The increasing penetration of renewable energy generation in recent years has introduced significant changes and challenges to modern power systems. One of the most critical challenges is the reduction in system inertia, which decreases grid stability and subsequently weakens the electrical network. To address this issue, grid-forming (GFM) converters have emerged as a promising solution to maintain stability in weak grids. This paper proposes three novel control schemes for GFM converters and compares them with the performance of another topology recently published by the same authors. The four evaluated control schemes are based on the virtual flux variable which allows current limiting without using internal current loops, improving the stability of the control system. The assessment includes methods based on PI regulators, using the mathematical flatness property of differential algebra, direct control (DC), and model predictive control (MPC). The results demonstrate the robustness and correct operation of all four control strategies as GFM converters. Furthermore, through tests involving disturbances such as frequency variations, voltage sags, phase jumps, and transitions to islanded mode, their differences in terms of dynamic response, switching frequency, and current quality are clearly evidenced.