Energy management made easy
Degree days are a simplified form of historical weather data. They are commonly used in monitoring and targeting to model the relationship between energy consumption and outside air temperature.
Weather normalization of energy consumption is one of the most common such uses of degree days. In theory, weather normalization (or "weather correction") enables a like-for-like comparison of energy consumption from different periods or places with different weather conditions.
Weather normalization techniques are often based around regression analysis of past energy consumption data, a method that is frequently used with degree days to:
Although much of the theory behind these methods is sound, the results are usually a lot less accurate than many people realize. Such degree-day-based methods are central to many energy management programmes, and, as a result, important decisions are frequently based on figures that can be misleading to those who put too much faith in them.
This article looks at some of the problems associated with the common uses of degree days in monitoring and targeting, and suggests a few ways that those problems can be mitigated. Its aim is not to denigrate the degree-day-based methods that are widely accepted in the energy industry, but to highlight the major sources of inaccuracy, and to encourage the reader to ensure the validity of degree-day-calculated figures before using them as a foundation for decision making.
If you are looking for degree-day data (rather than an article about it), you might want to head over to another of our websites: Degree Days.net.
First, this article looks at the basics of degree-day theory (you might want to skip this if you already know the basics):
Next, this article highlights problems with the ways in which degree days are commonly used, and then suggests ways in which those problems can be mitigated:
In heated or cooled buildings, energy consumption tends to depend on the outside air temperature:
"Weather normalization", or "weather correction", allows you to adjust your energy-consumption figures to factor out the variations in outside air temperature. In theory, you can then compare the normalized figures fairly.
Weather normalization is commonly used when analyzing changes in a building's energy consumption, and, when combined with other normalization techniques (such as normalizing for occupancy and building size), when comparing the energy consumption of different buildings.
Let's say you have several years' worth of energy consumption data for a building, and you want to compare the energy consumption in 2005 with that in 2006, to see if there was an improvement in energy efficiency.
|Year||Total energy consumption (kWh)|
The raw figures show that the building used less energy in 2006 than it did in 2005. However, let's say you know that a large proportion of the building's energy consumption went on heating, and you also know that 2006 was a warmer year than 2005. You would therefore expect less energy to have been used in 2006 than in 2005, as the warmer outside temperatures in 2006 meant that less energy was needed to heat the building.
So, less energy was used in 2006 than in 2005, but did energy efficiency improve, or was it just because 2006 had warmer weather?
This is where weather normalization can help. Provided you have the appropriate historical weather data (most probably heating degree days), you can calculate the weather-normalized energy consumption in 2005, and the weather-normalized energy consumption in 2006. These two figures can then, in theory, be compared on a like-for-like basis, enabling you to see whether or not there was an improvement in the building's energy efficiency.
Degree days are essentially a simplification of historical weather data - outside air temperature data to be specific. Degree-day data is easy to get hold of, and very easy to work with. This makes degree days popular amongst energy consultants and energy managers, certainly when compared with other forms of past weather data such as hourly temperature readings.
Degree days can come in any timescale, but they typically come as weekly or monthly figures. You can sum them together to make figures covering a longer period (e.g. sum 12 consecutive monthly degree-day figures to make an annual degree-day total). This is useful if you are working with, say, quarterly or annual energy-consumption figures.
There are two main types of degree days: heating degree days (HDD) and cooling degree days (CDD). Both types can be Celsius based or Fahrenheit based.
Heating degree days (HDD) are used for calculations that relate to the heating of buildings. For example, HDD can be used to normalize the energy consumption of buildings with central heating.
Heating degree-day figures come with a "base temperature", and provide a measure of how much (in degrees), and for how long (in days), the outside temperature was below that base temperature. In the UK, the most readily available heating degree days come with a base temperature of 15.5°C; in the US, it's 65°F.
An example calculation: if the outside temperature was 2 degrees below the base temperature for 2 days, there would be a total of 4 heating degree days over that period (2 degrees * 2 days = 4 degree days). In reality, the process of calculating degree days is complicated by the fact that outside temperatures vary throughout the day. Fortunately, however, you can use degree days in your own calculations without worrying about how they were calculated originally!
