Time delay required to change star to delta connection for motor

Star connection is for providing motor to sustain the high initial current to break the initial torque of motor to till it reaches its' steady state.

It depends on load, every electrical/electronic hardware has capacitance inductance, to transfer the current from power supply to another machine need these parasitic capacitances to charge which then acts as local load as it provides a discharge path for those charges accumulated in those contact capacitances & inductance. I told this because the delay very much depends on current & parasitic reactances offered by them which ultimately decides the charging time & discharging time.

Now, initially the motor is started with low speed, it has reasons, if we expect that motor reach to full speed instantly & try to increase the current tending infinity (max. current supply rating of P.S) then, an infinite voltage will be produced across the contacts & may experience a heavy arching / burn out the contacts/lines/P.S/motor windings them self.

As we know that hardware has parasitic capacitance & inductance, definitely their would be input to output delay of each & every component in the loop including the wires (ohm's law), so, we have combination of two types of delays at least, 1. Static Delay (to pure resistive components/parts )& other ir 2. Dynamic delays (due to inductance & capacitance).

You can not say that your loop has constant delays, as capacitances & inductances are switching current components (charging & discharging v/s time). So, you need to ether make estimated delay relations or do the experiment over varying loads & note down the min. typ. max delays for every load. This procedure is known as characterization of time delays.

As you are asking time required to switch from star to delta, your motor seed will be going on increasing till it reaches the steady state, and this current is directly proportional to speed, so, inversely proportional to delay. So, run your characterization experiment with varying speed/current instead if your load is not varying & note down the min/typ/max delays, the worst case can be worked out from the two experiments (not easily but, will give you a good estimate).

And to decide on turning on timers/alarms you should always consider the worst case delays (max. delays) to avoid the loss of response to critical situations.