For power current transformer, the secondary is not allowed to open when the primary is conducting current of several KAs. So I want to design a over voltage protection circuit for this situation, when there is over voltage (several KVs), then short out the secondary of the CT.
I want to use GDT or MOV for this purpose, but all they labeled as "transient". Is it suitable to use them under power frequency?
A current transformer has to be connected to burden resistor or short circuit. Your problem can't have a solution, since if you cannot ensure a burden resistor to be connected all the time, how can you ensure that MOV will be? Connect the burden resistor as you plan to connect the MOV and the problem is solved.
In the same way that a series circuit on a voltage supply needs a fuse, that burns open from overcurrent; a parallel branch on a current supply needs an antifuse, which burns short from overvoltage.
Unfortunately, this isn't a standard product, or not under this name at least. (The most common use of "antifuse" is in microelectronics, where a link is made to short out, rather than burn open, such as one-time-programming an error or code selection of an analog or digital IC.)
It does appear that there are existing solutions, CTPU (Current Transformer Protection Unit) for example:
However, without characteristics given, it's impossible to say whether these operate by clamping (the "varistor" part suggests so) or shorting (SiC, when hot enough, could indeed show reduced resistance; the ceramic body might support this mode of operation, but the 200°C rating suggests perhaps not). You would have to inquire with the manufacturer to find details.
You could potentially use a zener/TVS this way, as they fail shorted when overheated -- but this is problematic, as manufacturers do not rate them for fusing current, nor what resistance they attain when so shorted. It's not a very safe arrangement, lacking such assurance.
Incidentally, zeners are what they (anti)fuse when doing it in microcircuits; problem is, this is done to handle signal currents, the part/location never gets overheated again, and it's encapsulated afterwards. Whereas a TVS, the hottest (middle) portion of it might melt, but that leaves the bulk of the semiconductor alone (normal, nonconducting around the short); and the heat likely damages the packaging (releases magic smoke), so that the resulting short is subject to oxidation, corrosion, separation (the part might crack due to stress from melting and burning), etc. I can imagine a metal-ceramic packaged device could be made to fail in this way reliably, and to be qualified for such operation -- but you'll have to find a manufacturer that provides such parts with such ratings, and that seems a tall order.
The most conventional solution of all, is to simply ask around your local industrial suppliers and see what they suggest. They'll have manufacturers like the above (and their competitors, regional or otherwise) on the line card, and able to call in to sales/engineering to see what products they would recommend for an application. Or be knowledgeable enough as a representative directly, to have some idea what to do. Maybe they suggest a clamping method, like the above (varistor based or TVS) method, maybe there is something more specific (antifuse element, or mechanical equivalent).
This can also be solved by procedure -- if also unreliably, as procedure is subject to error as well. Before anything is disconnected from the CT, short out the terminals first. A CT must always have a low resistance across it, to reduce power dissipation, in precisely the same way that a voltage source must have a high resistance across it to reduce power dissipation.
