Writ large, around the world, liquid fuel (generally diesel) has a relatively small role in providing electricity and thus the “oil” and “electricity” domains have a minimal overlap. There are, however, exceptions that are notable generally in being “islands”. These islands can be temporal (power supply disruption leading to use of generators while the electric grid is restored), infrastructure (providing electricity to a site remote from the existing power grid — such as temporary or remote military bases) and/or traditional geographic islands — land surrounded by sea.
And, with oil prices above $80 barrel and unlikely to ever return to a few $10s per barrel, diesel-generated electricity is expensive, per kilowatt, compared to most other electricity options.
This makes these islands particularly appropriate for the introduction of renewable energy systems to displace oil. Especially as the prices have to account not just for the price of crude, but the the full price of 
transporting and storing the oil along with operating the diesel electricity generators. The U.S. military’s term for this: Fully-Burdened Cost of Fuel (FBCF). With a FBCF of $10s per gallon (plus lives at risk) in remote operating areas of Afghanistan, it isn’t surprising that solar panels have displaced traditional diesel generators for some Marines in Afghanistan. To date, however, such programs have been partial — perhaps even on the margens — reductions of island oil demand for electricity.
This, however, is changing.
The 
small Pacific island nation of Tokelau is to get a solar makeover. Right now, Tokelau is burning about 2000 barrels a year of diesel shipped in from New Zealand at a cost of NZ$1 millon (e.g., with shipping, about $500 per barrel or over $10 per gallon). That diesel provides Tokelau’s 1400 people about 16 hours a day of electricity.
This is about to change as New Zealand’s Power Smart Solar will replace the diesel generators with solar systems — and improve the electricity system to a 24/7 supply — and turn Tokelau to the first 100 percent solar electric nation.
The installation of 4,032 solar panels (one megawatt of solar) and batteries across the three atolls will eliminate
diesel fuel use and provide consistent high quality electricity. The original tender specification called for the solar systems to supply 90% of Tokelau’s electricity demand. Through creative design, project management methodology, and sheer scale Powersmart Solar will be installing solar systems capable of providing 150% of current electricity demand allowing the Tokelauans to expand their electricity use without increasing diesel use.
The following video provides a conceptual look at one of the coming installations. This is for Nukunonu Atoll by Powersmart Solar and IT Power. The system will comprise of 1152 x 230 Watt solar panels or 265 kW.
Using solar pv and batteries to provide 24/7 electricity in replacing part-time electricity that prices out, in a full system cost, at well over 50 cents per kilowatt hour (compared to a U.S. average of about 10 cents) is a ‘no brainer’. While, right now, solar PV is far from a ‘no-brainer’ for every electric consumer around the world, increasingly, as solar pv prices fall (and other electricity prices/costs rise), ever more ‘islands’ are joining Tokelau’s atolls as prime locations for major renewable installations.
PS: And, in that light, a story about Tonga’s 1st 1 MW solar pv installation going live:
Tonga currently generates electricity from costly imported diesel fuel.the facility will generate approximately 1880 megawatt hours of electricity per annum, meeting approximately 4% of Tongatapu’s total electricity demand.
And, as for another island (former nation), see this discussion of the challenges for Hawaii’s efforts to ‘go solar’.