Cooling degree days (CDD) are used for calculations relating to the cooling of buildings. For example, CDD can be used to normalize the energy consumption of buildings with air conditioning.
Cooling degree-day figures also come with a base temperature, and provide a measure of how much, and for how long, the outside temperature was above that base temperature.
Although this article talks mainly about heating degree days, much of the information is also applicable to calculations involving cooling degree days.
Celsius-based degree days are calculated using a base temperature that is measured in Celsius, and outside temperatures that are measured in Celsius.
In contrast, Fahrenheit-based degree days are calculated using a base temperature measured in Fahrenheit, and outside temperatures that are measured in Fahrenheit. Fahrenheit degree days are common in the US, where they typically come with a base temperature of 65°F (equivalent to 18°C). Since a temperature difference of 1°C is equivalent to a temperature difference of 1.8°F, Fahrenheit-based degree days are 1.8 times bigger than their equivalent Celsius-based degree days.
Although this article talks mainly about Celsius-based degree days, the theory and arguments presented are equally applicable to Fahrenheit-based figures and calculations.
Degree days are commonly used in monitoring and targeting of energy consumption. As an understanding of the popular methods is necessary for an understanding of the bulk of this article, they are briefly explained below:
Heating degree days are often used to normalize the energy consumption of a heated building so that, in theory, the normalized figures can be compared on a like-for-like basis. So, for the example given above, heating degree days would enable you to calculate normalized energy-consumption figures for 2005 and 2006 that, in theory, could be compared fairly.
The simplest way to normalize energy-consumption figures is to calculate the kWh per degree day for each kWh energy-consumption figure in question. Simply divide each kWh figure by the number of degree days in the period over which that energy was used. In theory, dividing by the degree days factors out the effect of outside air temperature, so you can compare the resulting kWh per degree day figures fairly.
The following figures continue the example explained above, using real degree days from the South Eastern region of the UK:
|Year||Total energy consumption (kWh)||Total heating degree days||kWh per degree day||Normalized kWh|
The last column in the table, normalized kWh, shows how you can multiply the kWh per degree day figures by a single "average year" degree-day value (in this case we used 2,027 degree days as the multiplier - an average-year value calculated from the last 10 years' worth of degree-day data from the South Eastern UK region). This gives you normalized equivalents of your original kWh figures that you can, in theory, compare fairly.
The normalized figures from the example above indicate that energy efficiency was actually slightly worse in 2006 than in 2005.
NB Some people use 5-year-average degree days as the multiplier, some use 10- or 20-year-average degree days, and others use "standard degree days" (to normalize figures in such a way that they can be compared between regions). Provided you use just one multiplier (e.g. do not use "rolling" averages) it should not matter much what multiplier you use, as your figures will at least be proportionally comparable.
Linear regression analysis is commonly used as a monitoring and targeting technique. Central to this is the assumption that energy consumption is caused by a "driving factor" (or "driver") - this could be the widgets produced by a production line, or, in the case of heating or cooling, the degree days. So, for a heated building, it is assumed that the energy consumption required to heat that building for any particular period is proportional to (or driven by) the number of heating degree days over that period.
Typically you would select a "baseline" set of energy consumption data: this would usually be weekly or monthly data from the past year or two. For each figure of energy consumption, you need a corresponding figure for the degree days (or whatever driving factor you are using) - you would then correlate these two sets of figures.
For example, the scatter plot below shows a years' worth of monthly degree days (x-axis) plotted against monthly kWh (y-axis). Specifically, the chart shows 15.5°C-base-temperature heating-degree-day figures from North West Scotland in 2006, and a very good correlation with the energy consumption data (an R2 close to 1):
The "regression line" is the line of best fit through the points in the scatter chart. It is often known as the "trend line" or the "performance characteristic line".
Once you've established the formula of the regression line, you can use it to calculate the baseline, or expected, energy consumption from the degree days. So, each time you obtain a new figure for the degree days (typically each week or month), you can plug it into the regression-line formula to get the expected energy consumption. You can compare this figure with the actual energy consumption for the period, to determine whether more energy was used than expected.
