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This paper deals with stabilization of an ideal transformer model (ITM) circuit, used as an interfacing algorithm for hardware-in-the-loop simulations. The ITM allows for the distribution of simulation model computations over multiple processors or can be used in power hardware-in-the-loop simulations. When specific impedance conditions of the partitioned circuit are not met, this interfacing algorithm becomes unstable. This paper first presents a new theoretical approach for representing the ITM interfacing algorithm that is based on delay differential equations. With a stability analysis of the obtained time-delay system, a stabilization method is proposed, which increases the stability boundaries of the ITM algorithm. Simulation examples, including the scenario of a two-level inverter system, are provided. [ABSTRACT FROM AUTHOR]

This paper discusses the back-flashover (BFO) phenomena in a high-voltage (HV) vertical double-circuit transmission line by means of numerical simulations. The single- and multiphase BFOs are analyzed considering 24 cases of AC-voltage angles and nonlinear characteristic of flashovers, taking advantage of the circuit analysis method in time domain. The models used in circuit analysis are the TEM-delay model, which can take into account the non-TEM characteristics of tower and line, and the conventional models. Prior to the BFO analysis, the characteristics of circuit models are compared and discussed with the numerical electromagnetic analysis results. In BFO analysis, it is clarified that the occurrence probability of the multiphase BFO is heavily depending on the bias AC-voltages. The relation of measured BFO phases and AC-voltages are well explained by the TEM-delay model with the valid lightning current magnitude. The conventional circuit models could have underestimated the occurrence of BFOs in HV transmission lines. The analysis and discussions shown in this paper can be utilized for advanced evaluation of lightning performance of transmission lines that considers the seriousness of lightning accidents. [ABSTRACT FROM AUTHOR]

Electromagnetic Transient (EMT) simulation tools are typically developed using conventional procedural programming languages. On the other hand, modern high-level and equation-based programming languages, such as Modelica, are currently available. Modelica allows formulating models that are easy to develop, maintain and understand by expressing what needs to be computed without stating how it should be computed. This paper presents a Modelica-based simulator for electromagnetic transients. It is demonstrated that this approach offers significant advantages for developing sophisticated models. Computational performance and accuracy are compared to a conventional EMT-type simulation tool. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive model of modular multilevel converter (MMC) for electromagnetic transient (EMT) simulations. The model is applicable to MMCs with arbitrary numbers of half-bridge and full-bridge submodules. The proposed design includes average value model, arm equivalent model, and detailed equivalent model. It allows smoothly transitioning from one model to another during time-domain simulations depending on the desired accuracy and execution time constraints. Modifications required in conventional MMC models to achieve smooth transitions are presented in the paper. Time-domain initialization methods are developed for each constituting model, including initialization of the appropriate control system blocks. Validity and effectiveness of the proposed adaptive model is demonstrated using EMT simulations of 401-level MMC-HVDC system. [ABSTRACT FROM AUTHOR]

Determining the Marx generator configuration, including the values of series and parallel resistors as well as the number of series and parallel stages to obtain standard lightning impulse (LI) waveforms, is usually done in a trial and error process in the high voltage test fields of power transformer manufacturers. This practical process may take excessive time and is boring for test engineers. In this paper, a simple simulation method is proposed to model the LI test circuit of the transformer by computer, which is helpful in identifying the Marx generator set up. This method is based on modeling the LI test circuit as well as the transformer's high frequency impedance in discrete frequency domain. The measured frequency response of the transformer is used to model its high frequency characteristics. Digital signal processing methods are used to simulate the circuit and obtain waveforms. The accuracy of the proposed method is validated using experimental tests performed on three transformers with different ratings. [ABSTRACT FROM AUTHOR]

This paper introduces an enhanced equivalent model of the half-bridge symmetrical monopole modular multilevel converter (MMC) topology for the analyses of the electromagnetic transients. Compared with the existing MMC models, the proposed model reduces the simulation computational time without compromising accuracy, and contrary to the existing models, it provides accurate representation of the MMC behavior with respect to the dc-side fault. This paper also evaluates and verifies the accuracy of the proposed equivalent model under various operating conditions, that is, startup, dc-side pole-to-pole fault, and ac-side three-phase-to-ground fault. The study results indicate that: 1) in contrast to the existing equivalent models, the proposed enhanced model accurately represents the MMC under various operating conditions; 2) the implemented simplifications to the model do not adversely affect the accuracy of the simulation results; and 3) a reduced-level approximated model of the MMC is also adequately accurate for protection studies. [ABSTRACT FROM AUTHOR]

