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"However, in Energyplus the loads from the HVAC Sizing Summary Report are still 1/3 from the sizes in the Equipment Summary Report. I will appreciate to know why this happens! "

The Design Load in the HVAC Sizing Summary is the zone sensible cooling or heating load only. It does not include any ventilation loads (outdoor air which is added by the HVAC system, this includes outdoor air added by ideal loads air systems). It also does not include any latent loads. The Equipment Summary and Component Sizing Summary report the capacity of the individual system components which includes latent and ventilation loads.

Regarding the differences in loads between programs, the ground heat loss is a common mistake. Any surface with "Ground" as the outside boundary condition will use the Site:GroundTemperature:BuildingSurface value as the outside surface temperature for that surface. The defaults for this as 18C (64.4F) which is nearly always wrong. These ground temperatures must be customized for the application or use one of the more advanced ground surface boundary conditions.