There are a number of other techniques that revolve around the degree-day-based regression analysis described here. The proximity of the points around the regression line is often used as an indication of the accuracy of the heating control (the greater the scatter, the worse the control), and it is common for people to plot a CUSUM chart of the difference between actual and expected consumption. Estimating "baseload" energy consumption is another typical application:
It is very common for a single energy meter to measure both weather-dependent and non-weather-dependent energy consumption together. For example, a building with electric heating might have a single electricity meter measuring all its electricity consumption (heating, lighting, office equipment etc.).
In degree-day analysis, energy consumption that does not depend on the weather is often referred to as "baseload" energy consumption. It generally comes from energy uses that are not directly involved with heating or cooling the building; examples include electric lights, computer equipment, and industrial processes. For the purposes of degree-day-based calculations, it is usually assumed that a building's baseload energy consumption is constant throughout the year.
It is worth nothing that the term "baseload" is often used to describe the total kW power of all the equipment that is on constantly, including when the building is closed. However, the baseload energy that we are talking about here is a total of all the non-weather-dependent energy consumption (including energy consumption from equipment that is only used during occupied hours), and is usually expressed as an average daily, weekly, or monthly kWh value.
Anyway, baseload energy consumption complicates the simple ratio-based approach to weather normalization that was described above. You can only apply that method to energy consumption that is 100% degree-day dependent, so, if the raw energy-consumption figures contain baseload energy consumption as well as degree-day-dependent energy consumption, you need to subtract the baseload kWh from the raw figures before applying the ratio-based method. (You would typically add the baseload kWh back on to your normalized figures afterwards.)
There are two methods that are commonly used to calculate the baseload energy as a monthly kWh value:
The same methods can be also be used on a weekly basis, if weekly data is available.
We've given a brief overview of the motivation and methods that are commonly associated with degree days in energy monitoring and targeting, and we shall now move on to the substance supporting the main theme of this article:
When applied to real-world buildings, common degree-day-based methods suffer from a number of problems that can easily lead to inaccurate, misleading results.
To explain how significant inaccuracies occur, following is an explanation of several major problems with the ways in which degree days are commonly used:
In degree-day theory, the base temperature, or "balance point" of a building is the outside temperature above which the building does not require heating. Different buildings have different base temperatures.
In the UK, for example, the majority of energy professionals primarily use degree days with a base temperature of 15.5°C. This is partly because 15.5°C base-temperature degree days are the historical norm in the UK, and partly because, unlike degree days with other base temperatures, 15.5°C figures have always been readily and freely available.
Use of a 15.5°C base temperature is often justified with arguments along the lines of:
The method of calculating an appropriate base temperature by subtracting the average internal heat gain from the building temperature is a sensible approximation. However, the figures used in the above arguments are where the problems lie:
In reality, 15.5°C is rarely the most appropriate base temperature to use for degree-day-based calculations. This is important, as degree-day-based calculations can be greatly affected by the base temperature of the degree days used.
The base temperature with which degree days are most readily available actually varies from country to country. For example, the "default" base temperature in the UK is 15.5°C, whilst, in the US, it's 18°C (65°F). This alone is a pretty strong indication that the one-base-temperature-fits-all approach to degree-day-based calculations is inappropriate!
The following chart is based on 2006 heating degree day figures for North West Scotland. Figures for three different base temperatures (18.5°C, 15.5°C and 10.5°C) are displayed as percentages of the March value (March being the coldest month in 2006 for that region). The figures are displayed as percentages (as opposed to absolute degree-day values) so that they can be compared easily.
This chart makes it clear that the base temperature of degree days has a big effect on the proportional difference between the degree days of one month and the degree days of the next. This is critically important to realize if you are weather normalizing monthly energy-consumption figures - getting the base temperature just slightly out can easily lead to misleading results.
To complicate things further, the base temperature of most buildings actually varies throughout the year. It is affected by the sun (solar heat gain), the wind, and the patterns of occupancy, all of which typically vary throughout the year. Even the internal temperature of the building will typically vary unless the building's heating control system is working perfectly.
As this section has shown, it's important to pick an appropriate base temperature for degree-day-based calculations, and degree days in the most appropriate base temperature are unlikely to be those that are most readily available. As a building's base temperature typically varies throughout the year, even the most appropriate base temperature is usually only an approximation.