In the companion paper, a methodology for computing transmission-line short circuits caused by direct and nearby ground lightning incidence was described. This paper presents the application of methodological and computational procedures of this methodology, regarding the calculation of lightning performance of transmission lines. From the computed results, focusing on 138- and 230-kV typical three-phase transmission lines, the effectiveness of the described process is clear, even when the line is modeled three-dimensionally or when nonlinear elements are present, for example, when arresters are installed in the line. [ABSTRACT FROM AUTHOR]

In this paper, a new synchronous machine model is developed for electromagnetic transients program type simulations. The stator circuit is expressed in the abc phase domain. The machine model is represented as a Norton equivalent with a current source in parallel with a constant Norton admittance. The machine equations are reformulated so that the computational effort required for the modeling of the machine is reduced. Test studies demonstrate the accuracy of the proposed synchronous machine model and show that the proposed model is computationally more efficient than the existing constant conductance phase domain model and voltage-behind-reactance model. [ABSTRACT FROM AUTHOR]

This paper presents a novel circuit model for eddy-current effects for multi-winding transformers. It presents the theoretical framework to model eddy currents applicable to layer or disk windings with n-layers for two-dimensional (2-D) transformer arrangements. The new white-box model is physical, dual, and leakage reversible. Additionally, it does not have mutually coupled elements or negative inductors. The paper presents a complete circuit for transformer windings (including capacitances) and core. The model accurately predicts the variation of resistance (dc component, skin, and proximity effects) and leakage inductance of windings from dc to hundreds of kilohertz. Being derived from the principle of duality, the circuit elements can be physically related one-to-one to the distribution of flux and current in the winding geometry. A practical winding discretization, based on field penetration depth for the given frequency, allows estimating the parameters using very simple formulae requiring only geometrical information and properties of materials. Model verification is done using finite element simulations. It is shown that the circuit model matches very well with 2-D FEM simulations. The circuit can be easily implemented in any circuit simulation software like EMTP-RV, PSCAD, ATP, etc., by simply dragging and dropping elements. [ABSTRACT FROM AUTHOR]

This paper presents a passive lumped model for DC cables and overhead lines, taking into account the frequency dependency of the per-unit-length parameters due to the skin and proximity effects. In comparison to distributed parameter line models, such as the Frequency-Dependent Phase model of PSCAD, the proposed model does not require line propagation delay extraction and does not impose any restrictions on the simulation timestep. As a result, for electrically short lines, the introduced model is more computationally efficient than distributed parameter models as it enables simulation using larger timesteps. The performance of the proposed model is evaluated in comparison with the PI model and the Frequency-Dependent Phase model through time-domain simulations of a DC microgrid and a radial DC distribution feeder. The studies performed in PSCAD focus on fault-induced transients. The results indicate that for electrically short lines the developed model is significantly more accurate compared to the PI model and provides similar accuracy with more computational efficiency compared to the Frequency-Dependent Phase model. [ABSTRACT FROM AUTHOR]

This paper presents a general method for building equivalent electric circuits of power transformers, including eddy current effects in windings and core. A high-frequency equivalent dual model for single- and three-phase transformers with two multilayer windings is derived from the application of the principle of duality. The model is built from elements available in circuit simulation programs, such as Electromagnetic Transients Program (EMTP)–Alternative Transients Program, EMTP-RV, PSCAD, and PSpice. The parameters of the frequency-dependent leakage inductance and winding resistance are computed with analytical formulae obtained from the solution of Maxwell’s equations that are based on the geometrical dimensions and material information. Ideal transformers are utilized to isolate the electric components (winding resistors and capacitors) from the magnetic components (inductors). The physically correct connection points for electric and magnetic components are clearly identified. The proposed methodology is successfully validated versus finite- element simulations and laboratory measurements. [ABSTRACT FROM PUBLISHER]

