “Grid,” and/or integrated battery back-up?
Choose <80% sized solar-only installation, not integrated with battery back-up (choose alternative 4 or 5 from the table below if you want back-up during power outages).
The expensive battery back-up portion of a solar panel/battery integrated installation has a very low benefit/cost ratio. The real benefit of the large, expensive battery pack is limited to very few days in the year, while they sit idle and do nothing during, perhaps, 350 days/year. In addition, depending on the type you would choose, the batteries will cycle every day, which will impact the life span of the battery and subject you to no-nonsense continual cycling efficiency losses. There are more arguments against a solar/battery “marriage” — inquire.
Instead, choose one of the much less expensive expensive separate emergency back-up measures, as described in (d) below.

(d) Solutions to bridge over brown-out periods
From lowest to highest cost, in Tab 10 we present a series of measures that can be considered to bridge over brown-out periods. We consider option (4) most effective, but, of course, there are valid arguments in favor of every other option.

CONCLUSIONS

The SOLARCALCS program accurately simulates the performance of any type of solar thermal and solar PV installation, taking all relevant system parameters and weather and site conditions into account, and making it extremely easy to analyze the effect of changing any one system parameter for design optimization purposes.

We present generic result tables for two specific locations, The Sea Ranch, CA, and Sunnyvale, CA. Similar tables for other locations can easily be established by users. These tables can be used as design tool for essentially any solar PV system in Northern California.

These theoretical results are corroborated with experimental results obtained for specific solar installations and found to be so accurate that they enable valuable insights into the effect of panel shading, which can otherwise only be empirically approximated.

Overall results include/emphasize:

— Collector azimuth and tilt are less critical for PV performance than is normally argued.
— 45-deg panel tilt balances seasonal collection for thermal pool heating in Sea Ranch; more tilt is preferable in Sunnyvale.
— As much as vertical (90-deg) panel tilt can be entertained for certain PV and thermal applications in Sea Ranch.
— Shading even from objects behind/above, not only in front of, the panels can significantly affect PV performance.
— Micro-inverters are strongly advised if there is any potential of shading (consider growth potential of nearby plants)
— Generally, Sunnyvale locations are better for PV, Sea Ranch locations are better for solar thermal performance.
— Noteworthy solar energy yield during overcast can only be expected for PV, not for unglazed solar thermal collectors.
— We find no measurable (<1%) performance degradation of our (Canadian Solar) PV panels over one year.