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The stability problem of low-voltage multi-terminal DC (MTDC) system has drawn lots of interest. This paper focuses on oscillation instability phenomenon of low-voltage MTDC system and analyses the interaction behavior between each voltage-source converter (VSC) and DC network oscillation modal. The typical structure and control strategy of low-voltage MTDC system under master-slave control is first described and its equivalent circuit is established. Then the interaction behavior analytical model is proposed and the source-network and network-load interaction characteristics are studied. Furthermore, a system stability analysis method is built based on the modularized modelling which can solve the problem of how to deal with the complexity of high-order low-voltage MTDC system. The transfer function of the whole system is conveniently established revealing the mechanism of system instability. The proposed method can provide effective stability assessment for low-voltage MTDC system. Finally, the results are verified using electromagnetic transient simulation and validated experimentally using a low-voltage three-terminal DC system test platform with AC 0.4kV/DC 800V. This research can be flexibly promoted to high-order systems for controller design and performance optimization.

Pulsed power sources provide high-power waves with high frequency (HF) content for a wide range of applications. Conventionally, a simple resistance is employed for the most prevalent pulsed power loads. However, the load model can highly affect the efficiency of source design. This paper contributes to fill this gap by considering the HF behavior of the loads. Accordingly, a new approach has been proposed to present a general HF lumped-circuit model for pulsed power loads. The frequency response of the loads is identified using the Finite Integration Technique (FIT). Subsequently, an equivalent circuit model is established based on the vector fitting (VF) algorithm. The applicability of the approach has been verified by comparison with two experiments, i.e. Vircator and coaxial reactor as the loads. It is indicated that the HF-based model can significantly improve the simulation results to be in good agreement with experiments. The results present that while a pure-resistive load model could lead to about 30% error in the estimation of the characteristics of output voltage, it is about less than 5% in the case of the proposed HF load model.

Modeling grounding systems is necessary for the calculation of ground potential rise (GPR), power system simulations and insulation coordination studies. In this work, a methodology for estimating equivalent circuit parameters through the optimization of the time-domain impulse response was developed. It allows to obtain equivalent circuits with positive parameters that accurately represent grounding systems considering both effects related to frequency and soil ionization. Additionally, linear and nonlinear equivalent circuits for calculating the impulse response of typical grounding systems were proposed. The Nelder-Mead optimization method was applied to adjust the circuit parameters. For evaluating the methodology developed and the proposed models, data from impulse current tests was used. It was found that the use of nonlinear circuits increases the accuracy of the simulated response, resulting in errors of less than 4% in the estimation of GPR. The proposed methodology allows obtaining representative circuits of typical grounding systems used in the electrical system. The circuits can be used for systemic studies and calculation of GPR considering short-circuit or lightning currents.

Insulator pollution flashover occurs frequently and is harmful to the power transmission and distribution network. But the randomness of the pollution flashover and the complex influencing factors make it difficult to be predicted. The objective of this paper is to study the mechanism of the discharging on insulator surfaces and design a the calculation method which derives flashover probability. By calculating the distorted electric field in the initial streamer discharge quantitatively and combining it with the equivalent circuit of the insulator surface, the initial discharge voltage is derived. By analyzing the change in power input and dissipation in the process of the arc discharge, we propose the criterion on arc development and extinction, and the critical flashover conductivity of the insulator is obtained. Based on the probability density function, the behavior of the factors on the critical flashover conductivity is described, and the probability of insulator pollution flashover is calculated under different environmental conditions. In the validation experiment, the measured initial discharge voltage and pollution flashover ratio are close to the calculated values. The methods proposed in this paper could be used in the quantitative calculation of the initial discharge voltage and the prevention of the pollution flashover on insulators.

The multi-terminal hybrid LCC/MMC HVDC has been applied to overcome the simultaneous commutation failure problem caused by the multi-infeed LCC-HVDCs in the East China. The high-speed and selectivity line protection method is required for the multi-terminal hybrid HVDC system. In this paper, the reflection and refraction of the fault traveling waves at different kinds of line terminals are characterized by transfer functions. Then the fault voltage as well as its first peak time at different line terminals when different internal and external faults occur are derived respectively. The conclusion proves that the first peak time of line-mode fault component voltage (FPTV) for internal faults is smaller than that for external faults, which is independent of fault impedance and fault type as well. Therefore, a FPTV-based non-unit ultra-high-speed dc line protection method is proposed. The algorithm is implemented in the developed protection prototype and validated in the Kun-Liu-Long three-terminal hybrid HVDC RTDS test system. The test results show that the proposed method can fast and correctly identify line faults in the multi-terminal hybrid HVDC system, even with 500 Ω fault impedance. Comparing with the traveling wave protection method of ABB, the proposed method improves the sensitivity when high-impedance faults occur.