The proper modeling of the transient thermal behavior of mutual heating effects between underground power cables is very important for the rating of transmission and distribution cables. The IEC standards proposed an accurate model based on exponential integrals that it can be difficult to implement in basic electrical software. The model is not consistent with the layered modeling of the cable thermal resistances. In this paper, a simple and easy-to-use alternative model is presented. It consists of injecting the correct current at the right position of the RC circuit representing the soil. The new model can accurately reproduce the full physics of the transient phenomenon and is consistent with the modeling of the cable used in the IEC standards themselves. The new model is tested and validated against numerous finite-element simulations for realistic cable installations. [ABSTRACT FROM AUTHOR]

A major issue in the modeling of harmonics dynamics via extended harmonic domain (EHD) has been detected and thoroughly analyzed in a recently published paper. It consists on incurred error of individual harmonic response when a step change in either source or parameter variable is applied to a system modeled in the EHD. This paper demonstrates that the error is due to incorrect initial conditions of the EHD state-space model at the time of step change and proposes an effective solution to achieve zero error. [ABSTRACT FROM PUBLISHER]

This paper proposes an optimal design method of modular multilevel converter (MMC) levels to approach the reasonable compromise between accuracy and computational efficiency. The entire procedure is benchmarked by a Thévenin equivalent 451-level MMC model. First, the calculation method of the critical maximum simulation time step is proposed to faithfully represent each voltage level of the staircase waveforms. Second, the previously developed improved analytic hierarchy process is adopted to integrate the relative errors of all the main electrical parameters into one comprehensive relative error at each MMC level. Third, the steady state, ac, and dc transient state relative error results as well as the central-processing unit times of all models are normalized and curve fitted based on the benchmark model. Finally, the optimal MMC level is obtained by the plotted curves and the given subjective weights considering the accuracy and efficiency. And the effectiveness and robustness of the proposed method are validated by various simulation scenarios on PSCAD/EMTDC. [ABSTRACT FROM PUBLISHER]

A real-time realistic framework for synchronous generator loss of field (LOF) protection studies is suggested in this paper by using the real-time digital simulator, which allows the user to realistically model the generator field supply circuit. By using such framework, the performance of LOF protection algorithms can be comprehensively evaluated in the face of the various LOF events including the short circuit and two types of the open circuit events, while the open circuit occurrence cannot be studied in the conventional simulation programs. The obtained results demonstrate that the generator dynamics are significantly different in the face of various LOF failures and then all of them must be regarded to develop the new LOF protection algorithms. By using the suggested framework, the performance of some recently proposed schemes along with the conventional impedance and the admittance relays are comprehensively evaluated. The obtained results from applying the various LOF failures show that, against the conventional relays, the new schemes cannot detect all types of LOF failures and so, they do not have enough reliability. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional electrothermal numerical model of the medium voltage outdoor circuit breaker. The model was validated by heat run test performed under the conditions required by IEC 62271-1 and IEC 62271-100 standards, as well as some other specific requirements related to the breaker overload under low ambient temperature conditions and natural cooling. The purpose of this study was to build a numerical model of the medium-voltage circuit breaker that could be successfully applied for the redesign of the breaker for more demanding operating conditions with minimum physical test iterations. The numerical results obtained were found to be in a good agreement with experimental values having the average discrepancy of 3 K with the maximum below 5 K on busbars. [ABSTRACT FROM AUTHOR]

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 Thévenin 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. [ABSTRACT FROM AUTHOR]

This paper presents a new passivity enforcement technique for frequency-dependent network equivalents expressed as rational models. The main feature of the proposed technique is that only a few residues of the rational model are perturbed, so that the passivity enforcement procedure becomes computationally more efficient compared to existing methods. The proposed technique is verified on practical network cases. It is demonstrated that the accuracy of the perturbed model is maintained in frequency-domain fitting and time-domain simulations of transients. [ABSTRACT FROM AUTHOR]

In this paper, an extension to the multiwinding BCTRAN model is proposed for the study of low-frequency saturating transients in single-phase transformers. The conventional experimentally obtained BCTRAN (winding leakage) susceptance matrix is retrofitted with a previously missing experimentally obtained nonlinear (core magnetizing) model. The assembled model gives accurate results for transients in all terminals. The model parameters can be acquired from information available in the nameplate plus terminal tests without the need of detailed transformer design or construction information. Only needed are standard no-load and impedance tests plus a newly introduced saturation test. Very simple formulas are proposed to compute the parameters. Illustrative examples on how the parameters are computed are given for three transformers rated 1.8, 5, and 75 kVA. For model validation, laboratory inrush currents tests are carried out and compared with simulations using the EMTP-RV. The results show that the simulations and experimental results match very closely giving great confidence in the model correctness and parameter estimation method. [ABSTRACT FROM AUTHOR]

