Inertia provision for frequency control is among the ancillary services that different national grid codes will likely require to be provided by future wind turbines. The aim of this paper is analysing how the inertia response support from a variable speed wind turbine (VSWT) to the primary frequency control of a power system can be enhanced. Unlike fixed speed wind turbines, VSWTs do not inherently contribute to system inertia, as they are decoupled from the power system through electronic converters. Emphasis in this paper is on how to emulate VSWTs inertia using control of the power electronic converter and on its impact on the primary frequency response of a power system. An additional control for the power electronics is implemented to give VSWTs a virtual inertia, referring to the kinetic energy stored in the rotating masses, which can be released initially to support the system's inertia. A simple Matlab/Simulink model and control of a VSWT and of a generic power system are developed to analyse the primary frequency response following different generation losses in a system comprising VSWTs provided with virtual inertia. The possibility of substituting a 50% share of conventional power with wind is also assessed and investigated. The intrinsic problems related to the implementation of virtual inertia are illustrated, addressing their origin in the action of pitch and power control. A solution is proposed, which aims at obtaining the same response as for the system with only conventional generation. The range of wind speeds near the power limitation zone seems to be the most critical from a primary response point of view. The theoretical reasons behind this are elucidated in the paper.