In this paper we propose a modular realization of the active capacitor, where each module is composed of a bidirectional converter and a buffering capacitor. This modular capacitor is a two-terminal device that can automatically adapt itself to different DC bus voltages, and is meant to filter out a wide range of low frequency ripples. Our plug-and-play control approach means that the modular active capacitor can be directly connected to the DC bus without any extra connections, just like a passive capacitor. The proposed modular design improves the overall reliability, providing fault tolerance operation. We investigate the application of our type of active capacitor in DC microgrids, where multiple active capacitors are distributed at different nodes. It is shown that ripple power can be shared in proportion to the storage capacity of the active capacitors without any communication between them. We also offer a mathematical stability analysis of a DC microgrid in which the admittances of all the devices satisfy a certain condition that is less restrictive than being positive-real (and which is satisfied by our proposed design). The modular active capacitor concept has been verified in simulations and experiments.

In order to reduce the influence of monitoring blind area caused by the uncertainty of fault resistance on voltage sag source location in transmission line short-circuit fault, a voltage sag source location estimation method based on optimal configuration of system monitoring points and fault parameter estimation is proposed. Considering the observability of voltage sag in various short-circuit faults, the importance index of measuring points in the system is proposed, so as to construct the optimal configuration model of monitoring points. Based on the optimal configuration scheme of monitoring points, the sag source location model is established, and the adaptive cuckoo algorithm is used to estimate the parameters of fault line, fault resistance and fault distance. Finally, the simulation is verified by IEEE-30 node standard test system. The results show that the proposed method has higher fault location accuracy and more engineering applicability than the traditional method.

To solve the power quality problems caused by freight railways in weak grids with high penetration of wind generation, this paper proposes a comprehensive control method for negative sequence current (NSC) suppression and reactive power compensation. Firstly, a co-phase traction power supply system (CTPSS) is introduced, and its compensation principle is analyzed. Secondly, to bring a doubly fed induction generator (DFIG) into full play in suppressing voltage unbalance (VU) in the grid, a VU compensation model of stator is developed. Moreover, a comprehensive compensation method is presented to achieve the dynamic compensation of VU and reactive power. Finally, the effectiveness of the proposed approach is demonstrated using a simulation, which can fully solve the power quality issues and effectively reduce the capacity of the CTPSS.

Compared with the conventional active power filter [4]–[6], but the operational power loss and the initial cost of the APF are much higher because of its high DC-link voltage requirement. The hybrid active power filter (HAPF) could be considered as a cost-effective solution to cancel out harmonic current as well as reactive power [7]–[11]. However, the conventional HAPF has a very limited compensation range. To extend the compensation range while keeping low DC-link voltage characteristics, a static var compensator (SVC) was applied to the HAPF to improve its compensation range. In 2014, the SVC coupling HAPF (SVC-HAPF) was first proposed [10], [12], in which its SVC part is used to dynamically compensate a wide range of reactive power, thus significantly reduces the current and voltage ratings of the active inverter part. And its active inverter part can also compensate the harmonic current. Due to the advantages of this HAPF topology, additional functions such as unbalance compensation and renewable energy integration are further investigated in the literatures [13]–[16]. The objective of the SVC-HAPF is to achieve power system current quality compensation, thus the current controller design is important for enhancing the compensating performance. However, the utilization of thyristors in the SVC part causes highly nonlinear dynamics, which leads to the controller design a challengeable task. In [13]–[16], a hysteresis current controller was applied for the SVC-HAPF. The hysteresis current controller is a simple and fast control strategy. However, its variable switching frequency leads to large output current ripple and grid stability issues, limit the usage of hysteresis current controller [17]. An alternative solution is applying the PWM-based control strategy which can fix the switching frequency. Recently, a multi-quasi-proportional-resonant (MQPR) controller with gain scheduling for the SVC-HAPF was proposed [18], which achieved a high steady-state accuracy as well as a fixed switching frequency. In the MQPR design, the nonlinear SVC part is modeled as two linear circuits for approximation. However, its gains design is not optimized, and the proportional gain is designed the same for both fundamental and all considered harmonics order [18], this also leads to slow transient response. Due to the nonlinearity caused by the thyristors in the SVC part, the control design with optimizing system performance is still not available for the SVC-HAPF among the existing literatures [10]–[18]. To overcome the nonlinearity and improve the control per-

The differences between the power quality at the AC and DC sides, caused by AC-DC converters with constant DC voltage control, commonly exist in low-voltage direct current (LVDC) systems. The voltage deviation isolation (VDI) is one of the typical phenomenons. A method is proposed to analyze the VDI performance and applied in two-stage high-frequency isolated AC-DC converters, which can isolate not only the faults but also the voltage deviation at the AC side and improve the voltage quality at the DC side. First, the voltage deviation isolation ratio (VDIR) is defined to assess VDI. Based on VDIR, the operation characteristics of AC-DC converters with constant DC voltage control are analyzed and the range of VDI is defined. Second, with considering the conditions for stable operation of AC-DC converters, constraints on power transmission limit and static stability limit are used to determine the range of VDI. Third, a simulation model is established and the feasibility and validity of the method are verified. Finally, the main factors affecting the range of VDI are analyzed. Actually, the method proposed is adapted to various types of AC-DC converters with constant DC voltage control.