Low-watt compact fluorescent lamps (CFLs) may account for significant energy consumption of power distribution feeders in future years. This can lead to power-quality concerns because these devices consume highly distorted currents. In order to predict CFL harmonic current emissions into networks, CFL models capable of predicting these emissions accurately are being studied. On the other hand, these models require great computational effort in large-scale CFL penetration studies. This paper presents and discusses several approximate CFL models based on the harmonic-coupled admittance matrix model which reduces the computational effort while maintaining reasonable accuracy. The performance of the models is validated with CFL laboratory measurements. [ABSTRACT FROM AUTHOR]

This paper proposes a graph-based matrix level partitioning methodology for parallel electromagnetic transient (EMT) simulation. By partitioning the graph associated with the admittance matrix, an efficient bordered block diagonal matrix form is obtained, which is particularly suitable for parallel implementation. Even without the presence of distributed transmission lines, fully automatic system partitioning and parallelization of the simulation are achieved. The parallelized algorithm is implemented on a shared memory computer and assessed using two scalable test cases. The first involves an underground cable with many distributed parameter cascaded sections. The second is an interconnection of multiple instances of the IEEE 14-bus system, where only lumped transmission-line models are used. The tests show that EMT simulation can be significantly accelerated. The scalability is tested with up to 64 cores. [ABSTRACT FROM PUBLISHER]

With the increasing penetration of renewable energies in modern power grids, large amounts of voltage source converters (VSCs) have been installed, resulting in many new transient issues. Electromagnetic transient (EMT) simulation plays an essential role in investigating and solving the issues. However, simulation efficiency plunges when object grids contain multiple VSCs, because each switching event incurs modification or re-decomposition of the network matrix in traditional EMT programs, which is very time-consuming. Thus, this paper proposes a VSC model represented by pulse voltage-current source pairs. Accordingly, a unidirectional loosely-coupled solving algorithm is designed. Synthetically, the authors propose a novel EMT simulation approach adaptive to systems with multiple VSCs. The proposed approach keeps the computational network invariable while sufficiently considers detailed switching events, thereby significantly improving the simulation efficiency of the EMTP program without precision loss. [ABSTRACT FROM AUTHOR]

Fast front pulses from lightning and switching conditions produce transient overvoltages and dielectric stresses that can result in premature deterioration or failure of transformer windings. Predicting these conditions in new transformer designs requires the implementation of internal winding models. This paper analyzes the accuracy and performance of different transformer winding models available in the literature, by means of comparisons with time- and frequency-domain measurements on a 2000-turns disk-type winding prototype, as well as evaluation of the computer time needed by each model to perform the corresponding simulation of the same prototype. The results show that including the frequency dependence of the model parameters is a decisive factor to accurately reproduce the measurements. They also show that a lumped parameter model described in a turn-by-turn basis can provide accurate results and requires shorter simulation time than a distributed parameter model. [ABSTRACT FROM AUTHOR]

The emerging voltage source converters (VSCs) such as hybrid cascaded multilevel converters (HCMCs) are promising converter technologies which enable higher converter efficiency, compactness, and DC fault resilience for high voltage direct current (HVDC) transmission. However, the large number of switching events due to the converters’ submodules introduces a heavy computational burden for electromagnetic transient (EMT) simulations. Efficient and accurate EMT-type converter models play a vital role in the control and design of HVDC converters. Several computationally efficient models for the HCMCs are proposed in this paper, including the detailed equivalent model (DEM) and several average value models (AVMs) of varying accuracy. Additionally, a combined model is proposed which allows the users to switch among the DEM and AVMs during dynamic simulations. The proposed models are validated against the DEM for dynamic transients. The simulation results demonstrate good modeling accuracy of the proposed models. The AVMs are also shown to significantly improve simulation efficiency compared to the DEM, which is very desirable especially for HCMCs with a large number of submodules. [ABSTRACT FROM AUTHOR]

