Electrical Engineering

Your question is not very clear.

Whether you run in star or delta, the speed of motor will be same ie synchronous*(1-slip). If you want to reduce the speed it goes into unstable region of slip-torque curve and stalls.

So there is no question of running in inching unless it is with a VFD or with the reducers.

As far as star is concerned, it is run either at start when the higher current will generate more torque or if it runs at the partial load (typically <50% of rating) in that case it improves the power factor as well as efficiency, but of course at the cost of the available power.

BTW: do not keep on switching it on and off in inching. Each time you switch on, the huge current passes through the motor, and is several times the rated current even in star. This is not healthy for the motor or for the insulation. Normal motors (unless specifically designed for inching) are only designed for a few times On/OFF in a given period. If you want then you have to get the specific motor, duly over rated that can handle this.

I do not know what duty class of motor u are using. If it is s1 its not suitable.For inching u should use s4 or s5 as required Like in Cranes where frequent starts and stops takes place.