Today's Energy Leader webinar is correlating energy use and weather data, and today's presenter is Steve Heinz. Steve is a professional engineer, certified energy manager, and certified measurement and verification professional. As the Founder and CEO of EnergyCAP, Inc., Steve has published software used by over 10,000 energy managers and 3,000 organizations to track more than 25 billion – yes, that's a "B" –billion in energy spending. Steve was also named by the Association of Energy Engineers as an International Energy Engineer of the Year. We are excited to have Steve on today's webinar. Steve, take it away.

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I've been amazed that we've had such interest in this topic that implies some discussion of statistics. If you would remember, statistics is the class that you went to great lengths to miss in college, so the fact that you've all signed up voluntarily is somewhat surprising to me! Thankfully, I will not be talking about a lot of statistics or going into a high degree of detail about that.

So let's get started: correlating energy use and weather data. So the need that I'm going to talk about is the need for a method to relate how outdoor weather conditions affect building energy consumption. Now, there's a few ways that a methodology can be developed to do this, and basically, the two approaches would be a statistical model or an engineering model.

Now, if you want to model a future building, a not-yet-built building, or a proposed renovation, or energy retrofit to a building and the question is, "How much energy am I going to use in this future building or how much energy will I use post-retrofit, and how sensitive is that energy consumption going to be to the outside weather?" I would recommend you use an engineering model, a building simulation. But typically, if you're modeling an existing building – so you have a building, you have information about the building, and you want to answer the question, "How sensitive is my

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energy consumption to outdoor weather conditions?" the better approach is typically to use a statistical model.

Some things that you have to consider when you make that decision is the cost. An engineering model, a full-blown building simulation is typically much more expensive – a factor of 10 or 50 or 100 times more expensive – than a statistical model because the statistical model doesn't require you to do any kind of building takeoff to do any measurements of building components; you don't have to do an inventory of mechanical systems or electrical systems. In most cases, you have everything that you need just from your prior utility consumption records. So cost is one driver of the decision. Another one is complexity. An engineering model or a simulation will typically be much more complex, require a higher skill level to use the tool, and hence, the cost of that.

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Another consideration is uncertainty – which approach would give you the least uncertainty in your results and to what degree is uncertainty something that is of concern to you. If you're going to use an engineering model, one resource where you can look up what models are out there is the Best Directory.

Best is Building Energy Software Tools, and if you look for simulations or calculations, you'll see in the directory links to various types of engineering models or simulation models that are out there. This Best Directory was initially created and hosted by the U.S. Department of Energy as a service by DOE. It has since been turned over to IBPSA, the International Building Performance Simulation Association, and they're currently moving the resources to their own format and getting that website up and running, so you can see the URL there on the screen. Something that you might want to check out if you're looking for simulation tools.

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But mainly, what I'm going to talk about today is statistical models. A statistical model that correlates historical energy use in a building with the weather is useful in several valuable ways – number one, in auditing. The audits of new utility bills can be made more accurate by understanding the impact of weather on building energy use. When your gas bill comes in or your electric bill comes in, you would typically compare that to historical trends to answer the question, "Is this bill reasonable or do I maybe have a problem?" The problem could be in the bill itself or the meter or the meter reading or something going on in the building you're not aware of, controls problems, something like that.

So it's valuable to have accurate audits, but any time you're comparing today's consumption, today's bill against historical data, the question that always comes up is, "Well, how much has today's weather changed from what the weather was in the historical period and how much has that affected the bill?" I don't want to go chasing down a suspected problem bill if, really, the bill was perfectly reasonable. It simply is reflecting the more severe or more mild weather. So a statistical model can help you with improved auditing.

Number two, it can help you in budgeting. When you're creating a future year budget,

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that's often based upon historical or most recent utility bills, but if those bills were the result of abnormal weather and you're projecting them into the future without taking that into account, it means the budget that you're creating is also implicitly assuming that the weather is going to be equally abnormal. So it might mean that there are some budget surprises in the future. When you create your budget, of course, you don't know what the weather's going to be next year, but it can be helpful to say, "I'm creating a budget based upon much more mild weather and I'm creating a budget based upon more severe weather and I expect it to fall somewhere in between." So it can help to inform the budgeting process.

