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DIGITAL COMPUTATION OF ELECTROMAGNETIC TRANSIENTS IN POWER SYSTEMS: CURRENT STATUS

Juan A. Martinez-VelascoDepartament d'Enginyeria Elèctrica

Universitat Politècnica de Catalunya, Spain

Abstract- This document presents an introduction to time-domainsolution of electromagnetic transients in power systems using adigital computer. Currently, the most widely used simulation toolsto solve electromagnetic transients are based on the trapezoidalrule and the method of characteristics (Bergeron's method). Onlyworks related to this solution algorithm are considered in thisdocument which covers two main topics : solution techniques andmodeling of power components.

Keywords : Electromagnetic Transients, Time-domainSimulation, Trapezoidal Rule, Numerical Oscillations, ControlSystems, Modeling.

1. INTRODUCTION

Transient phenomena in power systems are caused byswitching operations, faults, and other disturbances, such aslightning strokes. They involve a frequency range from DC toseveral MHz. A rough distinction is usually made betweenelectromechanical transients, traditionally covered by transientstability studies, and electromagnetic transients. The latter typeof transients can occur on a time scale that goes frommicroseconds to several cycles; they are a combination oftravelling waves on lines, cables and buses, and of oscillationsin lumped-element circuits of generators, transformers andother devices. Some electromechanical transients, such assubsynchronous resonance, for which detailed machine modelsare needed, are usually included in this class of transients.

Several tools have been used over the years to analyzeelectromagnetic transients. At early stages, miniature powersystem models, known as Transient Network Analyzers (TNA),were used. At present, the digital computer is the most populartool, although TNAs are still used; in addition, the newgeneration of real-time digital systems are probably the mostadequate tool in some applications for which either a veryhigh-speed or a real-time simulation is required.

Many techniques have been developed to solve electromagnetictransients using a digital computer. They can be classified intotwo main groups : frequency-domain and time-domain

techniques. The subject of this document is the digitalsimulation of electromagnetic transients in power systems,using time-domain techniques. Presently, the most widely usedsolution method is based on the application of the trapezoidalrule and the Bergeron's method, also known as method ofcharacteristics [1] - [6].

This document has been arranged as follows. Section 2 dealswith the basic solution techniques either already implementedor proposed for implementation in electromagnetic transientsprograms (emtps). It covers not only the algorithms aimed atsolving the transient solution, but procedures to reducenumerical oscillations produced by the trapezoidal rule,initialization methods, and procedures to solve the interfacebetween power networks and control systems.

Section 3 presents a summary of modeling works related to themost important power components taking into account theirfrequency-dependent behaviour.

Due to difficulties for developing power component modelsaccurate enough for a wide frequency range, much work hasbeen done to provide modeling guidelines for digital simulationof every type of transient phenomenon. Section 4 summarizesthe work done in this area and reports about works still inprogress.

Some topics, such as parallel computation or real-time emtp-based simulation of electromagnetic transients, which areclosely related to the main subjects of this document are notcovered here.

A selected bibliography related to topics of each part has beenincluded at the end of this document.

2. SOLUTION METHODS

2.1 TRANSIENT SOLUTION

The studies to solve travelling wave problems by means of a

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[ G] [ v( t )] [ i ( t )] [ I ] (1)

t )] [ iA( t )] [ I

A] [ G

AB (2)

vkm

vkm(0)

rthev

ikm (3)

km f ( i

km, dikm/ dt , t , ... (4)

digital computer were started in the early 1960's using twodifferent techniques, the Bewley's lattice diagram [7] and theBergeron's method [8]. These techniques were applied to solvesmall networks, with linear and nonlinear lumped- parameter,as well as distributed-parameter elements. The extension tomultinode networks was made by H.W. Dommel [1]. TheDommel's scheme combined the Bergeron's method and thetrapezoidal rule into an algorithm capable of solving transientsin single- and multi-phase networks with lumped anddistributed parameters. This solution method was the origin ofthe ElectroMagnetic Transients Program (EMTP), whosedevelopment was supported by Bonneville PowerAdministration (BPA).

The trapezoidal rule is used to convert the differential equationsof the network components into algebraic equations involvingvoltages, currents and past values. These algebraic equationsare assembled using a nodal approach

where [G] is the nodal conductance matrix[v(t)] is the vector of node voltages[i(t)] is the vector of current sources[I] is the vector of "history" terms.

