Journal of Halacha & Contemporary Society, No. XXI - Spring 91 - Pesach 5751 has an article by Rabbi Michael Broyde - Adjunct Assistant Professor of Law at Brooklyn Law School, and Rabbi Howard Jachter - Associate Rabbi of Congregation Beth Judah in Brooklyn which gives Rabbi Auerbach's opinion in his own words. The article concludes that current practice is that it is forbidden in any case.
The original quote from Rav Auerbach (Minchat Shlomo 74, 84) is
In my opinion there is no prohibition [to use electricity] on Shabbat
or Yom Tov... There is no prohibition of ma'keh bepatish or molid...
(However, I [Rabbi Auerbach] am afraid that the masses will err and
turn on incandescent lights on Shabbat, and thus I do not permit
electricity absent great need...) ... This matter requires further
However, the key point in my opinion is that there is no prohibition
to use electricity on Shabbat unless the electricity causes a
prohibited act like cooking or starting a flame.
The article goes through the various opinions on using electricity and concludes, in the relevant part:
Rabbi Auerbach additionally states that since the tradition forbids
the use of electricity, and this tradition received near unanimous
approval from rabbinic authorities in the normal course of events
observant Jews should accept this tradition (even though he feels it
is based on incorrect premises) and operate under the presumption that
the use of electricity without light or heat is a violation, of
rabbinic origin, based on molid.