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This paper reports a practical challenge in Distributed Energy Resources (DER) operation: open phase detection. The paper presents a wide variety of naturally occurred open phase events recorded by power quality meters in DER commercial operations. The events demonstrate the complexity of open phase detection due to electrical and magnetic interphase couplings through transformer winding and core configurations. The coupling effect could recreate the missing phase in various patterns so that the DER control and protection systems or control room operators may not detect the anomaly for prolonged period of time. This paper shares experiences of timely DER open phase detection by using power quality data and suggests practical detection guidelines based on waveform signature analytics. The original field records provide credible benchmarking references for algorithm development to meet the new DER open phase detection requirement in the IEEE Stdandard 1547–2018 revision. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of the magnetic effects of steel tanks on different three-phase transformers. Removable steel tanks are designed and built for transformers with distinct sizes and core topologies. Corresponding tanks of nonmagnetic materials are also built to study the effects of tank material. Zero-sequence tests, open-circuit (no-load) tests, ferroresonance, geomagnetically induced current (GIC), and energization (inrush current) tests are performed on the transformers with and without tanks. The results indicate that steel tanks have a significant effect on the zero-sequence impedance, ferroresonance performance, GIC, and no-load losses in steady state, while the tank has no appreciable effect on inrush currents. [ABSTRACT FROM AUTHOR]

Ferroresonance occurrence is a source of damage, causing overvoltage on voltage transformer (VT) and isolators of the grid equipment. Some solutions are available to protect VTs from the ferroresonance overvoltage. However, they just act after the ferroresonance occurrence. In this letter, to prevent the occurrence of ferroresonance, a dc reactor-based protection device is introduced. Analytical studies and simulations by MATLAB/Simulink and Maxwell ANSYS demonstrate the capability of the proposed protection device as a VT ferroresonance inhibitor. Experimental results from a scaled-down laboratory prototype are also provided to verify the proposed solution. [ABSTRACT FROM AUTHOR]

This paper presents the challenges that the power converters with $dq$ -frame-based control confront when subjected to ferroresonance. This is mainly due to two main properties of the widely used $dq$-frame control systems. It is demonstrated in this paper that regardless of the phase-to-ground or phase-to-phase voltage measurement, the $dq$-frame control only responds to phase-to-phase voltage variations. Furthermore, the PI controllers, which are employed in conjunction with the $dq$ reference frame, can inherently only track dc references and reject dc disturbances. Consequently, a $dq$ -based PI controller can only respond to the positive-sequence phase-to-phase voltage variations, effectively. This, in turn, limits the disturbance mitigation capability of the power converter. This study investigates the impacts of the ferroresonance phenomenon on the control system response and the operating conditions of the power converters. Based on a droop-based $dq$ frame controller, the behavior of an electronically interfaced distribution generation system is studied, under various transient conditions. In spite of a promising performance under the load change and islanding scenarios, the $dq$-frame-based controller of the power converter fails to detect and respond to the voltage fluctuation and excessive overvoltages as a result of ferroresonance. [ABSTRACT FROM AUTHOR]

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]

An improved scheme for coupling electromagnetic transients programs with finite element magneto-dynamic field programs is presented. The proposed scheme uses the compensation approach to build up a strong coupling between domains, with no time delay. This permits to fully take into account the spatial field distribution in the magnetic device as well as eddy currents in the conducting materials. The scheme is developed starting with the field equations for the Cartesian plane and axisymmetric cases, which are combined with the reduced circuit equations. The solution of the simplified circuit-field system is achieved by an efficient sequence of time discretization followed by the iterative solution of the resulting nonlinear equation. The implementation of the scheme and its validation are discussed. The results show a very competitive performance of the new approach. [ABSTRACT FROM PUBLISHER]

The predictive power of transient ferroresonance simulations depends mainly on the accuracy and fidelity of the power transformer model used for simulating complete systems involving all relevant network components. This paper considers three ways of transformer iron-core modeling relevant for ferroresonance simulations that are presented in detail. The presented transformer models are suitable for the state-space form of differential equation systems that describe the ferroresonance effect. Before solving the obtained differential equation systems, their numerical eigenvalues were analyzed in detail. This eigenvalue analysis has revealed a very stiff nature of the obtained equation systems. The obtained equation systems are solved by using a A- and L-stable numerical differentiation formulas (NDF) numerical technique, with the aim of suppressing undesired numerical oscillations. The obtained numerical results are verified by comparison against the available experimental results. The presented analysis shows that the suggested transformer model based on a hysteretic core inductor provides the most accurate results in terms of voltage and current waveforms and their peak values during the steady-state and transient ferroresonance. The analyzed transformer core models can be implemented in the existing Electromagnetic Transients Program-type simulation tools by using a combination of the trapezoidal and proposed NDF2 method. [ABSTRACT FROM PUBLISHER]

