To address the low inertia grid inverters sources provide, the virtual synchronous machine (VSM) has been one of the main approaches to regulate the active power in continuous time domain. However, continuous time solutions do not take into consideration some of the dynamic behaviors of the system, such as measurement delays and small number of samples per period, given by the limitations of the hardware used to implement these controls. This is where careful discrete design is important, taking into consideration these hardware limits to obtain reliable results. This paper presents a discrete implementation of the VSM using the direct discrete modeling method, along with a comparison between the continuous, exact discrete and an approximation. The finding highlights that the continuous and the approximation show deteriorating results the sample time increases. Only direct discrete modeling can match the ideal continuous domain design.