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This work proposes a fully circuit-based method for modelling electrical transformers. This method not only offers the advantages of circuit-based methods and can be implemented in electromagnetic transient (EMT) type software, but it can also provide a detailed representation of transformers, comparable to the finite element method (FEM). The proposed method enables a detailed geometrical modelling, as well as representation of magnetic flux paths and consideration of iron core saturation. It can be implemented in EMT-type software to see the effect of power networks on transformers. In addition, the proposed method can represent internal faults in transformers. The problem is constrained to a 2-D domain, which is often used in FEMs to represent the magnetic behavior of power equipment. Finite element analysis based on ANSYS Maxwell is used to verify the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the validity of two extended transmission line approaches proposed for calculating the ground-return impedance and admittance of an underground insulated cable is evaluated taking as reference a full-wave approach based on the 3-D finite-difference time-domain (FDTD) method. The transient responses of an underground cable with realistic radius are calculated for a wide range of soil resistivities and cable lengths. It is shown that the extended transmission line approaches lead to transient waveforms in good agreement with the FDTD method even for relatively short cables and high soil resistivity. The limitations of a traditional formulation that neglects the influence of the ground-return admittance on the calculation of the cable parameters are also demonstrated. Overall, the results confirm the accuracy of the newly-proposed expressions for the calculation of underground cable parameters. [ABSTRACT FROM AUTHOR]

This paper presents a simple yet effective method for locating faults in radial distribution networks where impedance-based methods are known to have limitations, especially in the presence of inverter-based power sources (IBPS). The proposed approach utilizes the Discrete Wavelet Transform (DWT) to capture the first arrival times of the fault-generated traveling waves. It is assumed that a digital fault recorder (DFR) exists at the terminal node of every lateral, as well as the beginning and end of the main feeder. The detailed derivation of the fault location method is presented, and illustrative fault scenarios are simulated to experimentally verify the proposed algorithm's performance under very diverse conditions. It is shown that the proposed approach performs successfully irrespective of the unknown fault impedance, inception angle, and type. [ABSTRACT FROM AUTHOR]

This application paper proposes a practical solution for transmission line records time synchronization based on the analysis of traveling waves (TWs) launched by internal faults, or by external events in the vicinity of the monitored line. Aiming on field applications, procedures that can be carried out by using commercially available TW digital recorders (TWDRs) are presented, allowing a practical computation of a synchronization factor which is used to align local and remote time references. Manual procedures are described and guidelines for the implementation of an automated scheme are presented. To evaluate the proposed procedures, the Alternative Transients Program (ATP) is used to generate realistic transmission line fault records, which are played back into real TWDRs. The obtained results show that the proposed solution is feasible, easy to apply in the field and reliable, being useful for multi-terminal records evaluation when no common time reference is available. [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]

This paper presents a novel leakage model for transformers that includes losses. This new model is physically based (topological) and it is possible to connect it to a topological core model without using any fictitious windings. The methods to calculate its parameters from standard test data and from design data are detailed within the paper. The results show that the new coupled leakage model with losses is able to match exactly the test report, when using standard test data. Preliminary investigations show that the results are very close to measurements, when using design data. [ABSTRACT FROM AUTHOR]

This paper proposes a set of fitting features that enables identifying propagation function of cables accurately in the form of multi-delay rational transfer functions while maintaining reduced order of approximation. Frequency domain partitioning and adaptive weighting techniques are applied directly in phase domain for the evaluation of poles and residues simultaneously to ensure the precision of fitting of all entries including the low-magnitude off-diagonal elements. The objective is not only to obtain a precise fitting in phase domain but also to account for intrinsic modal decomposition so that integration errors in time domain are not magnified. The order of approximation is considerably reduced by post-processing the fitting using the balanced realization technique. When the proposed fitting approach is combined with a precise integration technique in time domain, it leads to accurate evaluation of transients as demonstrated in this paper, eliminating the spurious oscillations or numerical instabilities that may be encountered in the universal line model regardless of the integration or interpolation technique. [ABSTRACT FROM AUTHOR]

