Renewables are increasingly penetrating power systems and impacting electricity Markets supported by the stricter energy and environmental policies. To handle the variability and uncertainty of renewable generation and to provide transparent economic incentives for resources to provide flexible services, a bid-based flexible ramping products market is proposed in the CAISO and MISO markets. To investigate the impact of these new products on the market equilibrium, a multi-period Nash-Coumot equilibrium model, formulated as a bi-level optimization problem, was proposed, and the Guass-Seidel iterative method was used to obtain the equilibrium. Moreover, a general framework of co-optimization of energy and flexible ramping products was established, and different types of generators, including thermal units, hydro units, renewable units and energy storage systems, are simultaneously considered to reflect their strategic interactions. Two cases with dominant solar power and wind power, respectively, have been implemented and are compared to demonstrate the impact of flexible ramping products on market prices, unit commitment and renewable integration. Additional energy storage systems are also included in the above case for further analysis. Simulation results show that when introducing the new products: the energy prices will increase slightly under normal conditions, more highly variable renewables can be integrated, the unit commitment will be changed, and more generators should be on line to provide flexible services, etc.