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That equation is a correct representation of the zone heat balance. All of the components of the heat balance are available as Output:Variables. My guess is that dividing the zone into two parts has changed the timing of when transmitted solar gains become a load. Start with these outputs for the two cases, and then you can add more detail once you know what area to focus on:

Output:Variable,*,Zone Air Heat Balance Internal Convective Heat Gain Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Surface Convection Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Interzone Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Outdoor Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance System Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance System Convective Heat Gain Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Air Energy Storage Rate,hourly; !- HVAC Average [W]

Also, try a case with a winter design day with no solar and constant temperature and see if the loads agree.

That equation is a correct representation of the zone heat balance. All of the components of the heat balance are available as Output:Variables. My guess is that dividing the zone into two parts has changed the timing of when transmitted solar gains become a load. Start with these outputs for the two cases, and then you can add more detail once you know what area to focus on:

Output:Variable,*,Zone Air Heat Balance Internal Convective Heat Gain Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Surface Convection Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Interzone Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Outdoor Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance System Air Transfer Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance System Convective Heat Gain Rate,hourly; !- HVAC Average [W]
Output:Variable,*,Zone Air Heat Balance Air Energy Storage Rate,hourly; !- HVAC Average [W]

Also, try a case with a winter design day with no solar and constant temperature and see if the loads agree.

Answer Part 2

Working with the actual files, comparing Zone Ideal Loads Zone Total Cooling Energy. This is not just a simple box divided into two boxes. This is an atrium embedded in a larger building, and the atrium has exterior, interzone, and ground contact surfaces.

  1. There are AirflowNetwork openings and cracks. Even with no venting, there is still infiltration flow through the cracks which will behave differently for two stacked zones than for one taller zone. Turn off AFN "NoMultizoneOrDistribution". Still different loads.

  2. A comparison of the two files showed a slight different in the per area internal gains for the upper atrium zone vs the lower. Remove People, Lights, and ElectricEquipment. Still different loads.

  3. The solar distribution is the defaul "FullExterior" which puts all incoming direct (beam) solar onto the floor. The original floor construction (Surface 21) interior material layer has a solar absorptance of 0.8, while the floor added to split the two zones has a solar absorptance of 0.5. Just to make things simple, changed all of the materials in the entire model to 0.9. Still different loads.

  4. The bottom floor (Surface 21) has an outside boundary condition of "Ground". There is no Site:GroundTemperature:BuildingSurface object, so the default temperatures of 18C are applied to the outside of this surface. So, this surface has a very different temperature dynamic that the rest of the surfaces. Changed this to be adiabatic. With this (and all of the above changes), the loads are now 5.17 for the single-zone case, and 5.37 for the two-zone case.

So, thinking back to the original models, the key driver is all of the incoming direct solar hitting the floor which has an outside temperature of 18C, so it sheds lots of the solar gains. The two-zone model takes the upper atrium solar and puts it on an interior surface where it isn't lost to the ground.