This paper proposes a technique to approximate a multi-layer earth structure by a homogeneous conductivity soil in ground return impedance calculations. An equivalent real-valued conductivity parameter is obtained, which can be used with reasonable accuracy in a simpler expression or in commonly available EMTP software, such as the Line Constants routine of the Alternative Transients Program (ATP). Several actual soil models are evaluated at frequencies ranging from 1 Hz to 2 MHz. Results show that the proposed method is accurate for modeling most power system problems, from steady-state conditions to transients commonly verified in electrical systems. The proposed expression is easy to use and introduces a considerable performance gain in terms of floating-point operations, compared to the analytical formulation of the general multi-layer soil structure. [ABSTRACT FROM AUTHOR]

Modern power systems face several problems at frequencies above the range of traditional stability studies due to the increasing penetration of power electronic devices. This phenomenon has been recently referred to as electromagnetic transient stability and is a growing issue in systems with power electronic converters at any power and voltage level, such as FACTS, high-voltage DC, interfaces for grid connection of renewable energies, custom power devices for power quality enhancement, among others. The study of power systems stability is usually carried out by simulation tools that represent the power system through phasor models. However, due to the faster dynamics of modern systems, the harmonic interaction among the controllers, converters, and electric power components, recent research results suggest that some stability analyses should be conducted with models suitable for wider frequency ranges, e.g., electromagnetic transient models. This paper reviews the use of frequency domain methods to analyze the influence of the modeling approach of passive power components on the results of electromagnetic transient stability studies. [ABSTRACT FROM AUTHOR]

Coupling capacitor voltage transformers (CCVTs) are the predominant devices used in high voltage systems to provide scaled-down voltage signals for metering, protection, and control devices. The performances of these devices are subject to errors due to the transient behavior of CCVTs, so that the use of CCVT digital models is essential for studying power systems in order to predict how the equipment dynamics affect protective relaying performances. In this review paper, the authors put together complete information regarding five realistic CCVT digital models available in the literature and perform a detailed sensitivity analysis of their magnitude and angle frequency responses, as well as their influence on phasor estimation, distance protection, and fault location techniques. [ABSTRACT FROM AUTHOR]

This paper analyses low-cost techniques for rural electrification based on the use of insulated shielding wires of extra-high-voltage transmission lines. The main idea is to use the line capacitive coupling as an auxiliary power supply to remote rural systems. The insulated shielding wire (ISW) will behave as a capacitive voltage divider, promoting low voltage on it. We introduce a comparison of different low-cost electrification methods used over the last years and present a careful analysis of different topologies, which have a major impact on rural voltage regulation. A transient study was implemented to observe the behavior of both the transmission system and the rural feeder under typical switchings. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of obtaining optimal black-box models of n-terminal power transformers for transient studies. We use actual transformer data to demonstrate that a transformer model endowed with both passivity and symmetry can be optimally achieved only if the corresponding constraints are formulated and simultaneously included in the parameter estimation problem as opposed to enforcing them independently as two distinct post-processing model adjustments. [ABSTRACT FROM AUTHOR]

This paper presents a new simulation approach based on the functional mock-up interface standard for parallel and multistep simulation of electromagnetic transients in power grids with computationally expensive control systems. The control systems are represented by slave subsystems, which are decoupled in memory from the power network and encapsulated in functional mock-up units. The simulation modes are either asynchronous or synchronous. In the asynchronous mode, the subsystems are simulated in parallel, whereas in the synchronous mode, the simulation of each subsystem is executed in a sequential multistep environment. Considerable computation time gains in both modes have been observed in power system protection studies on large-scale networks with accuracy properly maintained. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to perform application tests in protective relays. It is based on using the Gabriel graph to select, from a large number of events generated by a Monte Carlo-based procedure, a smaller subset that is able to predict the relay performance without compromising the quality of the estimator. The proposed methodology is successfully applied to test the behavior of differential protective relays in two situations: turn-to-ground faults and transformer energizations. In both cases, the proposed methodology significantly reduces the number of tests required to predict the success rate of the tested relays for a desired confidence level and variance. It is observed that the efficiency of the method increases as the estimated success rate of the relay increases. This means that if the estimated success rate is high, the proposed methodology leads to larger reduction in the number of events that are actually necessary to test the relay. The validity of the proposed methodology is demonstrated by means of tests performed with an actual protective relay. [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]

