There are a couple of dynamics at play. In the long term (10+ year range), I believe you are correct, that renewables will begin to have a significant effect on oil prices as natural gas power plants are shut down and replaced with solar and wind (oil is used primarily for transportation, not energy production; natural gas is replacing coal as the primary fossil fuel used for generating electricity as natural gas prices remain lower than coal for extended periods). For the short term, though, I think fracking has a bigger impact on prices.
Traditionally, oil prices had a long-term boom-bust cycle that lasted about 30 years...15 years of boom followed by 15 years of bust. This has been going on since the dawn of the oil industry, and is largely systemic: business cycles tend to be around 15 years, as in it takes about 10-15 years to go from discovery to production (gather data, drill exploration wells, drill production wells and production infrastructure). I'm not sure of any other industry with so long of a systemic business cycle.
Now, however, fracking has changed the game. So far, since "tight gas" is so new, we're able to use fracking in oil fields that have already been developed, to extract gas and oil from areas we knew it was at before, but thought it was too hard to extract (the term for where fracking is used--"tight" refers to the permeability of the rock...traditional oil comes from sources measured in the 10s of darcies...fracking is often employed in areas with <0.001 darcies, like shale rock). This means that production facilities, like pipelines and whatnot, are already in place. Furthermore, the discovery process is shortened, as these are already fields with known reserves, just in areas that we could not extract from efficiently before. Now, with fracking, we can. This means the investment cycle has been reduced from 10-15 years to 1-2 years.
With the old business cycle, new technology typically would be invented any time prices got high enough--generally following a business cycle where all of the "easy" oil has been found and extracted. New technology allows new fields to be produced "easily", causing a surplus of oil and a crash in oil prices. This continues until all the "easy" oil has been found, and the cycle continues. This cycle goes all the way back to the 1860s (whale blubber -> oil wells -> oil wells with pumps -> basic geology (drilling under hills) -> 2D seismic -> 3D seismic -> deep-sea/sub-salt -> fracking; pretty much follows a 20-30 year cycle). The concept of "peak oil" isn't new--people have been worried about peak oil since the mid-1800s.
Analysts aren't sure if the new reality we're in has fundamentally changed the markets. I say it hasn't--the cycles will return after all of this new "easy" oil, in the form of shale gas/tight gas, has been exploited. But we're only somewhere about 2-5 years into a 15-year bust cycle, if you ask me. I would expect prices to hover in the $40-$50 range for the remainder of this bust cycle, with a few rare exceptions (wars, disasters, etc). After that, I think you'll see prices return to the $100+ level (in 2016 terms--since the 1860s, prices have cycled pretty consistently between $10 and $100 for a barrel of oil, in 2016 terms) until the next technological revolution in oil exploration and production occurs. But it does mean less volatility in prices as business cycles shorten--at least for the remainder of this bust cycle. Maybe peak oil will become a reality right as demand for oil drops, making the next round of technology advances unnecessary.