Any baseload energy needs to be removed from energy-consumption figures before they can be weather normalized. This is fine in theory, but very difficult in practice.
As described above, linear regression is one way to calculate the baseload energy (plotting degree days on the x-axis against energy consumption on the y-axis, and taking the baseload energy from the point at which the regression line crosses the y-axis). However, the accuracy of this method is highly dependent on the degree days having an appropriate base temperature, which introduces all the base-temperature problems described above.
To illustrate the effect of base temperature on the baseload energy, the plot below extends the example correlation that was originally used to illustrate the method by adding a correlation of the same energy data with 18.5°C-base-temperature degree days. This is, in fact, made-up energy data (kWh and degree days don't correlate perfectly in the real world!), but the degree days are real, and show the striking effect of base temperature on the baseload energy calculated by this method.
The chart clearly shows that, although the 15.5°C and the 18.5°C base-temperature data both correlate very well with energy consumption, the 15.5°C data gives a baseload energy that is around 50% greater than that given by the "perfect" 18.5°C correlation. Choosing the the right base temperature clearly makes quite a difference to the baseload energy!
In reality, energy consumption will never give a "perfect" correlation with degree days of any base temperature, so, even if you do have degree days with a range of base temperatures available, you can never be certain that you are picking the appropriate base temperature just by looking at the correlations. And, since the y-axis intercept varies so significantly with the base temperature chosen, it will consequently be impossible to obtain the baseload energy accurately.
In fact, the whole concept of baseload energy is usually a pretty big approximation, as much of the energy consumption that typically contributes towards it depends on the time of year. For example: lighting energy consumption typically depends on the level of daylight, which varies seasonally and from day to day.
Baseload energy is certainly not suited to being wrapped up as a monthly kWh figure, as months are very different in calendar terms (this is explained further in our article on energy performance tracking). The simple fact that, in common 365-day years, March is over 10% longer than February makes it pretty clear that baseload energy consumption is unlikely to be constant from month to month.
Many buildings are only heated to full temperature intermittently, usually to fit around occupancy hours (e.g. 0900 to 1700, Monday to Friday). However, degree days cover a continuous time period: 24 hours a day, 7 days a week. This means that degree days are often not a perfect representation of the outside air temperatures that are most relevant to heating energy consumption.
Consider, for example, a building that is unheated overnight. The colder night-time temperatures do have a partial effect on the day-time energy consumption, as a colder night will typically mean more energy is required to bring the building back up to temperature in the morning. (Thanks to the complicated way in which buildings retain heat/coolth, there is a time lag, typically of the order of hours not minutes, between changes in the temperature outside and their effect on the energy consumption inside.) However, whilst this effect is only partial, the cold night-time temperatures are fully represented by degree days.
This problem is not only limited to day/night intermittent heating, as many buildings are also unheated through weekends, public holidays, and shutdown periods. When a particular weekend is uncommonly warm or cold, the degree-day total for that week or month will be affected accordingly, even though the outside temperature on that weekend is largely irrelevant to a building that is unheated on weekends.
With degree-day analysis of monthly figures, such intermittent heating also introduces a calendar mismatch: although monthly degree days cover the entire month, the proportion of days for which a building is heated typically depends on the calendar of the month in question. Consider the following example monthly figures for a building that is heated on weekdays only:
|Month||Total no. days||No. unheated days (weekends)||No. heated days (weekdays)||Proportion of days that are heated|
These example figures show that, for a building that is heated on weekdays only, the proportion of days that are heated varies quite considerably from month to month. This is a simple result of the way that the calendar works. Monthly totals of degree days do not take this calendar mismatch into account, giving another reason why they should not be expected to relate closely to monthly heating energy consumption (kWh). When bank holidays and shutdown periods are considered (as they should be), the effect of this calendar mismatch becomes more marked, and weekly degree-day analysis is also affected.
As mentioned previously, degree days typically come as weekly or monthly values. So, in order to compare or correlate energy consumption with degree days, you need meter readings that are taken at the start of each week or month. If you're taking those meter readings manually, you should take them at midnight, and often on weekends.
