Final answer:
The compound-motor connection to avoid is a counter-compound configuration where the series field winding opposes the shunt field winding, leading to instability and potential motor damage.
Step-by-step explanation:
In general, the type of compound-motor connection that should be avoided is one where the series field winding opposes the shunt field winding. This is known as counter-compound or differential compounding. Compound motors combine both shunt and series windings to take advantage of the characteristics of both. If these windings work against each other, the motor may experience instability in operation, potentially leading to poor performance or damage. Ideally, the series winding should aid (cumulative compounding) or at least not interfere with the shunt winding in maintaining motor speed under varying loads.