Design day and Runperiod value mismatch

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While the date is the same, the sizing period and run period use different weather data.

The DesignDay uses explicitly defined maximum/minimum temperatures and other weather variables and creates a day's worth of weather using a set of multipliers. See the EnergyPlus Reference for more details.

The run period uses the weather file data which is whatever the .epw file shows for that particular day. TMY3 files use a typical month from a 30 year average, and so it is unlikely that an average 5/21 will correspond to the design day 5/21.

Additionally, schedules for design days are usually different from the weather run period values. It's typical to have design day internal load schedules fully-saturated for cooling and zero for heating.