Generally, the small-signal model (SSM) of a modular multilevel converter (MMC) needs to consider the dynamics of equivalent arm capacitors, which inevitably increases the model order. In view of this, this paper proposes a general order-reducing approach based on balanced realization theory to reduce the SSM order of the MMC. In particular, two reduced-order models of an MMC-based HVdc grid are proposed with respect to different research objectives. To determine the potential minimum order of single MMC or MMC-HVdc grid, the criteria including singular values (SVs) of the frequency response, dynamic response in the time domain, and the largest absolute error of SVs are fully investigated. The simulation results of a four-terminal MMC-HVdc grid show that reduced-order models of the MMC and the HVdc grid can precisely predict both the stability and instability while the dynamic characteristics are retained.

The modular multilevel converter (MMC) is widely used in high and medium voltage applications. To improve the reliability of the MMC, fast and accurate submodule (SM) fault detection, location, and tolerant control are required to avoid the interrupted power transmission. Existing methods do not consider all fault characteristics of SM in different operation modes when MMC adopts nearest level modulation. This paper proposes a robust SM fault management scheme that enables uninterrupted operation of MMC with nearest level modulation under SM fault. The SM fault characteristics in different operation modes are presented. Then, the fault detection method based on measuring the compensation of the circulating current suppression controller is proposed. Three quantities, including accumulated discharge voltage, unbalanced charge voltage and capacitor voltage, are used to locate the faulty SM and identify the fault type. In addition, a fault-tolerant control method is proposed by injecting a symmetry compensation component into the modulation signals. Finally, simulation and experimental results are presented to verify the proposed fault detection, location and tolerant control methods.

The modular multilevel converter-based unified power flow controller (MMC-UPFC) is able to operate under unbalanced grid conditions with symmetric component decoupling. However, the constraint of the voltage limit of UPFC is not considered and no protection schemes are investigated to protect the UPFC from overmodulation under unbalanced grid conditions. To solve this problem, this paper proposes the cascaded control scheme for MMC-UPFC based on voltage limit control and symmetric component decoupling to balance the ac current of the transmission line. With appropriate transformer connections for MMC-UPFC, the negative- and zero-sequence currents are suppressed by the corresponding inner current loops. Considering the voltage limit of MMC, the operating ranges of UPFC-MMC under balanced and unbalanced grid conditions are investigated in both mathematical derivation and point scanning methods. The results are depicted and analyzed in 3-D vision. Based on the analysis of operating regions, the voltage limit control is proposed to protect the MMC from overmodulation and to maximize the controllable region under unbalanced grid conditions. Finally, the final cascaded control structure is constructed. The simulation results obtained in PSCAD/EMTDC are provided to validate the effectiveness and robust performance of the proposed control strategies.

The traditional proportional-integral control for a modular multilevel converter (MMC) design based on a two-level voltage source converter does not consider the dynamics of arm circulating currents and sub-module capacitor voltages, which will lead to the incomplete decoupling between powers and circulating currents for an MMC. In view of this, a nonlinear decoupling control strategy, which applies for two scenarios, e.g., active/reactive power control for a power controlled station (PCS) and dc voltage/reactive power control for a dc-voltage controlled station (DVCS), is proposed for an MMC station based on feedback linearization. First, the nonlinear feedback laws for PCS and DVCS are derived based on the nonlinear equations of an MMC. Next, the complete nonlinear decoupling control strategies for PCS and DVCS are developed. Following that, the zero dynamics stabilities of the two control schemes for PCS and DVCS are investigated. In addition, the method to design parameters of the outer linear controller is also proposed to satisfy the requirement of dynamic performance. Taking a two-terminal MMC-HVDC for example, the simulation in Simulink validates the good transient performance of the proposed nonlinear control, and its robustness is also validated against the changing of system parameters.

In 100% renewable energy power systems (REPSs), the frequency deviation is independent of the storage and release of rotor kinetic energy, and the essence of frequency control changes from energy balance to power balance. Thus, conventional LFC schemes are no longer applicable for 100% REPSs. To realize constant frequency operation of 100% REPSs, in this article, a novel load frequency control (LFC) scheme is proposed, for the first time. Furthermore, communication delays and packet losses are also considered. The proposed LFC scheme consists of two parts: a cascaded extended state filter (CESF) and a robust decision-making model (RDMM). First, the Padé rational polynomial is utilized to approximate the delay factor, based on which the LFC model with delays of the 100% REPS is established. Next, combining the Kalman-Bucy filter and extended state observer, the CESF is proposed to accurately estimate load variations. Then, taking both the renewable energy variation and the probability of packet losses into account, the RDMM is proposed to formulate the real-time power balance scheme. Finally, the proposed LFC scheme is verified on a modified IEEE 39-bus system with a pattern of 100% REPS.

Small-signal models (SSM) of modular multilevel converter (MMC) based HVDC grid under unbalanced grid conditions in recent literatures do not consider interactions between MMC and dc network. Therefore, it is necessary to correctly model the double-fundamental-frequency zero-sequence circulating currents (DFF-ZSCC) existing under unbalanced grid conditions, although they can be suppressed to avoid penetrating into dc side. In view of that, a general and modular small-signal modeling method of MMC-HVDC grid under unbalanced grid condition is developed. Firstly, a general d-q transformation process for multi-sequence and multi-frequency components is introduced to build the state-space model of MMC electric part in d-q frame. Secondly, the SSM of dc network, which is divided into dc- and double-fundamental-frequency parts, is developed based on the existing frequency-dependent-cascaded-pi (FDC-PI) cable model. Then, to interface MMC stations with dc network under unbalanced grid conditions, a general method to synchronize the variables of double fundamental frequency at dc side of each MMC station is introduced to compose the SSM of the entire HVDC grid from SSMs of each MMC and dc network. Finally, taking a three-terminal MMC-HVDC grid as an example, two SSMs of the MMC-HVDC grid with FDC-PI cable model and single-PI cable model are developed in Matlab, respectively. The small-signal dynamics and stability of both SSMs of the grid under unbalanced grid conditions are compared to validate the accuracy and stability of the proposed SSM of the whole HVDC grid. The simulation results validate the correctness and effectiveness of the proposed modular modeling method.