Define different HVAC operation trigger temperature and setpoint temperature

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This is commonly referred to as a deadband or driftpoint in the setpoint temperature range. For example say you have a setpoint range of 20-26 degrees, but you give it a deadband of 4 degrees, so the cooling won't actually kick on until 30 degrees, and the heating won't until 16 degrees. By convention this also means that the cooling system with overcool by the same deadband (in this case down to 22 degrees). (at least this is the most common control strategy that I see)

Another phrasing for this is throttling range, which in the example above would be 8 degrees, or twice the driftpoint. The only way I know how to do it natively and simply is with a ZoneControl:Thermostat:StagedDualSetpoint, which can define throttling ranges, as defined in the input output manual. If you need something more specific or more complicated, then I think you will need to look into EMS.

I find this as a major lacking point in EnergyPlus simple dual control thermostats, because it's such a common control strategy. In fact I have searched and found: https://unmethours.com/question/17507... and https://unmethours.com/question/17656... both of which are asking the same things as you, but neither have really been answered.

I believe you can do that with Availability Managers. You can read about that in the Input Output Reference. You would probably need to combine several Availability Managers in order to achieve on and off rules. Another option, a bit more complicated would be to use EMS.