In large compressors, there is a method we call 'pneumatic unloading' where at a preset pressure the compressor stops pumping air by pneumatically manipulating the valves but the motor drive is continuously running light. If this is what you mean when you say running continuously, then you should weigh it againts the pros and cons of frequent starting and stopping which could be detrimental to the motor windings and other related equipment. Actual costs will depend on specific situations and may be difficult to generalize.
Firstly, it depends how often you are staring and stopping? How large the motor is?
The motor must be allowed to cool adequately before attempting a restart. Noramlly no more than 4 starts per hour, not less than 15 minuts apart are recommended. If you have adequate winding temperature sensors, (no less than two per wdg) you may want to monitor winding temperature.
I am not sure what this has to do with star/delta starter mentioned in the heading of the question.
As for keepig the motor idling, it is very easy, measure the kW of the idling motor/compressor and calculate kW*H*cost/kwh.
Cost of risk on the other hand, is a subjective issue.