Very often the network contains voltage sources to ground, thenthe equation is split up into part A with unknown voltages andpart B with known voltages

The resulting conductance matrix is symmetrical and remainsunchanged as the integration is performed with a fixedtime-step size. The solution of the transient process is thenobtained using triangular factorization. One of the mainadvantages of this procedure is that it can be applied tonetworks of arbitrary size in a very simple fashion.

Bergeron's method can be efficiently used with lossless anddistortionless lines. However, parameters of actual transmissionsystems are frequency-dependent. The first works onfrequency-dependent models were performed for telephonecircuits in the 1920's [9]. The first frequency-dependenttransmission line model developed for EMTP simulations wasimplemented in 1973 [10]. Much effort has been made sincethen, and some other frequency-dependent line models havebeen developed and implemented, see Section 3.2.

The original Dommel's scheme could be used to solve linearnetworks. However, many power components - transformers,reactors, surge arresters, circuit breakers - present a nonlinearbehaviour. Several modifications to the basic method wereproposed to cope with nonlinear and time-varying elements

[11]. These modifications were based on a current sourcerepresentation, a piecewise-linear representation or thecompensation method. Some of the advantages and drawbacksshown by these approaches were discussed in [5] and [11].

Using compensation, nonlinear elements are represented ascurrent injections which are superimposed to the solution of thelinear network after this solution has been computed. Figure 1shows the scheme of the compensation method for a singlenonlinear element.

Figure 1. Principles of the compensation method.

Once the solution of the network without the nonlinear elementhas been computed, its contribution is computed from thefollowing equation

and the characteristic of the nonlinear element

vkm(0) in (3) indicates the voltage solution across the nodes "k"and "m" without the nonlinear element, while rthev is theThevenin equivalent resistance.

Iterative solution methods, such as the Newton's method, areused to solve this step.

The compensation method can be generalized to networks withseveral nonlinear components [12]. However, its application islimited to only one nonlinear element per node.

Other solution methods has been proposed to solve thislimitation. A very simple procedure based on a predictor-corrector method has been recently presented [13].

An interface for simulation of HVDC links and machines, alsobased on the Dommel's algorithm, was presented in [14].

The computation of electromagnetic transients with thetrapezoidal rule is performed in the time-domain. Some othertechniques have been developed to solve network equationsusing a time-domain solution (z-transform methods [15], wave

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digital filters [16]) or a frequency-domain solution [17]. Somealternative methodologies taking advantage of the Dommel'sscheme have been recently proposed, they use a hybridfrequency- and time-domain approach [18], or a state equationmodeling [19].

Programs based on the trapezoidal rule are currently the mostwidely used for simulation of electromagnetic transients. Thisis due to the simplicity of this integration rule, as well as to itsnumerical stability. The trapezoidal rule is an A-stable methodwhich does not produce run-off instability [20]. However, thisrule suffers from some drawbacks : it uses a fixed time-step sizeand can originate sustained numerical oscillations. During thelast twenty years several works have been presented to solve orminimize most of these drawbacks.

The step size determines the maximum frequency that can besimulated, therefore users have to know in advance what is thefrequency range of the transient simulation to be performed. Onthe other hand, both slow and fast transients can occur at thesame time in different nodes. A procedure by which two ormore time step sizes can be used in the trapezoidal integrationwas presented in [21].

2.2 NUMERICAL OSCILLATIONS

In many cases, such as switching operations or transitionsbetween segments in piecewise-linear inductances, thetrapezoidal rule acts as a differentiator, and introducessustained numerical oscillations. Several techniques have beenproposed to control or reduce these numerical oscillations.

One of these techniques uses additional damping to forceoscillations to decay [22]. This damping can be provided by theintegration rule itself or externally, by adding fictitiousresistances in parallel with inductances and in series withcapacitors. This method can have an important effect on theaccuracy of the solution.

Another technique is based on the use of snubber (RC) circuitsin parallel with switches. This option is particularly interestingin power electronics applications as snubber circuits are veryoften placed in parallel with semiconductors to limitovervoltages across them. Figure 2 shows a very simple case ofa half-wave single-phase rectifier. Plots without and withsnubber circuit in parallel with the diode illustrate thisdrawback of the trapezoidal rule, and one possible solution.

a) Scheme of the rectifier

b) Simulation result without the snubber circuit

c) Simulation result with the snubber circuit

Fig. 2. Numerical oscillations and their solution.

