In the UK - BS7671 requires both to bonded together - OK if your lightning electrode has a lower impedance than the system earth.
Prior to BS7671 our electricity companies use to specify an HRC fuse in any bond between the lightning earth and any earthed system connected to the suppliers companies earth facility.
I always make my lightning & earthing system one. I spend more on the below ground than I would on the above ground in industry practices. I don't know if you are talking residential, commercial, industrial, or utility application. Think of the basics. Current in and current out must always be equal. In your power system, a fault occurs at a motor. The faulted current must return to the source, i.e. transformer where the current is coming from in the ground path whatever that is, earth, conduit, conductor, etc. There could be shock hazard. This is what you are trying to avoid plus be able to clear the fault with a protective device. In a lightning strike you are trying to take the static charge to earth without it going through the path of electronics, instrumentation, computers, etc. If your building takes a hit, the charge will go to earth. The question is only how. I have no problem tying the two systems together.
There are several articles available on Lightning Protection Systems available on the net. The common thread between them is if you don't bond everything, your lightning protection system will not work.
Lightning ground rod is a part of ligntning protection. It is a path for large current to flow. When you want to provide ligtning protection, you must have some components such as Air Terminal, Air Rod, Down Conductor, Ground rod and other accessories. The grounding resistance must not be bigger than 4 ohms, otherwise, it could be not effective. In addition, after you install your ground system already, you have to bond metal components of your building to prevent from flashing as well.
Per NFPA 780, you must provide a separate ground electrode for your lightning protection system and you must bond that electrode to your building ground electrode system. Per the NFPA you cannot tie your down conductors straight to the building grounding electrode. But again, it is a requirement that both the lightning protection electrode and the building grounding electrode be bonded together. Many times IT providers will specify that a dedicated grounding electrode be installed for their system. This is only acceptable if that electrode is tied into the building grounding electode system. It is dangerous to not tie these together, due to the potential difference that would exist between electrodes. The myth that an isolated ground is necessary for sensitive equipment violates not only the NFPA/NEC, but Ohm's and Kirchoff's law.
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Here are a few instances when the ground is not tied together:
1. If the equipment cables are extremely long (i.e hundreds of miles), the ground loops can be hazardous separate grounds are used . In this case special equipment is added to monitor the ground potentials and short them out if necessary. This happens typically when one end is in the area of an electrical storm and the other is not . The capacitance of the long cable will pick up the changing ground potential caused before a lightning strike. The difference in potential between the two areas creates a situation dangerous to equipment and personnel. Usually a safety device will activate to short the two grounds.
2. When dealing with equipment in the ocean. Sea ground is at a different potential.
3. When dealing with secure data. It is possible to steal sensitive data by measuring noise on the ground of a grounded system. In this case an isolated ground and power supply is one of the steps used to make a system secure.
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