Today's power systems are subject to various challenges arising from the large-scale integration of renewable energy sources (RES), especially wind energy production. System flexibility, or the capability of a system to address deviations in variable RES production, is becoming more and more relevant. This paper aims to provide a systematic approach to evaluate the level of flexibility of a power system by unequivocally considering fast-ramping units (FRU), hourly demand response (DR) and energy storage (ES). In addition, to research the flexibility role in power system operation, an “online” index is considered to evaluate the technical aptitude of the FRU, hourly DR and ES system to deliver the required flexibility. The mathematical representation of day-ahead scheduling, with the added modeling of an online flexibility index, is a mixed-integer nonlinear program (MINLP). This paper presents a method to convert this MINLP into a mixed-integer linear program without loss of accuracy. The adapted 6-bus and IEEE 118-bus systems are employed to assess the suggested models and flexibility metric, demonstrating the proficiency of the online flexibility index.