Why we start motors at the bigging with star connection and after that we use delta connection?

During starting the torque requirment is very high and the starting current will be very high. A Star-Delta starter is used for starting motors to reduce the starting current. In star connection only phase voltage (0.707 X Line voltage) comes across each winding. hence during starting the current is lesser compared to applying Line votage across a winding. So you need a power supply source of lesser current capacity to start the motor while using Star-Delta starter than when using a direct on line DOL starter. But after starting, your motor needs to take load and for meeting the torque requirment, Delta is needed. Thats why these Y-D starters chage over to delta connection once sufficient speed is reached.