Several sources indicate that solar thermal water heating is the most cost effective because, "for less money, it will generate more energy and offset more energy that would otherwise need to be produced [1]." If this were not true, it would make sense to install a few more solar panels and just buy a standard electric water heater to avoid having a more complex water heating system with a much higher cost than a standard water heating system. I will investigate the worth of solar hot water by comparing the energy required by an electric water heater and estimating the number of solar panels needed to cover the energy difference between an electric water heater and a solar thermal water heater.

First, a conservative estimate of the amount of hot water used daily in a home can be found from various estimation tools online [2]. A daily home situation of five individuals each taking a 15 minute shower, washing one load of dishes and washing two loads of laundry, the hot water usage is estimated at 227.5 gallons/day. Using [3], and assuming water is heated from 60°F to 140°F and water heating process is 100% efficient, about (4186 J/kg°C)(145 kg)(227.5 gallon/40 gallon)(60 °C - 15.6 °C)(1kWh/26.9MJ) = 42.6 kWh is needed per day (40 gallons of water weighs 145 kg). Additional assumptions are that the heat loss through the plumbing system is ignored and the electricity required by a solar thermal water heater is negligible (or the extra energy needed by the electric water heater discounts from the small amount of electricity needed by the solar thermal water heater).

As a rough estimate of panel performance, we’ll use the estimate that 71.1% of the energy received by a region can be used by a fixed-angle PV array [4]. Reference [5] was used to determine the yearly average insolation for Melbourne, FL of 4.75 kWh/m2/day. The PV system efficiency (excluding panel efficiency) is assumed to be 90%. The DA100-A2 thin-film 100W solar panel has an active surface area of 16.84 sqft (neglecting frame thickness), which is 1.56 m2, so the thin-film material produces 64.10 W/m2. The panel was rated under STC of 1000 W/m2, so the panel efficiency is roughly 64.10/1000 = 6.41%. Combining the efficiencies yields 4.75(0.711)0.0641(0.9) = 0.195 kWh/m2/day (assuming no obstructions of light to the panels). Because the panel is 1.56 m2, each panel can produce 0.304 kWh per day. In conclusion, a PV system would require 42.6/0.304 = 140.16 solar panels, which seems outrageous.

Examining another case where the dishes and laundry are washed in cold water, 10 minute showers are taken and 14.7% efficient Sharp ND-240QCJ 240W panels are used. Also, the hot water temperature is adjusted to a more realistic 120°F. The differences in this case result in 125 gallons of hot water used per day requiring 17.5 kWh and a solar panel energy daily energy density of 4.75(0.711)0.147(0.9) = 0.447 kWh/m2/day. Adjusting for the panel surface areaw (roughly 1.63 m2) and again neglecting panel frame thickness, the solar panel average daily energy production would be 0.729 kWh. The resulting number of panels needed is then 17.5/0.729 = 24.02 solar panels, which is still a large number of panels.

So I ask the readers, is there an error in my calculations? Is the use of solar hot water really such a no-brainer?

Thanks,
Trevor

[1] Williams, C. Renewable Energy World. Retrieved from http://www.renewableenergyworld.com...ion-market
[2] Survey, U. G. Water Use at Home. Retrieved from http://ga.water.usgs.gov/edu/sq3.html
[3] Nave, R. Household Energy Use. Retrieved from http://hyperphysics.phy-astr.gsu.ed...nergy.html
[4] Landau, C. R. Optimum Orientation of Solar Panels. Retrieved from http://www.macslab.com/optsolar.html 
[5] Tukiainen, M. GAISMA Environmental Resource. Retrieved from http://www.gaisma.com/en/location/m...orida.html

Solar hot water panels heating water to 125 F (52 C) typically operate at 40% to 55% efficiency, while solar silicon photovoltaic (PV) panel efficiencies range from about 13% to 19%. Therefore, per unit area, solar hot water panels are more efficient for heating hot water since the PV panels use a narrower part fo the electromagnetic spectrum. You would have to check on cost per unit area for that comparison.

Storage of electrons and hot water both involve problems and expenses, so this is an advantage of grid-tie PV systems. Running wires is easier than running plumbing, and less likely to leak.