This paper investigates the numerical accuracy of currently employed methods for electromagnetic transient simulation with power electronics. Existing tools often employ the second-order accurate trapezoidal method for numerical integration. However, solution techniques employed to facilitate ideal power-electronic switches do not always preserve this second-order accuracy at switch events. As a result, the step size required to achieve the desired level of accuracy is often smaller than expected, affecting simulation speed. Therefore, this paper aims to assess and improve the tradeoff between step size and accuracy. First, currently employed solution techniques are reviewed by deriving asymptotic estimates of the rates at which approximation errors decrease as the step size reduces. Afterward, a benchmark method is proposed that preserves second-order accuracy at switch events. The tools EMTP-RV and PSCAD are compared with this benchmark method for elementary circuit examples. The results demonstrate the potential to improve accuracy, by several orders of magnitude in some cases, without increasing the number of linear systems to be solved. [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]

In this paper, we present a new black-box arc model that was validated using tests with short-line fault interruption of high-voltage circuit breakers. This new arc model shows superior performance compared with four types of existing black-box arc models. Black-box arc models are widely used to simulate current and voltage waveforms during the interruption process. Applied together with arc parameters, they determine arc conductance and interruption behavior. In this study, the arc parameters of each arc model are derived from an optimization approach in a defined time interval to minimize the difference between the measured and simulated arc voltages. The black-box arc models with optimized arc parameters are applied to a simplified circuit for short-line fault simulation, and the model accuracy of the interruption prediction and waveform fitting is quantitatively scored. [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]

Cross-bonded cable models are compared against their versions with normal bonding (no bonding) for propagation characteristics, frequency, and time-domain responses. Contrary to no-bonding cables, coaxial modes cannot propagate in cross-bonded cables. Instead, intercore modes propagate, being always accompanied by intersheath modes. The latter property cannot be observed if a cross-bonded cable is modeled with its homogeneous equivalent. It is shown that sheath cross-bonding induces intersheath modes circulating between grounding points and impacts on the cable response at resonant frequencies. Alternate models for cross-bonded cables, including both homogeneous and nonhomogeneous equivalents, are compared based on frequency- and time-domain responses, including a field test on a 225 kV 64 km cable with 17 major sections. [ABSTRACT FROM PUBLISHER]

Transformer terminal equivalents obtained via admittance measurements are suitable for simulating high-frequency transient interaction between the transformer and the network. This paper augments the terminal equivalent approach with a measurement-based voltage transfer function model which permits calculation of voltages at internal points in the regulating winding. The approach is demonstrated for a single-phase three-winding transformer with its tap setting in the middle position. Three internal points in the regulating winding are included that represent the midpoint and the two extreme ends. The terminal equivalent modeling makes use of additional common-mode measurements to avoid error magnifications resulting from the ungrounded tertiary winding. The final model is used in a time-domain simulation where ground-fault initiation results in a resonant voltage build-up in the winding. It is shown that the peak value of the resonant overvoltage can be higher than during the lightning impulse test, with unfavorable network conditions. Additional measurements show that the selected tap position affects the terminal behavior of the transformer, changing the frequency and peak value of the lower resonance point in the voltage transfer between windings. [ABSTRACT FROM PUBLISHER]

