Air Conditioner Thermostat Strategy

If you are a frequent reader of my infrequent writing, you'll know that last summer (2011) I installed a system to measure the temperature in and around our house as well as keep track of when the central fan is running (when the air conditioner or furnace is on). Last summer I ran two experiments

1. What is the effect on the attic temperature due to installing additional attic ventilation?
2. What is the effect on the amount of time the air conditioner runs during the day based on whether I turn it off or leave it on while the house is unoccupied?

The data from the first experiment showed about nine degrees of cooling after adding the extra ventilation determined simply by comparing the average temperatures before and after making the change.  The second experiment was far less conclusive and as I said at that time, a more complex statistical analysis would probably be necessary to make a determination.

That was a little over a year ago and I now have another season of data and the desire to jump into the statistics. You science nerds ready to rumble and see where this leads?

I made the choice this past summer to throw in another variable: rather than just measuring the effect of turning the air conditioner off during the day, I also investigated the effect of changing the thermostat set-point.  Every week on Monday morning I would re-program our thermostat with a different set-point and then each day of the week decide whether to bypass the schedule and leave it on all day or let the schedule run, cooling the house in the evening to the set-point I had chosen.  The three set-points I chose were 77, 78, and 79 degrees Farenheit; sadly, the 79 degree data set turned out smaller than I would have liked so I won't be able to use it for this analysis; hopefully by the end of next summer this will not be the case.  

I threw two summers of data into the statistics machine and hoped to answer a few questions:

Question 1 - Is it more energy efficient to turn off your air conditioner during the day (or when the house is unoccupied)?

This questions has been asked for many decades and the technical term I've found describing the strategy is "thermostat setback".  Much of the research seems focused on using this strategy during the winter for saving energy on heating and the internet is full of opinions.  I haven't looked very hard but I did find one academic paper from 1978 ("Energy Savings Through Thermostat Setbacks" by Nelson and MacArthur) in which the researchers used a computer simulation to try to answer the question.  Their general conclusions support the use of thermostat setback with an unsurprising caveat: the effect of the setback is most noticeable when the degree of the setback is large and the length of the setback is long.  The lower the change in thermostat setpoint and/or the shorter the duration of the change, the less significant the effect. In scenario at our house, both of these conditions are satisfied (roughly): the setback period is at least 8 hours and the change in temperature is high enough that the air conditioner does not run at all when setback.

To do the analysis on the data I had collected, I split the dataset into three parts based on the thermostat setpoint when it ran during the evening.  Each subset contained data showing the daytime state of the thermostat (cooling or not), the evening thermostat setpoint, the 2-hour average peak temperature of the day, and the number of hours the air conditioner ran that day.  I then ran a multi-regression analysis using the air-conditioner run-time as the dependent variable and the outdoor temperature and day-time state as independent variables. (For those of you who don't know, multi-regression analysis tries to determine the mathematical relationship between variables based on a set of data.  More importantly for our purposes, it will also calculate whether a given input variable has a significant impact on the stated output variable. Specifically, it will tell us whether the daytime state of the air conditioner has a statistically significant effect on the air conditioner runtime.)

Answer 1

• Thermostat setpoint = 77'F: Daytime state does have an effect on how long the air conditioner runs for the day.
• Thermostat setpoint = 78'F: Daytime state does not have an effect on how long the air conditioner runs for the day.

It looks like I just happened to stumble across the turning point.  The statistics imply that if I set the thermostat at 78'F, I will not experience longer run time if I just leave the air conditioner on all day rather than turning it off when I leave in the morning.  If I set the thermostat at 77'F and do choose the turn the air conditioner off during the day, the statistical model predicts a reduction in air conditioner runtime of almost 2.5 hours if I choose to do this. 

Question 2 - Does the thermostat setpoint have a significant effect on how long the air conditioner runs for the day?  If so, how much?

I haven't done the research on this one to have an informed opinion so I'm just going to jump to my analysis. Dataset was the same as above but this time was split into two datasets, one in which the AC was running all day and one in which it was off during the day.  I then ran the same statistical analysis to build a model of that would allow me to predict how long the air conditioner would run given the two-hour average peak outdoor temperature and the thermostat setpoint.

Answer 2 - The thermostat setpoint is statistically significant in determining how long the air conditioner will run each day regardless of whether the air conditioner is off or on during the day.

• Air conditioner off during day:  Each degree Farhenheit the thermostat is reduces saves 0.65 hours of air conditioner run time that day.
• Air conditioner on during day: Each degree Farhenheit the thermostat is reduces saves 0.80 hours of air conditioner run time that day.

Question 3 - How much money can be saved by using thermostat setback or increasing the thermostat set?

Answer 3 - I recently was able to measure the power of my air conditioner: 4kW when its running. Let's use the ballpark value of  $0.10/kWh for energy.  This means I'm charged $0.40 for every hour my air conditioner runs.

• Thermostat setback - If I choose to set my thermostat to 77'F and turn it off during the day (rather than leaving it running), I'll save almost 2.5 hours of air conditioner runtime which translates into $1.00 of savings per day.  Over a 30 day month this is $30 in savings.
• Thermostat setpoint increase - We can save $0.26 to $0.32 each day per degree the thermostat is increased.  This doesn't sound like much and over a 30 day month, this is a total reduction in the cooling costs of $8-$10 per degree.

All of the statistical models were linear in nature and we know from Newton's Law of Cooling that the heat loss rate of a house is non-linear; the hotter it is outside, the faster the house heats up. It should take much more cooling effort to keep a house 20 degrees cooler than the outside than just 10 degrees.  A linear model predicts it will take exactly half and this is not correct.  The model predicts the same amount of reduction in air conditioner runtime by moving the thermostat setpoint down one degree Farenheit whether it is 85'F outside or 110'F outside.  A non-linear model would work better here but until I figure out how to make the magic statistical software do this, we'll have to stick to the linear model.

That's what I've go for now.  Until next summer when I've got more data, this is what I know.