The transformer model developed in Part I is validated based on the zero-sequence test data, a ferroresonance event, and the geomagnetically induced current (GIC) measurements. Various transformer core constructions, including single phase, three limb, five limb, conventional shell type, and seven-limb shell type are represented, based on the proposed transformer model. The simulation results show high accuracy of the proposed transformer model in representing the studied cases. The study reveals that the saturation of the transformers at a given GIC level is more severe than that predicted by the existing transformer models. Furthermore, the proposed transformer model clearly explains the reasons for the previously reported discrepancies between the GIC experimental and simulation results. The study also concludes that for an accurate transformer model, particularly for the three-limb core type, the detailed representation of the zero-sequence characteristic is an essential requirement. Such a characteristic can be obtained based on either the proposed approach of the paper or a zero-sequence dc excitation test in addition to the test data at the power frequency. [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]

Ferroresonance is one of the most destructive transient phenomena in power systems. This complex phenomenon involves the association of nonlinear magnetizing inductances and capacitances, and may be initiated in many different ways, which makes its characterization very difficult. This work links EMTP and MATLAB and presents some computer tools that have been developed for assessing ferroresonance behavior. These tools allow users to visualize 2-D and 3-D bifurcation diagrams which can be used for performing sensitivity analysis, predicting the phenomenon at different stages, and finding safety zones for power system parameter design. [ABSTRACT FROM AUTHOR]

Increased ratio error of capacitor voltage transformers (CVTs) has been recently encountered in several substations in Iran. The results of the performed diagnostic tests indicate that short-circuited capacitor elements, especially in the low-voltage capacitor, have increased the CVT error. In this paper, some simple and effective techniques are suggested to solve this problem. One of the proposed methods to compensate the increased error is utilization of an auxiliary voltage transformer (AVT), which does not require disassembling the CVT. The practical aspects of this method, its effects on the CVT transient response, and the influence of the AVT improper design on the performance of distance relay are scrutinized in this paper. Furthermore, the design requirements of the AVT to avoid distance relay malfunctions due to the AVT ferroresonance are discussed. [ABSTRACT FROM AUTHOR]

Various catastrophic incidents and tripping events that have taken place in the power system of an oil and gas plant in Libya, initiated the investigation into transient phenomena in this site. A field survey was initially performed for this purpose. In addition, advanced measurement devices were installed in critical substations in order to monitor various routine switching operations that would help properly model the electrical network under investigation in an Electromagnetic Transients Program (EMTP). On February 7, 2010, a plant blackout occurred twice while the monitoring process was still in progress. Postmortem analysis of the event has been performed using EMTP and protection coordination software, based on the received oscillographs and measurements. The analysis as well as the simulations and the derived results are presented in this paper. Corrective measures are proposed to address transient phenomena and protection issues at this site. [ABSTRACT FROM PUBLISHER]

In-situ tests of coupling capacitor voltage transformers (CCVTs) in some of the high-voltage substations indicate that the ratio error of a considerable number of CCVTs has increased to more than 5%. Experimental analyses reveal that the CCVTs excessive ratio error is mainly due to the short-circuited capacitor elements of CCVTs. Comprehensive tests and investigations indicate that the occurrence of ferroresonance due to saturation of the auxiliary voltage transformers (AVTs) is one of the main reasons for this problem. These small transformers are usually utilized inside the protective relays and control and measuring equipment or are connected to the secondary side of CCVTs as an interface between the CCVT and the equipment. Imposed stress on CCVT components and the voltage oscillations' effect on transmission-line distance relay are also scrutinized in this paper. Finally, appropriate specifications for AVTs are recommended to prevent undesirable CCVT overvoltages and distance relay maloperation. [ABSTRACT FROM PUBLISHER]

This paper introduces the concepts of 1) dynamic inductance and 2) effective inductance based on the magnetic energy, and provides a new insight on the transformer core behavior during steady-state and transient regimes. Based on a newly developed core modeling approach, which is described in references one to four, this paper also: 1) addresses the intrinsic limitations of the single-valued magnetization characteristic-based core model; 2) uses the dynamic inductance as the key parameter to fully and accurately represent the core behavior; and 3) explains the reason for discrepancies among the reported core behavior based on the simulated and experimental results. In contrast to the widely accepted belief that a single-valued magnetization characteristic- based model can accurately represent the transformer core behavior, this paper demonstrates the necessity of a dynamic and physically correct hysteresis core representation. This paper also compares various core representations in terms of their accuracies for the ferroresonance simulation. This paper shows that: 1) the single-valued core model not only cannot accurately represent the core behavior under asymmetric excitation conditions, it may provide erroneous results even under symmetric excitation conditions and 2) the accuracy of specific transients highly depends on the precise representation of the hysteresis minor loops and the core dynamic inductance. [ABSTRACT FROM AUTHOR]