The large number of switching elements in the modular multilevel converter (MMC) is a challenging problem when modeling the MMC-HVDC systems for the computation of electromagnetic transients. The modeling complexity increases even further when a multiterminal (MT) MMC-HVDC system is used to integrate offshore wind farms (OWFs) with power-electronics-based wind energy converters, such as doubly fed induction generators (DFIGs). This paper compares modeling accuracy and computational performances for various combinations of MMC and OWF models. Onshore and offshore ac fault simulations are performed for an OWF system composed of DFIG-type wind turbines and connected to a practical ac grid through an MT MMC-HVDC system. The OWF system model includes the detailed representation of the offshore collector grid and the associated overcurrent protection. The offshore MMC controls include an offshore fault current limiter and fast OWF power generation reduction-based fault-ride-through function. [ABSTRACT FROM PUBLISHER]

This paper presents a methodology for the central-processing unit/field-programmable gate-array (FPGA)-based real-time simulation of a two-terminal MMC-HVDC of up to 501 levels using a detailed equivalent model. The proposed modeling approach is validated using case studies of 101-level and 501-level multilevel modular converter setups. FPGA-based models are designed using low-latency custom-made floating-point operators. The FPGA model is entirely reconfigurable in terms of the number of submodules per arm, as well as circuit parameters on an individual submodule basis. Real-time simulation performance is demonstrated in single-rate and multirate simulation environments and under various operating conditions. Limitations to the detailed equivalent model are identified and discussed. [ABSTRACT FROM PUBLISHER]

A methodology based on computer simulations and aiming to estimate the lifespan of transformer windings after the occurrence of short circuits is presented in this paper. The Von Mises and fatigue criteria are employed to determine the failure proximity of the windings. The obtained results contribute to the evaluation of the influence of electromechanical effects in transformer windings and to the determination of the number of short circuits that a transformer winding can support. The simulation results may also be employed in the design of transformers and failure diagnosis, to increase the security margin against mechanical failures. [ABSTRACT FROM PUBLISHER]

This paper proposes a new method of decoupling and subdividing electrical circuits, containing power-electronics devices, in order to achieve fast and accurate real-time simulation. In this technique, each state variable can be discretized using different discretization methods. Combining implicit and explicit ODE solvers, state-space equations are decoupled while remaining accurate and stable. Unlike most traditional decoupling techniques previously proposed, the proposed one does not require artificial delay or supplementary states to be added in order to decouple the system. Furthermore, this technique is meant to be implemented with commercially available simulation software. By doing so, a large and complex circuit containing several hundreds of state variables can be easily and accurately simulated with minor modification to the existing models. Finally, stability and accuracy of the proposed technique are thoroughly demonstrated in a numerical example during steady state and under faulty conditions. [ABSTRACT FROM PUBLISHER]

Electromagnetic transient-type (EMT-type) programs solve nodal analysis or modified-augmented-nodal-analysis (MANA) formulation-based power system network equations (PSNE). The PSNE coefficient matrix can be either constant or time varying depending on the utilized synchronous machine (SM) model. Therefore, a computational efficiency comparison for the SM models requires accounting for the refactorization scheme and the utilized sparse matrix solver (SMS). In addition, MANA formulation does not require or force admittance model usage and enables flexibility while representing the SMs in PSNE. This paper compares computational performances of various SM models for a practical case and accounts for the refactorization scheme, the utilized SMS, and the SM representation in MANA formulation. [ABSTRACT FROM PUBLISHER]

Nowadays, high voltage circuit breaker (CB) simulations are mostly based on Computational Fluid Dynamics (CFD) models. Such simulations require significant computer resources. An alternative approach is to use enthalpy flow models, which do not use space discretization of the interrupter unit chambers and valves. Gas flow is calculated based on state of gas in adjacent chambers and valve settings. However, the valve shape has significant influence on the effective flow cross section between chambers. Therefore, in order to ensure correct simulation results, it is necessary to determine the correct values of discharge coefficients for all valves in the interrupter unit of a circuit breaker. In this paper, the discharge coefficients were determined by combining a series of CFD and enthalpy flow simulations for each valve in the interrupter unit. After that, discharge coefficients are used as input for further simulations based on the enthalpy flow model. This way, benefits from both models are combined: more precise gas flow calculation and faster simulations. The proposed novel approach is validated in a high-power laboratory by pressure measurements on a 420 kV 63 kA self-blast circuit breaker. [ABSTRACT FROM AUTHOR]