White-box models are detailed models for the investigation of the internal behavior of transformers during dielectric design. A new model of this type with significantly improved characteristics is presented in this paper. The model has been developed in state-space form, which is more flexible than an equivalent circuit and also makes it possible to optionally hide proprietary information on internal voltages. The proposed parameter determination methodology is very robust and allows the adequate representation of the damping. The methodology for determining inductive impedances and capacitances as a function of frequency using the Finite Element Method is described first. Then the fitting of the impedances obtained in the frequency domain by means of rational approximation functions is presented, which is based on the Vector Fitting algorithm in combination with Particle Swarm Optimization. The state-space model is obtained next, which is then used to perform time and frequency domain calculations. This new model has been successfully validated by comparison with measurements on a large power transformer used as case study during the activities of the JWG CIGRE A2/C4.52.

This paper proposes a new method to select single-line-to-ground (SLG) fault feeder in resonant grounding power distribution system based on compensation characteristic of extinction coil in different frequencies. The proposed method is insusceptible to the influence of device polarity reverse installation. Firstly, through analyzing the zero sequence equivalent circuit under a SLG fault, the difference of zero sequence current share in fundamental frequency and second-harmonic frequency is investigated. And then, according to the change of current share (CCS), fault feeder selection criterion and steps are established. Finally, numerous simulation tests demonstrate the effectiveness of the proposed method in identifying the faulty feeder or the faulty bus. Besides, its reliability is also verified by tests with different system parameters and different fault conditions. Specially, device polarity reverse installation tests and comparisons are also implemented, which shows the advantages of the proposed method in dealing with device polarity reverse installation.

Single-phase auto-reclosing (AR) scheme is widely employed in extra high voltage (EHV) transmission networks to quench transient faults without completely removing the faulted transmission line (TL). Long EHV TLs are commonly equipped with shunt reactors to reduce the Ferranti effect overvoltages. It is common practice to disconnect these reactors under the heavy load periods during the year. Considering this point, the AR technique should be able to work properly not only when the TL shunt reactors are in service, but also when they are disconnected. This paper puts forward a novel adaptive single-phase AR approach for shunt compensated TLs based on the general mathematical model of faulted phase voltage waveform after the line isolation, which is obtained by analytical analysis conducted on the TL's equivalent circuit. The effect of capacitor voltage transformer (CVT) on the voltage measurement is taken into account using a proper model for the CVT. Performing some data processing on the faulted phase measured voltage, useful features are extracted which are used by the support vector machine classifier to reliably detect the arc extinction instant. The proposed approach performance is evaluated by extensive simulation studies, accounting for different TL compensation schemes, transposition configurations, and arc conditions. 1986-2012 IEEE. Manuscript received January 29, 2020; revised May 17, 2020; accepted June 26, 2020. Date of publication July 10, 2020; date of current version May 21, 2021. This work was supported by the National Priorities Research Program under Grant 11S-1125-170027 from the Qatar National Research Fund (a member of Qatar Foundation). Paper no. TPWRD-00150-2020. (Corresponding author: Majid Sanaye-Pasand.) Seyed-Alireza Ahmadi and Majid Sanaye-Pasand are with the School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran 1439957131, Iran (e-mail: s.alireza.ahmadi@ut.ac.ir; msanaye@ut.ac.ir). Scopus 2-s2.0-85106618619

The high-speed accurate electromagnetic transient (EMT) simulation of the power electronic transformers (PET) has become a challenge, due to the microsecond-range time steps and the large number of high-frequency semiconductor switches and isolating transformers. Taking the input-series-output-parallel (ISOP) connected cascaded H-bridge (CHB) type dual active bridge (DAB) based PET as an example, this paper proposes a general high-speed equivalent EMT modelling method of PET. First, the isolating transformer within each DAB is discretized into two-port Norton circuits. Second, each CHB-DAB is equivalent to two single-port circuits by eliminating the internal nodes. And the input-side is represented by a Thevenin circuit and the output-side is represented by a Norton circuit. Third, all the CHB-DABs are equivalent to a two-port circuit with all the internal node information preserved. Fourth, the implementation of PET blocking is also considered for startup and fault protective actions. Fifth, the stability of the proposed discrete decoupling method of the PET is verified that it does not introduce specific limitation on the simulation step size. Finally, the developed PET models on PSCAD/EMTDC are shown to be two orders of magnitude faster than the currently available fully-detailed models with negligible loss of accuracy.