Of course, it is rarely convenient to take manual meter readings at midnight or on weekends, so it is common for such readings to be taken up to several days early or late. This can introduce a significant inaccuracy into degree-day-based calculations.
For example, the month of June 2006 ended at midnight on Friday 30th June. If, for convenience, the meter reading was taken at 0900 on Monday 3rd July, June's energy consumption would cover a period that was around 8% longer than it should be, and July's energy consumption would cover a period that was around 8% shorter than it should be. The degree-day figures would match the calendar months exactly, but the energy consumption data would not. It's not difficult to see that this would introduce a significant inaccuracy!
(This is as much a symptom of the base temperature problem and the intermittent heating problem as it is a problem in its own right.)
When the outside temperature is close to the base temperature of the building, the building will often require little or no heating. Degree-day-based calculations are particularly inaccurate under such circumstances:
Matters are complicated further if the building has both heating and air conditioning. Under such conditions (an outside temperature close to the base temperature), a building will often require both heating and cooling to maintain a constant inside temperature over the course of a single day.
An energy-efficient building would usually sacrifice the maintenance of a constant temperature by ensuring that the temperature above which the air conditioning came on was a few degrees higher than the temperature below which the heating came on (a "comfort zone"). However, it is rare for real-world buildings to have perfect HVAC control. In fact, poor HVAC control can often result in a building being heated at the same time as it is being cooled - not very energy efficient at all!
Anyway, the upshot of all these complexities is that, when the outside temperature is close to the base temperature of the building, degree-day-based calculations are typically much less reliable. The inaccuracies introduced by the base temperature problem and the intermittent heating problem are exaggerated, making it difficult to place much confidence in results.
This article has highlighted several significant problems with the popular degree-day-based calculation methods. The greatest danger with these methods is that they are used without an awareness of their shortcomings - inaccurate figures that are thought of as accurate can easily lead to bad decision making.
Following are a few suggestions for how you can mitigate the problems highlighted above, and improve the accuracy of your results from degree-day-based calculations:
You should aim for data that is:
When we originally wrote this article, it was very hard to get data that satisfied the above criteria. We consequently included Hitchin's Formula - a rather inaccurate and esoteric way to estimate degree days in any base temperature using mean temperature readings. However, since then we have set up the Degree Days.net website, which offers free heating and cooling degree days, in any base temperature, in daily, weekly, or monthly format, for locations worldwide. You can also now get weekly degree-day data for 77 UK weather stations from The Environmental Change Institute of Oxford University. Given that these sources make it much easier to get good data for locations worldwide, we decided that there wasn't much point in including Hitchin's Formula any more.
The "ideal" temperature problem occurs when the outside temperature is such that the building requires minimal heating or cooling. Since the standard approaches to degree-day-based analysis are particularly inaccurate under such circumstances, it's often best to simply leave these periods out of your regression analysis.
Interval metering has only become readily available in recent years, and much of the energy-management literature has yet to catch up. Analysis of the high-resolution detail contained within interval data such as half-hourly data can, in seconds, reveal patterns of energy wastage that could never be revealed by weekly or monthly regression analysis.
Other benefits aside, interval meter data can help in overcoming the degree-day problems that this article has highlighted. An interval meter can completely solve the problem of taking accurate meter readings at exactly the right times, as interval meters automatically take readings at the start and end of each week and month (in fact, they typically take readings every 15 or 30 minutes). Software such as Energy Lens can be very useful for splitting interval meter data into the weekly or monthly totals that are usually necessary for degree-day analysis.
Interval metering helps further if several interval meters are fitted:
Separate submetering can significantly reduce or even eliminate the baseload energy problem. If the heating energy consumption is metered separately, any baseload energy will be minimal, so there will be minimal potential for inaccuracies to be introduced by a fluctuating or poorly-estimated baseload. You should therefore be free to perform degree-day-based calculations on the heating energy consumption data without having to worry about inaccurate estimates of baseload energy.
Submetering can also give you greater confidence in your analysis of the non-heating energy consumption of the building. If the non-heating energy consumption is metered separately, it will be unlikely to be affected by variations in outside temperature, and you should be able to make more accurate comparisons of week-on-week and month-on-month energy performance, without need for degree-day normalization techniques.
