how much time delay required to change star to delta connection for motor and how we can calculate the time delay

If what you are asking is how much time delay you require from when the motor starts in star to when it should switch to delta, it always depends on the load and varies considerably.
It basically depends on how long the motor takes to reach full speed in 'star'. When it reaches full speed you then switch it to delta.
For example, a pump may take 1 second to reach full speed so the timer should be set for 1 second. The flywheel of a press may take 30 seconds to reach full speed in star, so the timer should be set for 30 seconds.
Setting the timer to switch to delta before the motor reaches full speed may blow the fuses or trip the circuit breaker.
Many customers today are opting for a 'soft starter' instead of star / delta contactors too.

Motor must reach full speed and current must drop to running current before switching over to delta. Switch over time depends on load inertia and load speed.
There is no formula to calculate the time. Set timer to high value say 60 second. Connect a tongue tester to motor line side 1-phase before star-delta connection. Start the motor and observe the time taken when starting current drops to running current. Set timer slightly higher the observed time. It will work satisfactorily.

Star Delta motors are not two speed motors. The star delta configuration is used to keep start-up current for large inertia loads or high horsepower motors to 300% of the nameplate current or less. With todays Solid State starters, the need for Star Delta starters has all but disappeared. The time to transition from Star to Delta is determined by the load's inertia. I doubt that you can calculate the time mathematically since there are numerous variables. The time tested method is with an ammeter and a stopwatch. When the current starts to fall rapidly, it's time to switch to Delta. If this time exceeds 20 seconds, you need to resize the motor and starter otherwise nuisance tripping of the overload will occur not to mention a reduction in the life of the windings.

Jean, completely correct....just FYI
It is still quite common in industrial automation to use wye-delta for two speed rather than controlling inrush on high HP.
I do it all the time with under 5 HP SEW
The trick is ... you cannot stay in slow all the time... only for decel or recovery mode in slow for one cycle. Too long in slow and you let the magic smoke out. This is done because it mimics the torque speed curves of a demag micro speed multi ratio gear box.
A whole lot cheaper. . It is a Euro thing for sure....I first seen in a French Design...
Works exceptionally well for high inertial decels. I do it all the time on very Large Dial Tables.

Why would you use a wye-delta motor and starter in the firsl place?

1. Use a solid-state starter and wire the motor for high voltage.
2. Use a standard motor and a solid-state starter

Wye-Delta is Prehistoric

David,
Star Delta starters are far from obsolete. For example YD starter for 250kW price is about few hundred bucks, soft starter is around five thousand bucks, and VFD is around 30k$. Both SS and VFD require additional cost in protection switchgear. If you need constant speed YD is far cheapest solution, even in longer term. On other side if you need or your process allows you to change speed, then VFD is far best solution, also considering economy.

Considering the cost of rewinding a 250kw motor, not to mention removal and reinstallation, I would strongly recommend a solid state starter (different from a Soft Starter) as economically a better value overall.
Longer motor life, and depending on the type of load (a rock crusher for example), longer mechanical life.
Total cost of ownership is more important than the price of components.

Why should I rewind motor? Here in Europe we have 230/400V 50Hz (or 220V/380V) network, like in most of world.
Also applications for the motor that big, are usually requiring 1 or 2 start per day.
In my country for 250kW load almost always electricity company will supply you only from MV network, so it means that you have MV/LV transformer at your plant, and you pay the price per KW at rate 0,039$ for higher tariff or 0,013$ for lower tarif.
I have seen many installations with YD starters that are working over 30 years without any problem, with practically zero maintenance.
So, please explain me, for applications where we need constant speed, and we don't require frequent starts and stops, where is economy with solid state starter,considering TCO.

If I am not mistaken, the question originally pertained to how much time delay is required for a YD starter.
It sounds like Karimulla already has a YD starter in place and is merely asking how long to set the timer. Maybe the original timer quit and he had to replace it, I have seen this issue before when someone replaced a timer but kept blowing the motor fuses due to the time being too short and not allowing the motor to reach full speed (for a press flywheel).

If he has a YD already in place there is nothing wrong with it and unless there is an energy savings issue then stay with it.
However if he needed to replace the starter then he could consider going to a soft starter which saves energy and mechanical wear and tear.
I recently priced a YD starter combination against a soft starter for a 400V 150HP pump motor and the soft starter was by far less expensive.

The comment on rewinding referred to the fact that the MTBF (mean time between failures) would be less than with a Solid State Starter therefor the need to rewind more often. Effectively if the motor starts only once a day or less, then stay with your current starter.

The motor will never reach its running current in star mode since the lower voltage will produce higher slip and therefor more current. When the current falls from the 300% level down to a steady state current which will vary according to the load inertia, then its time to switch to delta.