is a surge protector necessary for a basic travel trailer?

I have seen 100 volts NOT under load. I regularly use an autoformer and have tweaked it to "cut in" about 113 volts. My heaters produce more wattage, and the motor devices such as the air condtioner are much happier.

On the above mentioned 100 volts, I was able to safely run my air conditioner, but it did eventually trip the shore breaker.