I know the Great Northern Railroad used electric locomotives through
> mountain passes in Washington State because electrical locos could out
> pull steam locomotives on the steep grades encountered there.
The Great Northern initially ran electrics through the Cascade tunnel to prevent asphyxiation from steam engine flue gas. Later they extended the run from Wenatchee to Skykomish. They could have extended the run to improve engine rotation issues or to take advantage of the increased efficiency of electrics. I've never seen a definitive reason in print.
The Milwaukee Road, which also ran through the Cascades about 50 miles south of the Great Northern, was electrified from Othello to Renton, about 200 miles and from Harlowton Montana to Avery Idaho, 207 miles. The two electrified divisions spanned the Cascades, Saddle Mountain (the ruling grade) and the Bitterroots in the Rockys. The electrification was clearly done for the improved performance and cheaper crew and operating costs.
Another, less often mentioned, reason for the electrification had to do with members of the Milwaukee's board of directors having financial interests in both General Electric and Anaconda Copper, two companies which stood to make a lot of money on the deal.
At the time running two steam locomotives on a train required two engine crews. The electrics were configured in permanent two-locomotive sets, could be operated from a single control stand and were treated as a single locomotive by union rules.
The electrics were far more reliable than steam, rarely requiring service. Steam on the other hand required maintainance every 100-200 miles, frequent stops for water and loss of performance in cold weather. The electrics could also use regenerative braking, giving back about 12% of the total electricity cost.
I know a little about these things because my dad was a brakeman and conductor on the Milwaukee for 33 years.