It’s an age old dilemma for efficiency advocates: how do you calculate how much energy you didn’t use or how much money you didn’t spend? You can’t put a yardstick up against something that doesn’t exist.

We tend to rely on models and predictions of what might have happened, and calculate the savings based on that hypothetical case.  But it all feels a bit like a house of cards, with our arguments and calculations set on a soft foundation.  Even if stakeholders understand the base-case model (many don’t), they may be skeptical of the savings estimates.

To gain confidence and a voice in energy decision making, we need a few improvements:

1. A simple model for the base case, that anyone can understand with a brief explanation.
2. A way to compare different models to each other, so we can choose the best one.
3. An measurement of the uncertainty in our models and predictions, to set boundaries on our confidence.
4. A quick way to calculate the difference between the model and what really happened, also known as “savings.”

Here’s my workflow for addressing some of these problems and needs, using my own home’s energy.  The process needs improvement, but I think it’s a start.

This method assumes you’re familiar with a bit of weather normalization.  If not, check out my previous article on how your energy use changes through the seasons.

First, plot your building’s energy use versus the monthly average temperature:

Electricity Consumption vs. Temperature

In the graph above, I’ve plotted all of my house’s energy data before September of last year – data for the baseline months before I insulated the attic and bought a new programmable thermostat.  I’ve normalized the kWh consumption to a 30-day cycle for consistency.  And remember, I’m using color intensity to give a sense of time; darker blue points are more recent.

You’ll note that there’s a distinct “curve” shape to the data, where my house consumes substantially more electricity in the cold-temperature months, less between 60 and 70 degrees, and a little more when it gets hot.  This mirrors the energy consumption of my heat pump in cold and warm months.

It’s clear there’s a relationship between temperature and electricity use, so we can make a model of this relationship.  “Make a model” is a fancy way of saying “fit a line.”  This is not a simple linear (straight line) relationship, though.  A polynomial (curve) fits much better.

Polynomial model of energy consumption

Nice.  Now we’re getting somewhere.  Check off requirement #1.

The line, and the 95% confidence intervals shaded in light blue, give us a way to predict how much electricity I would use if the month were 56 degrees.  How?

That line is an equation.  Specifically:

30-Day Normal kWh = 1912.9792 – 17.5737*AverageTemp + 1.2035871*(AverageTemp-61.491)^2

All we have to do is plug 56 into the equation for the AverageTemp and we get approximately 900 kWh.  Great!

Our “model” of energy use has some additional benefits.  It comes with an R Square value of 0.96, which means our model can explain 96% of the variation in the data.  Put another way, 96% of the change in my monthly electricity bill is captured by the equation above, and is explained just by the temperature change.  Only 4% of the variation in my bill is caused by other factors – the randomness inherent in our daily habits, how hard the wind blows, and who stands with the refrigerator door open.

We could add other factors to our model, like how many nights we cook every month, or change the type of curve we fit, and these would possibly improve our R Square.  But it’s very simple to find out the temperature, and I’m happy with the fit.  We’ll leave it alone.   Still, it’s nice to know we could develop better models and objectively compare them with one another based on R Square and other metrics.  Check off requirement #2.

Okay, let’s go ahead and add in my September-January data (red crosses) to see where it falls on the model.

Electricity Model with Savings Period

Eyeballing the data, it looks like the September data point is close to the prediction and lies inside the blue shading at 70 degrees.  Moving left through the colder months, the deviation starts to stand out, and we see that the red points don’t fit well with the previous model.

Keep in mind – we’re looking only at the vertical distance to get a sense of the changes.

Vertical distance = kWh savings

Thankfully, we don’t need to measure each point individually with a ruler, we can use our model curve to speed up the process.  Just use the equation for the line to calculate the difference between the model and each point.  In effect, we’re flattening out the curve, removing the effect of temperature on electricity consumption.  The result is called the “residual” – the 4% of variation left over when we remove the 96% of variation accounted for in our model so far.

Residuals from the Electricity Model

Requirement #4 – Check.

You can see that we’ve flattened the line, and only the difference between each point and the model’s prediction is left.  You’d expect these residuals to look randomly scattered – if you see a pattern, your model missed something!

You’ll also notice that the baseline (blue) points are scattered around the zero line, deviating by plus or minus about 100 kWh.  You can make a measure of this variation, but we’ll just eye-ball it for now (I’m still working on Requirement #3)  and consider anything within those boundaries to be “normal” or expected.

You have no doubt noticed by now a couple of red crosses WELL below the line – those are my energy savings for December and January!  Multiply the residual by the price per kWh for that month (and yes, this changes…) and you’ll get this:

Savings over time

The line hovers around zero, meaning my model did an okay job at fitting the data.  It has a slight upward angle, indicating that my energy use was increasing over time, independent of the temperature changes.  Not good!

But take a look at the month after I insulated (the first red cross).  Energy use was below the expectation.  It’s not huge, but I wouldn’t expect a lot of savings in a month where my HVAC doesn’t run very often.

It’s not until December when you see some serious savings.  I attribute the $47 drop to a couple of things

1. better insulation
2. better control by the thermostat, avoiding the use of my auxiliary heat
3. we traveled over Christmas and were gone for a week 

January’s savings weren’t quite as good, but still respectable for a single month.  I figure I’ve spent under $400 on insulation, thermostats, caulk and foam, and I’ve recouped about $100 of that in just five months.  Not bad, and I feel good knowing I can demonstrate the savings with some solid numbers, rather than guesstimates and a vague hunch.

Sadly, I’m excited to see what next month’s bill brings…

So the question is: how do YOU measure what didn’t happen?

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