Question-and-Answer Resource for the Building Energy Modeling Community
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It is difficult to pinpoint an answer given this much information, but here are some possible reasons to explore:
The summer design day is of the type that has high drybulb with mean coincidenct wetbulb, but often cooling coil loads are larger for high wetbulb with mean coincident drybulb. The program will select the design day with the highest sensible zone load, so sometimes you have to remove the DB->MWB day from input to force it to use the WB->MDB day. This often comes up for dry climates, which I would think is the case for Lima.
The schedules that are important for controls are setup one way for the design days, but then differ for the regular types of days so that the system is not really running properly when changing from design days to annual run.
Sun angles for a mid-summer are high, but shoulder seasons have lower sun angles which actually lead to higher gains in the space, regardless of outdoor temperatures. Add some additional design days that cover shoulder seasons, even covering all twelve months.
As always, you'll want to study detailed timeseries results for air system nodes to diagnose what is really going on during those hours not met.
