Also, ungrounded 3-wire 3-phase systems that have no transformer + light bulb ground detector or similar means to drain direct current from the system can build up EXPLOSIVE amounts of static electricity during rain if there is any amount of overhead line. At 1 factory where they had 480 volts ungrounded a 600-amp motor circuit blew up right in front of me during a rain storm and that was the only place where lightning was heard. It does not matter what the voltage is whether it is 240, 480, or 4,800 volts. Low energy lightning can do a lot of damage. A cable plant technician for Ohio Bell told me that 97% of lightning damage to outdoor telephone cables comes from silent lightning or invisible lighting. Telephone cables have to be able to carry 300 VAC so that they can carry 105 VAC ringing current and so that they have an insulation level that is protectable to some extent. THWN wire is essentially a 600-volt building wire version of telephone wire. As the voltage goes up you will have smaller percentages for low level lightning damage but it will still be a lot.
There are some things you can use:
1. Convert the system to solidly grounded using a zig-zag set or a wye delta transformer with the wye side connected to your 4.8 KV distribution. The delta side would be corner gvrounded with nothing else connected. Either way you need to use 4 current transformers 2 of them in 1 of the phases so that they can be subtractively in pairs to 2 fault relays to protect the zig-zag set or other grounding transformer from internal faults. THe CTs for the A and B phases would be subtractively connected to 1 relay the other B phase and the C phase CT connected to the other relay. The 2 differential fault relays need to have a long time ( overload ) setting, a short time, and an instantaneous setting with the last setting above the inrush current of the grounding transformer. You also need to protect the grounding transformer from overload such as a CT in the comon ground wire or 3 relays using 3 of the first 4 CTs.
2. You could convert this system to resistance grounded. The 3 voltage transformers for monitoring the voltage to ground of each phase should be rated 7,200 volts at system frequency so that you can impose a 2.5 hertz 10 volt subsonic tracing tone that is compatible with the Merlin Gerin Vigilohm system or the Megger Geolux system. Each transformer 120-volt secondary would need to be connected to a 130-volt indicator lamp, a direct reading voltmeter, and if you want a voltage sensor that sends the voltage reading back to your dispatching center. The former system is the only one that offers both permanently mounted and portable transmitters and receivers and the Geolux system using portable transmitters and receivers only. You would need to build a heftier than stock subsonic transmitter using say a 140-volt "direct current" pulse width modulated servo drive to generate a 100-VAC subsonic tracing tone 2.5 Hertz or 5 Hertz. You would also need a parallel resonant 50-Hz or 60-Hz blocking device in series with the servo amplifier output plus a damping resistor. I do not remember if the Geolux system will receive 2.5 Hertz but I do remember that it can receive 5 Hertz.
You will also need 3 7,200-volt primary 240-volt secondary transformers connected in the wye primary broken delta secondary configuration. The 7,200-volt primaries would each be connected from each phase to ground. The 240-volt secondaries would then be connected in the broken delta configuration and neutral grounding resistor across the 2 open ends of the secondary. The secondary resistor needs to be able to withstand 720 volts continuously from a heat dissipation standpoint e.g. three 240-volt heating elements connected in series. There are different formulas for sizing the transformers and resistors to damp out voltage excursions.
ON this system you should run an overhead ground wire over the 4,800 volts close to and over the substation to help absorb lightning. You need to sink the ground rods as deeply as possible. See US Patent 8,439,125 for directions on how to do this plus some articles by Martin Conroy wrote on what he and the patent holder Richard Teebken did when their company Grounding Perfection was in business. Remember, a lightning arrestor will only be as good as its ground. This applies whether your system is solidly grounded or resistance grounded.
3. You could also do a delta to wye voltage raise to 4,800Y8,320 volts solidly grounded. Along New York 17 right before or after the Pennsylvania/New York line there are 3 4,800:4,800-volt power transformers that step down to 4,800 delta from 4,800Y8,320 volts. That was back in 1989 - the location could have been moved or the rest of the circuit voltage raised. That is, some power companies have both voltages.
4. You could also do a raise to 13,800 volts. Apparently your 13,800-volt system does not have sustained overvoltages that are blowing out the lightning arrestors. If the source is 7,970Y13,800 volts lime on Cleveland Public Power you can start installing dual voltage transformers and a Protective Earth neutral conductor on the 4,800-volt system. I have seen dual voltage transformers of these voltages:
4,340x7,620 volts single phase and 4,340 delta x 13,200 delta on Cleveland Electric Illuminating Company.
4,800x7,620 volts single phase on the Holmes-Wayne power cooperative.
A photo of a 4,800x16,000-volt single phase on a Canadian electric utility.
2,400x7,200 volts single phase and 7,200x13,200 volts single phase on Ohio Edison.
A 4,800x7,970 volt or a 4,800x13,800-volt single phase transformer is theoretically possible.