Should we normalize electricity data by HDD in a not electrical heating systems?

I have been analyzing energy consumption for more than 40 sites for the last 6 months and now it is the time to calculate the energy savings from the previous electrical saving projects that we had in the last couple of years. But wait, how do I compare the electricity consumption for these different years? Should I normalize it by Heating Degree Days (HDD) because we had different temperature patterns each year? Or it doesn't matter because our heating systems run by Natural Gas! But wait, the more heating needed, the more and harder electrical systems such as fans and pumps would work.

These were some of my thoughts when I wanted to start my analysis. Regardless of if you asked these question from yourself, or you never thought about this, you should pay attention to some points:

1- Your electricity bill is not only based on your fans and pumps'electrical consumption. You have a lot of electrical systems that are consuming the same amount of energy throughout the whole year, such as lighting systems, or electrical stoves, or vacuum cleaners...

2- Even if some of your electrical systems are affected by the temperature profile, they might not follow the linear correlation. Here is a simple test you can run to figure this out by yourself:

Collect your electrical bill data for each month and look up the HDD number for each of those months. You can easily find HDD data for your area by searching in internet. Sort you HDD from smallest to biggest. Then graph your data to find the linear equation, and R squared value:

Now if you do the same process with Natural Gas data you see a totally different result:

This graph clearly shows that despite electricity consumption, NG consumption has a very good correlation (R squared = 0.9691) with HDD. 

3- Now if you are really insisting that electricity consumption of your electrical systems such as fans and pumps are correlated to HDD, you should try to find an approximate electricity consumption of the systems that are not dependent (like lighting, electrical stove  carpentry machines, vacuum cleaner etc.) and take them out of your electricity consumption data and then try to graph it by HDD. if you see R Squared value higher than 0.8, then I would say you can go ahead and normalize your data by HDD. If not, just forget about normalizing by HDD, it just doesn't have that simple linear correlation.