How Does EnergyPlus Determine When Refrigeration Compressors Start or Stop in a Parallel System?

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Here is a link to the documentation: https://bigladdersoftware.com/epx/doc...

The quote appears twice, one for normal refrigeration systems and another time for CO2 transcritical systems: "Once the corrected capacity is calculated for each compressor, the compressors are dispatched one at a time until the system load is met. The last compressor dispatched is assumed to run at full load for the fraction of the time step necessary to meet the load, That is, the model neglects compressor cycling losses at part-load conditions. "

Thus the answer to your question is there is no control strategy nor thresholds based on anything but load, they work from first to last from partial to full power.