Lee,

Thank you for your reply. I like your explanation of efficiency differences between the two technologies based on the electromagnetic spectrum. Your explanation is similar to http://greenrednecks.com/2009/05/09/solar-thermal-vs-photovolatic-pv-%E2%80%93-which-should-you-choose/. I can relate to this explanation, but it lacks a lot of detail. I was hoping for a more scientific response and a review of my arithmetic and sources.

I did find an error in my calculations after posting, but I don't have an immediate remedy. The insolation numbers I used are total solar energy received for the average day, but the data lacks information on intensity. Solar panel efficiencies are rated by STC, which uses 1000W/m2 irradiance and 25C. In short, the efficiencies solar panels at different temperatures and irradiance levels will vary and probably for the worse, making my calculations above weigh even more in favor of solar thermal water heating.

Thanks,
Trevor

Trevor-

You are trying to "reinvent the wheel" in terms of computing energy collection for solar PV and solar thermal, and you would like the forum members to help educate you. That is not an efficient use of our time. For solar PV, the answer to how much energy you can collect is already known. Just use PVWatts version 2.0, http://www.nrel.gov/rredc/pvwatts/grid.html (it is free) to compute the power for Melbourne, FL, which it shows with an insolation of 5.08 kWh/m^2/day, which is close to your value. So PVWatts gives the answer of 3.57 kWh/day per kW DC rating for the panel. If you want to reinvent the wheel with your own calculations, feel free, but make sure you match the answer of PVWatts (within 10% or so). Note that your 90% efficiency is too high. Look at derate factors for PVWatts (e.g., see table titled Solar Photovoltatic Derate Factors as Provided by SunPower at http://www.residentialenergylaboratory.com/rel_energy_use_pv.html).

If you want to know why solar PV systems are inefficient compared to solar thermal, use Excel to plot out the solar spectrum using a black body temperature of 5800 K using Planck's Law. Then compute the effect of the tranmission range of glass, and the reflectivity. Then multiply that by the response factor for a silicon photodiode. To compare with solar thermal, just use an absorptivity for black paint, maybe 0.95 at all wavelengths, in place of the response factor for the photodiode.

For solar hot water, use calculators at Build it Solar (http://www.builditsolar.com/References/references.htm) like http://www.infinitepower.org/calc_waterheating.htm.

This is your homework problem, not mine.

Posted By Lee Dodge on 13 Feb 2012 06:27 PM
Solar hot water panels heating water to 125 F (52 C) typically operate at 40% to 55% efficiency, while solar silicon photovoltaic (PV) panel efficiencies range from about 13% to 19%. Therefore, per unit area, solar hot water panels are more efficient for heating hot water since the PV panels use a narrower part fo the electromagnetic spectrum. You would have to check on cost per unit area for that comparison.

Storage of electrons and hot water both involve problems and expenses, so this is an advantage of grid-tie PV systems. Running wires is easier than running plumbing, and less likely to leak.

But the efficiency of either depends a lot on the operating temp, and the delta-T between thermal panels and the ambient outdoor air.  In very cold climates the wintertime uptake of PV can approach that of a thermal panel running at 130F+ water in crisp 0F air, but if you're using the panels for radiant-slab space heating with only 80F water, maybe not.

And a 15% PV system running a mini-split heat air-source heat pump at outdoor temps of 45F can beat 130F solar thermal on  effective-efficiency for space heating due to the COP of the heat pump.

But under the summer sun when PV hits 140F+ it's output will be significantly lower than it's 25C rating due to thermal electron leakage effects.

Sundrum marries PV panels to thermal panels to maximize total collection efficiency at domestic-hot water pre-heating temperatures. By using the thermal panel to cool the PV it runs at higher effective efficiency than if they were separate.

Bottom line, there's no easy math, you still have to design your solar for the actual application to optimize it's actual efficiency, and it WILL vary.

Dana1-

The original poster (OP) said: "I will investigate the worth of solar hot water by comparing the energy required by an electric water heater and estimating the number of solar panels needed to cover the energy difference between an electric water heater and a solar thermal water heater."
So I think his interest is in domestic hot water. Therefore, we do not need to venture off into air source heat pumps for space heating. Let us keep it simple and straight-forward to address the question asked by the OP.

