Energy Analysis: CUSUM Questions
Looking for any help I can get from facility managers/engineers:
I am attempting energy analysis for a building, and am looking to use the CUSUM regression technique comparing CDD/day to kWh/day, examining for differences between 2006 and now, given certain efficiency improvements.
When I compare the CDD/day to kWh/day of 2006 and 2007 for the baseline fit, however, the trend is contrary to expected, with a DECREASE in energy usage given more CDD. On top of that, the R-squared indicates that CDD/day are not predictive of the kWh/day- it is at ~0.10.
Is it possible to run the CUSUM analysis given these parameters?
My second question is: how do I go about normalizing for a change in building occupancy over the months? I normalized the billing period lengths of dividing CDD and kWh by billing days, but is it legitimate to also divide by sq feet (obtaining the kWh/day/sq ft)? Or is there a better way.
Thanks in advance for any help you can provide.
-Paul Coraggio, Student
Ramapo College, Presidents Climate Commitment Task Force
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Using regressions with kWh/day should be valid BUT you need to correlate it against more than only Cooling Degree Days. From a statistical standpoint, correlating usage data (dependant variable) that doesn’t go to zero with a factor (independent variable) that can approach (or be) zero (such as HDD or CDD), presents inherent problems. As a minimum, include avg. temp. (daily or monthly to match the data) as well as CDD and/or HDD. If the building has both electric cooling and electric heating, try performing separate regressions for summer vs. winter.
Surprisingly, modest occupancy variations have little impact on energy consumption for most buildings. In general assume that lighting (if off) would save 1.5 watts/SF. If a large area is unoccupied AND the HVAC is OFF (generally not likely), more adjustment may be called for. You could do your regressions using the dependant variable kwh/SF/day.
For colleges setting up a baseline and looking for weather adjusted results going forward, the regressions approach is very useful in part because it allows results to be checked at least monthly. Use energy units/SF/day so you can make future adjustments when adding new buildings.
As some may have found, simply dividing monthly or annual heating energy by HDD can deliver widely variable results with big variations in actual HDD (or skyrocket when it goes to zero). A fixed base-load adjustment can help accuracy, but a regressions based adjustment is the answer.
A regression analysis can be done in MS Excel by downloading an add-in called Analysis Tool pack. Once installed, a new option called Data Analysis will appear under the Data tab. By selecting the Regression tool, a range of y-values (dependant variables) and x-values (independent variables) can be chosen and evaluated. The tool will output the results of the regression analysis in a new worksheet including the R-squared value and coefficients for the corresponding equation. Be happy if the R-squared is over .8.
It is best to try different combinations and once a formula is initially selected, test fit the "actual vs. projected" using the baseline period to help pick up any abnormalities. Weather is clearly the most important variable. Even if adding other variables increases R-squared, it may not really create more accuracy unless the reason for the correlation can be justified.
Like with buildings that have electric heat, special attention is required for sites that use thermal cooling (absorption or steam turbine chillers), or have cogeneration as the energy consumption will increase with both cold & hot weather. Again, try separate regressions for different periods.
Note that weather data is available on many web sites and the location of the weather station itself may not have to match exactly as long as the site's weather correlates well to the location of the energy user (inland 50 miles away from an inland user may be better than coastal 20 miles.
Good luck!