"Damage" is an all-encompassing term for "It Doesn't Work Anymore". The AVR (Automatic Voltage Regulator) could be damaged by something internal, like a failed component, or the AVR could be damaged by something external, like a short-term transient voltage spike (short-term voltage surge) on the power line caused by lightning, or even work on the outside power lines next to the building. The external-to-the-AVR-Box damage cause could even be a backward voltage spike from the elevator motor, although the chances of that are very slim.
The Automatic Voltage Regulator is an electronic device. As such, it is itself capable of being damaged from transient voltage spikes that come in on the power line. Yes, it is designed to reduce voltage spikes that come in on the power line, but the voltage spikes that it's designed to correct are relatively long. Lightning strikes or work on the outside power lines can induce voltage spikes that are far shorter.
Voltage Level Protection
On the incoming utility power, at least under normal circumstances, if the voltage is too low for proper running of the elevator, the AVR increases the voltage to normal. If the voltage is too high for safe elevator operation, the AVR reduces the voltage to normal.
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Protect Electrical Products from Surges
Nothing provides perfect protection. The AVR is a relatively slow-reaction-time adjustment device to regulate the normal voltage variations on the utility power. According to the literature provided by the manufacturers of some AVRs, its typical reaction time is about 1/10 of a second. It protects from voltage dips, swells, over-voltage and under-voltage events. However, it will not protect from transient voltage and surge voltages which last less than a millisecond (one thousandth of a second).
Transient voltages caused by lightning are really fast, and the AVR cannot properly deal with such fast transient voltages. Remember, the AVR is an electronic device, and it also can be damaged by lightning.
The AVR protects the elevator from varying AC voltage. To protect the Automatic Voltage Regulator from high-speed transient voltage surges, like the ones caused by close lightning strikes, there should be a Surge Protective Device (SPD) or a Transient Voltage Surge Suppressor (TVSS) in the power line between the AVR and the incoming utility power.
An SPD or TVSS doesn't regulate voltage, an SPD or TVSS protects from short term voltage surges. But sometimes, after repeated transient voltage surges, it too can be damaged.
By comparison to the cost of replacing the AVR, a surge protector is inexpensive. You might wish to replace the surge protector at the same time that you're replacing the AVR. Just in case it, too, is damaged.