Posted By engineer on 01/17/2009 8:14 AM
Tough to quantify - so many different thermostat and control systems give a myriad of alternative scenarios.
Some thoughts:
1) Bin data (hourly average temperatures) coupled with an accurate Manual J building load calculation should predict # of hours of 'legitimate' stage 2 operation (as well as stage 3 hours)
2) From that data you'd need to try to winkle out the 'extra' hours caused by suboptimal zone control board or overactive thermostat(s) Not sure how to go about that other than via placing hour meters on stage 1 and stage 2 signal wires and comparing it using actual weather data (not BIN - every year is different from averages)
Calculating the efficiency difference between stages is not trivial - certainly one would use the manufacturer performance tables as a starting point. Then actual data would have to be gathered at the system in question - ARI efficiency ratings assume a specific drop in EWT when 2nd stage kicks in. EWT will drop (closed loop, not open loop - yet another consideration) but not exactly as ARI assumes.
Another complication is that for most systems no effort is made to increase GPM at 2nd stage. However, manufacturer performance tables use different, higher flows for stage 2 tables.
Finally there is the need to interpolate, probably 2 dimensionally, using the tables - EWT data is only provided every 10 degrees, and flow in even or odd values every 2 GPM. Rounding for simplicity could introduce errors near or greater than the calculated loss of efficiency.
Finally finally, all of this assumes airflow is at rated CFM. ECM blowers supposedly deliver specified CFM to within 5% but ONLY IF duct ESP is within bounds - for many duct systems it isn't. For zoned systems, ESP may be in bounds only if large zones are calling, but not in the case of small zones, a design compromise sometimes tolerated under the theory that single small zone operation is relatively rare and short-lived. If CFMs aren't where they need to be, all bets are off with efficiency calculations. There are correction tables, but knowing the CFM in a high static situation isn't easy.
I'm okay with 15% as a basis for back-of-envelope estimates, but determining the fraction of 2 stage hours that are unnecessary (and therefore available for optimized controls) vs those legitimately needed owing to building load is not trivial.
Whew. Thanks for the effort you put into that. It makes a lot of sense & is very educational. I guess its all moot if one uses a differential up-staging control system.
Anybody out there care to take a crack at: "determining the fraction of 2 stage hours that are unnecessary (and therefore available for optimized controls)"