As promised, today’s post will be all about how I modeled domestic hot water (DHW) energy consumption in the homes I studied for my PHD thesis. Please, stifle your yawns!
Before I dive into that, however, a couple of quick notifications. I will soon have two articles published on this research. One is in the Sep/Oct issue of HomeEnergy Magazine (http://www.homeenergy.org/show/article/id/1903/nav/default). This one is all about the financial side of building and owning a net-zero or near net-zero energy home in New England. I know many of you are very interested in those results, so I strongly urge you click on over to HomeEnergy.org and take a look. Like most things in life, you will have to pay to read the full article. For copyright purposes, I won’t be able to simply cut and paste it into this blog. Also, its going to be a while before I get to the financial section of my thesis anyway, so rather than wait several more weeks or months even, you can get the info right now at HomeEnergy Magazine.
The second article will be published in Energy and Buildings, a peer-reviewed international journal (http://www.journals.elsevier.com/energy-and-buildings/). The article has been approved and I am waiting for them to send me the final proof. Once I know it is published, I’ll let all of you know. That article is all about the energy results of my research project, with no mention of finances at all. Okay, on to DHW modeling.
Remember, the whole point of creating my own custom energy model (CEM) was to have a model that could estimate energy consumption over a year in each of these houses, so that I could have something against which to compare the measured consumption. I couldn’t use “off the shelf” modeling software (see my previous post), so, using things like the ASHRAE Fundamentals Handbook and the DOE Building America Benchmark, I came up with my own models for the four categories into which energy consumption falls in a home: HVAC, DHW, lighting, and appliances & miscellaneous loads. Here’s an excerpt from my thesis with accompanying equations:
Energy consumed to heat a home’s DHW is dependent upon a number of variables. These include: the number of occupants in the home, the temperature of both the source cold water and the set point temperature of the DHW, the efficiency of the heating system, and significantly, whether the home uses a solar thermal system for DHW. The first step is to determine the daily DHW load in gallons, and for that a series of simple equations from NREL’s Building America Benchmark are used. These calculate the average daily amount of DHW used for clothes washers, dishwashers, showers, baths and sinks. The sum of these load yield the total daily DHW load in gallons. Multiplying the daily load by the number of days in each month yields the monthly load.
In the equations below, “Nbr” refers to occupants (see the footnote on the bottom). Also, just click on the equations and a new tab will open up where you’ll actually be able to read them.
Then, knowing the set point temperature of the hot water (which was one of my questions to each homeowner) and using the heat capacity (4187 J/kg-C) and density (1 kg/liter) of water, I determined how much energy is required to heat the amount of water consumed, i.e., the energy DHW load.
Note that I assumed that tank and line losses amounted to 13% for each house. Thus, the actual energy required to heat the water would be 113% of the load. You’ll see I ended by converting the energy into kWh. BTW, these are screen shots from “MathCAD”, a very cool program (http://www.ptc.com/product/mathcad/). I use MathCAD ver 15.0. I tried using the latest iteration, which is called MathCAD PRIME 2.0, but I did not like the new interface.
Of the 20 houses I studied, nine had solar thermal systems, and most of those used them to heat DHW. So, I had to estimate how much of the required energy load could be met by these solar thermal systems, i.e., how much energy would the solar thermal systems produce and transfer to the hot water systems during the course of a year. I’m referring to the “solar fraction”–the fraction of DHW load met by the solar thermal system each month (you have to break it down by month; though I assume the homeowner consumes the same amount of water month to month, the amount of solar energy of course varies with the season…). More excerpts from my thesis follow:
The third step is calculating the solar fraction (SF) using the f-chart method. The SF is the fraction of DHW load met by the solar thermal system each month. This fraction greatly depends on the load, the size and efficiency of the solar thermal system, and the time of year. Generally speaking, a correctly-sized solar thermal system may supply most of or even exceed the energy load during summer months, but produce only a small fraction of the load during the cold winter months.
The last sentence applies to homes in cool, snowy locations like New England. Homes in warmer climates (Florida, Arizona, Hawaii, etc.) may be able to generate all their energy for DHW from solar thermal systems year round.
This step is broken down into two parts: part A calculates the average daily radiation on a surface of the solar thermal array for each month, Hc, in kWh/m^2; part B then uses the monthly values of Hc plus various parameters of the solar thermal system itself to calculate the SF for each month. The equations in part A are essentially identical to those used in calculating Hc during the PV production modeling, taking care to use the tilt (β) and azimuth (aw) of the solar thermal system rather than the PV system (see equations 5 – 15 above). The equations for part B follow, with “…PL representing the long term thermal loss per unit load and PS representing the long term insolation gain of the solar thermal collectors” (Goswami, Kreith, & Kreider, 2000).
The fourth and final step calculates the DHW load, taking solar fraction and energy factor of the hot water heater into account. Ld (monthly DHW load) is multiplied by (1 – solar fraction) to get the DHW load required to be met by the home’s hot water heater. For homes w/o solar thermal, the SF = 0 for every month. Finally, these values are divided by the hot water heater’s Energy Factor (EF) to convert from load to consumption, and by 3.6*106 to convert into kWh:
As an example, the figure below gives the results of these DHW calculations for House W, which has a solar thermal system. Note that between March and October the DHW load goes “negative” in this graph. This means that the solar thermal system can supply a greater than required amount of energy for DHW during this period, and hence the electric back-up system should not have to supply any energy during the same time period.
 Note: the author has modified these equations by substituting the number of occupants of each house for the number of bedrooms. The primary reason is that in several of the homes studied, the relationship between number of bedrooms and occupants varies greatly. For example, House A has seven occupants but only three bedrooms, whereas House N has five bedrooms but only two occupants. Clearly, the people in House A would use more DHW than those in House N, but if number of bedrooms is used as the variable, then the equations would yield the opposite results. In the cases where number of bedrooms equals number of occupants, then substituting the variables makes no difference to the results.