This article presents a nonlinear equivalent circuit model of an isolated dc-dc converter with a 3-phase medium frequency transformer. The model takes into account the magnetic cross saturation of the 3-phase core-type magnetic circuit. The model is suitable in detailed electromagnetic transient simulations of power systems involving isolated dc-dc converters. The model is developed using the Lagrange energy method. It involves a matrix of dynamic inductances containing a nonlinear term resulting from core magnetization and a linear term resulting from leakage flux. The model parameters are determined based on a series of magnetostatic finite element method simulations. This approach is convenient when applied to high power transformers offering a limited characterization effort, or if the transformer prototype does not exist. The experimental validation performed on a novel 3-phase MFT prototype in a 100 kW 1.2 kV 20 kHz dual active bridge converter has proved the validity of the model and model parameters. The no-load steady-state and inrush tests and the full-load test show a very good fit between the simulated and experimentally measured waveforms. The comparison with a classical simplified model neglecting magnetic cross saturation shows a significant difference in the no-load inrush test.

This study develops a high-speed protection method for a modular multilevel converter (MMC)-based DC grids. The method utilizes the single-end derivative of common-mode (CM) and differential-mode (DM) currents to construct a protection phase-plane that divides different DC fault types into different regions. When the protection starts, the first sampling point that enters the fault regions of the protection phase-plane has the largest value. When five sampled data satisfy the corresponding fault conditions, the protection signal will be sent. This scheme ensures the rapidity of protection. CM and DM circuits of MMC, DC transmission line, and fault transition resistance under different fault types are derived following the principle of modulus decomposition. Finally, the synthesized equivalent circuits are obtained. On this basis, the expressions of CM and DM currents are derived to analyze the characteristics of fault currents on the protection phase-plane and provide the rules for distinguishing different fault types. A four-terminal MMC-based DC grid simulation model is established in PSCAD/EMTDC. The rapidness and reliability of the proposed protection method are then verified using different simulation cases. The proposed method is also validated on a scaled-down hardware setup in the laboratory.

This paper yields a systematic scientific foundation for the evaluation of responsibility of utility and customer to the harmonic distortions at the point of common coupling (PCC). In this regard, this paper proposes a technical process for the evaluation of harmonic distortions. This technical process provides a way to answer some technical questions related to harmonic issues based on the following aim: identifying the dominant side, determining the responsibility of each side to harmonic distortions, determining the influence of the utility on harmonic current distortions at the PCC, and determining the influence of the customer on harmonic voltage distortions at the PCC. This paper deciphers these technical questions in the concrete “relevant factors” for the evaluation of harmonic distortions. These “relevant factors” are systematically classified based on the equivalent circuits of utility and customer side for harmonic studies. In this regard, six well-defined “relevant factors” for the Thevenin equivalent circuit and six analogue “relevant factors” for the Norton equivalent circuit are formulated. Some of these “relevant factors” are proposed, for the first time, in this paper. Furthermore, this paper explains the relations between the “relevant factors” to ascertain their interdependence. In addition, the usefulness of the “relevant factors” to answer the technical questions related to the harmonic issues is illustrated using a calculation example.

High inrush current severely threats the safe operation of the power system and transformers, which may lead to mal-operation of overcurrent protection device, internal short-circuit fault in transformers. Phase-controlled switching technology is an alternative method to reduce inrush current effectively by controlling the front-mounted circuit breaker (CB) to break or make at the predetermined phase angles of current or voltage. In this paper, a new simplified phase-controlled switching strategy is proposed for three-phase unloaded transformer with Y-connected windings in the primary side, which can limit the inrush current under 46.7% of the captured maximum inrush current. Meanwhile, this strategy is independent on the residual fluxes in the iron cores. The optimal making angle is obtained by theoretical analysis based on an equivalent circuit model of unloaded transformer. The comparison of the proposed method and the random switching approach is also presented with considering residual flux. A simulation model is established to calculate the amplitudes of inrush currents against various residual fluxes when using the proposed phase-controlled switching strategy and random switching method. The simulation results show that the proposed strategy can limit the inrush current under a low value. A test platform with high and low voltage instruments is built and some measurements are carried out. The experimental results are in good agreement with the theoretical analysis and simulation results, which verifies the effectiveness and practicability of the proposed strategy.

Due to a lack of high and stable power supplies for large-scale online monitoring devices, the intelligent development of high voltage transmission lines has always been restricted. This paper presents a method for capacitive power tapping from an insulated shield wire of overhead high voltage transmission lines with tuning. A general equivalent model, which considers the influence of line sag and landform on the equivalent circuit parameters, is established. The calculated equivalent circuit parameters show good agreement with the field measured data obtained by a 220 kV single-circuit transmission line. In order to maximize the tap-off power, a nonlinear tuning method is proposed since linear tuning can cause an overvoltage problem, and a tuned reactor is developed. Based on the measured equivalent circuit parameters, an experiment platform is built in the laboratory to measure the tap-off power under different resistive loads. The experimental results indicate that the maximum power is about 900 W, which represents an improvement of 80% compared with the maximum power without tuning. Additionally, the tuned reactor shows good robustness to the perturbation of equivalent circuit parameters, which validates the effectiveness of the proposed power tapping method.