Some of the most efficient techniques developed to avoidnumerical oscillations are based on the temporary modificationof the solution method, only when numerical oscillations canoccur, without affecting the rest of the simulation. One of thesetechniques is based on the CDA (Critical DampingAdjustment) procedure [23], [24]. During a switchingoperation, CDA uses a backward Euler rule and two half-sizeintegration steps. This method does not require recalculation ofthe admittance matrix.

Another technique is based on interpolation [25]. Severalapproaches have been developed. The procedure presented in[26] uses two time step sizes and represents switching devices(power electronics components) by means of characteristiccurves. A modified linear interpolation to solve problemsmanifested not only in the network solution, but in the controlsystem too, has been presented in [27].

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[ Y] [ V] [ I ] (5)

YAA] [ V

A] [ IA] [ Y

AB] [ VB (6)

2.3 INITIALIZATION

The solution of a transient phenomenon is dependent on theinitial conditions with which the transient is started. Althoughsome simulations can be performed with zero initial conditions,for instance some lightning surge studies, there are manyinstances for which the simulation must be started from power-frequency steady-state conditions. Capabilities to obtain theinitial steady-state solution are of great importance in emtps. Inaddition, an initialization procedure can be a useful tool on itsown, for instance to calculate resonant voltages due to couplingeffects between parallel transmission lines.

The steady-state solution of linear networks at a singlefrequency is a rather simple task, and can be obtained usingnodal admittance equations [5]

where [Y] is the nodal complex admittance matrix[V] is the vector of node voltages[I] is the vector of current sources.

Elements of both [V] and [I] are complex phasor values.

As for the transient solution, this equation is partitioned whenthe network contains voltage sources to ground

However, this task can be very complex in the presence ofnonlinearities. Saturation effects in transformers and shuntreactors, rectifier loads and HVDC converter stations canproduce steady-state harmonics.

The initial solution with harmonics can be obtained using somesimple approaches. The simplest one is known as "brute force"approach : the simulation is started without performing anyinitial calculation and carried out long enough to let thetransients settle down to steady-state conditions. This approachcan have a reasonable accuracy, but its convergence will bevery slow if the network has components with light damping.A more efficient method is to perform an approximate linear acsteady-state solution with nonlinear branches disconnected orrepresented by linearized models. Some emtps have either a"snapshot" or a "start again" feature. The state of the system issaved after a run, so later runs can be started at this point.Using a "brute force" initialization, the system is started fromstandstill, once it reaches the steady-state, a snapshot is takenand saved.

A significant effort has been made during the last years to

develop efficient procedures for implementation in emtps andaimed at calculating ac steady-state initial conditions with thepresence of nonlinear components. The techniques can bedivided into three groups : frequency-domain, time-domain,and hybrid methods.

One of the first methods, known as Initialization withHarmonics (IwH), was presented in [28]. This procedure usesan iterative solution based on the superposition of the steady-state phasor solutions at the fundamental frequency and at themost important harmonic frequencies, with a representation ofnonlinear inductances as harmonic current sources.

An improved version of the IwH method was presented in [29].This procedure uses a harmonic Norton modeling of nonlinearbranches and a quasi-Newton type method.

Several procedures have been proposed to calculate initialconditions using time-domain techniques. The search of theperiodic steady-state solution is presented as a two-pointboundary value optimization problem. Techniques developedduring the last years are based on an iterative Newton method.More recent procedures use a shooting method [30], or awaveform relaxation technique [31]. The latter paper presentsa procedure with a fast and efficient convergence in networkswith nonlinear power elements and ideal diode-type devices.

Hybrid approaches to calculate initial conditions in nonlinearnetworks using both frequency- and time-domain techniqueshave also been developed [32].

A different solution method to obtain steady-state solution isneeded when initial operating conditions are specified as powerconstraints. An initialization procedure, kown as MultiphaseHarmonic Load Flow (MHLF), was presented in [33] and [34].In this method, static compensators and other nonlinearelements, under balanced or unbalanced conditions, arerepresented by harmonic Norton equivalent circuits. Furtherimprovements incorporated a synchronous machine model intothe initialization procedure [35]. A simpler multiphase powerflow solution based on the MHLF procedure was presented in[36]. If this approach is used for emtp initialization, sourcesneed to be defined to drive the transient solution at those nodesfor which load flow models were specified.

