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To guarantee the frequency stability of renewable energy sources (RESs) generation integrated into the power system, primary frequency regulation (PFR) for RES generation controlled by virtual synchronous generator (VSG) has been concerned extensively. This study mainly focuses on the dynamic and steady-state characteristics of VSG in the PFR dead-band. Based on the typical structure of VSG, small-signal model of the conventional VSG is established to analyse the issue of the sharp change of angular frequency. Consequently, a novel modified VSG (M-VSG) controller is proposed, which can ensure a stable angular frequency and synchronise with the grid without the phase-locked-loop. The inertia and damping properties of M-VSG are studied theoretically by eigenvalue analysis, and the design procedure of control parameters is presented. To enhance the practicability, a flexible PFR strategy of M-VSG is added considering inertia mode, bidirectional mode, and unidirectional mode according to the operation state of RES generation. Moreover, after PFR is added, the proposed controller is analysed with eigenvalue loci to guarantee the stability and dynamic characteristics outside the dead-band. Finally, hardware-in-the-loop experiment results based on RT-LAB demonstrate the validity of the theoretical analysis and the superiority of M-VSG in participating in flexible PFR. [ABSTRACT FROM AUTHOR]