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An assumption for the traditional predictor/corrector solution includes that for step 3, the HVAC calculation assumes perfect control. If this is relaxed, then the traditional predictor/corrector methods are not applicable.
In Modelica based simulations (as in other simulations that are using an ordinary differential equation solver) there is no "load" and then "system" simulation, but rather a simultaneous solution of these equations. This may or may not require iterations depending on the HVAC system, its control, and the (optional) computation of the pressure drop in the duct network.
Modelica based tools have the "awareness" to only iterate when needed, this is determined automatically by these tools.
Comparing computing time among this approach and today's building simulator is an open-end question as people that use Modelica generally have more detailed models (but of coarse simpler models could be used as well) and R&D is ongoing for how to best simulate large buildings with very slow dynamics (e.g., heat conduction in walls) and fast dynamics (e.g., control loops). Here, it is important to note that this is not a question specifically to Modelica (which is for the simulation converted to C code that is likely more efficient than a human programmer could reasonably write) but rather a question of what numerical methods are best suited for this application domain. IDA/ICE has very promising results for such integrated solution that do not use a predictor/corrector method.