2.4 CONTROL SYSTEMS

The development of a section for representation of controlsystems in transients programs was initially motivated bystudies of HVDC links. The Transient Analysis of ControlSystems (TACS) option was implemented in the BPA EMTPin 1976 [37]. Although the main goal was the simulation of

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X( s) G( s) U( s) (7)

) KN

0� N

1s �... � N

ms m

D0 � D1s �... � Dns n (8)

( t ) K d u( t ) � hist ( t (9)

Axx

] [ x] � [ Axu

] [ u] [ his t (10)

HVDC converters, it soon became obvious that TACS hadmany other applications, such as the representation ofexcitation of synchronous generators, dynamic arcs in circuitbreakers, or protective relays.

Control systems are represented in TACS by block diagramswith interconnection between system elements. Controlelements can be transfer functions, FORTRAN algebraicfunctions, logical expressions and some special devices. Thesolution method used by TACS is also based on the trapezoidalrule. A control block in the s-domain can be described by thefollowing relationship

where U(s) and X(s) are respectively the input and the outputin the Laplace domain, and G(s) a rational transfer function

Transfer functions are converted into algebraic equations in thetime-domain

where K is the gain, while c and d are obtained from thecoefficient of the rational transfer function G(s) [5], [37].

A control system with many linear blocks results in a system ofequations with the following general form

The resulting algebraic equations of a control system are bynature unsymmetrical. Due to this fact, the electric network andthe control system were solved separately in the original TACSrelease. The network solution is first advanced, networkvariables are next passed to the control section, and thencontrol equations are solved. Finally, the network receivescontrol commands. The whole procedure introduces a time-stepdelay, see Figure 3.

Figure 3. Interface between a network and a control system.

Components other than transfer functions can be included in aTACS section, but they are seen as nonlinear blocks and notdirectly added into the simultaneous solution of transferfunctions.

When a nonlinear block is inside a closed-loop configuration,a true simultaneous solution is not possible. The procedureimplemented in the TACS solution is simultaneous only forlinear blocks, that is s-transfer functions, and sequential fornonlinear blocks. When these blocks are present, the loop isbroken and the system is solved by inserting a time delay.These delays inside control loops, as well as the delay betweenthe network and the control system, are the sources of differenteffects. Instabilities, inaccuracies and numerical oscillationsproduced by delays have been reported.

Although the first release of TACS was a powerful and flexibletool, new applications have been demanding other capabilitiesthan those implemented in the original version. One exampleare the new digital controls used in static compensators, HVDCconverters and other FACTS devices. The execution of tasksonly when needed, the simulation of conditional branching(IF-THEN-ELSE) or the manipulation of vector arrays arecapabilities not available in the first TACS releases.

Several works have been performed to overcome mainlimitations and minimize problems originated by TACS :

* Improvements to solve internal time delays, initializationproblems and some FORTRAN code limitations, wereimplemented and presented in [38].

* Limitations in FORTRAN code capabilities were solved bydeveloping an interface between TACS and FORTRANsubroutines. The interface presented in [39] maintains fullTACS capabilities and takes advantage of the FORTRANflexibility to represent digital controls.

* Another approach to overcome these limitations was providedby MODELS [40]. Initially known as "New TACS", theMODELS program was developed to substitute the TACSprogram. However, it became obvious that both optionsprovided alternate approaches, and therefore TACS waspreserved in those emtps in which MODELS was imbedded.

* Several techniques can be used to solve simultaneously powernetwork and control system equations and avoid problemsrelated to the interface delay. Two procedures usingcompensation have been recently developed [41], [42].

* A different and simple solution using filter interposition tosolve inaccuracies caused by the interface time delay wasrecently presented in [43].

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3. MODELING OF COMPONENTS

3.1 INTRODUCTION

An accurate simulation of every transient phenomenon requiresa representation of network components valid for a frequencyrange that varies from DC to several MHz. An acceptablerepresentation of each component throughout this frequencyrange is very difficult, and for most components is notpractically possible.

Modeling of power components taking into account thefrequency-dependence of parameters can be practically made bydeveloping mathematical models which are accurate enough fora specific range of frequencies. Each range of frequenciesusually corresponds to some particular transient phenomena.One of the most accepted classification of frequency ranges isthat proposed by the CIGRE WG 33-02 [184]. According to theCIGRE document, frequency ranges can be classified as fourgroups with some overlapping

* low-frequency oscillations, from 0.1 Hz to 3 kHz

* slow-front surges, from 50/60 Hz to 20 kHz

* fast-front surges, from 10 kHz to 3 MHz

* very-fast-front surges, from 100 kHz to 50 MHz.

