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This article shows engineers and energy data analysts how to “normalize” energy consumption or production to account for the variation in weather over time. By the end of the article, you should understand why normalizing for weather is important, and how it can be done, either in a spreadsheet or using a free tool called RETScreen® Plus.

Why Normalize for Weather?

The need to “normalize” for weather arises very often. For example, you have a year or two of utility bills for a facility, you plan on improving the energy efficiency of the facility, and you need to estimate what the energy savings will be in the future. One challenge is that the past energy consumption is determined not just by the equipment at the facility, but by the variations in the weather experienced by the facility. What if the winter covered by the utility bills was especially cold, and as a consequence gas consumption was higher than typical? Basing your estimates of savings on a single year, without “normalizing” for weather, or explicitly adjusting the consumption to reflect typical weather conditions, will cause you to overestimate the typical savings in the future.

Normalizing for weather is a good idea whenever an accurate understanding of the current energy consumption of a facility (a “baseline”) is needed; otherwise, as suggested in the previous example, estimates of future savings arising from improvements to the existing facility may be too high or too low, and consequently inferences that a proposed improvement is cost-effective may not turn out to be correct (or, conversely, a truly cost-effective opportunity may be missed).

The need to normalize may also appear in energy production projects. For example, a photovoltaic system might produce more electricity in one year than in the previous year. Is this merely because there was more sunshine in the second year? If so, did this additional sunshine hide deterioration in the system operation?

Sometimes normalizing for weather is not merely a good idea, but rather a requirement of a client or a utility or government funding program. For example, I recently conducted a study for a client who was seeking funding from the Federation of Canadian Municipalities (FCM). The client needed to show how much connecting his building to a district heating system would reduce overall natural gas consumption (and thereby greenhouse gas emissions). The FCM program stipulated that any study had to first normalize past energy consumption for variation in the weather, and then project savings into the future based on typical weather.

Normalizing for Weather: the Theory

Normalizing for weather is, in principal, straight forward: you “fit” a statistical model (i.e., an equation) that relates you consumption data (e.g., utility bill consumption) to one or more variables that you think exercise an influence on consumption (e.g., heating or cooling degree days). When “fitting” the model to the data, you adjust the coefficients of the equation until sum of squared differences between the actual consumption data and the modeled consumption data is minimized. Often a linear equation is used for the statistical model, and the process is called “linear regression”.

So, for example, you might produce a scatterplot of daily average gas consumption for each billing period against the average number of heating degree days per day for the billing period, as shown in the figure below.

I’ve superimposed a straight line on the scatterplot to make it evident that there is a linear relationship between the fuel consumption and the heating degree days. That is, I should be able to estimate with some accuracy the fuel consumption using an equation of the form[1]:

This equation has the right form, but what should I use for the coefficients a and b? A common approach is to select a and b in such a way as to minimize the “sum of squared errors”, or SSE. To do this manually, I start out with a guess for these coefficients, and then I use this equation to estimate the fuel consumption for each billing period. I then compare these estimates with the actual fuel consumption for each billing period. If I square the difference of the two and sum over all billing periods, I’ll have the SSE. This is a measure of how well my choice of coefficients fits this equation to the data; I adjust the coefficients until the SSE is as small as I can make it (unless the line passes through every data point exactly, the SSE will not go to zero).

Then I’ve got my equation. For the data from the example above, it would be:

I can then use this equation to estimate the gas consumption based on the heating degree days. So, for example, imagine that for the location of this building, a typical month of March will have 620 heating degree days (°C·day). That works out to 20 heating degree days per day. If I wanted to know what the facility’s gas consumption in a typical March would be, I’d plug this into the equation:

This would tell me that on an average March day, I’d require 6.6 GJ of gas, so over the whole month I’d consume around 206 GJ of gas. To determine the gas consumption in a typical year, I do this same exercise for each month’s typical number of heating degree days.

Normalizing for Weather Using RETScreen® Plus

While this normalization can be done using a spreadsheet, my tool of preference is RETScreen® Plus, a sister program to the better known but completely different RETScreen® 4. (Both tools are available for download, for free, from the Government of Canada: www.RETScreen.net).

RETScreen® Plus is designed precisely for this type of exercise (as well as much more in-depth analyses to be discussed in later articles), and consequently much quicker and (less error-prone) than doing the manual exercise outlined above. The main program features that make it quicker and easier than the manual exercise are:

1) Rapid access to up-to-date daily weather data for locations across the globe

2) Tools for combining and regrouping data sets on different time bases.

3) Automatic fitting of equations

4) Optimization of the heating degree day reference temperature

Let’s examine each of these advantages by going through the key steps for normalizing for weather data using RETScreen® Plus.

I’ll start by asking my client for utility bills. He sends me a spreadsheet for the period of 2012 through 2013, indicating for each bill the billing date and the billed gas consumption (in GJ) for the period:

Note that the “monthly” bills are not all dated on the same day of the month, and the number of days in the billing period changes from bill to bill. Also note that I’m missing the bill for May 23. Such are the complications of the real world.

Next, I open RETScreen® Plus. The first key step is to tell it where my building is located; it will be apparent why we need to do this when we need to get weather data. There are a variety of ways to specify the project location, but the fanciest is through a map interface that lets me indicate the project location with a thumbtack:

Then I import my Excel spreadsheet of utility data into RETScreen® Plus. I tell it that the data I want to investigate is for “Fuel Consumption”, specifically natural gas measured in GJ. It opens a blank table:

I fill this table by “Importing from file…” and selecting my Excel file. A dialog box pops up and I see that it has correctly interpreted the headers in the file, with the exception of the gas consumption, which I have to pick from a drop down list:

When I click on the green checkmark, I get another dialog box identifying the missing data for May and giving me some choices for dealing with this, such as using the average for the whole data set, interpolating between adjacent data points, deleting the whole row, or repeating the previous value. I chose to simply ignore the missing data for now. RETScreen inserts this data into my table, automatically calculating the number of days in each billing period:

With that half my data is in the tool. But now I need to tell RETScreen what the “factors of influence” in this data are: that is, what variables are likely to exert an influence on the gas consumption. When normalizing for weather, the answer is pretty clear (it’s the weather, obviously), but in different applications of the tool it might be factory production, hotel occupancy, or something else.

Thus, I need to get weather data for 2012 and 2013. Ideally, this weather would be on the same time basis as my utility bills. That is, I’d have the average weather conditions for my site for the first, second, etc. billing periods.

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