A frequency-dependent transmission line model for multi-scale simulation of diverse transients over a wide range of frequencies is developed, implemented, and validated. It makes use of the concept of frequency-adaptive simulation of transients in which the Fourier spectra are adaptively shifted in the frequency domain to reduce the discretization time-steps in the time domain. The transients are modeled through dynamic phasors comprising the real and imaginary parts of analytic signals to facilitate the frequency shifting. In the proposed line model, all mathematical operations such as numerical recursive convolutions are, therefore, expressed in terms of analytic signals. A modal decomposition is performed to attain decoupled modes for the multi-phase case. The transition from the representation of electromagnetic traveling waves with time-steps below the wave propagation time to the tracking of slower electromechanical transients at time-steps above the wave propagation time is achieved by the automatic insertion of a $\pi$-segment to represent the galvanic coupling within one time-step. Accurate and efficient simulation of both electromagnetic and electromechanical transients within a simulation run is so supported. The validation is verified through comparison with a staged field test covering the diverse transients of line energization, transient recovery voltage, and steady state. [ABSTRACT FROM PUBLISHER]

Electromagnetic time reversal (EMTR) has been shown to be an efficient method for locating faults in ac and dc power grids. In the available literature, the back-propagation medium has been considered to have identical losses as the direct-time medium. However, the telegrapher's equations describing the traveling wave propagation are time-reversal invariant if and only if inverted losses are considered in the back-propagation phase. This paper presents an analysis of the impact of losses on the performance of the EMTR-based fault location method for power networks. In this respect, three back-propagation models are proposed, analyzed, and compared. It is shown that a lossy back-propagation model, for which the wave equations are not rigorously time-reversal invariant, results in accurate fault locations. Finally, an EMTR fault location system based on the lossy back-propagation model and a fast electromagnetic transient simulation platform is developed and its performances validated. [ABSTRACT FROM PUBLISHER]

This paper proposes an equivalent winding capacitance network for the transformer low- and mid-frequency transients analysis, based on the standard test data. The proposed model can accurately represent the positive- and zero-sequence winding capacitances. Therefore, it is physically correct and more accurate than the existing modeling approaches. Based on the winding voltage profile, the equivalent winding capacitances are analytically determined using the measured capacitances in the dielectric test, winding connection, and vector group which are available in the transformer standard data. The calculated capacitances are validated with the time-domain simulations. A general method based on complex turns ratio and complex ampere's law is also proposed to obtain the equivalent winding capacitance seen from the energized winding and thereby determine the lumped capacitances to be connected at the terminals of the transformer model. The methods to estimate the missing parameters in the standard data are also discussed. Furthermore, the differences with the existing modeling approach in estimating the winding capacitances and the analysis of transient phenomena are highlighted through the analytical solutions and time-domain simulations. [ABSTRACT FROM AUTHOR]

In June 2014, the French transmission system operator (Réseau de Transport d'Électricité—RTE) performed a field test on a 64 km 225 kV XLPE underground cable. This paper presents the validation of the cable model from field test measurements. In the first part, the cable impedance and admittance calculations are compared to the per-unit-length parameters evaluated from field test results. In the second part, the field tests are simulated in an Electromagnetic Transients Program (EMTP) to validate the cable model. [ABSTRACT FROM PUBLISHER]

This paper proposes a startup sequence for a modular multilevel converter (MMC) HVDC-connected offshore wind farm (OWF) and demonstrates how it can be simulated using an electromagnetic transient-type tool. The objective is to analyze inrush currents of transformers and cables (HVAC and HVDC). Modeling accuracies and computational performances are examined using three existing modeling methods for the MMCs. [ABSTRACT FROM PUBLISHER]

This letter presents a closed-form expression for ground return admittance for a system of underground cables. It is based on the approximation of the infinite integral found using a quasi-TEM (transverse electromagnetic) formulation of the electromagnetic field. The results indicate that the frequency behavior of the closed-form expression provides useful responses up to a few megahertz, thus being a suitable alternative to the numerically challenging infinite integrals. The agreement of the closed-form results and those obtained using the infinite integrals is very good regardless of the ground conductivity considered. [ABSTRACT FROM AUTHOR]