This part discusses modeling works for some of the mostimportant network components - overhead lines, insulatedcables, transformers, arresters, network equivalents, rotatingmachines, circuit breakers - taking into account theirfrequency-dependent behaviour.

3.2 OVERHEAD LINES

Two types of time-domain models have been developed foroverhead lines and insulated cables :

a) Lumped-parameter models, that represent transmissionsystems by lumped elements whose values are calculatedat a single frequency

b) Distributed-parameter models, for which two categoriescan be distinguished, constant parameter and frequency-dependent parameter models.

The first type of models is adequate for steady-statecalculations, although they can also be used for transientsimulations in the neighbourhood of the frequency at whichparameters were evaluated. The most accurate models fortransient calculations are those which take into account thedistributed nature of parameters and consider theirfrequency-dependence.

A significant number of papers dedicated to analyze thefrequency-dependence behaviour of overhead lines andinsulated cables for digital simulation has been presentedduring the last 30 years. And although some efficient modelsare presently implemented in the most widely used emtps, newefforts are being now devoted to the development of moreefficient models.

Some of the first papers presenting frequency-dependent linemodels for digital simulation were published during the late1960's and early 1970's [44], [45]. Most models were aimed atsolving transmission-line equations using a time-domainsolution. Those models were based on the modal theory :multiphase line equations are decoupled through modaltransformation matrices, so that each mode can be separatelystudied as a single-phase line. For unbalanced anduntransposed lines, transformation matrices are frequencydependent. However, it is possible to obtain a good accuracyusing constant transformation matrices [46], [47].

Several approaches using modal theory have been proposed:weighting functions [10], recursive convolutions [48] - [50],state-space formulation [51]. One of the most popular modelswas presented in [52]; the paper proposed the solution of atransmission line model using a modified recursive convolutionand assuming frequency-independent transformation matrices.The transient solution of this model is based on the rationalfunction approximation of the propagation and characteristicadmittance functions. The order of the rational functions willdepend on the line geometry, the frequency range and thedesired accuracy. A high accuracy can only be obtained with alarge number of real poles. This can slow down the simulationof large networks. Low-order fittings have been proposed as acompromise between the solution accuracy and the modelsimplicity [53], [54]. The validity and limitations of constanttransformation matrices, as well as guidelines on how to choosethese matrices, were discussed in [55].

A procedure for representing dissipative multiconductortransmission lines with frequency-dependent parameters in awide frequency range has been recently proposed [56]. Theprocedure is aimed at evaluating the correcting terms to beadded to the propagation and characteristic admittancefunctions calculated according to the solution presented in [52].

New methods using frequency-dependent transformationmatrices have been recently proposed. They are based on aNewton-Raphson iteration technique [57], vector fitting andmodal decomposition [58], or polar decomposition [59].

A different solution method based on the superpositionprinciple and the Hartley transform was presented in [60].

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Some recent works have shown that the solution of lineequations can be efficiently performed using a phase-domainformulation, instead of modal-domain [61] - [68]. Reference[68] uses a second method which combines modal and phasedomain solutions.

All the previous papers consider transmission linerepresentations taking into account only conductor geometry.Some other parts of a transmission line, such as the towers,have an important influence on its performance in lightningstudies. The concept of nonuniform transmission lines includesthe effect of towers and grounding resistances, as well ascorona effect [69], [70]. In lightning studies, towers arerepresented by a surge impedance with an associated traveltime. Literature related to tower modeling can be found in [71]- [74].

A source of attenuation and distortion of surges andovervoltages in overhead lines is corona. An important efforthas been made during the last 20 years to understand this effectand for its representation in transient studies [75] - [79]. Manyinteresting papers dealing with corona representation in digitalsimulations have also been published [80] - [86].

3.3 INSULATED CABLES

The formulation of insulated cable equations and their solutionare similar to those used with overhead lines. However, thelarge variety of cable designs makes very difficult thedevelopment of a single model for representation of every typeof cable.

One of the first works dealing with a general formulation ofimpedances and admittances of single-core coaxial andpipe-type cables was presented in [87]. The cable models couldbe used to evaluate matrices and equivalent pi-circuits of cablesand to obtain steady-state initialization at a single frequency,but they should be used to perform accurate transientcalculations. The validity of this formulation is restricted, asmentioned above, to transient calculations in theneighbourhood of the frequency at which parameters areevaluated. The derivation of cable impedances and admittanceswas the subject of some previous works, see [88] for coaxialcables and [89] for pipe-type cables.