You said: "In very cold climates the wintertime uptake of PV can approach that of a thermal panel running at 130F+ water in crisp 0F air..."
Let us examine that statement. Currently it is 31F (-0.6C) outside here, and my Viesmann Vitosol 200F solar thermal system is operating with a 125 F (52C) inlet antifreeze temperature and 138 F (59 C) outlet temperature. If I use Andy Schroder's solar thermal model at http://andyschroder.com/cgi-bin/FixedTilt.cgi?collectorID=Vitosol_200F&Tin=50&Tout=60&Collector_Altitude=35&Collector_Azimuth=0&location=724660&NumberDaysAveraged=5&GrossAreaPerCollector=1 for Colorado Springs, CO (the closest location to me that he lists), then for an inlet temp. of 50C and an outlet temp. of 60C, he predicts the solar thermal power output over the year, and he shows output varying from 1.3 to 2.8 kWh/day m^2. Multiplying 365 days/year times an average daily value of 2.05 kWh/day m^2, then the annual collection is 748 kWh/m^2. How does this compare to solar PV in the same area?

Using data for my neighbors solar PV system which has a more typical efficiency (14.4%) than my own, he has a Sharp system that is rated at 2.82 kW DC, and the panel area is 19.6 m^2. Running this system in PVWatts 2.0 for Colorado Springs, the predicted output is 4214 kWh per year, or 215 kWh/m^2 annually.

So, annual averages for Colorado Springs, a relatively high solar insolation area:
solar thermal = 748 kWh/m^2
solar PV = 215 kWh/m^2
solar thermal / solar PV = 748/215 = 3.5 on an area basis

The area advantage for solar thermal is not surprising. Solar thermal collects most of the energy that comes through the glass cover plate, say from 0.33 micrometers to 3.0 micrometers. It does lose some of this energy through reradiation. In contrast, a silicon photodiode has significant response only over the range from 0.4 micrometers to 1.2 micrometers, and the quantum efficiency is low on both ends. The OP was surprised at the large area of PV panels required to heat water. It is clear that a much smaller area of solar thermal panels should be required. There are significant losses in storing thermal energy, but there are also losses in storing electrical energy.

You (trevdog122) may be mixing a few numbers here.

If you use numbers from PVWatts, then you may not need such complexity.
 
There are 2 solar insolation numbers, expressed as kWh/m2/day, available from PVWatts; a number that reflects historical weather changes (clouds, air mositure content, etc.) that's at STC 25° C.  For a Dallas location, this number is approximately 5.46 kWh/m2/day yearly average.

The other number additionally includes historical temperature changes.  For a Dallas location, this number is approximately 5.00 kWh/m2/day yearly average.

Solving for the number of 100 W thin-film panels needed:

Daily PV system output = 42.6 kWh/day = (5.00 kWh/m2/day)(0.1 kW/panel)(x panels)

# 100 W thin-film panels needed = 42.6 kWh/day / (5.00 kWh/m2/day)(0.1 kW/panel) = 85.2 panels.

This number assumes theoretical perfect PV system efficiency.  Now apply an efficiency factor.  PVWatts uses 77% as a default number to represent deviations from true south, imperfect tilt, constant tilt, wiring sizes, etc.

85.2 panels / 77% = 110.6 panels.

Hope this helps.

Best regards,

Bill

Lee- at ambient-to-water delta-Ts of 130F+ flat panels are already running less than 40% collection efficiency, and if you subtract out the pumping power it's looking even less great, and the difference between that and a better-than-average PV system isn't very big, which is all I was saying with that comment. I wasn't talking about annual uptake, only mid-winter performance of PV vs thermal systems in very cold areas as "the exception that proves the rule", but wasn't being very clear about it. (Alas, my whole discussion was indeed a ramble, not actually addressing the OP's question- call it a mush-brain Monday. ;-) )

Using PV for thermal in resistance-heaters (without any heat pump leveraging) will ALWAYS be a net-loser in low-mid-temp thermal applications (such as DHW) and yes, it really IS a no-brainer.

I like Sundrum's consolidated hybrid approach for getting the most out of small-roof applications though.

It appears there is good reason to have both solar thermal and photovoltaic panels. I'll be building in Michigan. The solar thermal panels will harvest much more in the winter if they are more nearly vertical, I'm thinking of about 60 degrees. How can one intelligently chose the ratio of thermal panels to PV panels? From what I've been able to calculate, it is very difficult to fully cover winter space heating with solar thermal panels. "Borrowing" some energy from the grid which can later be "repaid" is the best argument for grid tied PV and a good heat pump. My plan which is honestly based on pure guesswork is for 160 sq ft of thermal panels and 550 sq ft of PV (7500 dc watts).

