Improve regression results by taking thermal inertia into account

[steevschmidt]

Background
Buildings have different thermal characteristics which can create a delay between outdoor temperature changes and the resulting heating and cooling energy loads. For example, an uninsulated wood home from the 1950’s will respond very differently to a winter cold snap than a new highly insulated straw-bale home with high thermal mass: the heater will turn on almost immediately in the former, but may not respond for several days in the latter. As a result, increased HVAC energy use may lag temperature changes by several days. While these lags are most apparent during extreme temperature swings, they are caused by fixed building characteristics: the same delay occurs with every outdoor temperature change, no matter how small.

Likewise, the opposite may also occur, if buildings incorporate automated pre-cooling or pre-heating strategies. In these cases – which we expect to become more common in the future as we shift to TOU rates -- the associated increase in HVAC energy consumption may precede a change in temperature. Examples:

1. Since 1991 PG&E’s Pacific Energy Center can consume more electricity the day before a very hot day by making and storing ice in the basement, which is then used to cool the building in following days.
2. Stanford's new SESI facility represents an extreme case: it can start chilling water up to 7 days (!) before a heat wave.

Issue
We understand current CalTRACK methods look for correlations between weather and energy use only on a day by day basis (i.e., Tuesday’s outside temperature is only compared to Tuesday’s energy use). If so, any significant delay between cause and effect will obfuscate the true amount of energy correlated with weather, and regression results may be inaccurate.

Internally, HEA correlates a single day’s temperature with a moving 5-day average of energy use covering two prior days and two days post. We implemented this in 2011 after finding it to significantly improve regression results for many homes, with no noticeable degradation of existing “good” regression results for other homes. (We documented our testing methods in CalTRAK Issue #109 .)

Validation
There are at least two issues to validate: (1) the building behavior and (2) the potential impact on NMEC results.

(1) Regarding the building behavior:
HEA confirmed this issue with a variety of building science experts including Gil Masters at Stanford. But this group likes data, so we recently ran a simple test to try to directly measure this “lag”.

Test methodology:

1. Use hourly natural gas data from 29 gas-heated homes in SoCalGas territory.
2. Find all “cold snap” dates, defined as the first day when the local weather average temperature dropped by 5 degrees (F) compared to a 5-day rolling average. Weather data came from the KONT weather station very near these homes.
3. Exclude those dates with any similar cold snaps within five days before or after.
4. For each home, determine the maximum gas use within 5 days after the cold snap date. Record the difference in hours between cold snap date and the timestamp of the observed maximum gas use.

Results:

1. We identified 28 such cold snaps between October of 2015 and last week.
2. The median lag across all homes was 41 hours, with an average standard deviation of 31 hours.

Nearly two days! This is longer than we expected and the variation is quite high, so hopefully someone can run a better analysis, perhaps using regressions with varying offsets. But we believe even this simplistic analysis demonstrates the presence of meaningful delays.

(2) Regarding the impact on NMEC results:
HEA’s internal analysis produces significantly lower CVRMSE values than CalTRACK (see table in Issue #103). In other posts we've documented a number of issues we believe contribute to these improved results, but we have not been able to quantify the impact of each issue independently. The test results described above, if accurate, indicates that many more homes than [we] expected have significant delays between weather and energy use. If this is the case, the delay would undoubtedly impact CalTRACK's existing day-by-day weather-energy correlations, making this issue a significant contributor to lower CVRSME values.

Requested CalTRACK change
Investigate and characterize the effectiveness of alternate methods to better handle timing differences between weather changes and associated energy use in different building types. This could reduce CVRMSE for CalTRACK methods and improve accuracy.