Electric company found an open neutral at home yesterday, my kwh usage, has been high, would an open neutral cause my kwh usage to increase?

Probably. The reason is because the open neutral is likey an intermittant connection and many devices draw a much large current on startup.

Motors will all the time.

Incadescent lamps draw about 10x their rated current when cold, so they would have to cool first..

About how high in %?

3500 to 4500 kwh/monthly

That does seem excessive, since the average use is about 500 kWh for someone with non-electric heat. I'm surprised the utility company didn't catch it. Someone "siphoning" power is yet another possibility.

Watch for hot tubs and swimming pools.

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