This paper provides a detailed core model for the step-down transformer (SDT) of the coupling capacitor voltage transformer (CCVT) to investigate the CCVT transients and ferroresoriance behavior. The core model represents hysteresis symmetric and asymmetric minor loops, remnant flux, and the eddy current effects. Based on the developed model, the impacts of passive and active ferroresonance suppression circuits (PFSC and AFSC) and overvoltage protection devices (OPDs) for fast suppression of the CCVT ferroresonance phenomenon are also studied. This paper also presents a generalized methodology to select the AFSC parameters. The simulation results, in the PSCAD/EMTDC environment, indicate that the hysteresis and eddy current effects of the SDT core significantly influence the CCVT ferroresonance behavior. The study results also show that: 1) in both the presence and the absence of arresters and spark gaps, the AFSC can mitigate the phenomenon faster than the PFSC, i.e., in about two cycles and 2) the output fidelity of the AFSC-based CCVT is less dependent on the burden as compared with that of the PFSC. [ABSTRACT FROM AUTHOR]

The key concern for transformers experiencing ferroresonance is whether the energy transferred into the transformer body during core saturation by the nonsinusoidal currents is damaging. Saturation and the consequent incompetency of the core to contain the flux manifests itself as current induced in parts of the transformer body not foreseen to conduct current. Sustained ferroresonance may last for minutes (or even hours), when no intervening operations are carried out, and may cause local overheating and thermally degrade surrounding insulation. In this paper, transient electromagnetic analysis was conducted by using 2-D finite-element models of a 240-MVA 400/132/13-kV autotransformer. As a continuing effort, the main objective of modeling is to visualize the flux flow in parts where transformer designers have not anticipated its presence. A quantitative assessment of the flux, the induced currents, and the power dissipated in these parts has been carried out to determine the degree of risk imposed on a transformer under ferroresonance. [ABSTRACT FROM AUTHOR]

Abstract-This paper investigates impacts of various formations of hysteresis on the stability domain of ferroresonance modes of a voltage transformer (VT). Based on four different hysteretic and two single-valued polynomial models, ferroresonance behaviors of the VT are studied. The hysteretic models are developed based on the Preisach theory. The first hysteretic model accurately duplicates the measured hysteresis loops of the VT in a wide variation range of the core excitation level. The other three hysteretic models represent different hysteresis loop formations. The polynomial models are based on identical single-valued polynomial magnetization characteristics but represent different core loss resistances (i.e., constant and dynamically varying core loss resistances, respectively). All of the models represent the same core losses as the measured value to investigate impacts of hysteresis loop formations on ferroresonance modes, independent of the corresponding hysteresis losses. The studies are conducted in time domain in the PSCAD/EMTDC software environment. The studies indicate that the VT model, which duplicates the measured hysteresis loops and the measured core loss over a wide range of excitation levels, results in more ferroresonance modes, expanded stability domains, and higher overvoltages. This paper concludes that formation of hysteresis is an independent factor which significantly impacts the ferroresonance phenomenon. Not only is it a single-valued magnetization characteristic but also a generic hysteretic characteristic; if it is not accurately constructed based on the measured core hysteresis data, it can result in significant error in determining the ferroresonance overvoltages and stability domains of the ferroresonance modes. [ABSTRACT FROM AUTHOR]