Power flow controllers and circuit breakers are important devices in a DC grid, and combining them and expanding their ports can save many components. This paper proposes an integrated multiport DC power flow controller with a DC circuit breaker that can achieve power flow control and fault removal on multiple DC lines during steady and fault states, respectively. First, the device's topology based on modular multilevel converters is proposed, and the principles of power flow control and self-power balance based on bridge arm voltage are introduced. Second, it is improved by adding a fault removal capability. The equivalent circuit and fault currents in different time sequences are analyzed, and the component parameter selection method is designed. Third, in the PSCAD/EMTDC, the power flow control and fault removal capabilities are verified using three conditions: flow control, line fault, and bus fault. Finally, the number of components and steady-state losses are analyzed. Overall, the proposed device has power flow control and fault removal functions as well as a certain limiting effect on the fault current, which greatly reduces the system construction cost.

Transient voltage and current stresses are essential for the design and protection of multi-terminal DC (MTDC) transmission systems, especially under the short-term dynamics after severe grid faults. In this paper, we propose a discrete-time model for the modular multilevel converter based MTDC (MMC-MTDC) system considering the DC-side disturbances in the system. Based on the piecewise linear modeling, the state variables such as the transient voltage on the sub-module (SM), arm current, etc., can be calculated analytically for the critical short term (within 10 ms) after the severe DC fault while the system protection is yet to be activated. Parameter sensitivity analysis is also performed to give a better system design guideline. The estimation results are validated by detailed electromagnetic (EMT) circuit simulations and the scaled-down experimental laboratory prototype.

In compensated distributed networks (CDN), minimizing the asymmetry in the shunt parameters of the power lines is a key factor for avoiding excessive neutral voltages which is necessary not only for safety but also for improving the sensitivity of detecting ground faults, particularly when bush-fire mitigation is a major concern. This paper offers a comprehensive analysis and modeling of the asymmetry of the power lines in CDN. Unlike the existing analyses which assume the asymmetry can be lumped in one phase, the proposed analysis is based on more practical assumption by considering the asymmetry in all of the phases of the power lines. The proposed analysis is used to develop an equivalent circuit for asymmetrical CDN which then used to develop a new method for calculating the per-phase asymmetries in the shunt parameters. The proposed method has been validated based on simulations of real networks.

To analyze interference induced by transient overvoltage, this article proposes an impulse injection technique for determining the impedance of a high-voltage air-core reactor over a wide frequency range. By injecting nanosecond pulses into reactor in open-circuit, short-circuit and loading conditions, the linear characteristics of air-core reactor can be revealed up to several MHz. Then the equivalent two-port impedance including stray parameters can be derived from the measured current waveforms. Using vector fitting and impedance synthesis, the equivalent circuit is obtained and can be further applied in transient simulation. As an example, a 110 kV reactor is studied in this paper and its equivalent circuit is deduced in the frequency range of [2.5 kHz, 10 MHz]. The accuracy of the model is validated based on the measurements of a loading experiment.

DC distribution network has a lot of advantages over traditional ac distribution network and it is considered as one of the best power supply modes in the future. However, protection relay design for dc distribution network is a major challenge due to the requirement of high speed fault detection for the vulnerability of converters. In this paper, it is proposed that the boundary protection is very suitable for dc distribution network since it can protect the whole line only based on local measurement and does not need to coordinate with neighboring relays. However, it needs to find suitable line boundary for dc distribution network. Impedance features of magnetic ring is tested and difference in steepness and peak time of voltage travelling wave in case of internal and external faults when magnetic ring installed at both ends of dc distribution line is analyzed. Results show that magnetic ring is feasible to be used as line boundary. Besides, a wide band model of magnetic ring is proposed based on vector fitting and circuit synthesis method. It paves the way of analysis on features of internal and external faults at dc distribution line and validation of proposed fault detection method.

Frequency response analysis (FRA) has become a widely accepted technique by worldwide utilities to detect winding and core deformations within power transformers. The main drawback of this technique is its reliance on the personnel level of expertise more than standard or automated codes. To establish reliable FRA interpretation codes, accurate high frequency transformer model that can emulate the frequency characteristics of real transformers in a wide frequency range is essential. The model can be used to investigate the impact of various winding and core deformations on the transformer FRA signature. The transformer equivalent high frequency electric circuit parameters can be calculated based on design data, which are rarely available, especially for old transformers. As such, this paper presents an artificial intelligence technique to estimate these parameters from the transformer FRA signature. The robustness of the proposed technique is assessed through its application on three, 3-phase power transformers of different ratings, sizes, and winding structures to estimate their high frequency electric circuit parameters during normal and fault conditions. Results show that the proposed technique can estimate equivalent circuit parameters with high accuracy and helps interpret the FRA signature based on the numerical changes of these parameters. The main advantage of this approach is the physical meaning of the model parameters facilitates reliable identification of various faults and hence aids in establishing reliable interpretation codes for transformer FRA signatures.

