Smart-thermostat setback saving

How hours of lower setpoint become heat that was never lost

The relation prices restraint. The whole-house conductance says how much heat the envelope leaks for each degree of indoor-outdoor difference held; the saved degree-hours say how many degree-sized, hour-long slices of that difference the schedule declines to hold. Their product is heat that was never lost — not generated more cheaply, simply never demanded. Dividing by the system’s efficiency turns unneeded heat into unneeded purchased energy, and the tariff prices it.

The saved degree-hours input is the schedule made measurable, and building it is where the honesty lives: setback depth below the normal setpoint, times the hours per day the lower setpoint actually holds, times the days the routine survives. Every term is a behavioural claim — an abandoned schedule saves nothing, however it was programmed. A shallow setback kept through every sleeping night can outsave an ambitious one dropped by the first cold morning, and an occupancy-sensing thermostat earns its keep by finding away-hours a programmed schedule would miss.

What the simple product ignores is the recovery. When the setback ends, the system must climb back to the comfort setpoint, running harder than it otherwise would; the house’s thermal mass — furniture, slab, the walls themselves cooling and rewarming — smooths and delays everything. Over a season those effects mostly borrow heat rather than create it, which is why the degree-hour method stands as the standard first estimate — and why a measured winter wanders around it rather than landing on it.

The efficiency input ties this page back to the machines. For electric-resistance heat it sits at unity — a saved unit of heat is a saved unit of electricity — while for a compressor the seasonal coefficient from the heat-pump page divides the saving: a machine that made the heat cheaply saves less per unit avoided. The same schedule is worth most in the worst-heated house — the quiet logic of doing the cheap behavioural fix first and letting the equipment decision follow.

One caution belongs in the arithmetic rather than the footnotes: heat pumps complicate deep setbacks. A steep morning recovery can push a compressor into its backup strips, buying the recovery at parity instead of at the machine’s multiple — a smart controller’s gentle early ramp exists to avoid exactly that. A schedule aggressive enough to change HOW the machine heats has stepped outside what the seasonal average can see.

When this calculation is used

• Pricing a schedule before adopting it: a proposed overnight and workday setback, as degree-hours, valued against this house’s conductance and this bill’s tariff.
• Auditing a thermostat’s promise after a season — the degree-hours its logs claim, run through the envelope and tariff, against what the bills did.
• Comparing routines rather than gadgets: a deeper-but-shorter night setback against a shallower all-day one, holding house, system and tariff constant.

Worked example

Run the pack’s declared reference schedule: a home of moderate envelope conductance, a season’s worth of saved degree-hours from a routine nightly setback, electric-resistance heat, and a mid-range residential tariff.

The engine returns the annual saving and, separately, the electricity never consumed. Read the electricity against the winter’s consumption first: it states what share of the season the schedule quietly removes — the number to weigh against the comfort the setback costs.

Every figure in this example is produced by the certified engine when the calculator loads, checked against the signed pack’s declared test vectors; nothing on this page stores an answer. Raise the coefficient from resistance to a heat pump’s and the same schedule shrinks in value — the efficient machine already banked most of what restraint was going to save.

What each input represents

Assumptions and limits

• Heat loss is proportional to the indoor-outdoor difference through one constant conductance; solar gain, internal gains, wind and hour-to-hour envelope variation are averaged away.
• Recovery energy and thermal-mass effects are not separately modelled: the degree-hour product stands in for the true trajectory, which measured winters wander around.
• One seasonal coefficient prices the avoided heat; a setback deep enough to force a heat pump into backup-strip recoveries changes the machine’s own average and steps outside this relation.

What the guards protect against

• Zero saved degree-hours is refused — the pack ships the refusal as a declared test vector — because a schedule that never lowers the setpoint has nothing to price, and a zero-cost answer would dress a non-schedule up as a result.
• The envelope conductance must be positive and is capped far above any dwelling, catching wrong-unit figures or a compound’s worth of building pasted into a house-sized relation.
• The coefficient’s band tolerates the sub-unity averages of a hard-driven machine but refuses fractions describing a system that wastes most of its electricity — a mistyped decimal, not a heater.

Provenance

Degree-day and degree-hour heat-loss estimation: envelope conductance times temperature-difference hours, with purchased energy scaled by system efficiency

The whole-house conductance is multiplied by the saved degree-hours to yield the heat never lost, divided by the heating system’s coefficient to yield the electricity never purchased, and priced at the tariff to return the annual saving.

Screening and reference material, to be checked against the governing standard and a qualified engineer; not a design determination. The signed pack carries its own citation, which displays from the verified leaf when the calculator loads.