Power system transient analysis relies on the deployment of models with ever-increasing accuracy that represents the system's frequency-dependent components with respect to the phenomena being scrutinized. A key issue in this context is the construction of a model yielding passive properties for each system component. Such properties are commonly compromised by corrupting noise in measurements that serve as input to the computation of blackbox models. In addition, model passivity could be further compromised during parameter estimation. This paper undertakes the task of developing a proposal to build an optimization methodology based on linear matrix inequalities (LMI-based) which is intended for obtaining an optimal, passive, blackbox model for a n-terminal power transformer. The resulting model can be further realized as a circuit representation in order to simulate the transformer dynamics in an Eletromagnetic Transient program (EMT type). The results derived from two operating power transformers are later provided to confirm how effective the procedure herein proposed is. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

The behavior of a grounding system can be predicted by using either the electrical equivalent circuit models or electromagnetic computation. Despite its advantages over the latter, the equivalent circuit model fails to accurately predict the behavior under transient conditions due to the absence of two key factors, namely: 1) the current rate-of-rise and 2) soil ionization. This paper proposes a method to enhance the performance of the equivalent circuit model by taking into consideration of both mentioned factors. It is discovered that by using the proposed method, the estimated values of R and L of the equivalent circuit model are improved. The computed inductance dynamically changes with the change in the lightning current parameters, thus improving its accuracy for all current rate-of-rise conditions. The soil ionization effect is implemented as recommended by CIGRE, and this further improves the accuracy of the model. As a result, the voltage response of the model becomes more accurate and comparable to the electromagnetic computation results. Another important feature of the proposed model is that it can be directly applied or connected to power system equipment. Thus, an accurate grounding system effect on the transient performance of key power equipment, such as surge arresters, can be obtained. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

The computation of the electromagnetic transients in a power transformer with nonlinear material using the finite element method (FEM) is so dense that the traditional nonlinear solver employing the Newton–Raphson method can hardly execute in real time. In this paper, we emulate the finite-element computation of electromagnetic transients of a transformer in real time for the first time. The transmission line modeling (TLM) method employed in the FEM successfully decoupled the nonlinear elements from the linear network so the nonlinearities could be solved individually, which is perfect for parallel processing. The parallelism of the TLM-FE solution is sufficiently explored and realized on a field-programmable gate array with deep data pipelining, and the implementation can execute in real time and provide detailed field information of the transformer during the transients. The proposed noniterative field–circuit coupling enabled the transformer to interface with an external network and the comparison with commercial FEM software proved the accuracy and computational efficiency of the real-time FE model. [ABSTRACT FROM PUBLISHER]

The model of a modular multilevel converter (MMC) determines the extent of critical circuit information that electromagnetic transient simulations can reveal. In this paper, two MMC models are proposed for efficient real-time hardware-in-the-loop (HIL) emulation on the field-programmable-gate-arrays (FPGA). The nonlinear switch-based model employing the insulated-gate bipolar transistor (IGBT) dynamic curve-fitting model considers factors affecting its transient performance so that device-level behavior such as power loss and junction temperature can be reproduced accurately in the electro-magnetic-thermal simulation of a power converter for its design evaluation. Meanwhile, regarding the MMC submodule as a transmission line stub achieves faster computation speed and enables the formation of a hybrid arm to save FPGA hardware resources. As the large network that the MMC presents is burdensome for real-time execution with a small time-step, circuit simplification based on partitioning and merging is conducted. Hardware implementation of a three-terminal high-voltage direct-current system containing an MMC-based dc–dc converter is carried out and the efficacy of proposed models is validated by comparing HIL emulation results with the offline simulation tool PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

In electromagnetic transient (EMT) simulation, 80–97% of the computational time is devoted to solving the network equations. A key observation is that the sub-matrix representing the interaction between two far-away groups of buses is usually sparse and can be approximated by a low-rank matrix. Based on this observation, we propose a novel low-rank approximation method which permits ${O(N \log N)}$ -time matrix-vector multiplication for each network solution time step. Comprehensive numerical studies are conducted on a 39-bus system and a 179-bus system from the literature, and large cases created from the two systems. The results demonstrate that the proposed approach is up to $2.8\times$ faster than the state-of-the-art sparse LU factorization based network solution, without compromising simulation accuracy. Since our low-rank approximation is highly parallelizable, further speedup may be possible. [ABSTRACT FROM AUTHOR]

