Research On Key Issues Of Stability Of A Modular Multilevel Converter Based HVDC System

Modular multilevel converter (MMC) has been attracting increasing attention of the scholars and engineers since it was proposed, owing to its advantages over the traditional 2-level converter such as the low harmonics, modular design, low switching frequency and loss and so on. An important issue concerned for the MMC based high voltage direct current (HVDC) system is its stability and damping, which decides whether the system can operate steadily and also the recovery performance form some faults. The main aim of design and optimization of the controller parameters is to improve the stability and damping. So it is important for the engineer to research the factors influencing the stability of an MMC-HVDC system and propose efficient strategies to improve the stability.In this paper, the mathematical model and the basic control strategies of the MMC-HVDC system are first researched, and then key issues on the stability of the MMC-HVDC system are analyzed. The key issues include the damping of the global asymptotic stability, the internal harmonic stability and the interaction of the MMC with the ac and dc side circuits. To do these research, analytical mathematical models are developed. A lot of conclusions are derived on the stability of the MMC-HVDC, which is of significance for the real engineering. 1) Mathematical model and control strategies of the MMC-HVDCThe basic operation principle including the SM operation mechanism, the basic mathematical model, the average switching function model is researched, which is the basis for the stability analysis of the MMC-HVDC system. Then the control system of an MMC-HVDC system is established, including the decoupled d-q control strategy, the nearest level control, the capacitor voltage balancing control based on sorting algorithm and the circulating current suppressing controller and so on. Then the operation characteristics of the MMC with asymmetrical arms owing to sub-module fault is researched. The fault characteristics, including the asymmetrical capacitor voltage between the upper and lower arm, the asymmetrical circulating currents of all harmonics, the DC current fluctuation, the voltage offset at the DC or AC side, and the asymmetrical DC components of the arm current of the arms are revealed. A circulating current suppressing controller with the SM fault-tolerant ability is proposed. The controller is designed to rebalance the fundamental frequency components of the upper arm voltage and the lower arm voltage. A fundamental frequency resonant controller is added to the traditional second-order frequency proportional resonance circulating current controller, hence the series of problems caused by asymmetrical arms can be solved. A 201-level MMC-HVDC system is established in PSCAD/EMTDC and the simulation results validate the efficiency of the proposed control strategy.2) Research on the damping of the internal global asymptotic stability of the MMCThe balancing between arms of the MMC is an important issue on the internal stability of the MMC, which is in essence the internal global asymptotic stability. The damping of the global asymptotic stability directly decides the recovery performance from a fault resulting in forced charging or discharging of the capacitors. A detailed dynamic model is developed to calculate the recovery speed of the unbalanced capacitor voltage, based on the average switching function. Then factors influencing the damping of the global asymptotic stability are analyzed. It is found that the damping is dependent on the arm resistance, the modulation index and the SM capacitance. There exists a contradiction between good damping and low loss, and a small arm resistance can result in poor damping. To improve the damping of the internal global asymptotic stability, a supplementary control strategy based on the concept of "virtual resistance" is proposed, which can improve the damping significantly without adding the converter loss. Finally, the simulation with PSCAD/EMTDC is implemented to validate the analysis and the efficiency of the controller.3) Small signal model of the MMC with consideration of the internal dynamics and the internal harmonic stability analysisSmall signal model is an important method for stability analysis and controller parameters design. In the most ealier work, the internal harmonics dynamics including the capacitor voltage fluctuations, the internal circulating current and the circulating current suppressing controller are always neglected when establishing the small signal model of the MMC-HVDC sytem. In this way, the state-space model is simplified significantly, but it will bring in significant errors to the eigenvalue analysis of the MMC-HVDC system. A detailed small signal model with consideration of the internal dynamics is established, based on the concept of "dynamic phasors". The established small signal model provides interface with the external controller and the ac/dc side circuit. The model is validated by the comparion with the electromagnetic transient simulation. Also, the simplified terminal model is also established without specializing the internal harmonic dynamics. The dynamic response results of the simplified model and the detailed model are compared. It is demonstrated that a simplified model can bring in some errors to dynamic performance evaluation, and the establishment of a detailed small-signal model is necessary.Based on the established detailed small signal model of the MMC, eigenvalue analysis and mode identification of a one-terminal MMC-HVDC system is implemented. The modes of the MMC-HVDC system are divided into "external modes" and "internal harmonic modes" by participation factors. It is demonstrated that the simplified model can not be used to analyze the internal harmonic modes. Besides, the internal harmonics modes and the factors influencing these modes are analyzed. It is found that the internal harmonic modes are always poorly damped, and they can not be neglected in stability analysis. The circulating current suppressing scheme, the arm resistance, the outer loop controller parameters all have great impact on these modes. The "harmonic instablity" phenomenon is also revealed. A lot of conclusions on the internal harmonic stability are derived, which is important for controller parameters design in real engineering.4) Interaction analysis of the MMC with the ac and dc circuitThe stability of the interaction of the MMC and the ac and dc circuit is analyzed in this part. To do this research, the small-signal model of a 54-order point-to-point MMC-HVDC system is established, based on concept of "dynamic phasors", and the eigenvalue analysis and mode identification are implemented. For the interaction of the MMC with the ac side circuit, the impact of the ac system on the internal harmonic stability of the MMC is analyzed. It is demonstrated that the variation of the ac system can result in internal resonace of the MMC, i.e. harmonic instability, especially when no circulating current controller is adopted or the circulating current controller gains are small. Then a frequency-domain stability analysis method is derived based on the impedance-frequency characteristics under d-q rotating axis, the nyquist stability criteria is used to research the stability of the system. Such frequency-domain analysis method under d-q rotating axis avoids the frequency coupling problem under a-b-c static axis, and the results are more reliable and accurate.For the interaction of the MMC with the dc side circuit, the impact of the main controller parameters, the circulating current controllers on the dc interaction modes are analyzed. It is found that using a one-terminal MMC-HVDC system to research the system will bring in significant errors for the the dc interaction modes, the stability can be even evaluated mistakenly. It is interesting to find that the dc interaction modes are more sensitive to the control parameters of the converter regulating the dc voltage than that of the converter reglating the power. Also it is found that the dc interaction modes can be coupled with the internal harmonic dynamics, and they can be influenced by the circulating current controller parameters.