Zero Energy Home: Introduction to the Numbers

I'm a numbers guy. In college, I majored in Math, but that wasn't enough numbers, so I added a second major - Computer Science. So when I started thinking about our new, energy-efficient home it was in terms of numbers.Before we started building, I looked for numbers. There were numbers out there, but I couldn't figure out how to make those numbers tell me what I wanted to know: how does what I put into the design and construction of my new home affect the performance - in detail - of my house? In particular, I wanted to come up with a good estimate of my annual energy consumption, so I could figure out how to size my solar PV array.

My wife and I had initially planned to live in our new home for a year before we installed the solar electric system, but we're not very patient, and our electric provider had rebate money available now, but perhaps not later. So now I had to figure this out, and there just didn't seem to be any reliable sources of information on the web that could help me.

So I decided that what I needed was data and some sort of model of my home's energy performance. Some of the data I knew I needed is easy to collect - just step outside to the side of my house and read my electric meter every day and record how much energy I've used.

Since I started doing this in August (in central Texas), it's readily apparent that the major portion of our energy usage is to cool the house. It has, in fact, been a rather hot August, and our energy bills reflect that. But just how much is the outside temperature affecting our energy usage?

It's relatively simple to look up the daily high (and low) temperature for each day, but I found that to be too simplistic. That doesn't tell me if the temperature hovered near the maximum all day, or if it was just a brief spike. I wanted to know how the temperature fluctuated throughout the day. I wanted more numbers.

So I bought a small weather station. It sends the data wirelessly to a small console that displays the data on a LCD screen, and records the data (including indoor and outdoor temperature and humidity) every half-hour. It has a USB connection that I use to download the data once a day to my computer.

Now I've got enough numbers! Almost. There are a couple of appliances that we use rather erratically, but have a significant effect on the daily numbers. Primarily, the clothes washer and dryer, and the dish washer. So I started recording the number of loads of laundry and dishes we run each day.

But what do I do with all of these numbers? What do they mean? Somehow, I have to use my rudimentary knowledge of how a house works to develop some sort of performance model, and then use the numbers to calculate the various parameters that exist in the model.

A lot of my model is speculative, and I'm certain I'm omitting critical elements from it (or at least I'm aware that there could be significant refinements to it). But this is where I'm starting. If you have suggestions, or more concrete knowledge of home energy modeling, please feel free to educate me!

Since I now have access to all of this data, I started thinking about how it fit into the model. I have the outdoor temperature recorded approximately every half-hour, which started me thinking about "degree days", which is a sum of the difference between the high (or low) daily temperature and some ideal temperature. But we don't have our thermostat set to an "ideal temperature", and it the thermostat has different setting for different time periods.

However, I also have recorded the indoor temperature. And I recall from high-school physics that the rate that heat flows is proportional to the temperature differential. So I decided to take the difference between the indoor and outdoor temperatures, add them up for each 24-hour period (normalized for a 24-hour periods, in case I don't have exactly the same number of records for each day).

I'm currently calling this value the "differential", but for the mathematically inclined, it's more like a "degree day integral approximation". That's the first element in my model. It's a value that is proportional to the amount of energy that is used to keep my house at the desired temperature. In the model it will be multiplied by an unknown factor that is an indication of how much energy is lost through the exterior of our house.

That's just one factor that will end up in my model. In future posts, I'll describe the other elements, and attempt to perform some analysis on the numbers.

Date1 Indoor F° Outdoor F° Differential2 Dishwasher Loads Laundry Loads kW·h
Min Max Min Max
8/6/2010 78 80 78 104 165 0 0 25
8/7/2010 77 80 78 99 163 0 0 25
8/8/2010 79 81 79 97 145 1 3 32
8/9/2010 79 80 78 98 152 0 0 29
8/10/2010 76 81 77 99 154 1 0 23
8/11/2010 81 81 79 99 149 0 0 26
8/12/2010 79 80 76 100 120 0 1 26
8/13/2010 79 80 77 98 155 1 0 23
8/14/2010 77 79 80 100 171 0 1 27
8/15/2010 79 80 79 100 173 1 1 30
8/16/2010 79 80 78 102 176 1 1 27
8/17/2010 79 79 76 102 99 0 0 27
8/18/2010 78 78 79 101 177 1 0 28
8/19/2010 77 81 76 100 88 0 2 24
8/20/2010 79 80 79 98 137 1 0 27
8/21/2010 78 80 79 100 150 0 1 29
8/22/2010 79 79 78 101 165 0 0 25
8/23/2010 78 80 76 103 170 1 2 34
8/24/2010 78 80 78 105 185 0 0 27
8/25/2010 78 81 78 94 81 0 2 27
8/26/2010 78 80 77 92 83 0 0 21
8/27/2010 78 79 69 96 71 1 1 27
8/28/2010 78 79 62 97 46 1 1 25
8/29/2010 78 80 72 97 104 0 0 20
8/30/2010 79 80 80 97 134 0 2 29
8/31/2010 77 80 79 98 135 1 0 23
9/1/2010 78 80 79 99 127 0 1 29
9/2/2010 79 81 79 98 115 0 0 25

1Calculations are approximately 5:00PM to 5:00PM 2Differential is the absolute value of the calculated difference between indoor and outdoor temperature summed over the 24-hour period.