HVAC systems with start time optimization

A method for controlling HVAC equipment to affect at least one physical property of an environment of a building zone, the method comprising:

• obtaining a schedule for the environment comprising at least (i) a first time period and a third time period during which a criterion for the at least one physical property of the environment is to be satisfied and (ii) a second time period occurring between the first time period and the third time period and during which the criterion for the at least one physical property of the environment need not be satisfied;
• determining a transition time during the second time period at which to start pre-conditioning the environment based on an intersection of (i) a first timeseries comprising predicted values of the physical property when the HVAC equipment are operated in a first control mode during the second time period and satisfying the criterion at a beginning of the third time period, wherein the first timeseries is initialized at the beginning of the third time period and determined by backward simulation using a thermal model of the building zone and (ii) a second timeseries comprising predicted values of the physical property when the HVAC equipment are operated in a second control mode during the second time period and satisfying the criterion at an end of the first time period, the intersection defining a temperature-time point at which the predicted values of the physical property in the first timeseries and the second timeseries are equal;
• and
• operating the HVAC equipment in the first control mode during a terminal portion of the second time period beginning at the transition time.

One or more non-transitory computer-readable media having instructions stored thereon that, when executed by one or more processors, cause the one or more processors to perform operations comprising:

• obtaining a schedule for an environment of a building zone comprising at least (i) a first time period and a third time period during which a criterion for at least one physical property of the environment is to be satisfied and (ii) a second time period occurring between the first time period and the third time period and during which the criterion for the at least one physical property of the environment need not be satisfied;
• determining a transition time during the second time period at which to start pre-conditioning the environment based on an intersection of (i) a first timeseries comprising predicted values of the physical property when HVAC equipment are operated in a first control mode during the second time period and satisfying the criterion at a beginning of the third time period, wherein the first timeseries is initialized at the beginning of the third time period and determined by backward simulation using a thermal model of the building zone and (ii) a second timeseries comprising predicted values of the physical property when the HVAC equipment are operated in a second control mode during the second time period and satisfying the criterion at an end of the first time period, the intersection defining a temperature-time point at which the predicted values of the physical property in the first timeseries and the second timeseries are equal;
• and
• operating the HVAC equipment in the first control mode during a terminal portion of the second time period beginning at the transition time.