We examine the changes to the electric power system required to incorporate high penetration of variable wind and solar electricity generation in a transmission constrained grid. Simulations were performed in the Texas, US (ERCOT) grid where different mixes of wind, solar photovoltaic and concentrating solar power meet up to 80% of the electric demand. The primary constraints on incorporation of these sources at large scale are the limited time coincidence of the resource with normal electricity demand, combined with the limited flexibility of thermal generators to reduce output. An additional constraint in the ERCOT system is the current inability to exchange power with neighboring grids. By themselves, these constraints would result in unusable renewable generation and increased costs. But a highly flexible system - with must-run baseload generators virtually eliminated - allows for penetrations of up to about 50% variable generation with curtailment rates of less than 10%. For penetration levels up to 80% of the system's electricity demand, keeping curtailments to less than 10% requires a combination of load shifting and storage equal to about one day of average demand.