Electricity!

The electric power companies has made a significant contribution to the evolution of the this modern society.

The electric power companies have made a significant contribution to the evolution of this modern society.

The principle of all of the electric companies has been exceedingly simple, to provide a supply that corresponds to a demand.

The principle of all of the electric companies have been exceedingly simple, to provide a supply that corresponds to demand.

But In actual fact, there are various limitations that restrict the electricity supply: such as the total generation capacities, the transmission capacities, and so on.

Electricity!

There is a mismatch between the title of this article and the overall tone of its content.
The title "Electricity!" would be fine for a very informal and light discussion. However, the
content of the message is somewhat academic and serious. This sort of title is probably better:
Reevaluating Electric Consumption in Japan after Fukushima". (What genre do you wish to
write in? Casual and light? Or scholarly and precise? This article mixes genres, so I am confused.)

In Japan, Electricity is indispensable to most people in OECD countries the backbone that supports our lives, and the amount of the demand worldwide is growing. relatively quickly as the result of the growth in its economy in the recent years.

電力需要は、日本独自のものではありませんので、OECD諸国に変更した。
Also, the data I have read suggests Japan's electric consumption has alreafy peaked:
in recent years it has decreased. Worldwide, however, electric consumption is growing.

The electric power companies has made a significant contribution to the evolution of the this modern society.

すみませんが、上記の文書は曖昧過ぎる。You should specify *which* electric power companies have
made a "significant contribution" to society. (If you mention TEPCO, I am afraid people will laugh.)

But at the same time, they brought some abuses have occurred.

The main principle of all of the behind electric companies in Japan has been exceedingly simple: to provide enough power a supply that corresponds to meet consumer a demands.

This is a topic I have done some research on and it seems like an over-simplification. Japanese electric power companies have a number of agendas to fulfill, and some of those agendas conflict.
If you look at the situation closely, I believe it is anything but simple.

Such intention has been encouraging the use of electricity for a long time.

上記の文書は意味不明。。。これをどう補正すれば良いかわかりません。

But concurrently, In the term of the use of electricity, it caused the circumstance that many people believe that the electricity supply is an inexhaustible. COMMENT: Here is my guess at what you are trying to say:"Since the Fukushima Disaster, many Japanese have come to realize that electricity is not an unlimited resource to be taken for granted."

COMMENT: The previous sentence needs to specify the context as Japan. It should also clearly
indicate that the 3/11 Fukushima Disaster was a key event that changed public thought about
electricity in Japan.

But In actual fact, there are various limitations that restrict the electricity supply: such as the total generation capacities, the transmission capacities, and so on.

Hmm. This sentence would be much better with a concrete example. It sounds too vague and theoretical. Also, you are stating facts that any educated reader already knows. (Either delete entirely or else provide a clear example with new information that readers do not already know.)

*ADD NUMBER* months after the 2012 Tohoku Earthquake all of the nuclear plants in Japan are suspended operations because of on safety concerns, and it is concerned that Japan will may faces power shortages this summer.

Please indicate the time lag between the 3/11 mega-quake and the decision to suspend nuclear power in Japan. Also, didn't the decision to suspend operations come from the Prime Minister's
Office? (If I remember correctly, it was *not* a decision by the electric power companies, but a
mandate from the Prime Minister's Office directly.)

Therefore, this is a time that the renewed principle of the electric supply that will induce people to manage in a limited supply must be considered.

I am afraid I could not figure out the meaning of this sentence. It seems you will need to reword this sentence a bit more before the meaning is clear.