I have heard that some don't use electricity made by the Israeli Electric company on Shabbos and only use generators.
However, I have seen people who do use public electricity on Shabbos.
What are the reasons to permit it and forbid it?
Reasons to prohibit: Electrical generation in Israel involves a Jew doing melacha on Shabbat, and since it is forbidden to benefit from such work, one shouldn't use electricity from the public utilities on Shabbat.
Reasons to permit: Electricity is required to power hospitals and other life-saving functions. Therefore, it is permitted for Jews to generate electricity on Shabbat. According to R' S.Z. Auerbach, use of electricity is permitted
based on a Talmudic precedent: if a sick patient requires meat for survival, and no dead meat is available, a live animal may be slaughtered (otherwise in violation of Shabbat) and its excess meat may be consumed by others on Shabbat. Since in this case there is no way to cook any meat without slaughtering a whole animal, the rationale that the violator might do more than necessary does not hold.
Some authorities say Jews may use electricity generated in violation of Shabbat because the violation itself was not wilful. The violation of Shabbat by the Jewish workers at the power plants is considered unintentional (Hebrew: שוגג, shogeg), not willful (Hebrew: מזיד, meizid). Some authorities prohibit benefiting from products of unintentional violation of Shabbat, not only for the violator but also for the beneficiary, who is in this instance the user of electricity.
In 2011 the Israeli government announced that
The Rabbanut would devise ways to produce “mehadrin” electricity – without the need for direct violation of the Sabbath by Jews – that would be acceptable to all circles.
The plan is quite simple: Applying automation procedures in the power stations on Shabbat and leaving non-Jewish workers to observe the automatic production.
For more information, please see:
Chaim Jachter and Ezra Frazer, Gray Matter, volume 2, pages 54-66.