Switching- on a power transformer creates energizing inrush current (EIC) which in turn leads to sympathetic inrush current (SIC) in adjacent in-service transformers (ITs). Sympathetic inrush current changes the waveform and prolongs the duration of its origin EIC. This makes the analysis and estimation of EIC complicated. Occasionally, the stress of EIC can cause internal short circuit in energizing transformer. Detecting short-circuit fault current during EIC is a challenge for transformer differential protection. On the other hand, SIC may mislead the earth-fault protection of in-service-transformer. This paper, first, proposes a new dc equivalent-circuit based on the dc-component of inrush current, which is efficient in analyzing concurrent EIC and SIC. Next, based on this equivalent circuit, new predictive formulas for EIC and SIC are derived. By employing these formulas, the transformer internal fault during inrush current can be detected based on the comparison between the predicted and measured waveforms, which prevents differential protection from fail-to-trip. Also, the predicted SIC waveform can be compared with the measured waveform to prevent IT earth-fault protection from mal-trip, during inrush current. Finally, the proposed equivalent circuit and formulas are verified using the EMTP simulation results of a real grid, under different system conditions.

This paper proposes three different black-box models for a 10-kVA 7.967 kV–120/240 V distribution transformer that is suitable to narrowband power line communication studies. One is valid in the 3–500 kHz range, while the remaining two are simpler models valid for the CENELEC band (3–148.5 kHz). The models are represented as equivalent circuits derived from the rational approximation of the transformer admittance matrix using either phase- or modal-domain theory. All parameters needed for their implementation in electrical circuit solvers are given. Validation is performed not only in frequency domain, but also in time domain, with the application of voltage signals that excite the 3–500 kHz and 3–148.5 kHz frequency bands uniformly. The models are shown to accurately predict the attenuation and distortion of signals transferred through the transformer for a wide range of load conditions for both downstream and upstream signal transmission. Signal attenuation is shown to be load dependent, frequency dependent, and sensitive to the considered transmission path (downstream or upstream).

The overhead line will be widely applied in the future flexible high-voltage dc (HVDC) grid. Correspondingly, effective reclosing strategy which can identify the fault property must be configured for the dc circuit breaker (DCCB) to improve the system power supply reliability. However, if the DCCB is reclosed directly, large second overcurrent may occur to damage the vulnerable devices in the system. Therefore, the inherent voltage characteristic difference between different dc faults (nonpermanent or permanent) is analyzed in the paper. And then a novel DCCB reclosing strategy for the flexible HVDC grid is proposed. Compared with the method which recloses DCCB directly, the proposed strategy can avoid the second damage under permanent fault condition, because it can identify the fault property without completely reclosing the DCCB (only the residual dc current breaker is reclosed before fault property identification). Moreover, compared with the typical sequential auto-reclosing strategy, the proposed strategy significantly reduces the additional control and design requirements on the DCCB. Finally, simulation cases based on the PSCAD/EMTDC are carried out to verify the correctness of the theoretical analysis and the superiorities of the proposed reclosing strategy.

The power system planning and protection studies are becoming more challenging due to the rapid increase in penetration levels of converter-interfaced renewables. Type-IV wind turbine generators (WTGs) and photovoltaic panels are interfaced to the grid through a full-scale converter, and their short-circuit current contributions are mainly designated by the converter control and associated current limits. This paper proposes a new phasor domain modeling approach for the wind parks (WPs) with Type-IV WTGs, using the concept of control-based equivalent circuits. The proposed model precisely represents the detailed electromagnetic transient (EMT)-type model in steady state, and is able to account for the fault-ride-through function of the WTG control as well as its specific decoupled sequence control scheme in addition to the traditional coupled control scheme. Although the collector grid and WTGs inside the WP are represented with their aggregated models, the overall reactive power control structure of the WP is preserved by taking the central WP controller into account. The accuracy of the proposed model is validated through detailed EMT simulations.

This two-part paper proposes a revised method for calculating high voltage (HV) cable sheath currents, and for fault location of cross-bonded HV cable systems. The equivalent circuit and the cable impedance per unit length under short-circuit fault conditions are revised from those under non-fault conditions. Part 1 of this paper proposes a revised phasor domain mathematical model for the sheath current calculation under fault conditions, following demonstration that short-circuit faults can cause changes in the equivalent circuit of the cable metal sheath, and cause changes in the cable impedance per unit length. The calculation results, as given in a case study, show that there exists a unique relation between the fault position and the sheath fault currents, making it possible to locate a fault by analyzing the characteristics of the sheath currents during a fault. Part 2 of the paper focuses on the fault location method via sheath current monitoring.

