This paper presents a design-oriented analysis on the voltage stability and the transient fault current limitation of voltage-controlled modular multilevel converter (MMC) with Lfilters. First, a dual-loop voltage control based on the L-filter plant is systematically designed, where the upper limits of controller parameters for ensuring the small-signal stability are identified. Then, considering the transient current limitation during faults, the lower boundaries of inner current controller parameters are derived. Within the region of allowed controller parameters, the optimization is further made to minimize the closed-loop output impedance of MMC, which enhances the output voltage stiffness against the load current disturbance. Lastly, time-domain simulations corroborate the theoretical analysis. Keywords-Modular Multilevel Converter (MMC), voltage control, controller design, fault currentNOMENCLATURE Pw, Qw Active power and reactive power of wind farm uw, iw Voltage and current of grid connection point of wind farm Zw Impedance of the transmission line us Voltage of PCC of MMC uc, is Voltage output by MMC and current input into MMC ug Voltage of the location of the fault uα, uβ, Voltage in two-phase stationary frame iα, iβ Current in two-phase stationary frame idc, udc DC current and DC voltage of MMC Leq, Req Equivalent inductance and resistance of MMC Lg Equivalent inductance from fault point to PCC of MMC fc, ωc Crossover frequency and angular frequency ω0 Resonant frequency of PR controller u * s , i * s Reference value of voltage and current. I * smax Maximum value of the current limiter Tabc2αβ Clarke transformation Gd ,Td Time delay and time constant Hu , Td1 Filter of voltage feedforward and time constant Gi, Gv Transfer function of inner current loop regulator and outer voltage loop regulator. Kpi, Kii Proportional gain and resonant gain of inner current loop regulator Kpv, Kiv Proportional gain and resonant gain of outer voltage loop regulator δ1%, ts Overshoot and convergence time I.

Right-half-plain (RHP) zeros can significantly deteriorate a control system's dynamic performances as it exhibits non-minimum-phase behaviors. In this paper, we investigate the occurrence mechanism of RHP zeros in weak-grid-tied VSCs as well as provide guidance for minimizing their effects. A reducedorder multi-input multi-output (MIMO) transfer function of the weak-grid-tied VSC is firstly obtained. Then, the single-input single-output (SISO) transfer function to study the impact of the RHP zeros on the power response is further derived. The existence of RHP zeros is examined by applying the Routh criterion on the numerator of the SISO open-loop transfer function. We find that RHP zeros can exist either when the VSC works as an inverter or a rectifier. Furthermore, large grid impedance values as well as operation points with high active power values can result in a non-minimum-phase system. It is also shown that RHP zeros limit the minimum PLL bandwidth. Simulation results and RTDS experiments validate the correctness of the analysis and the conclusions obtained.

Low-frequency oscillations have been reported in several weak-grids-connected voltage-source-converter(VSC) systems. Although efforts have been devoted to understand the parametric and sensitivity impact of the VSC controller gains, a general formulation of the oscillation mechanism is still missing. Using transfer function dynamic modelling approach, we find that the outer loop active power control's bandwidth mainly determines the oscillation frequency. The PLL introduces a large phase lag around the frequency of the PLL bandwidth in weak grids which decreases the oscillation damping. A simple but effective PI+Clegg integrator (CI) compensator is proposed to replace the standard outer loop active power controller compensating the PLL's phase delay and increase the oscillation damping. The results are verified in a real time digital simulator.

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This paper analyzes the transient stability of an offshore wind farm connected via modular multilevel converter (MMC)-based high-voltage direct-current transmission system. The wind farm is composed by full-scale type-4 wind turbines, whereas short-circuit faults occurring in between the MMC and wind farm are considered. The MMC tends to be switched to the current limiting mode or the overmodulation mode during the ac-side fault, which further interacts with the control systems of wind turbines, complicating the transient stability problem of the system. Hence, in this work the parametric impacts of the phase-locked loop of wind turbine converters and over-current/modulation limiters of the MMC are revealed analytically, and further corroborated by time-domain simulations.