Nobody invented electricity. Ligtning has existed since before there were people around.
There have been a whole hoast of stages for discovering electricity starting with the persians about 1400BC, way before the greeks, and if you want something odd to look at look up the "Baghdad Battery". It is thought that low voltage electroplating was being done before people knew what electricity was.
You also need to look up Tessla, Voltaire, and many others to get a good over-all picture.
There may be quite a no. of ans. The Greeks are known o produce static electricity by rubbing amber.
Benjamin Franklin discovered that lightning is electricity when he got slight shock via a metal wire.
Botanist Galvani discovered electricity flow through solutions when different metals are touched to them in pairs.this was the basis of Alessandro Volta making the electrochemical Voltaic Cell.
Michael Faraday discovered electromagnetic induction and designed various appliances based on it.
There was no invention, there was a long progression of science advancements that developed materials and mathematics that made electricity easier to understand and control.
The modern method of calculations were invented by Oliver Heaviside.
These methods made it possible to easily calculate power flows in electrical power circuits, for the power you get out of wall circuits.
http://en.wikipedia.org/wiki/Oliver_Heav...
Nobody invented electricity. It has always been there, it just wasn't being used.
A better question would be, "Who first harnessed energy to create usable amounts of electricity for human use?"