Reference [90] presented a method to solve cable equationsconsidering the frequency-dependence of cable parameters. Thesolution of the cable equations is performed in the modaldomain and assumes frequency-dependence of modaltransformation matrices. The model is valid for transientsimulations over a wide frequency range. Recent works havepresented new approaches based on vector fitting and modal

decomposition [58], or polar decomposition [59].

Additional works related to cable modeling and some casestudies are presented in [91] - [93].

As mentioned above, a new trend in the solution of cableequations taking into account frequency-dependence ofparameters is to carry out calculations in the phase-domain[62], [63], [64], [67].

A method for simulating electromagnetic wave propagation incoaxial cables represented by finite sections, taking intoaccount the frequency dependence of cable parameters, waspresented in [94].

3.4 POWER TRANSFORMERS

An accurate representation of a power transformer over a widefrequency range is very difficult, despite of its relatively simpledesign. In addition, two alternative transformer models can beused whether surge transfer from one winding to another is notof concern, or surge transfer has to be computed.Representations for both situations were proposed in thedocument written by the CIGRE WG 33.02 [184].

A significant effort on transformer modeling has been madeduring the last twenty years. Some modeling approaches for usein transient programs follow :

1) The representation of single- and three-phase n-windingtransformers is made in the form of a branch impedanceor admittance matrix [95]. This approach is generally usedto derive models for low-frequency and slow-fronttransients. Transformer parameters are both nonlinear andfrequency-dependent. Major causes of iron core

nonlinearities are saturation and hysteresis; one of themain causes of frequency-dependence are eddy currents.This approach cannot include nonlinear effects of ironcores. They are incorporated by connecting nonlinearinductances at winding terminals. Many built-in modelscurrently available in several emtps use this type ofrepresentation; their derivation is made from nameplatedata.

Iron core nonlinearities have been the subjects of manyinteresting papers [96] - [102]. The representation of eddycurrent effects has been analyzed in [103] - [106].

2) Detailed models incorporating core nonlinearities can alsobe derived by using the principle of duality from atopology based magnetic model [107] - [110]. Thisapproach is very useful to create models accurate enoughfor low-frequency and slow-front transients.

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A different approach to obtain the equivalent circuit of athree-phase five-legged transformer, valid also forlow-frequency and slow-front transients, was proposed in[111]. A hybrid model based on core topology, andconsisting of electric and magnetic circuits was presentedin [112].

3) Previous approaches do not consider frequency-dependentparameters, they are not useful to represent a transformerat high frequencies, although they can be improved iflumped capacitances are connected across transformerterminals. Models taking into account frequency-dependentparameters can be divided into two groups : models witha detailed description of internal windings [113] andterminal models, based on the fitting of the elements of acircuit that represents the transformer as seen from itsterminals [114] - [118].

Reference [119] presents a simplified model based on theclassical T-form model; this model is extended to highfrequencies by adding winding capacitances and representingshort-circuit branches by RL frequency-dependent equivalentnetworks.

A hybrid model for internal resonance studies, and valid for awide frequency range - from a few kHz to a few Mhz -, waspresented in [120]. The model is based on a coil-by-coildetailed model plus intercoil black box models.

Detailed models are needed to obtain internal transient voltagedistribution. These models are reasonably accurate forinsulation design, and generally consist of large networks.However, they make system models unnecessary large when theconcern is the response at the transformer terminals. Someefforts have been devoted to obtain reduced transformer models,using either linear or nonlinear techniques [121] - [124].

Other models, including saturation, hysteresis, as well aseddy-current losses, have been proposed in [125] - [127]. Theperformance of different transformer models, most of themcurrently implemented in many emtps, for the simulation offast switching transients was analyzed in [128].

Usually models are derived considering the behaviour of thetransformer from its terminals, a method for simulation ofinternal faults in power transformers using capabilitiesavailable in some emtps was presented and validated in [129].

3.5 SURGE ARRESTERS

Two basic types of surge arresters are now in use : gappedsilicon-carbide arresters and gapless metal-oxide surge arresters

(MOSA). Although many of the arresters still in use are theolder type gapped silicon-carbide, the majority of the newinstalled arresters are the gapless metal-oxide type. Literaturerelated to modeling of surge arresters can be found in [130],[131], [132].

MOSAs present a frequency-dependent nonlinear characteris-tic : the voltage across the arrester is a function of both the rateof rise and the magnitude of the current conducted by thearrester. Modeling of MOSAs was the subject of a paper writtenby the IEEE WG on Surge Arrester Modeling [133]. The paperproposes a procedure to obtain the parameters of the equivalentmodel from manufacturer's data.