This two-part paper is intended to clarify definitions in dual transformer modeling that are vague, provide accurate modeling guidelines, clarify misconceptions about numerical instability, provide a unified dual model for a specific type of transformer, and introduce new paths of research to the power systems/electrical machinery community for low-frequency transients. Part I discussed the topology of duality-based models and some important issues, such as the most common approaches to derive dual models and their variety, the equivalence of negative inductance and mutual couplings to represent the leakage inductance of three-winding transformers, and the numerical oscillations caused by the use of nontopological models. This part of the paper discusses and compares white-, gray-, and black-box models. The paper also reviews hysteresis models (static and dynamic) and highlights the differences between the air-core inductance and saturation inductance. The available dual models for the representation of the transformer tank are then presented. A unified and accurate model of a three-phase core-type transformer adequate for all low-frequency transients is presented. Finally, concrete guidelines are presented for the appropriate selection of the model topology and parameters for different low-frequency transient studies. [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]

A saturated core fault current limiter (FCL) essentially utilizes the dynamic and nonlinear magnetic behavior of steel cores to operate as a variable reactor. However, the nonlinear characteristic of magnetic materials has made modeling this unique device a difficult task. Hence, experimental measurements and finite-element method (FEM) analysis are the most common techniques used to characterize the transient behavior of the device. Both of these techniques, while accurate, cannot be used to analyze the transient electrical behaviour of FCLs in complex power systems, particularly when investigating power system switchgear behavior during fault events. FEM-based FCL modelling, despite its usefulness as a design verification tool, cannot be easily coupled to all electromagnetic transient programs that are in use today. This paper presents two modeling approaches to represent the saturated core FCL in transient network simulators: 1) the nonlinear reluctance model and 2) the nonlinear inductance model. Both models are implemented in pscad/emtdc and are validated by experimental results of a single-phase prototype saturated core FCL, where excellent agreement between the experimental and the modelling approaches is achieved. [ABSTRACT FROM PUBLISHER]

A mathematically rigorous framework combining diffusion map analysis techniques with simulation data from electromagnetic transient programs is proposed to characterize the collective dynamics of transient processes. The framework can be used to compress and analyze large and complex data sets obtained from transient simulations. Through this formulation, the structures that dominate the system response, and the global measurements that contribute most to this response can be directly calculated. The resulting coordinates can be correlated with the time scales of specific motion or be effectively used to extract spatiotemporal features of high-dimensional data. The application of the method is illustrated on both, electromagnetic transient simulations and transient stability data. Simulation studies reveal that diffusion-map data-analysis techniques generate accurate estimates of modal parameters even in the presence of measurement noise. [ABSTRACT FROM PUBLISHER]

This paper presents the development and validation of an accurate and computationally efficient wideband reduced-order dynamic equivalent model for the Type-3-based wind power plant (WPP). The proposed Type-3 WPP equivalent model reproduces the dynamic behavior of the WPP in response to an electromagnetic transient in the host power system and is composed of two parts: 1) a static frequency-dependent network equivalent model which represents the response of all passive components of the WPP in a wideband frequency range, and 2) a dynamic low-frequency equivalent model that represents the aggregated dynamic model of the doubly-fed asynchronous generator (which is also referred to as doubly-fed induction generator) wind turbine generators, their local controls, and the WPP supervisory control. The proposed model significantly reduces the hardware/software computational burden and the computation time, as compared to the WPP detailed models, without compromising the accuracy of the simulation results. The proposed model is incorporated as a software module in the PSCAD/EMTDC environment and its computational efficiency and accuracy are verified based on comparing the results with those of a detailed model. [ABSTRACT FROM PUBLISHER]

Co-simulation opens new opportunities to combine mature electromagnetic transients (EMT) and phasor-mode (PM) solvers, and takes advantage of their respective high accuracy and execution speed. In this paper, a relaxation approach is presented, iterating between an EMT and a PM solver. This entails interpolating over time the phasors of the PM simulation, extracting phasors from the time evolutions of the EMT simulation, and representing each subsystem with a proper multiport equivalent when simulating the other subsystem. Various equivalents are reviewed and compared in terms of convergence of the PM-EMT iterations. The paper also considers the update with frequency of the Thévenin impedances involved in the EMT simulation, the possibility to compute the EMT solution only once per time step, and the acceleration of convergence through a prediction over time of the boundary variables. Results are presented on a 74-bus, 23-machine test system, split into one EMT and one PM subsystem with several interface buses. [ABSTRACT FROM PUBLISHER]

