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I'm not sure exactly what your definition of 'the useful energy' is, but the sum of Cooling Coil Total Cooling Rate does not consider the effect of Pump Shaft Power, which heats chilled water and becomes a load on chillers. The cooling load from Pump Shaft Power is normally 3 to 5% of total cooling load. I think we should not ignore it.

When I want to know the the total cooling load of a whole building, I select Chiller Evaporator Cooling Rate in Output Variables and sum up the cooling rate of all chillers. Below is my understanding of the relationship between each Output Variable.

Σ(Chiller Evaporator Cooling Rate)

= Σ(Cooling Coil Total Cooling Rate) + Σ(Pump Shaft Power)

= Plant Supply Side Cooling Demand Rate + Plant Supply Side Unmet Demand Rate

When I use not chillers but VRFs, I select VRF Heat Pump Total Cooling Rate and sum up the cooling rate of all VRFs.

Please refer to here or other description of Output Variables.