A different model that represents the frequency-dependencebehaviour by means of a nonlinear inductance in series with anonlinear resistance was proposed in [134]. An algorithm toderive parameters of the arrester model from test data was alsoincluded.

Modeling guidelines of gapped silicon-carbide surge arrestersfor digital simulations of slow-front transients were presentedin [135]. The proposed model is based on current-limitingarrester design. Recommendations to adapt the model forlightning studies were also included.

Metal-oxide varistors (MOV) models suitable for digitalsimulation of series compensated lines have been the subject ofsome recent works [136], [137].

3.6 NETWORK EQUIVALENTS

The simulation of transient phenomena in power systems veryoften requires a detailed modeling of just a small part of thesystem to be studied. Network equivalents can be used torepresent those parts of the system for which a detailedmodeling is not needed. The goal is to reduce the complexityand the computation time, while the simulation accuracy ispreserved. Several procedures have been proposed since early1970's to obtain single- and multi-port network equivalents[138] - [142].

Most of these procedures are based on the frequency responseof the network to be represented by the equivalent and on theapplication of a fitting technique to synthesize either a single-or a multi-port circuit which matches the response of thenetwork over a wide range of frequencies.

3.7 ROTATING MACHINES

The need for detailed synchronous generator models intransients programs was motivated by some serious

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subsynchronous resonance (SSR) incidents in the early 1970's.Utilities were concerned about some problems involvinginteractions between synchronous generators and powersystems.

The simulation of torsional interactions between themechanical turbine-generator system and the power systemneeds a very detailed representation of the generator and thepower system. Several dynamic three-phase synchronousgenerator models were developed and implemented in the BPAEMTP at mid 1970's [143], [144]. All those models were basedon the Park's transformation for solving the electricalequations. They incorporated a detailed representation ofmechanical and electrical parts, used a sophisticated solutionmethod to solve machine-power system interface, and includedinterface to control systems.

Although its development was raised by SSR problems, thosemodels could also be used for other studies, such as loss ofsynchronism, load rejection or transmission line reclosure.Magnetic saturation effects were not included at early stages.A simple and efficient representation of magnetic saturationwas added to one model in the late 1970's [145].

Interests in the analysis and simulation of renewable energysources motivated the demand for other machine models. Avery powerful and flexible module, known as UniversalMachine (UM), was implemented in the BPA EMTP in 1980[146]. The UM module allowed the representation of up totwelve different machine models and expanded the applicationsof the program, for instance to the simulation of adjustablespeed drives. The first UM release had several limitations thatwere solved in subsequent versions [147]. Two interfacemethods, compensation and prediction, are currently used withthis module.

All the machine models above mentioned are based on thetransformation of phase-quantities into dqo-quantities. Thematrix of self and mutual inductances becomes then constant.With models based on compensation methods no more than onemachine connected to the same nodes can be simulated. Thislimitation is avoided with a prediction-based interface.However, with this solution method, the prediction of severalelectrical variables is needed. This can originate numericalinstability.

The development of a synchronous generator model usingphase-domain equations instead of Park's transformation tosolve the electrical equations has been recently presented [148].This solution is numerically stable, as no prediction of anyelectrical variable is made, and simplifies the inclusion ofsaturation effects. With this approach, the matrix of self and

mutual inductances changes with the rotor position, then theadmittance matrix of the network has to be recalculated at eachtime step, which generally increases the simulation time.

Different techniques to solve machine-power system interfacehave also been developed and implemented in other transientsprograms [149].

Models currently implemented in all emtps are adequate forsimulation of low frequency transients. They are sufficientlyaccurate to analyze the interaction between the machine andthe power system, as well as torsional oscillations in themechanical part. However, these models are not adequate forsimulation of fast-front transients. Some switching motoroperations can originate steep-front surges and cause largeturn-to-turn winding stresses. Lightning surges transferredthrough transformers are also a source of high stresses anddielectric failures. Recent works have proposed computermodels for analyzing machine behaviour in fast-front transientsand predicting distribution of interturn voltages caused bysteep-fronted surges [150], [151], [152]. Some of these modelshave been represented and simulated using emtp capabilities[150], [152].

Techniques to develop machine models based on theirfrequency response have also been proposed [118], [153].

Most emtp studies are dealing with large three-phasesynchronous and induction machines. The analysis andsimulation of small and special machines were presented in[154], [155].

