Why Surge Arrester Doesn't Work?

something wrong PHASE wise. May not get values as replied on point at which SA is connected

exactly the phase "S" in 220KV connected with phase "T" in 66KV

I'll accept your argument that I didn't do vector math, but you didn't include the vector group either. Assuming that the 220kV line is the source for the transformer then the 66kV output will be shifted by the vector group and one phase.

Using the 220kV S phase as reference then we have 127kV 0º plus 38kV +/- 30 or 60º for example. 127 + 33 = 160 and 127 + 19 = 146, you still have a blown arrester.

Even if the 66 kV side were somehow de-energized at the time of the contact, you would still have had 127 kV on an arrester with a MCOV of 72.5, that "extra" 45 kV is going to do a lot of damage very quickly. No arrester rated 72.5 MCOV can withstand 127kV continuously for very long.

As a matter of fact if you tell us the make and model number plus the number of cycles the fault persisted, it's possible to estimate how long it took to cook the arrester. You cannot argue your way out of this one.

"you still have a blown arrester."

The problem is the arrester didn't blow

...and you know that how? If the function of a lightning arrester is to protect downstream equipment from failing, and by your own words "...causes breakdown of the insulation..." then one might logically assume that the lightning arrester failed to do its job of protecting the equipment's insulation.

Please provide satisfactory engineering proof that the arrester is still functioning, dude.

There you go. Simple math.

I under stand this math but my question is if the voltage which the insulation exposed to is 140 KV as you say, why the insulation was breakdown while it exposed to this voltage at insulation test?. And is this voltage isn't high enough to make surge arrester work?

Let me clarified it again,you said "There are many different ratings that apply, and the voltage yours was exposed to, 165kV, exceeded them all thereby guaranteeing that it would fail." isn't supposed that when the voltage exceed them all then it works and decrease the voltage or destruct itself

There's only really one way to solve the problem.
Take the lower voltage UG where it passes under the transmission lines.

Unfortunately it costs money but is more effective than relying on surge arresters.