Switching of shunt capacitors can cause transient overvoltage. The voltages are traditionally evaluated with electromagnetic transients (EMT) simulation programs. It is a very time-consuming process mainly due to the need to convert a power-flow (or short-circuit) case to the EMT case. This paper proposes an idea to conduct capacitor switching studies directly inside commercial power-flow/short-circuit tools such as PSS/E, thus avoiding the data-conversion process. The idea is to conduct switching studies in the frequency domain. The frequency response of the study network is determined using the short-circuit solution engine of the host commercial software. This paper presents the theory, unique issues, and implementation details of the idea. The effectiveness of the proposed method is verified by comparing the results with those of the EMT simulations. [ABSTRACT FROM PUBLISHER]

This paper describes the application of a controlled switching device to energize a 500 kV/230 kV/46 kV, 1200 MVA autotransformer in Manitoba. The development of a detailed electromagnetic-transient (EMT) simulation model of the transformer formed the basis of the work described. The transformer model includes an accurate representation of hysteresis and remanance, which was validated using recorded waveforms and manufacturer data. This paper discusses a feasibility study conducted using this transformer model to evaluate the suitability of controlled switching to energize this transformer. A series of real-time hardware in the loop tests was conducted using a real-time simulator as part of precommissioning tests. The real-time simulation (RTS) tests and phase 1 of commissioning tests conducted in October 2014 showed that the controlled switching device would produce inaccurate residual flux estimates when it integrates the secondary voltage waveforms of a capacitive voltage transformer. Based on these RTS test results and EMT simulations, the installation of a wound potential transformer (PT) was recommended. This paper also discusses simulation studies conducted to manually program the controller until the PT was commissioned. During phase 2 of testing conducted in October 2015, a wound PT was commissioned and the controller was tested. The recorded waveforms showed good agreement with simulation results. The controller has accurately predicted residual flux and minimized inrush currents during transformer switching events. [ABSTRACT FROM PUBLISHER]

The objective of this two-part paper is to provide clarity to physical concepts used in the field of transformer modeling, to dispel common misconceptions regarding numerical instabilities, and to present unified modeling techniques for low-frequency transients. This paper focuses on proper modeling of nonlinearities (magnetizing branches) since these components are critical to determine the low-frequency behavior. A good low-frequency model should properly represent: normal operation, inrush currents, open and short circuit, out-of-phase synchronization transient of step-up transformers, geomagnetic-induced currents, ferroresonance, and harmonics. This paper discusses the derivation of electrical dual models from the equivalent (magnetic) reluctance networks and the direct application of the principle of duality. It is shown that different dual models need to be derived for different transformer geometries and the advantages and disadvantages of each method are discussed. This paper also compares double-sided versus single-sided dual models, and shows that the double-sided model is a more general approach. The mathematical equivalency of several leakage models (negative inductance, mutual coupling, and BCTRAN) is demonstrated for three-winding transformers. It is also shown that contrary to common belief, a negative inductance is not the source of numerical oscillations, but they occur due to the use of noncorrect topological models for representing the core. [ABSTRACT FROM PUBLISHER]

In this paper, the behavior of three-phase transformers in the presence of geomagnetically induced current (GIC) is investigated. The associated phenomena involve very slow transients, in the millihertz range, while representing significant magnitudes of even and odd harmonics of power frequency. As a result, the transformer response involves nonlinear and frequency-dependent effects. This paper considers the impact of variations in the transformer core construction and design parameters on its saturated behavior and the resulting reactive power absorption, when subjected to GIC. A detailed transformer model is described including air-gap and tank effects. The study results highlight significant parameters that can affect transformer reactive power and promote them as being important parameters for GIC studies. Furthermore, the transformer dynamics during the slow transient of the GIC variations and polarity reversal are discussed. [ABSTRACT FROM PUBLISHER]