With the development of HVdc transmission technology, the isolation of dc faults is becoming increasingly important. As the most effective solution, hybrid HVdc circuit breaker (CB) is not mature enough, which has restricted its engineering application. Accordingly, this paper proposes an auxiliary dc CB scheme suitable for HVdc grid. In this scheme, the traditional half-bridge modular multilevel converter (MMC) is partially innovated to have the ability of auxiliary breaking operation. With the effect of the MMC auxiliary breaking (MAB) operation at both ends of the fault line, the dc fault current can be easily interrupted and isolated by low-cost CB unit installed in the dc transmission line. The equivalent circuit under MAB process is analyzed, and the fault isolation sequences are designed. Furthermore, the economic comparative analysis among three schemes is performed. Finally, a four-terminal bipolar HVdc grid test model is built in PSCAD/EMTDC; in addition, an MMC prototype with proposed scheme is also developed. The simulation and experimental results validate the effectiveness of the proposed scheme.

Among different modular multilevel converter (MMC) submodule (SM) topologies, the clamp double submodule (CDSM) has the capability of dc fault current limiting and utilizes a relatively small number of switching devices. Since CDSM has a more complex circuit structure than half-bridge or full-bridge SM, it is a significant challenge for the real-time electromagnetic transient (EMT) simulation for a multiterminal dc (MTDC) system containing CDSM MMC.This paper proposes the device-level electrothermal model of CDSM for real-time EMT simulation, which can accurately present the power losses, the junction temperatures, and the switching transient waveforms of individual switches consuming more computation resources. The individual insulated-gate bipolar transistors of the CDSM MMC during fault clearance transient are evaluated from both electromagnetic and thermal perspectives, which interact with each other dynamically. To ensure the real-time performance of the proposed model, the equivalent circuit model is combined with the device-level model. The system-level and device-level waveforms during normal operation and dc fault transient for a three-terminal dc system are both presented and compared with PSCAD/EMTDC and SaberRD. The simulation system was implemented on the Xilinx Zynq UltraScale+ ZCU102 multiprocessor system-on-chip (MPSoC) platform, and the results were captured by the oscilloscope in real-time.

This paper proposes a unified high-speed electromagnetic transient (EMT) equivalent and implementation method for modular multilevel converter (MMC) with arbitrary single-port submodule (SM) structures. The proposed method, interacts with the users by the incidence matrix, branch admittance matrix and the column vector of the current sources as input, then a nodal admittance matrix is automatically generated for each individual SM and the internal node information of the SMs are transferred to the interfacing nodes. Hence, the internal nodes are eliminated without obtaining the complicated analytical solutions, the reduced-order equivalent circuit of each SM is obtained and all the SMs within each arm are cascaded into one ultimate Thevenin equivalent. At the end of each time step, the EMT solver updates all the previously eliminated internal node information so that nothing is lost under steady and transient states. The proposed approach is validated by EMT models of an enhanced double half-bridge sub-module based MMC-HVdc system on power systems computer aided design (PSCAD)/EMTdc.

The power direction method is a widely used method for harmonic source identification. This method can work with no harmonic impedance information but is not theoretically rigorous. To overcome this theoretical shortcoming of the traditional power direction method, six existence criteria and two dominance criteria are proposed in this paper. These are all sufficient conditions that are mathematically derived based on the widely used utility–customer equivalent circuit. The existence criteria can be used to determine whether some harmonic source exists on the customer or utility side, and the dominance criteria can be used to identify whether the customer side is the dominant harmonic source. These criteria can be regarded as an improved power direction method, and the key improvement is the establishment of a rigorous theoretical basis. These criteria were tested using a MATLAB program, and no counterexample was found. Their practical application for harmonic source identification in a transformer substation is also introduced and discussed.

In order to select a reliable and economical type of transformer on-load tap-changer (OLTC), it is necessary to accurately determine the maximum step voltage in the process of engineering design. Because both configuration and operating conditions of a phase-shifting transformer (PST) are more complicated than those of conventional transformers, it is far harder to accurately calculate the maximum step voltage. The existing calculation methods have the shortcomings of inadequate accuracy or weak applicability. To solve these problems, based on the equivalent circuit of a PST, this paper at first derives the quantitative relations between operating conditions and the step voltage. Subsequently, the effect of different load conditions, including the load current and the phase angle difference between the load voltage and current, on the step voltage is fully investigated. This investigation reveals a law about the changes in step voltage under different load conditions. Next, a new calculation formula for the maximum step voltage is proposed, and its accuracy is verified with two practical examples. Finally, an error analysis is carried out to demonstrate the generality of this approach. The calculation method offers appealing accuracy and is very suitable for the economical and reliable selection of OLTC for symmetrical two-core PSTs in the process of engineering design.

