Heat transfer & efficiency

When you say "Both options are tested" - what is the match between the two tests? Do you have 2 identical buildings? Where all the conditions identical for each test?

Also, why don't you tell us what X was, to save some brain-strain!

What does "generator" mean? If it means the same as CHU, then you cannot be doing what you think you are doing, because (10-hours of X<100%) is very much less than (14-hours of 20% +2-Hours of 100% + 8-hours of X<100%).

If the system was thermostatically controlled at 20-degC, rather than by running for a fixed proportion of the time, you can reduce heat loss by maintining the building just warm enough to avoid condensation reducing the insulation in the walls - but the 20% for 14-hours seems too high for this to work out in this case.

Sorry, but methinks your simplifications have yielded a question with no logical answer, as it is currently defined.

The only way for these two situations to have equal performance AND for them to have a simultaneous solution for the same value of X% is for X to be 240%, which is invalid. Therefore, you have not properly defined the parameters of your situation. And since your "real" location likely does not have outdoor temperatures that remain constant from night to day for three months, you cannot simplify this out of the problem. Solar loads matter, and outdoor temperature compared to the indoor setpoint during night (unoccupied) versus daytime (occupied) determines the energy required to equalize heat loss.

The most efficient way to run a building similar to the one you describe is usually to allow the temperature to drift during UNoccupied time period to a minimum (in cold weather) set by the requirements of the owner or objects in the building, and raise it to the occupied setpoint just prior to the start of the work day (if a business or school) or a similar but smaller difference if residential.

In the US, this is typically no colder than 15-18 deg C for non-residential. Either way, the building CHU is run at whatever percentage of fire maintains the hydronic loop at a temperature setting that is dependent upon the current outside temperature. This is initially programmed based on instructions from the design engineer who probably used software to "model" the building heat loss per room and read the optimal heating loop temperature off of the heating plant printout - this is generally a simple linear system called "outdoor reset" and a couple of endpoints are programmed into the boiler sequencer/controller. In other words, as it gets colder outside, the temperature of the hydronic loop is raised to allow for more efficient transfer of heat from the mechanical systems and radiators into the building.

If you are burning gas to heat water, this should be done with a "condensing" type of boiler, preferably with several in parallel and raised together so that maximum condensing will be attained when not at peak load conditions, for as close to the 97% capability of these systems at minimum load (maximum 'turn-down'/minimum fire/whatever your brand calls it) as possible.

If you are running a condensing boiler at 20% for any length of time, it's probably close to 97% efficient.

All boilers, in non-condensing situations, such as at maximum fire, are max'ing out their efficiency at about 85%, which is why standard atmospheric boilers are "just about as" efficient as expensive condensing boilers at anywhere near full (100%) fire.

In general, modern boiler sequencers can be programmed or some can "learn" to anticipate the time required for the system to go from it's UNoccupied setpoints up to the initial temperatures required for the OCCupied time period.

So when comparing two ways of controlling your system, whichever control scheme maximizes the time spent at lower firing rates will always save you gas, and it would NOT surprise me in the least to find that your plan "B" saved energy, since "A" assumes the system is burning at at a higher rate (lower thermal efficiency) for the entire time it is on.

It is not unusual for one of my multiple-condensing-boiler designs to cut a large percentage off of a school's gas bill compared to the replaced single atmospheric boiler that was removed, and was often oversized to begin with. We always combine these systems with controls to maximize the time the boilers spend at the minimum firing rate possible to equalize the heat input to the system with the heat lost by the building as the outdoor temperature changes. The old systems were often setup as your example "A," with the boiler % fire based on outdoor temp, but simply set to fire ON or OFF, and usually at 80% efficient or less.

Thanks ...