This paper investigates the dynamic interactions of a modular multilevel converter (MMC) -based HVDC grid and its host ac system during ac-side disturbances. The HVDC grid is composed of five MMC stations that are interconnected through a network of cables and overhead lines. The ac grid includes ten turbine generators. The studies are conducted in the PSCAD platform, including the detailed models of the ac and dc subsystems. The reported case studies indicate that without the HVDC supplementary control functions and based on the conventional dq-frame control structure: 1) each MMC behaves as almost a fixed sink/source of power during the ac-side electromechanical transient oscillations; 2) the MMC-HVDC grid effectively improves dynamic interactions between ac subsystems that are connected only by the HVDC grid; 3) without appropriate provisions, the embedded MMC-HVDC grid can aggravate the transients of the host ac system, for example, interarea oscillations. The observations also contradict the widely accepted notion that even without supplementary controllers, the MMC-HVDC grid necessarily improves the dynamics of the ac system. The study results provide a comprehensive insight into the transient behavior of the MMC-based HVDC-AC grid. Such an understanding is essential to design the protection and control systems of the future HVDC-AC grids. [ABSTRACT FROM AUTHOR]

The passivity enforcement problem is always a key issue when estimating passive black-box models. Passivity has been broadly scrutinized in the literature and is known to yield stable time-domain simulation; thus, passivity is a much-desired model property which cannot remain an unmodeled effect. Many successful algorithms exist that accomplish the enforcement task by model parameter perturbation, with the caveat that the passivity violations to be suppressed are not large. This paper proposes a novel approach to address this issue. We propose four different mathematical formulations to preprocess the measurement of admittance parameters. Preprocessed data serve as inputs to parameter estimation algorithms to obtain passive models for power system applications. This approach is particularly adequate to use with model parameter perturbation methods. Three examples containing data of actual measurements illustrate the advantage of using the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper introduces a new frequency-dependent cable model for the simulation and analysis of electromagnetic transients. The model belongs to the traveling-wave class. The key feature of the proposed model is the correct representation of modal propagation function contributions in the phase domain. The challenge is in fitting modal contributions that are nonsmooth due to their eigenvectors. Since the nonsmooth behavior is associated with similar eigenvalues, the problem is solved by reducing the rank of the propagation matrix. The proposed new approach eliminates numerical instability problems that can be encountered in the universal line model. [ABSTRACT FROM AUTHOR]

Accurate knowledge of the per-unit length impedance of power cables is necessary to correctly predict electromagnetic transients in power systems. In particular, skin, proximity and ground return effects must be properly estimated. In many applications, the medium that surrounds the cable is not uniform and can consist of multiple layers of different conductivity, such as dry and wet soil, water, or air. We introduce a multilayer ground model for the recently proposed MoM-SO method, suitable to accurately predict ground return effects in such scenarios. The proposed technique precisely accounts for skin, proximity, ground, and tunnel effects, and is applicable to a variety of cable configurations, including underground and submarine cables. Numerical results show that the proposed method is more accurate than analytic formulas typically employed for transient analyses, and delivers an accuracy comparable to the finite-element method (FEM). With respect to FEM, however, MoM-SO is over 1000 times faster, and can calculate the impedance of a submarine cable inside a three-layer medium in 0.10 s per frequency point. [ABSTRACT FROM AUTHOR]

This letter proposes a two-stage fitting procedure for transmission line/cable functions in which low-frequency samples are exclusively considered. At the first stage, fitting is performed for a reduced band by excluding frequencies close to DC. Reducing the fitting range improves the numerical conditioning of the overall system of equations and relieves fitting. The second stage consists of finding a correction term for the out-of-band samples close to DC. The procedure, when used with the recently introduced frequency-dependent cable model approach, allows modeling transmission lines and cables with improved fitting precision at low frequencies. Overall, the new approach is called frequency-dependent model (FDM) with DC correction, i.e., FDM/DC. It can be used to complement the prevailing universal line model in two ways: for reducing the integration errors due to unbalanced fitting and for improving the precision of DC response. Two examples are provided to demonstrate the utility of the new approach. [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]

