With an increasing integration of converter-based power generation into the power system, concern regarding the stability and availability of future power systems has emerged. In order to address this, fault ride-through capability is required by installed generation to avoid a network collapse due to large disconnection of distributed generators. In addition, the interest in controlling grid-connected converters as synchronous generators is increasing, but little research has been done to uncover how such a control structure will perform during grid faults. Therefore, this project develops a state-of-the-art current-mode controller for a grid-connected converter and compares it to a described voltage-mode controller during both symmetrical and asymmetrical grid faults. It is shown that a voltage-mode grid-forming control structure, which emulates the principal parts of a conventional synchronous machine, can provide inherent grid-supporting functionalities, making it advantageous compared to a conventionally used current-controlled grid-following strategy. However, during grid faults, the fundamental principle of the grid-forming control makes a mandatory current limitation cumbersome. This project describes the advantages and disadvantages of the voltage-mode controller compared to the current-mode controller and proposes an enhanced grid-forming controller enabling the voltage-mode structure to be fully applicable for future control of grid-connected converters.