Liebler said: "How can one intelligently chose the ratio of thermal panels to PV panels?"
I do not see any reason to consider this ratio. You have implied three uses for some type of solar energy:
1. Space heating
2. Domestic hot water heating
3. Electrical generation

The normal approach to defining these requirements is as follows:

1. Space heating (typically the least attractive solar option, since the energy is only needed in the cold months, where in almost any climate it is the most difficult to collect solar energy). Perform heat loss calculations for the house design to define the load. Use computational tools such as those provided at BuildItSolar website to see what size system in terms of panels and storage would be required. Examine the cost compared to conventional heating to see if solar heating can be justified economically. Solar space heating is usually not economically justified, so then the system size can be determined by what "contribution" to green energy that you would like to make, which could still be 100% of the expected load if you desire.

2. Domestic hot water heating. How much hot water does the family use currently? Assume that same amount will be used in the new house. Size the solar hot water system using computational tools at BuildItSolar or at solar thermal system vendors.

3. Electrical generation. How much electrical energy does the family use currently? Assume that same amount will be used in the new house, with whatever adjustments you want to guess at for changes in heating system, fans, lighting, etc. Or use BEOpt to compute electrical loads. That defines the load. Let us assume that you will have a grid-tie system? Use PVWatts Version 2 (available for free) with input for your actual address that will customize the solar insolation, and then see what system size is required to meet your load. Look at any restrictions based on roof area, utility restrictions, etc. That should define your system size. Utilities in some areas will not allow you to oversize the system based on expected electricity use, in some areas they will not pay for excess energy generated, while in other areas, you can be paid a handsome profit for excess generation capacity.

Liebler: The rule of thumb (almost always guaranteed to be imperfect, if less imperfect than something else) is that for space heating from a simple solar geometry point of view you want set them up oriented due south, pitched at latitude +10 degrees. But if you usually have snow cover during the coldest months you can set them up steeper, soaking up the very considerable reflected gains, and have less of a heat-dumping issue in the summer.

If your grid tied with an annualized net-metering basis you should set up the PV for maximum annual gain, not optimal winter gain, which will be a more like latitude -10 degrees, but local weather (including the fog, snow, & air-clarity/haze data) can alter that quite a bit.

Any home where you want the solar to pick up a large fraction of the heating load needs to be substantially above code on R values (like 2x the code-min whole-wall R), and properly assessed SHGC vs. U values for the size & orientation for the windows, and as air-tight as possible (under 3 ACH/50 is good, under 1.5 is better.) At code min R & air leakage the size of the array necessary to handle the lion's share of the space heating load won't come anywhere near to fitting on the house. A good place to start is table 2, p 10 of this document:

http://www.buildingscience.com/documents/reports/rr-1005-building-america-high-r-value-high-performance-residential-buildings-all-climate-zones

MI is zones 5 & 6, and note the R-values are "whole-assembly" R, not center-cavity R. eg: 2x6 framing with R20 batts come in at about R14 after factoring in the thermal bridging of the studs, so to hit the recommended ~R30 walls for climate zone 5 would take 3" of exterior rigid foam sheathing, either XPS or polyiso outside the structural sheathing on your 2x6 fiber-insulated wall. At R values less than that the lifecycle cost of the solar required to support the loads will be substantially more expensive than going higher R. There's a big gray area starting around those whole-assembly values, and subsidies can skew the economic analysis by quite a bit. At 2x those values the cost of the higher performance building will likely be more than the lifecyle costs of PV + heat pumps supporting those loads, but the crossover points will vary depending on site & climate factors as well as the actual costs of building envelope improvements.

In any new design using DOE2 and BeOpt (both are freebie downloads, and pretty good) to simulate the building in it's site factors & climate is useful for determine which improvements are and are not "worth it". Most of the time going higher-R on the building and optimizing the passive gains will be cost effective, where active solar-thermal space heating is not.

When & where PV is heavily subsidized, heating with heat pumps as your primary heating system gives you a large base load by which you can then maximize the amount of cheap subsidized PV. In a high-R solar-tempered building in climate zone 5, split system air source heat pumps (mini-splits) can be as efficient as much more expensive ground sourced (geothermal) heat pumps, and need very little in the way of backup. But mid-winter performance is marginal in areas with January mean temps of less than +10F & heating design temps below -10F, so whether that's an option for you depends on your location and local subsidies.

