Thoughts on Efficiency Derates

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Proper field work for existing buildings should necessarily include thorough testing. For example, for boilers you should really do a combustion test at different part loads (unless the burner is On/Off only) to capture the burner efficiency across the modulating range. The idea is to try and nail as many parameters as you can: there will always be some that can't measure or even estimate with more than a broad qualitative judgment, for example infiltration.

I'd also be pretty skeptical about trying to derive general rules of efficiency versus aging. Something old but very well maintained might be working just like on the first day, and generally a system is a combination of individual components. A 50 year-old cast-iron scotch-marine boiler on which you just recently replaced the burner and the jacket insulation shouldn't be much different than an actual brand new boiler (we didn't get that much better at making giant kettles basically). On the other hand a two year old boiler that hasn't been well maintained - no bleeding nor water treatment leading to water-side scale, soot in the fire tubes, burner not tuned across the entire modulation range, controls overridden - might be a lot worse than planned if not a safety hazard (incomplete combustion => CO).

Coils need cleaning, filters need changing, burners need tuning, everything needs servicing.

Anyways, after proper field work, you will need to take an educated guess for the initial value of some parameters you couldn't measure. Start by trying to assess what the rated efficiency of the unit is (nameplate, or common efficiency ratings at the time, look at older codes for example), then derate that based on whatever information you have such as visual inspection (dirty coil, coil fins bashed in, etc)

After that, these parameters will be refined during the calibration process where you'll try to get your model to match the utility bills.

This basically amounts to a linear regression problem in which you have naturally quite a few parameters (some matter a lot, others much less so, a sensitivity analysis is useful for that).

In many cases you'll use 12 monthly bills as the independent variable for the calibration. If you're familiar with the problem of overfitting, this should really stress my earlier point about "nailing every parameter you can".

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

-- John von Neumann

(For fun, see a Python implementation of this quote)