The Modular Multi-level Converter (MMC) topology is one of the most important switch mode converter topology and provides indispensable potential applications in the power systems industry, specifically, for High Voltage Direct Current (HVDC) transmission systems. Recent applications of MMC in HVDC transmission systems has posed problems such as circulating currents in the converter legs, which threatens the safe operation and also deteriorates the system’s performance. The circulating currents occur mainly due to the fluctuations in the capacitor voltages in the Sub Modules (SMs) of the MMC. Hence, in order to nullify the SM’s unbalanced voltage, this article aims to use a new counting sort based technique in conjunction with Carrier Phase Disposition Pulse Width Modulation Technique (CPD PWM). The increased harmonic content in the output voltage and current waveforms may be attributed to the unpredictable dynamics of capacitors. To address this, the article also proposes a cascaded voltage and current H∞ repetitive control scheme under normal and fault conditions. This entire scheme has been applied for back to back connected HVDC systems for mitigating the Total Harmonic Distortion (THD) in current and voltage respectively. Further, stability analysis for the proposed controllers has been performed to prove its robust operation and finally all the results have been explored.