Lee & Dana1,
Thank you both for your insights! Yes, I'm planning on building a "high R" tight home! It seems prudent to go a bit overboard on the insulation as it is not a costly "error". I'll be aiming for r40 whole wall r and r80 ceiling with an r24 unheated basement. I've used PVwatts and the tools at Build it Solar to estimate heat losses from the house and gains by hypothetical solar installations. I find it near impossible to do space heating fully with solar thermal panels, even 100% domestic hot water is iffy in mid winter. I'm inclined to totally give up any space heating by solar thermal as not economically justified. Pushing for 100 % solar fraction of DHW also seems uneconomical as well, the last 20% requires doubling the panel area. How does one make these trade offs?

"I'm inclined to totally give up any space heating by solar thermal as not economically justified. Pushing for 100 % solar fraction of DHW also seems uneconomical as well, the last 20% requires doubling the panel area. How does one make these trade offs?"

It sounds like you have already made reasonable tradeoffs. I forget your location, but wonder if it was the Midwest, like Illinois? I think most folks target for 50% to 70% of DHM, because, as you have said, it is unfavorable economically to get the last 30% or so, except for maybe Florida. But the economics are reasonable for the first 50% to 70%. Passive solar heating from high SHGC windows, insulating shades, proper overhangs, window placement, and home orientation is fairly easy and inexpensive if performed in the design phase. For your "high R" home, you should be able to meet 30% or more of your heating needs from passive. I compute that I am around 30% or 35% for a production house that is not laid out well for passive solar, but I am in a very favorable location for solar insolation on windows. If you want to be closer to net-zero energy, you can consider adding solar PV beyond your usage to make up for energy used for space heating and hot water beyond what can be done with solar. That was my approach to net-zero source energy -- high R (but not as high as yours), passive solar (tempering), solar DHW, very low electrical consumption, and excess PV even using a small system. Depending on the net metering rules by your utility, this is usually not economically justified, and it may not even be allowed by the utility, but net-zero energy can be psychologically rewarding.

BEOpt is made to help with these decisions, and includes the economics as well as the heat loss calculations. Version 2 has more reasonable costs for solar PV than version 1, but is maybe still a little on the high side at $5.50 per installed DC Watt, while others are quoting $4.50 to $5.00. I think version 1 was using $7.50 per DC Watt.

Posted By Liebler on 21 Feb 2012 04:17 PM
Lee & Dana1,
Thank you both for your insights! Yes, I'm planning on building a "high R" tight home! It seems prudent to go a bit overboard on the insulation as it is not a costly "error". I'll be aiming for r40 whole wall r and r80 ceiling with an r24 unheated basement. I've used PVwatts and the tools at Build it Solar to estimate heat losses from the house and gains by hypothetical solar installations. I find it near impossible to do space heating fully with solar thermal panels, even 100% domestic hot water is iffy in mid winter. I'm inclined to totally give up any space heating by solar thermal as not economically justified. Pushing for 100 % solar fraction of DHW also seems uneconomical as well, the last 20% requires doubling the panel area. How does one make these trade offs?

The spreadsheet based heat loss calculator on BuildItSolar is really crude. There's a better spreadsheet heat loss freebie downloadable from Crown Boiler, as well as pretty good  free pro-type heat loss tool available from Taco.


hose are pretty reasonable tools to use for designing heating systems, but using a heating design tool to optimize a building design is a bit like using a rock for a hammer. It's not even half the tool you're really looking for- they don't have the total-energy-use simulation you get out of DOE2 or  BeOpt.  The Hot2000 freebie is also pretty good.  The more site & climate information that goes into it, the easier it is to assess the relative performance & value of changes, beyond mere  BTU/hour loading @ outside design temperature.

For very-high-R homes the PassiveHouse modeling tools are pretty good- it's cheap, but not free, and they have been criticized by the NetZeroEnergy types for promoting R values (particularly for sub-slab foam) with lifecycle costs considerably more expensive than PV + heat pumps.

