Research contribution

1.4.1.Mathematical model

The mathematical model of the MMC is used to describe the converter behaviour during the regular operation. The proper selected mathematical model can precisely define the switching losses, the junction temperature of the power switches, or the electromagnetic inter- ference generated by the high speed switching action. Since they are derived from the funda- mental theoretical model of the MMC, the common mathematical model was derived by in- serting controllable voltage or current sources to reveal the controllability of the MMC. It has been proven that the conventional VSC control approach can be used in the control method for MMC. The outer power control loop and inner current loop are provided to guide the de- sign of the MMC modelling and control. The average MMC model is built in MATLAB to verify the proposed mathematical model. The junction temperature and the electromagnetic interferences are not considered in the simplified model.

1.4.2.The modulation methods

Because of the series-connected structure of the MMC, the modulation methods are based on the sinusoidal methods. In the PWM methods used for MMC, the number of the carriers can be as same as the number of the submodules depending on the structures of the submod- ules. Therefore, the computational requirement of generating the PWM is high when there are many submodules in each arm of the MMC. The implementation of the PWM methods is pro- vided, and the comparison among the Phase Shifted Pulse Width Modulation (PS-PWM) and Phase Disposition Pulse Width Modulation (PD-PWM) are presented. The interleaving tech- nology is also discussed to illustrate the benefits and the drawbacks of such modulation meth- ods. The hardware implementation of the PWM is also shown to demonstrate the realization of selected PWM in the control unit for MMC.

1.4.3.The capacitor voltage balancing control

A large number of the submodules provide smaller voltage steps and lower converter out- put harmonics on the AC side of the converter. However, similar to the conventional multi- level converters, such as the diode-clamped converter or flying capacitor converter, the MMC

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can have problems caused by the imbalanced voltage distribution among the submodules. The magnitude of the current, the turn-on and turn-off period, and the effects of the sampling fre- quencies affect the voltage distributions across all the capacitors in the submodules. The dy- namic capacitor voltage monitoring of all the submodules and the arm currents are required to balance the energy distributions. Therefore, the conventional voltage balancing processes can be slower when the converter submodules are more than the conventional multilevel con- verter. However, one of the advantages of the MMC is the large number of the submodules in each arm. Thus the benefits of reducing the complexity of the voltage balancing control can be significant. The predictive voltage balancing control is proposed to further simplify the voltage balancing processes. Compared to the conventional voltage balancing control, the pre- dictive voltage balancing control has a better performance at the same sampling rate and the current measurement is not necessary as the control approach is improved. On the other hand, the effects of the communication delays between the circuit and the control unit can also be minimized. It makes it much more favourable in the Ultra High Voltage (UHV) applications for its fast and simple control approach. However, the arm currents are still required to be monitored to achieve the circulating current regulation in the circulating current suppressing control.

1.4.4.Circulating current suppression control

The circulating current is caused by the imbalanced capacitor voltages of the upper and lower arms and the resonance currents generated by the arm inductor and capacitors. Because this current flows among the arms of the MMC, it can increase the stresses of affected compo- nents hence increasing the power rating of the components and initial investment regarding the submodules. The implementation of the arm inductor can suppress the circulating cur- rents, but that will affect both the size and the investment of the power plant. In that case, the generation of the circulating currents according to the mathematical model is investigated, and the suppression method is developed. The proposed circulating current control is based on regulating the circulating current to its DC components to minimize the AC components which are at the double-fundamental frequency. Its simplicity and fast response to the dy- namic changes are favourable in MMC when the number of the submodules is significant. As a result of the suppression control, the circulating current harmonics at the switching fre- quency are observed while most of the AC circulating current at the twice fundamental fre- quency are eliminated. Both simulation and experiment results demonstrated the effects of the circulating current suppression approach in eliminating the most of the AC components and

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reducing the capacitor voltage ripples. Because the voltage ripple in the capacitors are smaller than before applying the suppression control, the converter output can have smoother voltage patterns which lower the converter harmonics on the AC side. This results in further lowering the requirement of the AC side filter and reducing the costs.