This paper introduces a new realization for a phase-domain line model and proposes methodologies to increase its numerical performance. The new realization is based on the management of complex poles that may arise when deriving rational models by means of second-order states. The accuracy and numerical performance of the proposed realization is assessed through its application to representative examples and the comparison against other methodologies. It is demonstrated that the proposed methodology can increase substantially the numerical efficiency of the model. [ABSTRACT FROM PUBLISHER]

This paper contributes to the accurate and efficient computation of control system equations in electromagnetic-transient simulation tools. The proposed approach is based on the formulation of a reduced rank Jacobian matrix in a fully iterative Newton method. In addition, this paper compares the accuracy and efficiency for the proposed method's variants, including a hybrid approach with a fixed-point solution. [ABSTRACT FROM PUBLISHER]

In this paper, a critical review of existing methods to couple magnetic circuits to electric circuits is provided and explained using a two-port element called mutator. In order to couple magnetic circuits in electromagnetic transients-type programs, a new implementation of mutators is described, which uses the commonly available coupled series R-L branches. The practical case of a single-phase two-winding transformer is studied, and the results show that the new method is equivalent to the dual (inductive) model. However, it is concluded that the new method is more interesting than duality to couple large 3-D topological models (transformers, lines, motors, etc.), because it avoids difficulties of duality associated with nonplanar magnetic circuits. [ABSTRACT FROM PUBLISHER]

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 availability of accurate and broadband models for underground and submarine cable systems is of paramount importance for the correct prediction of electromagnetic transients in power grids. Recently, we proposed the MoM-SO method for extracting the series impedance of power cables while accounting for the skin and proximity effects in the conductors. In this paper, we extend the method to include ground return effects and to handle cables placed inside a tunnel. Numerical tests show that the proposed method is more accurate than widely used analytic formulas, and is much faster than existing proximity-aware approaches, such as finite elements. For a three-phase cable system in a tunnel, the proposed method requires only 0.3 s of CPU time per frequency point, against the 8.3 min taken by finite elements, for a speed up beyond 1000 X. [ABSTRACT FROM PUBLISHER]

Based on an enhanced topological representation of the transformer core, flux air paths, and tank, a duality-based transformer model is proposed for low and mid-frequency transients analysis. In the developed transformer model, the core and tank iron are represented based on a frequency-dependent hysteresis model. The winding capacitances and the frequency dependency of the winding resistance are also incorporated in the developed model. Furthermore, a detailed model is developed for the air gap and tank, and the corresponding average equivalent is presented which is more appropriate for extracting the parameters from the measurement. In addition, the nonuniform air gap and the fringing flux effects are taken into account, and an approach is presented to obtain the corresponding parameters. The developed models also include the equivalents of the tank magnetic shield and the structural parts. Part II of this paper provides validations and further simulation results. [ABSTRACT FROM PUBLISHER]

In this paper, a previously published model for the representation of the leakage inductance of multiwinding transformers is enhanced to support accurate calculations of low-frequency transients, including inrush currents, series ferroresonance, and geomagnetic-induced currents. The new circuit is obtained from the principle of duality and, therefore, is physically consistent. The unique characteristic of the improved model is that the very deep saturation behavior of the iron core is properly represented for each winding simultaneously (reversible model) without changing parameters. The hysteresis cycle and iron-core losses are also included. In addition to its reversible terminal behavior coupled with physical consistency, the proposed model can be built with circuit elements available in Electromagnetic Transients Program-type programs, and all of the parameters can be computed from terminal tests. The model is validated by comparing computer simulations versus laboratory measurements for three- and four-winding transformers. [ABSTRACT FROM PUBLISHER]