The reduced amount of rotational kinetic energy in power systems has significant detrimental impacts on system frequency behaviour. To ensure system security, this issue must be addressed in a systematic way. Given this, we consider three different metrics, namely i) minimum power penetration from synchronous generators, ii) minimum rated power of synchronous generators, and iii) minimum synchronous kinetic energy, as frequency control constraints in the market dispatch model, and assess frequency behaviour of the system for these metrics. The results show that each metric has a different impact on market dispatch, and, accordingly, on the system frequency behaviour. It is shown that with high penetration of converter-based generation, we need to consider a minimum kinetic energy requirement as a frequency control security constraint in the market dispatch model to guarantee the frequency stability of power systems.