This paper introduces an accurate transformer core model, using the Preisach theory, to represent the core magnetization characteristic. This modeling approach provides the required precision to match major and minor hysteresis loops of the model with those of the actual transformer core material. Using the proposed model, the ferroresonance phenomenon of a voltage transformer (VT) is simulated and compared to the corresponding experimental results. In addition, the simulated ferroresonance behavior of the VT based on: 1) the Electromagnetic Transients Program (EMTP)-RV hysteric reactor model, 2) the EMTP reactor type-96 model, and 3) a single-valued polynomial as magnetization characteristic, is also deduced and compared with the proposed model and the experimental results. The investigations conclude that the proposed model provides the most accurate results in terms of the VT core losses and the VT voltage waveforms and their peak values during 1) normal operating conditions, 2) ferroresonance transients and jumping from normal to ferroresonance operating conditions, and 3) ferroresonance steady-state conditions. Furthermore, higher accuracy of the proposed model in representing the hysteresis loop provides the highest and the most accurate bifurcation point and the transient loss when compared with other models. This paper also concludes that major and minor hysteresis loops must be represented in the core model to accurately simulate ferroresonance phenomenon of the VT. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that ferroresonant oscillations involving voltage transformers (VTs) may be initiated by switching transients in ungrounded medium-voltage networks. It was demonstrated that various modes of ferroresonant oscillations may exist for the same VT type depending on the initial conditions and on the network capacitance. As the ferroresonant oscillations pose a risk to the VTs due to large overcurrents in the primary windings, the VTs operating in ungrounded networks should be protected against this phenomenon. The analysis of the classic method of protecting the VTs by means of connecting the damping resistor to the open-delta-arranged auxiliary winding has shown that often a very low ohmic value of the resistor is required to provide reliable protection. A new method of protecting the VTs against ferroresonance with a compact active load was thus developed. [ABSTRACT FROM AUTHOR]

The magnetic hysteresis phenomenon plays an important role in the ferroresonance behavior of a transformer. however, most existing transformer models for the analysis of the ferroresonance phenomenon either ignore the hysteresis effects or represent it based on the hysteresis major loop and scale it for lower current levels. Such a modeling approach does not reflect the actual physical behavior of the magnetic core with respect to the ferroresonance phenomenon. This paper, based on Preisach theory, introduces an accurate model of hysteretic inductor to represent a single-phase transformer for the investigation of the ferroresonance phenomenon. Based on the developed model, time-domain simulation studies show that even in the case of a single-phase transformer where no magnetic coupling exists between the three-phases, all known types of ferroresonance, including fundamental, sub-harmonic, quasi-periodic and chaotic modes, may occur. The effects of hysteresis and its initial conditions, grading capacitors and transformer winding capacitance on occurrence of ferroresonance and its change of mode are also discussed. [ABSTRACT FROM AUTHOR]

For ferroresonant circuits, the sufficient condition for preventing fundamental ferroresonance (FF) from occuring is that there is no intersection between the voltage-current characteristic of the linear part of the circuit, and the saturated power frequency excitation characteristic of the nonlinear part. Based on this understanding, part II of this paper has presented a criterion for the possibility of FF in the form of an analytical expression which is composed of the essential parameters of the circuit. By giving the critical resistance value for damping FF, the expression clearly indicates not only the possibility of FF but also the methods for eliminating the FE The possibility of FF is judged by comparing the critical resistance value with the real value. In the meantime, the expression suggests how to adjust the essential parameters to suppress FE The criterion has been proven by both simulation results and field tests. With this criterion, the possibility and elimination of FF can be studied for the first time by a simple yet effective analytical method. [ABSTRACT FROM AUTHOR]

This paper has highlighted a major problem with the traditional excitation characteristic (TEC) of nonlinear inductors, in that the TEC contains harmonic voltages and/or currents, and has been used the way as if it were made up of pure fundamental voltage and current. In comparison to the TEC, a new concept, namely the power frequency excitation characteristic (PEC), which contains no harmonics, has been put forward. Two methods have been presented in obtaining the PEC. The first method is based on Electromagentic Transients Program simulation, resulting in discrete voltage and current pairs. This method essentially acts as a reference to validate the second one. The second method em- ploys Fourier and Maclaurin series approximation techniques, and brings forth a simple yet effective analytical expression. The expression is proven to have satisfactory precision in the saturated region of the PEC, especially in the extremely saturated region. [ABSTRACT FROM AUTHOR]

A three-phase, two-winding transformer model is presented in this paper. Nonlinear magnetizing curves are piece-wise linearized, while the input winding capacitances are lumped onto the transformer terminals. A stiff system of differential equations in a state space, describing the transformer transient behavior, is solved using the L-stable backward differentiation formulas (BDFs) numerical rule. It has been shown that using the BDF numerical rule has resulted in better stability properties than using the trapezoidal rule. A computer program has been developed for generation of variable-state waveforms. The developed program is suitable for simulations of low-frequency three-phase transformer transients such as inrush currents and ferroresonance. This computer program has proved to be nu- merically stable for the problems investigated in this paper. The results acquired in this way are compared to results obtained using MATLAB/Power System Blockset, as well as to results of laboratory measurements. [ABSTRACT FROM AUTHOR]

The performance of the T and the \pi equivalent models used to represent transformers are tested under ferroresonance. Comparisons between simulations and laboratory experiments show the superiority of the \pi equivalent circuit. [ABSTRACT FROM AUTHOR]