This paper presents a method on order-reduction of interharmonic analysis based on the principle of interharmonic interaction. First, we obtain the transformation between dynamic phasors in dq coordinate and dynamic phasor sequence components (DPSCs). Then, a full-order interharmonic analysis model is developed taking the voltage and current double closed-loop controller into account via the transformation mentioned before. The principle of interharmonic interaction is studied based on the full-order DPSCs model. On the basis of the principle, the dominant frequencies for all kinds of variables are selected and a reduced-order interharmonic analysis model is derived. Finally, two examples are presented for illustration of the proposed method. It is shown that the reduced-order interharmonic analysis model based on the principle of interharmonic interaction keeps high accuracy with substantial computational savings.

Multilevel inverters have been widely used in high voltage and high-power applications on account of their remarkable performance in recent years. The multilevel inverters have an increased chance of switch fault due to a considerably large number of semiconductor switches associated with the power conversion. Therefore it is crucial to detect and locate faults quickly. In this context, an open-circuit fault diagnosis method for cascaded H-bridge multilevel inverter (CHBMI) based on the level-shifted pulse width modulation (LS-PWM) technique is proposed. Unlike the fault diagnosis based on the algorithm, the proposed method only needs a certain logical judgment to diagnose the fault based on subtle fault characteristics. The output voltage of the H-bridge and load current are used for fault diagnosis.

A reactive power optimization algorithm for distribution network with photovoltaic (PV) generation is proposed to address the problems of power quality degradation, system active power losses increase and system instability caused by the connection of PV generation. Firstly, a multi-objective reactive power optimization model is established with the objective functions of minimizing system active power losses, controllable loads reduction, and PV active power reduction. Secondly, the PV power generation system is modeled mathematically. Thirdly, using the non-dominated sorting genetic algorithm (NSGA-III) to solve the model. Finally, the feasibility and validity of the proposed method are verified by the simulation with the modified IEEE123-bus system.

Due to the environment concerns, energy risks, fossil fuel loss reduction, controllable loads reduction and also the PV ac-tive power reduction. The validity and the effectiveness of the proposed method are verified by the simulation with the modified IEEE123-bus system. The paper by G. Zhang and J. Yu from Central South University, China presents an open circuit fault diagnosis method for cascaded H-bridge multilevel inverter based on the level-shifted pulse width modulation. The fault diagnosis is done based on the logical judgement instead of the conventional algorithms, thus improving the detection time. The proposed fault diagnosis method can also work for more number of levels and higher switching frequency of the multilevel inverter compared with the prior state-of-the-art scheme. As the interharmonic generated by the grid-connected PV system has attracted widespread attention recently, the paper by Q. Luo and his co-authors from South China University of Technology, China and Guangdong Power Grid Corp Guangzhou Power Supply Bureau Co Ltd, China presents an order-reduction method of interharmonics analysis model based on the principle of the interharmonic interaction. The proposed reduced-order interharmonic analysis model shows substantial computational savings while keeping accuracy. The paper by Y. Qiu and his co-authors from South China University of Technology, China and Shenzhen Power Supply Bureau Co., Ltd., China presents a method for analyzing the voltage deviation isolation (VDI) performance for a two-stage high-frequency isolated AC-DC converters in LVDC systems, which can isolate not only the faults but also the voltage deviation at the AC side and improve the voltage quality at the DC side. The range of VDI can be determined with considering the conditions for stable operation of AC-DC converters, constraints on power transmission limit and static stability limit. Simulation model is established to verify the feasibility and validity of the proposed method. The paper by C. Gong and his co-authors from the University of Macau, Macao, China presents a H∞ optimal controller design based on harmonic state-space modeling for the static var compensator coupling hybrid active power filter in reactive power and current harmonics compensation. The proposed controller achieves high steady-state accuracy, fast transient response, and fixed switching frequency simultaneously, which shows superior control performances in comparison with the recent developed state-of-the-art multi-quasi-proportional-resonant controller. Both simulation and experimental results verified the effectiveness and performance of the optimal controller design. The paper by D. Xiao and her co-authors from Southwest Jiaotong University, China addresses the power quality problems caused by freight railways in weak grids with high penetration of wind generation. This paper proposes a comprehensive control method for negative sequence current suppression and reactive power compensation for a co-phase traction power supply system connected with doubly fed induction generators. The proposed approach can fully solve the power quality issues and effectively reduce the capacity of the co-phase traction power supply system. The paper by G. Lv and his co-authors from Nanjing Institute of Technology, China presents a voltage sag source location estimation method based on optimal configuration of system monitoring points and fault parameter estimation. The adaptive cuckoo algorithm is used to solve the three optimization variables of fault line, fault distance and fault resistance. The validity and the effectiveness of the proposed estimation method is verified by the simulation with the IEEE-30 node standard test system. • Ken King Man Siu, University of North Texas, USA • Minwu Chen, Southwest Jiaotong University, China • Qing Zhong, South China University of Technology, China • Xiaorong Xie, Tsinghua University, China • Yongheng Yang, Zhejiang University, China We would like to express our deep gratefulness to Prof. Jinjun Liu, Editor-in-Chief, for his tremendous support from the initiative throughout the final stages of this Special Issue. Finally, we would like to thank the CPSS TPEA staffs involved with the production and technical support of this Special Issue. We look forward to seeing more great papers on Power Quality Conditioning in Modern Power Grids Integrated Emerging Power Electronic Systems in CPSS Transactions on Power Electronics and Applications in the time yet to come and your continuous support to the journal.