DC short-circuit current calculation is necessary to design and protect modular multilevel converter-based (MMC-based) multiterminal dc (MTDC) grids. In this article, a general and analytical short-circuit current calculation method is proposed for bipolar MTDC grids. For pole-to-pole (P2P) faults, the superposed fault equivalent network of the MTDC grid is first developed in the frequency-domain. Then, a decoupling method based on the network inductance ratio is proposed, which simplifies the high-order network into the superposition of several independent two-order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC circuits. As a result, the short-circuit current can be expressed as the sum of the currents of these <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC circuits. For pole-to-ground (P2G) faults, the phase-domain dc line impedance considering the coupling effects is determined based on its modal-domain parameters, so that the P2G fault current can be calculated using the method of the P2P fault. The proposed method’s effectiveness is verified through simulations and experiments, and the calculation error is classified and analyzed. Compared with the existing methods, the proposed method is more accessible, more accurate, and available for hand-solution.

Analytical Calculation of Transient Short-Circuit Currents for MMC-Based MTDC Grids

Survey of Relay Protection Technology for HVDC Transmission Lines

In a small-current grounding system, the pole-to-ground fault may cause the voltage drop in the fault pole and the voltage rise in the other poles. In flexible DC distribution systems, Severe voltage variation may shorten the insulation lifetime of the equipment, which leads to great concerns on the safety issue. In addition, the existence of high transition resistance degrades the accuracy of fault detection methods, thus further affecting the reliability of the system. Therefore, it is essential to explore an advanced technology for faulty feeder detection. This study proposes a faulty feeder detection method based on the characteristics of transient zero-mode current (TZMC) in multi-frequency bands. The change rate of zero-mode voltage is applied as the protection activation criterion. Then, the characteristic matrix is constructed via computing the fuzzy entropy of TZMC in each frequency band. Finally, the faulty feeder can be identified by conducting fuzzy C-means on the characteristic matrix. This proposed method is tested through simulations on the PSCAD/EMTDC platform, which successfully demonstrates its outstanding adaptability, reliability, and accuracy. 

Multi-Frequency bands based Pole-to-Ground fault detection method for MMC-Based radial DC distribution systems

The multiple reignitions of vacuum circuit braker (VCB) while switching off the shunt reactor in an offshore wind farm (OWF) would produce a high overvoltage. The post-arc process of ion movement in the vacuum interrupter is analysed. Considering the sheath growth and ion concentration variation, the expression for dielectric recovery strength inside the VCB interrupter is derived. A novel VCB model is implemented in the environment of electromagnetic transient programme based on the new reignition criterion. Then, the switching overvoltage is computed and analysed in detail. For the OWF with high rising rate of transient recovery voltage, the sheath growth must be considered in the VCB model; otherwise, the overvoltage may be underestimated. Using resistor–capacitor (RC) snubber, a new installation scheme is proposed to suppress the overvoltage in the OWF. The results indicate that the proposed scheme can not only reduce the peak and steepness of overvoltage but also damp the high-frequency oscillation. It would not affect the steady-state operation of OWF. Besides, the capacitor of RC snubber normally does not bear the electric stress, and its life expectancy would be greatly enhanced. 

Investigation on overvoltage caused by vacuum circuit breaker switching off shunt reactor in offshore wind farms

This paper proposes a joint limiting control strategy for suppressing DC fault current and arm current in modular multilevel converter-based high-voltage direct current (MMC-HVDC) systems, which includes two target-oriented current limiting controls. To limit the DC fault current in the early fault stage, an equivalent modular multilevel converter (MMC) impedance is obtained, and its high-frequency part is reshaped by introducing virtual impedance, which is realized by adjusting the inserted submodules adaptively. Following the analysis of MMC control characteristics, the arm current limiting strategy is investigated, with results showing that the inner-loop control has significant effects on arm current and that a simple low-pass filter can reduce the arm current in the fault period. Finally, by combining the virtual impedance shaping and inner-loop control, the fault currents of DC lines and MMC arms can be suppressed simultaneously, which can not only alleviate the interrupting pressure of the DC circuit breaker, but also prevent the MMC from being blocked by the arm overcurrent. Theoretical analysis conclusions and the proposed strategy are verified offline by a digital time-domain simulation on Power Systems Computer Aided Design/Electromagnetic Transients including DC platform, and experiment on a real-time digital simulator platform. 

