Estimating Heating Energy from Utility Bills

More on the “Phase 2” AdjustmentEcotope, Inc

BACKGROUND MATERIAL AND COMMENTS ON VBDD

What is Variable Base Degree Day Regression (VBDD)?

Base Load

Energy = Base Load + Heating Slope * Heating Degree DaysDegree Day Base

Heating Slope

Sometimes it works very well (like for example this home)…

And other times it doesn’t work at all.

Site level VBDD seems to work pretty well on gas bills! It does not seem to work very well across electric bills. These are all RBSA SF sites, where “Gas n=667” refers to any site with gas bills and “Electric n=699” refers to any site without.

Let’s reiterate. Site level VBDD seems to work pretty well on gas bills! It does not seem to work very well on electric bills. Ecotope’s implementation of VBDD here performed a brute-force search over balance points 48F to 70F. Anything that hit the boundary of the search is not believable or usable.

So we were looking at all bills before – what about just bills from Josh’s spreadsheet.

[These] are homes that have some form of permanently-installed electric heat (FAF, BB, or HP). These are meant to represent an electric utility's program-eligible homes with minimal screening.

Shown in vertical dashed line is the cutpoint of 0.45. This looks better than the previous plot for all sites, but it still does not inspire confidence in site-level VBDD with an R^2 cutpoint.

BAD GOOD

Similarly for the balance points, the picture is better for this smaller set of homes, but still doesn’t look good.

PRISM: An Introduction. MARGARET F. FELS Center for Energy and Environmental Studies, Princeton University, Princeton, NJ 08544 (U.S.A.) (Received January 1986)

In general, the NAC estimate [Normalized Annual Consumption] provides a reliable consumption index from which energy savings and conservation trends may be accurately estimated. The small standard error of NAC for our sample house… is typical of PRISM results. On the other hand, the three parameters, α [base load], β [heating slope], and τ [balance point], which define a house’s energy signature, are less well determined.

VBDD, or PRISM, typically works great on total normalized consumption, but gets a bit dicey when you try to pull out the specific parameters such as base load, heating slope, or balance point. The original PRISM people asserted as much:

Annualized kWh is the total consumption as reported by bills. Normalized Annual Consumption (NAC) is the weather adjusted total. As seen from last slide, NAC is pretty close to AC. Unlike the normalized heating estimate, NAC doesn’t do crazy things.

Back to the R^2 plot, all results from a site-level VBDD investigation must be qualified:

BAD GOOD

Conditional on the R^2 from an unusual regression model exceeding a mostly arbitrary cutpoint of 0.45, here are the savings.

What does that even mean? What does that mean for program savings?

CORRECTING FOR HOMES THAT GOT CAUGHT IN THE “BILL FILTER”

BAD GOOD

GOOD

BAD

BAD

The Main Idea:We want to estimate heating energy from utility bills. We use the Variable Base Degree Day (VBDD) Regression model to do this. The VBDD model works great on some homes, but does not work great on all homes.

To separate the two, we have a “bill filter.” The bill filter decides in a crude way whether the VBDD model was appropriate. It excludes sites with low R^2 or with balance points at the boundary of the search 48-70F.

For bill streams set aside in this fashion, we cannot use the VBDD estimates for any purposes. We cannot use the heating estimates from VBDD when we acknowledge that the VBDD model has failed.

Back to this example site in which VBDD failed, VBDD cannot tell us anything about the amount of heating energy used at this home.

25% failed bill filter

So what can we do?

We can look at the difference in annualized energy between the homes that pass the filter and the homes that fail the filter. “Annualized” refers to a weighted average of the observed bills and not a model-based weather normalization.

The homes that failed the bill filter used less total energy on average than those that passed the bill filter.

+ +

Coefficient Description Estimate* Standard Error p-valβ0 Intercept 10140 547 <.001β1 Floor Area (ft2) 3.6 0.49 <.001β2 UA * HDD65 (kWh/yr) 0.12 0.03 <.001β3 Heat Pump (TRUE/FALSE) -60 75 0.43β4 Failed Filter (TRUE/FALSE) -2796 76 <.001

• 100 ft2 higher area 360 higher annualized kWh• 1000 kWh higher UA * HDD65 120 kWh higher annualized kWh• Presence of Heat Pump 60 kWh lower annualized kWh (not significant)• Failed Bill Filter 2800 lower annualized kWh

*Estimated w/ RBSA survey weighting

Raw kWh Adjusted kWh

Passed Filter 19493 19449

Failed Filter 17889 16653

Difference 1604 2796

Adjusted Estimate: 14% less annualized energy

• Started with primary electric homes• Homes with gas usage removed• Homes with missing data removed• Homes with Tbal 48F set to failed• Regression with RBSA Survey weights to adjust for house size, UA,

climate, and heat pump• Estimate: 14% lower annualized energy in houses that failed the bill

filter (19450 vs 16650 kWh / year on average)• Assuming houses on both sides of filter use the same proportion of

electric use as heat

𝑂𝑣𝑒𝑟𝑎𝑙𝑙𝑈𝑠𝑎𝑔𝑒=𝑝∗ 𝑋+ (1−𝑝)∗𝐶∗ 𝑋

Let X denote heating usage estimated from well-behaved billsLet p denote proportion of well-behaved billsLet C denote a correction factor for misbehaved bills

Proposal: C = 1 - .14 = 86%. If we take p=25%, then this would downgrade the usage of 25% of the homes by 14%, for an overall reduction of 0.25*0.14 = 3.5%.

Proposed Correction Approach

Recap

3.5%

8.3%

35% 45%

Here are the consequences of the adjustment based on annualized total. It is very sensitive to the assumption of how much heat the “mis-behaved” homes use as a fraction of their total bills. For the well-behaved homes, the heat fraction was estimated as 45%. If you assume the mis-behaved homes also use 45% heat then that leads to a 3.5% overall reduction. As an example, if you assume the mis-behaved homes use 35% heat then that leads to an 8.3% overall reduction.

Example Alternate Choice

RbsaM Case Studies SummarySiteid Reason Failed Diagnosis Heating Energy

10887 Tbal 70F and Low R^2 Malfunctioning Heat Pump (?) High

11418 Tbal 48F Probably real Normal

12507 Tbal 70F Spa Normal

13912 Tbal 48F No utility heating Low

14140 Tbal 70F Shop (?) Normal

20020 Tbal 48F Spa Normal

20230 Tbal 70F Possibly real Normal

20469 Tbal 48F Large cooling load Normal

20998 Tbal 48F Cooling, Spa, & Well Pump Normal

21143 Tbal 48F Bad Read Low

23960 Low R^2 Bad Read Normal

24203 Tbal 48F Probably real Normal

24375 Low R^2 Vacations & Spa Low

24684 Low R^2 Possible Bad Reads Normal

Final Thoughts:

When using site level VBDD we must adjust for the homes that got caught in the bill filter – that didn’t show energy use linear in heating degree days.

We don’t know anything about how much heating energy those homes used.

We know that overall they used about 14% less total energy

A crude adjustment based on the 14% less total energy is unfortunately very sensitive to small changes in the assumption of how much heat the “mis-behaved” homes used, something we know nothing about.

Large changes require compelling and conclusive evidence. We do not have compelling and conclusive evidence.

We recommend, for now, assuming 45% heating energy for the mis-behaved bills and applying an overall downward adjustment of .25* .14 = 3.5% to usage or savings estimates computed from site level VBDD. The 45% heating energy is equal to the fraction of heating observed from the population for which VBDD reports useable results.