Renewable energy sources are expected to take a very large share of electricity production in 2 degrees scenarios. The main objective of the study is to analyze the use of the demand response (DR) in high variable renewable depending electric power systems and explore the potential advantages of using DR to compensate intermittency. We also considered the interactions of DR with the entire power system, including the other flexibility options (storage, electric grid, and dispastchable power plants) using European Unit Commitment And Dispatch (EUCAD) model. In the supply and demand balance modelling, DR is similar to electricity storage: they both displace an electric load between two time-periods, although their technical operating constraints differ which makes their economic models and behaviours slightly different. We perform studies with very different renewable shares which are expected to be representative of different time horizons, today, in 2030 and 2060, years. We found that the need for implicit DR grows up to 20 % of the peak load but might have a value after which its use is saturated. Surprisingly, the competition with storage capacities appear to be very limited. Regarding to explicit DR, the level of usage is more sensible to the price when the high VRE claims for more flexibility.