Joint Limiting Control Strategy Based on Virtual Impedance Shaping for Suppressing DC Fault Current and Arm Current in MMC-HVDC Systems

The pole-to-ground fault is one of the most typical faults in modular multilevel converters (MMCs) based DC grid. Analyzing the transient characteristics of fault voltages and currents is of great significance for fault identification, configuration of protection, and optimization of system parameters. This paper proposes an equivalent transient characteristics calculation method for pole-to-ground faults for symmetrical monopolar MMC based DC grid. Firstly, according to the mechanism of the pole-to-ground faults, the fault network and the steady-state network are formed. Then, the star-delta transformation is performed on modelling the MMCs in the fault network, which overcomes the problem that the number of the inserted sub-modules (SMs) in each arm is time-variant. Based on the discrete adjoint model, the pre-fault and faulted matrices describing the voltages and currents are established, and a general method for solving the transient voltages and currents is proposed. Finally, the proposed method is validated in a four-terminal symmetrical monopolar MMC based DC grid. The results show that the proposed method is of high accuracy, and is much more time efficient than time-domain simulation.

/pdf/an-equivalent-calculation-method-for-pole-to-ground-fault-2hioioieav.pdf

An Equivalent Calculation Method for Pole-to-Ground Fault Transient Characteristics of Symmetrical Monopolar MMC Based DC Grid

Hybrid HVDC circuit breakers with an energy absorption branch of a parallel arrester structure

Symmetrical monopolar configuration is the prevailing scheme configuration for modular multilevel converter based high-voltage direct current (MMC-HVDC) links, in which severe DC overvoltage or overcurrent can be caused by the DC faults. To deal with the possible asymmetry in the DC faults and the coupling effects of the DC lines, this paper analyzes the DC fault characteristics based on the phase-mode transformation. First, the DC grid is decomposed into the common-mode and the differential-mode networks. The equivalent models of the MMCs and DC lines in the two networks are derived, respectively. Then, based on the state matrices, a unified numerical calculation method for the fault voltages and currents at the DC side is proposed. Compared with the time-domain simulations performed on PSCAD/EMTDC, the accuracy of the proposed method is validated. Last, the system parameter analysis shows that the grounding parameters play an important role in reducing the severity of the pole-to-ground faults, whereas the coupling effects of the DC lines should be considered when calculating the DC fault currents associated with the pole-to-pole faults. 

Fault Current and Voltage Estimation Method in Symmetrical Monopolar MMC-based DC Grids

There is active power coupling between ac system and dc system in ac/dc interconnected power grid, and modular multilevel converter based HVDC (MMC-HVDC) system could not completely isolate the fault from ac system to dc system or dc system to ac system. In order to achieve the effect of independent decoupling operation of HVDC system and make full use of "firewall" function of the MMC-HVDC system, the battery energy storage system (BESS) based MMC-HVDC system is a preferred choice. For the BESS based MMC-HVDC system, this paper firstly analyzes the basic structure and operation principal. Then, based on numerical integration and nested fast and simultaneous simulation approach, this paper derives the Thevenin equivalent circuit of BESS based SMs and BESS based MMC. The case studies are performed on a ± 500 kV 2-ternimal MMC-HVDC system. The time-domain simulation results show that the ac side active power and the dc side power of the BESS based MMC-HVDC system can be decoupled from each other, and the transmitting power during and after the ac or dc fault can be kept.

Modeling and Simulation of Battery Energy Storage System based MMC-HVDC

Fast detection and isolation of direct current (DC) faults are key issues for DC grids. Therefore, it is very necessary to study the fault protection principle for DC grids. This paper firstly presents the main difficulties in DC fault protection. Then, a local protection and local action strategy for isolating the DC faults is proposed. To illustrate the performance of the proposed protection strategy, a four-terminal DC grid with the hybrid high voltage direct current (HVDC) circuit breakers (HVDC CBs) is constructed in the time-domain simulation software PSCAD/EMTDC as the test system. The systematical comparison between the ordinary protection strategy and the proposed strategy is carried out. The protection selectivity of the proposed local detection and local action strategy is thoroughly studied through complete DC line fault scanning of the test system. The simulation results show that the proposed strategy is of high protection selectivity and speed. In addition, the current rating and the voltage of HVDC CB could be greatly reduced with the proposed strategy, which proves the economic benefits of the proposed strategy.

https://www.mdpi.com/1996-1073/13/18/4795/pdf

A Local Protection and Local Action Strategy of DC Grid Fault Protection

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