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And finally, using correlation of use versus weather is valuable for cost avoidance calculation, M&V, the measurement and verification of energy savings. To illustrate that, here's an example we've pulled from EnergyCAP. When we're doing measurement and verification of savings, if this is per IPMVP, the International Performance Measurement and Verification Protocol Option C, the whole facility approach – that approach says we're fundamentally looking at the utility bills in the base year, the utility bills today, and we're comparing, but before we make that comparison, we have to adjust the baseline to current conditions. In other words, what would we have consumed today – sorry, what would we have consumed in the base year if the base year's weather had been equaled to today? So we're normalizing for weather.

Well, this is an illustration out of EnergyCAP that shows how important this can be. The orange bar, the 412, is the decatherms that I consumed currently. This is from last year, but it's illustrating today's utility bill. So I just got a gas bill where I consumed 412 decatherms.

Now, I'd compare that to the baseline. In the base year, I consumed 754. So if I simply compared those two raw numbers – the raw baseline with the raw today – it shows

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my savings were 342 decatherms. But that is not really a fair comparison because the weather today was more mild than it was in the base year, and I shouldn't get credit in my M&V for more mild weather because I don't control the weather.

So, before I compare, I have to adjust the baseline, I have to say, "What would I have consumed in the base year if the weather was as mild in the base year as it was today?" Well, in this case, because the weather was more mild, the adjustment is downwards and the correlation analysis we've done that comes up with an adjustment factor says, "Had we had mild weather in the base year, I would have consumed 548. So, now, when I want to calculate the savings attributable to my efforts, it's the difference between the adjusted baseline – the baseline that has been adjusted to current conditions – versus the actual bill.

So my true savings due to my efforts were 138. They weren't 342. And obviously, if a fee is going to be paid to a consultant or an ESCO based upon the savings, you would be overpaying for those savings if you didn't make the weather adjustment. So you can see how valuable the process can be.

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Now, potential weather data variables – what weather data variables do we want to use in this analysis? Well, there's a number of different variables that you can consider, and different people have used different variables in different kinds of analyses.

Number one, most commonly used would be daily dry bulb temperature. That would be the average outside temperature for the day, and when I say average, typically, the way that's taken, it's not the average of 24 hourly readings; it would be the middle value between the daily high and the daily low.

Another potential value would be daily wet bulb temperature. This would be the same process to calculate it, but the wet bulb temperature takes humidity into effect. So, in some climates, particularly Gulf Coast states, that might be found to be a better weather variable than dry bulb temperature. Possibly most commonly used would be degree days. Degree days would be an expression of dry bulb temperature, but the advantage of degree days is they are specifically designed for use in building energy analysis because we're tallying up the days when I need heating separately from the days that I need cooling. I'll talk some more about that later.

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Now, I've seen some systems that, instead of using daily data, it just uses a monthly average – monthly, dry bulb, wet bulb, or maybe monthly total degree days. The problem with that is that if you're using raw utility bills, those are very seldom rendered on a strict calendar month basis. So if you are going into a statistical correlation phase and you're using a calendar month utility – sorry, a calendar month weather average and correlating that with the utility bill that was not calendar month – 15th to 15th would be the worst case – then you're skewing your results right there. You're mismatching the data. So be cautioned about that.

And people ask about other weather variables – should we take wind into account and humidity and cloud cover? Those variables do have an impact on the amount of energy that a building uses, it has an impact on the heat loss of the building or the heat gain of the building, but there's certain problems inherent in using more variables in a calculation, and I'll talk a little bit more about that later.

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Okay, so let's start off now with a statistical analysis in Excel. If you're going to do this in Excel, you need the Excel analysis tool pack that might not be preloaded into your version of Excel. You can see if it's there or not by using the data tab in Excel. If it's not there, you can install it; there's no cost.

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You go to Options, and from Options, you go to Add-Ins, and you should see if it's active or inactive.

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In this example, it's inactive but we can activate it. So we simply go to Manage, click on Go, check the tool pack, Okay, and then it will install it.