It is best to be sceptical when comparing weather-normalized figures from one week or month to the next, as inaccuracies caused by the base temperature problem, the baseload energy problem, and the intermittent heating problem are likely to be exaggerated by natural changes in those properties throughout the year.
However, provided the size and general operational patterns of the building do not change from one year to the next (energy-efficiency improvements aside), a comparison of yearly weather-normalized figures is less likely to suffer to the same extent, as the changes throughout any one year will usually be approximately repeated every year. Comparisons of year-on-year weather-normalized energy consumption are not infallible, but they should be less prone to the problems highlighted in this article than weekly or monthly comparisons.
Remember that the figures calculated using degree-day-based methods are usually only approximate.
Plugging numbers into a formula will almost always give a result, but the accuracy of that result can only be trusted if the formula is sound and the numbers that went into it are accurate themselves. This is essentially the main problem with the common uses of degree days in monitoring and targeting: the calculations have no difficulty producing "results", but the combined effect of the problems highlighted in this article means that the overall accuracy of those results is often very low (despite the fact that they may appear with several figures after the decimal point).
After reading about the inaccuracies introduced by each of the problems that this article highlights, it should not be difficult to see how simple, justifiable changes to input parameters could easily turn a supposed 3.74% improvement in energy efficiency into a supposed 1.12% overspend (figures after the decimal point are shown here to highlight the misleading nature of numbers that appear more accurate than they really are).
Unless you have accounted for the problems highlighted in this article, figures that you calculate using standard degree-day-based methods will usually only be very approximate. There is no danger in using these methods to give you an indication of what may be happening with the energy consumption you are analyzing. However, before placing too much confidence in the figures, be sure to consider how different those figures might be if you had changed your approach to calculating them just slightly (e.g. by using degree days with a slightly different, but no less "correct", base temperature).
The degree-day-based techniques described in this article are just as applicable to buildings with consumption figures in the millions of kWh as they are to buildings with consumption figures in the hundreds of kWh. However, the magnitude of the absolute numbers has no bearing on their accuracy - it's the proportional differences that matter.
For example: if you use regression analysis to calculate that, over the last month, a building consumed 2% more energy than expected (a relatively low proportional difference), that might be more likely to be a symptom of inaccuracies in the calculation than an indication of a real problem. And, if you have little confidence that a 2% difference means anything, it's irrelevant whether that 2% difference equates to 200 kWh or 2,000,000 kWh.
In contrast, a 20% proportional difference may well be high enough for you to consider it meaningful. If you have confidence in the proportional difference, you can also have confidence in the corresponding absolute numbers, and can confidently use them for deciding priorities and so on. The critical point is that only the proportional difference can enable you to judge whether the result of a calculation is likely to be meaningful, and, until you have judged that, the absolute numbers can only be a distraction.
By looking at the general accuracy of your calculation process (e.g. how many of the problems highlighted in this article apply), and by looking at the quality of your baseline correlation, you should be able to get a feel for the level of proportional difference that makes a figure worthy of your attention. It's only worth looking at the absolute numbers (e.g. excess kWh or cost) once you've determined from the proportional differences (e.g. percentage above expected) that they are likely to be meaningful (and not just a symptom of calculation inaccuracies).
Degree-day-based monitoring and targeting is a central part of many energy management programmes, but degree days are commonly used in ways that can easily lead to inaccurate, misleading results. If you are using the popular degree-day-based methods, it's important that you have an understanding of the sources of inaccuracy, and a sense for the reliability of the figures on which you base decisions. Otherwise you will frequently find yourself chasing excess consumption that doesn't really exist, and highlighting improvements that haven't really be made.
On the plus side, any monitoring and targeting, however inaccurate, will probably still result in energy savings: it's almost always possible to find energy wastage if you go looking for it, and anything that builds energy awareness is generally good. However, separating the real indicators from the blind alleys will help you to focus your time as effectively as possible, and achieve significantly greater energy savings as a result.
First, congratulations for reaching the end of this article - it's a long one! If you found it useful, might you consider telling your colleagues or mentioning it on your website?
You might also be interested in our other articles on energy management / energy monitoring and targeting.
And you might like to take a look at our Energy Lens software: