Does anyone know what should be Arc Duration(cycles) on 345kV and 138kV bus?

There isn't a "typical" duration to be used. Someone will need to review the protection (relays, fuses etc.) time current curves using the available fault curve for different locations/conditions to determine the clearing time. The breaker opening time and safety margins also need added to the relay time. The NESC has tables based on PPE levels using ranges of fault currents and maximum clearing times.

It's unlikely that time/overcurrent would be the primary protection used at those voltages. More likely distance relaying either with or without communication assistance is used; or line differential. Check with the protection department of the line owner/operator. Don't forget even "instantaneous" tripping has both relay and breaker time adders needed to get to arcing time.

Even catastrophic overcurrent is not really high for transmission lines. This being the case and leaving some allowance for tolerating faults on the subtransmission/distribution side of things, generally the modelling looks at sag and thermal limitations of the lines for the lower current limits and outright melting at the upper limits. Either way there is significant thermal mass and thus time delay in a transmission line before tripping MUST occur so trip times will be longer.

For our 230 kV lines I just assumed 2 seconds since trip times are so long.

Definitely not true at all. This statement may be true for 480 V systems but not transmission lines. Physics gets in the way of high voltage (high by IEEE standards). For relaying with a 1 cycle delay although I haven't seen much of even this for high voltage systems, I'll grant you that 1 cycle relaying is at least commonly available these days.

1 cycle clearing is difficult to achieve on any system except for very low current/voltage molded case breakers. "Instantaneous" tripping at medium voltage (1-35 kV) these days is achieved with vacuum interrupters that with 1 cycle allowed for relaying open in 3 cycles. Those devices typically require on the order of a 1/4" movement to open so mechanical motion required to open/close and inertia is very small. Scaling up to a high voltage SF6 switch pushes the opening times out to several cycles as the contact size and physical arc gap dimensions grow although puffer switches reduce this requirement somewhat by using a bellows to blow out the arc. This is the fundamental problem for the mechanical side of things.

On the electrical side, we have an even bigger problem that is not significant at low voltage (<1 kV). The fundamental difficulty is that if the contacts do not open at a zero crossing, not only does an arc form, but the result of the arc suddenly extinguishing causes ringing in the circuit due to impedance. At low voltages this is barely noticeable except with a very high speed oscilloscope and it is generally tolerable to a point. But at transmission voltages even "small" transients of say 200-300% of nominal voltage would require subsequent doubling or tripling of the insulation system. The solution is to increase the impedance during contact opening (and to a lesser degree, closing). So the actual switch design first closes onto a resistor or an inductor. Then the main contacts open, transferring the load onto the impedance. Finally the smaller resistor contacts open which interrupts the circuit with a drastically reduced transient.

The combined mechanical movement of the electrical contacts and transient control requirements combine to where a "1 cycle" opening" is never going to happen. By way of example, the S&C 2000 switch which can go up to 230 kV is pretty fast at interrupting at a 6 cycle time. That is nowhere near a 1 cycle opening time.

Since bus protection was brought up, don't forget to add the time of the lockout relay if used. Another half cycle for a high speed Electroswitch LOR.