Dana1,
At your suggestion I've downloaded and tried BeOpt and Hot2000 freebie. I'm not at all impressed. They do more but force more assumptions and limit choices to what is in their library. What is the precise definition of "framing factor" and how is it applied? I am building with double 9 'tall 2x4, 24"0C stud walls with 11 1/2" cavity filled with dense pack cellulose (r3.8/") using single top plates & "advanced" framing. I calculate my whole wall r at 40.76, using r1/" for wood, ignoring sheating, drywall and "air films". ( cavity r=43.7)

Dana1 may have a different definition of framing factor but I think of it as a percent of the total wall area occupied by framing members.  Framing in a typical 2x4 wall can occupy almost 30%.  This means that a significant percentage of the wall is not insulated unless there is insulation placed beyond the studs.  I believe 25% is the figure that was detrmined by ASHRAE in one of their studies although the hot box test uses figures between 11% and 14%.

The real question is how will the percentage be computed for the wall you intend to build.  In your case, is the framing factor applicable?

Alton,
      I computed the whole wall r value by using the cavity r for the relative area(91.1%) occupied by the full cavity and the 7" wood+ 4.5*3.8)=r24.1 for  the portion (8.8%) of  area occupied by framing.  Does that mean I have a framing fraction of 8.8%?

Posted By Liebler on 23 Feb 2012 07:57 PM
Alton,
      I computed the whole wall r value by using the cavity r for the relative area(91.1%) occupied by the full cavity and the 7" wood+ 4.5*3.8)=r24.1 for  the portion (8.8%) of  area occupied by framing.  Does that mean I have a framing fraction of 8.8%?

That's an insanely low framing fraction, that must simply be ignoring all  headers & plates, code-required firestop blocking, band joists, window & door framing, etc.  What you've calculated would be something similar to the portion used for defining the "clear wall" R values, which aren't very useful for homes with windows & doors, and walls of non-infinite height.

30% would be on the high side unless there are lots of cute bump-outs, double plates top & bottom, etc.  In "typical" tract housing 25% might be more common, but framing fractions of 20% are easily achievable even with 16" o.c. framing if one pays attention to window placement & sizing to minimize the number of studs & cripple-studs, and use single-plates where-appropriate.  To get it as low as 15% takes 20" o.c. advanced-framing/optimal value engineering (AF/OVE) approach to everything from wall lengths to window & door sizing, but not impossible.  But 8.8% isn't.

To get a better handle on it, study this document:


http://www.buildingscience.com/docu...gh-r-walls

In particular, look at the table 3, p.13 (and the stated framing fraction assumptions behind the calculated whole wall values.)

Dana1,
      OK, what I calculated is more properly called the clear wall r value.  This is the r value for a straight wall with no openings.  In my analysis, I've considered the "rim joist" area as a separate wall area that is r30 (without interior spray foam but I'll probably add it for better air sealing).  This seems to be what was done in the paper you reffered to.  Including the rim joist with the wall results in an r38.5 .  Window and door framing (including headers) is, in my mind, more properly accounted for by enlarging the window/door area which is what I've done.  It is my intention to have no thermal bridging below the roof trusses, which sit on both inner and outer exterior stud walls, except at window and door openings.  This is not like any of the wall systems in the paper.  I'm hoping I can convince the authorities that dense pack cellulose doesn't require added fire stopping.  My current thought is to use EASI-WALL with 4" concrete on each side of 4" foam for the basement so the thermal break is maintained down to the footings.

Liebler said:
"At your (Dana1's) suggestion I've downloaded and tried BeOpt and Hot2000 freebie. I'm not at all impressed. They do more, but force more assumptions and limit choices to what is in their library."

I do not understand your comment about being limited to choices that are in their library. When using BEOpt, you can right click in the "Double Stud options" box (under Walls) and that takes the user to the "Options editor." There the user can define the wall with any thickness, cavity R-value, and framing factor, and it will compute the overall R-value for the assembly. It is easiest to do this by copying the data for a wall similar to yours, pasting that at the bottom, and then editing it. However, you must use their definition of framing factor. It will not work correctly when you make up your own definition of framing factor. See the notes in the bottom frame in the "Double Stud options" box to follow their definition. There will be some uncertainly in estimating the framing factor, but if that is of concern, simply define two different walls with the lowest and highest reasonable framing factors, and evaluate the sensitivity by calculating overall home heat losses for both. BEOpt appears to be very flexible for these purposes.