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Over the last decade, with the merits of high efficiency, compactness, and flexibility, energy conversion systems based on multiple-electrical-port and multiple-mechanicalport electrical machines have attracted widespread attention from both academia and industry. This concept has been adopted in many industrial applications, such as wind power generation, ship shaft power generation, ship electric propulsion, electric vehicles, rail transportation, more/all electric aircrafts, and ac/dc microgrids. Due to the ever-increasing demand for highly reliable and cost-effective energy conversion systems, advanced machine/converter topologies, modeling approaches, control strategies, and reliability, evaluations of multi-port electrical machines and drive systems are in great need.

This article develops a new closed-loop analytical steady-state model of low-capacitance half-bridge Modular Multilevel Converters (MMCs) operated with the average arm energy control and Sub-Module Capacitor Voltage (SMCV) ripple above the conventional value of 10%. In this control approach the level of average SMCVs is regulated directly. As has been already shown in the literature, if the average SMCVs are not controlled, the circular interactions of the inherent low-frequency SMCV ripple and the modulation signal which affect the dc arm voltages will also lead to the variations in the average SMCVs. In order to compensate for these variations a dc component has to be introduced in the modulation signal (in addition to the 2nd harmonic which suppresses the 2nd order circulating currents). This is included in the proposed analytical modelling where the three key non-linear equations are established and solved iteratively using Newton Raphsons method to calculate the steady state modulation signal parameters. The effects of the introduced dc component in the modulation signal on the MMC electrical quantities are demonstrated and analyzed. The developed model is also compared with the existing analytical steady-state MMC models in the literature. It is further employed to optimize the parameters of the grid connected MMC. The optimization is based on the improved utilization of the available modulation signal window and is performed with the aim to minimize the voltage stresses on the power devices. The analysis is supported by simulation and experimental results.