The integration of wind power plants introduces new dynamics into power systems, forcing reconsiderations of how they are studied, planned, and operated. High quality models are essential to these studies. Manufacturer-specific electromagnetic transient (EMT) wind turbine models are usually available only as black-boxes, which hinders analysis and research. To overcome this issue, this paper proposes a generic EMT-type model for a specific type-IV wind turbine system, which is validated against field measurements from a wind turbine of the same type. More precisely, it proposes a wind turbine model based on an externally excited synchronous generator system connected to a full converter composed of a six-pulse diode rectifier, a dc–dc boost stage and a two-level voltage source converter. The required control features and internal protection schemes are considered and described. Two different fault ride-through control strategies, in line with existing grid codes, are implemented. A corresponding EMT-type hybrid model representation is also developed based on newly proposed switched equivalent circuits and average models for the considered hardware, control, and power electronics stages. It allows for the use of larger simulation time steps, hence considerably improving computation times.

Frequency response analysis (FRA) is an effective approach for detecting mechanical damage in the windings of a transformer. However, the application of FRA to estimate the winding condition of autotransformers (ATs) employed in the China High-Speed Railway is problematic. Because the split windings of the ATs are connected inside the tank, it is impossible to measure the FRA curves for each split winding outside the tank directly. Therefore, it is difficult to identify fault winding and effectively diagnose the overall condition of the windings. This paper explores the features of FRA curves under different fault conditions to help distinguish the fault winding. An equivalent circuit model is built for the AT with split windings, and the electrical parameters of the windings are determined using the finite-element method. The model is then employed to simulate typical axial displacement faults. The results show that the first antiresonance and resonance of the frequency response for connections involving series windings or series and common windings may be visible features for diagnosing winding faults and the fault level. Specifically, the first and second resonances of the frequency response for the common winding connection may be regarded as the primary feature for identifying fault windings.

Analyzing the harmonic distortions at the point of common coupling is thoroughly addressed in this two-part paper. The main aim of such an analysis is to identify which of the utility and customer sides is significantly responsible for the harmonic distortions at the point of common coupling. In Part I, the meaning of the dominant side is challenged fundamentally. Here, two different definitions for the dominant side are discussed: The side with the larger equivalent harmonic “voltage” or “current” source. It is shown that these definitions are not identical. Subsequently, common methods are categorized in three general concepts based on: the direction of active power flow, the reactive power, and the voltage-current ratio. These three categories as well as their validity are analytically reviewed for both the definitions. The concept based on the voltage–current ratio has been explicitly presented in the original work for identifying the dominant equivalent harmonic voltage source. This concept is developed in this paper for identifying the dominant equivalent harmonic current source as well. In Part II, the application of the methods is illustrated using some common calculation examples. In addition, these methods are described verbally to provide a physical interpretation. Some practical aspects regarding the implementation of the methods are discussed as well.

In order to improve features, such as fault current blocking and capacitor voltage balancing, modular multilevel converter (MMC) topologies incorporating multiport submodules (SMs) are being considered as candidates for HVdc transmission applications. This paper presents high-speed and accurate electromagnetic transient (EMT) models for MMCs composed of such multiport SMs. The approach uses the Schur's complement technique to recursively eliminate internal nodes of the converter structure to create a multiport Norton equivalent that connects to the external network. Thus, the final admittance matrix seen by the EMT solver has a dimension orders of magnitude smaller than that of the unreduced structure. As with previously developed approaches for MMCs with single-port SMs, all internal information, such as individual SM capacitor voltages, is preserved and can be output by the program if needed. This increases the bookkeeping effort, but the overall reduction in matrix size more than compensates for any resulting time penalty. Approximately two to three orders of magnitude speedup over a straightforward implementation in an EMT program is achieved.

Transient enclosure voltage (TEV) induces a relative potential difference between grounding conductors and then couples to secondary cables and may cause malfunction and even damage to secondary equipment. This study investigates the coupling mechanism of TEV to secondary cables from an experimental point of view and presents a cable model suitable for calculation. Experiments are carried out on test platforms established in a laboratory. The experimental results indicate that the magnitudes of port voltages are roughly 1.5‰ of TEV magnitudes, and the waveform of the start port voltage has the same profile but in antiphase with that of the end port voltage. Moreover, only common-mode voltage with no differential-mode voltage exists for the twin core cable. Based on these results, an equivalent circuit for a secondary cable is proposed. This circuit can generate similar waveforms as those measured in the experiment. The experimental and theoretical results presented in this paper should prove helpful for evaluating the interference severity of secondary cables resulting from TEV for the electromagnetic protection of secondary ports.