White-box transformer models are used by transformer manufacturers during the dielectric design of windings. The models are often based on constant parameters (RLCG matrices) with the high-frequency losses accounted for by a scaling of the dc resistance (k-Factor). We show an efficient procedure for interfacing such models with Electromagnetic Transients Program (EMTP)-type circuit simulators via state equations and a Norton equivalent. The approach makes no approximations except for the discretization in the time domain. Diagonalization is utilized for achieving high computational efficiency. Proprietary information about internal voltages is optionally hidden from the user. Internal surge arresters are handled by the EMTP circuit solver by declaring their connection points as external nodes. The model interface includes automated initialization from 50/60-Hz initial conditions. The proposed interfacing capability permits manufacturers to apply their models in complete network simulations, and to share their models with users. [ABSTRACT FROM AUTHOR]

The effect of splitter plates (SP) on current interruption at medium voltage (MV) level is theoretically investigated in the framework of Mayr's arc model, which is generalized to take into account the electrode fall voltage, V0, of the SP. The model is analytically solved in the current zero (CZ) region where the current (before CZ) and the voltage (after CZ) can be linearized with respect to time. The current turns out to be successfully interrupted if the total electrode fall voltage, NV0, for N − 1 SP plus contact electrodes, is larger than twice the transient recovery voltage, ${\boldsymbol{U}} \approx {\dot{\boldsymbol{U}t}}$ , at the characteristic arc decay time, t = τ, after CZ: ${\boldsymbol{N}}{{\boldsymbol{V}}_0} > 2{\dot{\boldsymbol{U}\tau }}$. For ${\boldsymbol{N}}{{\boldsymbol{V}}_0} < 2{\dot{\boldsymbol{U}\tau }}$ , an additional thermal condition must be satisfied, where also the current rate, ${\dot{\boldsymbol{I}}} = {\boldsymbol{\ dI}}/{\boldsymbol{dt}}$ before CZ, and the arc cooling power, K, are involved. The intuitive results lead to a simple understanding of the electrical effect of SP on current interruption at MV and serve as an initial design rule for the number of SP in different gases. [ABSTRACT FROM AUTHOR]

Domain decomposition of the network conductance matrix is one of the efficient approaches to solve large-scale networks in parallel, wherein the most commonly-used non-iterative method is the Schur complement (SC) method. However, the SC method could not obtain the network conductance matrix inversion directly, and the computational cost will increase fast when the overlapping domain expands. In this work, a novel Linking-Domain Extraction (LDE) based decomposition method is proposed, in which the network matrix is expressed as the sum of a linking-domain matrix (LDM) and a diagonal block matrix (DBM) composed of multiple block matrices in diagonal. Through mathematical analysis over LDM, one lemma about the nature of LDM and its proof are proposed. Based on this lemma, the general formulation of the inverse matrix of the sum of LDM and DBM can be found using the Woodbury matrix identity, and based on the formulation the network matrix inversion can be directly computed in parallel to significantly accelerate the matrix inversion process. Test systems were implemented on both the FPGA and GPU parallel architectures, and the simulation results and speed-ups over the SC method and Gauss-Jordan elimination demonstrate the validity and efficiency of the proposed LDE method. [ABSTRACT FROM AUTHOR]

Transformer manufacturers make routine use of white-box detailed transformer models for ensuring that the transformer will pass the lightning impulse test. For use in general simulation studies, the model should additionally be multiphase and properly reproduce the transformer's input impedance characteristics and voltage ratios at 50/60 Hz. One challenge in such general modeling scope is to properly represent the frequency-dependent damping of the transformer's many resonances. In this work, we show how to properly include empirical damping factors in a multiphase admittance-based formulation of the state-equations. It is shown that the substitution of the real part of the state matrix eigenvalues causes some undesired changes to the model's behavior at lower frequencies, but this deficiency is mitigated by a correction to the output matrix. The resulting model can be directly included in EMTP-type simulation programs via a companion model, or via a terminal model with an add-on model for optional calculation of selected internal node voltages. Application of the modeling approach to a single-phase three-winding transformer demonstrates its merit in terms of accuracy and efficiency. Finally, the limitations of the model are discussed regarding accuracy and applications scope. [ABSTRACT FROM AUTHOR]