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Okay, so now we have it in our version of Excel and we have to prepare the data set.

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So I pulled some raw data out of the system that has billing period, the number of days in the billing period – and notice that these number of days are not equal to the length of the calendar month. I pulled heating degree days. Now, these are the sum total of all of the heating degree days in the billing period calculated by taking the day the consumption started up to the day the consumption ended and adding together all the degree days. So these are the degree days in the billing period, not in the calendar month. It's in the actual days represented here, so that way, I know that my consumption and my heating degree days are for the same calendar days.

And here's my consumption, and then I divided heating degree days by the number of days in the billing period and I divided the usage by the number of days in the billing period so that in my analysis, everything is normalized on a per-day basis.

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Next step is, in this case, I made some adjustments to the data set. Number one, for the summer months, when there were virtually – when there were no heating degree days or virtually no heating degree days, those are the months that I know that the heating system in the building is turned off, and I don't want to try to correlate usage with a very, very low number of heating degree days when I know that there should be no correlation, and because the system's not even activated.

So I remove those rows from the data set. And I also added another month so that it starts in January, ends in next January, because these billing periods are not calendar month; it's sort of ragged as far as when it starts, and so I wanted to roll it over into the next January to make sure that all the days of the year were represented.

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So I remove those rows from the data set. And I also added another month so that it starts in January, ends in next January, because these billing periods are not calendar month; it's sort of ragged as far as when it starts, and so I wanted to roll it over into the next January to make sure that all the days of the year were represented. Okay, so to do the – a single linear regression in Excel, single linear regression has the form y equals mx plus b; in other words, a straight line where y is the dependent variable of usage, and that dependent variable of usage depends upon the independent variable, x, of degree days times the slope of the line, plus a constant, b, which is the vertical or y-intercept.

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So that's the general form of the equation, single regression. I select Regression in Excel and then I have to tell Excel what the input range is, what the output range is, and it gives me a result.

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So in this case, my single linear regression result is an R-square of 0.95, a very high R-square; in other words, the correlation is – fits very well. The b factor, the y-intercept of 12, and the slope of the line is 3.2.

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Now, I put the same data in EnergyCAP and this screenshot from EnergyCAP shows the same thing: R-squared of 0.95, the y-intercept – which is right here – is 12, and the weather factor, which is the slope of the line, is 3.2.

Now, in this illustration from EnergyCAP, we're showing, visually, how we did the linear regression. We took all of the utility bills in the base year – so every dot is a utility bill – and we plotted these utility bills, usage on the vertical – so the vertical coordinate is the therms per day – and weather on the horizontal. The horizontal coordinate is heating degree days per day in that billing period, and we simply plot the points.

Now, because I had that data set in Excel, you could plot these in Excel as well; would end up just the same. We plot the points and it shows that the points tend to rise to the right. That means that in the months with more heating degree days – in the colder months – my usage is higher, and in the mild months, with very few heating degree days, the usage is lower, as you would expect a gas meter that's providing heat to a building.

The green line is the regression line. That's the best fit statistical regression line. The

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two gray lines are the two standard deviation lines. So in a typical statistical analysis, you'd calculate standard deviation, and we plot two standard deviations. Any point outside of that, above it or below it, would be considered an outlier.

And finally, the blue line – the blue line shows where the y-intercept is, which is the point right there. So, to explain the meaning of that, we're saying that even when we have zero weather – no heating degree days, therefore, no heating use – we're still using 12 therms a day. What are we using that for? Probably domestic hot water, maybe cooking, those kinds of things – not for heating because we had no weather on that day.

So we draw the blue line horizontally to indicate that in any month, we're probably using those same 12 therms every month for domestic hot water and other non-heating needs. So in this very mild month, we're using 12 for domestic hot water and just a little bit for heat. In this month, we're also using 12 for domestic hot water but we're using all of this for heating, and that makes sense because this is our coldest month.

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One thing that you'll have to deal with is outliers. Now, what happens if we do this analysis and I have one utility bill that was way up here? It's outside of two standard deviations. That means that it's an outlier. What do you do with it?

