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When referring to outputs from EnergyPlus, it is important to specify the exact report name and column heading. In this case, "total cooling load of the entire facility" is probably the "Zone Sensible Cooling" loads from the "HVAC Sizing Summary" table output. The coil design load will include the zone sensible load plus outdoor air load, fan heat, and latent loads. The coil sizing relative to zone load can also be impacted by inconsistent inputs for supply air temperatures in the Sizing:Zone and Sizing:System objects. For more details, see answer in the (nearly duplicate) question here.