Deploying high penetration of variable renewables represents a critical pathway for decarbonizing the power sector. Hydro power (including pumped-hydro), batteries, and fast responding thermal units are essential in providing system flexibility at elevated renewable penetration. How to quantify the merit of flexibility from these sources in accommodating variable renewables, and to evaluate the operational costs considering system flexibility constraints have been central challenges for future power system planning. This paper presents an improved linear formulation of the unit commitment model adopting unit grouping techniques to expedite evaluation of the curtailment of renewables and operational costs for large-scale power systems. All decision variables in this formulation are continuous, and all chronological constraints are formulated subsequently. Tested based on actual data from a regional power system in China, the computational speed of the model is more than 20,000 times faster than the rigorous unit commitment model, with less than 1% difference in results. Hourly simulation for an entire year takes less than 3 min. The results demonstrate strong potential to apply the proposed model to long term planning related issues, such as flexibility assessment, wind curtailment analysis, and operational cost evaluation, which could set a methodological foundation for evaluating the optimal combination of wind, solar and hydro investments.