What we do in EnergyCAP is outliers are thrown out of the model. We say that we don't know what goes on in this month, but this month does not fall in the model that is described by the other months. So, rather than try to fit it in the model and therefore make the correlation much worse for all of our months, we're saying that something strange, something different must go on in the building in this month.

Now, it could have just been one month in this particular base year and never occurred again. All we know is that this utility bill was abnormally high. We would've expected the consumption to be down here. It was really up there. So we should check the bill, make sure that the bill was entered correctly, that it was received correctly, but beyond that, maybe there's some activity in the building in that month that causes it to fall way outside of the norm.

What we do in EnergyCAP is, once we identify it as an outlier, we say we cannot reliably make a weather adjustment for this month because we can't model it. We

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don't know what goes on, but it doesn't fall in with our general model. So we simply exclude it and flag it and say, "We're not going to try to make a weather adjustment because we don't understand how to do it." But that doesn't affect our ability to make weather adjustments for the other months. You might want to treat outliers in some other way, but that's how we do it in EnergyCAP.

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Okay, moving on. Well, that was a single linear regression. What if you don't want linear? What if you want something that's non-linear?

So I took the same data set and now, for a non-linear correlation, not using degree days but using average temperature – so using average temperature, it could be the average dry bulb temperature; it could just as easily be the average wet bulb temperature if you wanted to try that. So now, my data set is ready to go. I have usage and I have the average temperature across the period of that usage. And when I do this – I did this for two years – I charted this using a quadratic equation. A quadratic equation is a higher order equation – in other words, a curve – that has the general form, x-squared plus x. And we have two different coefficients and then a third coefficient, c.

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So this is a more complex equation, and again, Excel can handle that or other statistical tools, and it gives me a slight curve based upon temperature, whether dry bulb or wet bulb. So it might be something that you might want to consider to see if that's going to give you a – what you might consider a better result.

It's really hard to say which result is best. What I would say is you need to decide how you're going to do it and be consistent, because once you develop the model, whether it's the quadratic model or the single linear regression model and apply that consistently, month after month, year after year, you're keeping the rule the same, and you might find that, in some cases, the quadratic would calculate a higher savings than the linear regression, in some cases, the other direction, but if you consistently apply it month after month, year after year, over the long run, you're not biasing the methodology.

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Some people ask about additional variables, variables beyond weather, such as occupancy or production, number of widgets produced or number of meals produced. If you're going to add additional variables, some of the considerations are the availability of historical data. If you want to try to correlate occupancy with usage, are you going to be able to get accurate historical records of occupancy, probably on a day by day by day basis, and the same thing for production. That might be hard to do. Maybe not for one building, but if you have a hundred buildings, that could be a very daunting problem. And ongoing – how are you going to get the data, how are you going to get it into the system?

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You have to consider the cost versus benefit. I wouldn't dispute the fact that additional variables eliminate some uncertainty in the result, and you might say that gives you a "better result," but you're paying quite a cost for that, and is that worth the benefit? Something that I keep in mind is the idea that, as we try to increase the accuracy of measurement and verification in general – weather correlation, weather versus use correlation, specifically in this case – so you wanna increase the accuracy, the cost is gonna go up. We have more variables, we have more work to do, higher skill level to do it, more time to do it. So if the energy manager is the person doing it, instead of the energy manager spending his or her time with other activities or out doing building walk-throughs or any other energy management function, that person's gonna be sitting at a PC doing additional data collection and additional statistical correlations. So all that comes at a cost.

Increasing accuracy will cause the cost to go up. If you look at the benefit, most of the benefits are derived – so you might look at this sweet spot, and then as we get much more accurate or we really – adding bottom line value or benefit to the system. I find that the sweet spot fits pretty well with single linear regression, using utility bill data and degree day data. That data is available for free. You very well might be tracking it anyway. So it's very economical.

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The considerations, time, and complexity – whatever process you create, it has to be very readily usable, it has to be sustainable. If the person, let's say, the audience I'm speaking to right now, if you establish this, ask the question, "Well, if I were to leave this position, could the next person coming in pick this up and keep it going or would it just get put on the shelf because someone's not going to understand it or have the skill level or have the background in statistics?" So it has to be usable, has to be sustainable.