Modular multilevel converter (MMC)-based multiterminal HVdc (MTdc) transmission is a favorable option for asynchronously interconnecting several weak ac systems. This paper investigates the potential resonance of such an MMC-MTdc system excited by background harmonics in any of the MMC's ac systems and the undesirable transfer of these harmonics to the remote ac systems. First, the harmonic transfer rule across one MMC is established using phase leg voltage analysis and it is then used to develop an equivalent circuit model of the MMC-MTdc system. This model is used to investigate the mechanism of resonance excited by ac-side background harmonics. Finally, a control strategy is proposed to mitigate this resonance. Analytically calculated results from the derived model and the proposed control strategy are validated via electromagnetic transients simulation of a five-terminal MMC-MTdc network.

The residual axial magnetic field (AMF) at current zero, which is caused by large $\mathrm{d}i/\mathrm{d}t$ during the forced current-zero stage of DC interruption based on the technique of artificial current zero, has a significant influence on the interruption performance of the vacuum circuit breaker. In this paper, a model of AMF contacts system is developed by finite-element-analysis software Ansys. The eddy current induced in the contacts system is also analyzed by an equivalent circuit. The influence of the frequency of countercurrent and the characteristics of saturable reactor, which results in the change of $\mathrm{d}i/\mathrm{d}t$ before current zero, are investigated. The results demonstrate that the frequency of countercurrent has a significant influence on the residual AMF at current zero. The residual AMF decays exponentially after current zero with a time constant independent of the countercurrent frequency. The residual AMF can be reduced by using a saturable reactor. The effect of a saturable reactor depends mainly on the duration of the low $\mathrm{d}i/\mathrm{d}t$ stage before current zero.

Cables in ventilated and ladder-type trays have been extensively studied and are rated according to ANSI/NEMA standards. The National Electric Code (NEC) provides guidelines on ampacity for cables installed in ventilated and ladder-type trays. However, for solid bottom trays, there is very little published material; there are neither standards nor guidelines. This paper proposes a methodological approach for the thermal rating of power cables installed in solid bottom trays with and without cover. An analog thermal–electrical circuit is derived from first thermodynamic principles. The circuit parameters are easy to compute. The method is completely general and is applicable to trays with any number of cables (not only to integer fill depths). The validity of the method is corroborated with numerous finite-element method simulations and laboratory experiments. A hand-worked example is given for illustration.

High-impedance faults (HIF) occur frequently in resonant grounding systems and are difficult to detect. Thus, an effective HIF feeder identification technology is urgently needed. This paper establishes an HIF equivalent circuit in a resonant grounding system. The change rule of transient zero-sequence voltage, transient zero-sequence currents, and their projection components with respect to the transient zero-sequence voltage of the bus are analyzed in both underdamping and overdamping resonance conditions. Furthermore, the variation ranges of the resonant frequency, the magnitude, the attenuation factor, and other parameters are specified in detail. The magnitude and phase relationships of zero-sequence currents among the faulty feeder, healthy feeders, Petersen coil, and fault points, as well as the relationships between their projection components and quadrature components with respect to the transient zero-sequence voltage are analyzed and compared. A novel faulty feeder identification method based on a comparison of the magnitude and polarity of the transient zero-sequence current's projection component is proposed. The accuracy of the transient characteristics and the feasibility of the proposed method are verified by simulations and field data.

The well-known and widely applied Thevenin theorem is applied to the operational analysis of ac transmission circuits. The approach is to model the transmission circuit AI as an n-port. The calculation of the Thevenin equivalent impedance is found by applying an n-vector of currents to AI and observing the behavior of the terminal voltages of AI. The Thevenin equivalent voltage is an n-vector and this is simply the open-circuit voltage of AI. The equivalent circuit is applied to conveniently study the transmission circuit performance for a range of different operating conditions. The treatment of controlled sources in the model is described. The application of Thevenin's theorem to a class of multiport circuits has been described before, and the application to three-phase circuits has been suggested; however, the contribution in this paper is the treatment of transformers and modeling mutual coupling between phases in transmission components, and the application to general polyphase circuits.

With the high penetration of distributed generations (DGs), the conventional radial distribution network is becoming an active distribution network (ADN). It has the characteristics of multisource, multibranch, bidirectional power and fault current flow, as well as weak infeed. To provide effective protection for such a network, a novel current differential protection scheme, together with new implementation technology, is proposed in this paper. In this scheme, instead of using phase currents, a positive-sequence fault component (PSFC) is introduced into the differential protection. By building the PSFC equivalent circuit of the ADN, the distribution characteristic of PSFC within the ADN is theoretically analyzed in detail, especially for the case when the ADN contains inverter interfaced DGs. The PSFC-based differential protection criteria for different types of feeder are then established and simulated. To put the scheme into practice, data self-synchronization and peer-to-peer communication techniques are established. Based on this principle and using an advanced hardware platform, a protection prototype is successfully developed and tested. The test results verify the feasibility of the proposed protection scheme.