Outliers – how are you gonna deal with outliers? Are you gonna try to incorporate all outliers into the model or, as I mentioned earlier, are you going to say, "Here's a month that we just – that doesn't fit into the model, so we're not gonna make any weather adjustments in that month. We can't explain it." So you have to deal with that up front.

Weather data availability – what's the cost and availability of weather data? Easy if you're looking for dry bulb temperature or degree days; different question if you need wet bulb temperature or you want to get wind chill, wind, solar, things like that. Potentially, they add some value, but you might not be able to get those variables for historical time periods. You might have to pay to get the data. So you need to take

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that into account.

Also, you have to be careful with weather variables and that you can't just say dry bulb temperature, wet bulb temperature, wind velocity, cloud cover; you can't assume those are independent variables because there's a high degree of cross-correlation between, for instance, dry bulb and cloud cover. So if you treat them truly as independent variables from a statistical standpoint, you're at fault because those are not truly independent. So you have to be careful about that, again, adding cost and complexity.

I wanted to end up just mentioning that a good resource for weather data is the website, Weather Data Depot. Here's some seven talking points about Weather Data Depot. Number one, the data comes from http://www.accuweather.com. AccuWeather is the number one provider of weather forecasts and data in the U.S., so it's a very authoritative source.

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In Weather Data Depot, you can enter a zip code or city, state. We import about 14,000 weather stations every morning. We get that data downloaded from AccuWeather, so basically, every zip code (see #2) is mapped to weather data. Now, there aren't that many physical stations. The majority of those stations are, you might say, virtual stations where the data for a zip code is created by a computer simulation at AccuWeather taking into account adjacent physical stations and satellite data and ground observations and so on. That's the way most weather forecasts are created. There's not always a physical station right in your zip code. You can set the balance point (see #3) to whatever point you need. If you don't understand what balance point means or what a degree day is, if you go to the FAQs at the website, it will explain balance point and how degree days are calculated.

Anyway, we default balance point at Weather Data Depot to 60 degrees F. If you go to NOAA, the government site, they use 65. When the degree day concept was first created back in the 1930s, it was based upon the need to forecast the amount of natural gas that residences were going to use, and 65 made perfect sense back then because residences were not insulated the way they are today; they weren't looking at institutional- or commercial-type buildings, and there was a minimum amount of internal heat gain in buildings back in the 1930s, so 65 made a lotta sense. Today, 65

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is just too high. We default to 60. We find a lot of buildings maybe more appropriately set to 55, but you can set it to whatever you want and all the data will instantly update.

In this particular weather report (see #4) , you can compare any two years. So you can set a base year, 1995 up until 2015, and then set the comparison year in a like way, and when you do that, the report here is going to compare what you have set as your base year to the comparison year and it will show heating degree day and cooling degree day and total degree day comparison. So, in this case, it's saying that January of 2015 had seven percent fewer heating degree days than the base year, January of 2014. In other words, my winter weather that month was seven percent more mild, meaning I would've expected to have a lower heating requirement on the building. We show you the year-to-date numbers down below as well. You can click on a month and drill into that to see the daily data and you can copy the data to Excel just with one click. You can only do one station at a time.

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And there's some other functionality in the site. There's some tabs up top that give you some other charts. One of them that I like to point out is the heating degree day chart. I have this set to seasonal. Seasonal means we run from July to June, in other words, the entire heating season, and it's a cumulative chart. That means, in every month, what we show in the chart is the sum total of all of the heating degree days to date in the heating season. So you notice the numbers keep growing, the lines keep going up because we're adding every month onto it. What's nice about this is when you get to the end of the heating season, you can see what we ended up with, and we also show that in tabular format that you, again, can download to Excel. So this shows me that my heating season 2011 to 2012, because it's the lowest line on the chart, which is right here, had the fewest cumulative heating degree days of any year in ten years. So 2011, 2012 was very, very mild. The worst winter in that ten-year period was the one up top with the most heating degree days. That was the winter of 2013–2014.

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Thanks for attending the webinar!

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