The simulation of an induction machine using the existingsynchronous machine models available in some emtps wasdetailed in [156].

3.8 CIRCUIT BREAKERS

A circuit breaker opens its contacts when a tripping signal issent to it. The separation of the contacts causes the generationof an electric arc. The phenomenon by which the arc is actuallyextinguished is very complicated. Although a large number ofarc models have been proposed, there is no general acceptancefor any of them.

Several approaches can be used to reproduce the arcinterruption phenomenon; the most suitable representations ina transients program are the so called black-box models [157],[158]. The aim of a black-box arc model is to describe theinteraction of an arc and a electrical circuit during aninterruption process. They consider the arc as a two-pole, anddetermine the transfer function using a chosen mathematical

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gt

1- i , g

viP[ i , g] (11)

form and fitting free parameters to measured voltage andcurrent traces. Rather than internal processes, it is the electricalbehaviour of the arc which is of importance. Several levels ofcomplexity are possible [159], [160] :

1) The breaker is represented as an ideal switch that opens atfirst zero current crossing, after the tripping signal isgiven. This model can be used to obtain the voltage acrossthe breaker, which is to be compared with a pre-specifiedtransient recovery voltage (TRV) withstand capability forthe breaker. This model cannot reproduce any interactionbetween the arc and the system.

2) The arc is represented as a time-varying resistance, whosevariation is determined ahead of time based on the breakercharacteristic. This model can represent the effect of thearc on the system, but requires advanced knowledge of theeffect of the system on the arc.

3) The most advanced models represent the breaker as adynamically varying resistance or conductance. They canrepresent both the effect of the arc on the system and theeffect of the system on the arc. No precomputed TRVcurves are required. Most of these models rely on a firstorder differential equation

where g is the arc conductancev is the arc voltagei is the arc current- , P are black-box model parameters.

These models are generally developed to determine initialarc quenching, that is to study the thermal period only,although some can also be used to determine arc reignitiondue to insufficient voltage withstand capability of thedielectric between breaker contacts. Their most importantapplication cases are short line fault interruption andswitching of small inductive currents.

Many models for circuit breakers, represented as a dynamicresistance/conductance, have been proposed. A survey onblack-box modeling of gas (air, SF6) circuit breakers waspresented in [158]. The emtp implementation of three dynamicarc models, adequate for gas and oil circuit breakers, waspresented in [161]. All those models are useful to represent acircuit breaker during the thermal period, models forrepresentation of SF6 breakers during thermal and dielectricperiods were discussed and used [162], [163]. The developmentof a user-defined model based on the Newton's method wasproposed in [164]. A new model also based on the Newton'smethod and a predictor for calculation of the arc resistance was

recently presented [165].

A vacuum circuit breaker has a different performance, itsrepresentation has to consider its statistical properties. Modelsfor this type of breaker were presented in [166] and [167].

Several models can also be used to represent a circuit breakerin closing operations [5] :

1) The simplest model assumes that the breaker behaves asan ideal switch whose impedance passes instantaneouslyfrom an infinite value, when open, to a zero value at theclosing time. This performance can be represented at anypart of a power cycle.

A closing operation can produce transient overvoltageswhose maximum peaks depend on several factors, forinstance the network representation on the source side ofthe breaker, or the charge trapped on transmission lines ina reclosing operation. One of the factor which has moreinfluence on the maximum peak is the instant of closing,which can be different for every pole of a three-phasebreaker.

Most transient programs allow users to analyze theinfluence of this factor and obtain a statistical distributionof switching overvoltages, usually provided in the form ofan accumulative frequency distribution. Two types ofswitches can be represented :

a - The closing time of a switch is systematically variedfrom a minimum to a maximum instant in equal

increments of time; this type is known as systematic switch.

b - The closing time is randomly varied according toeither a normal (Gaussian) or an uniform distribution; thistype is known as statistical switch. Data required torepresent these switches are the mean closing time, thestandard deviation and the number of switching operations.When a pre-insertion resistor is used to mitigate switchingovervoltages, the closing time of both main and auxiliarycontacts are statistically determined.

2) The breaker model assumes that there is a closing timefrom the moment at which the contacts start to close to themoment that they finally make. The withstand voltagedecreases as the separation distance between contactsdecreases, an arc will strike before the contacts havecompletely closed if the voltage across them exceeds thewithstand voltage of the dielectric medium. Modeling ofthe pre-strike effect and its influence on the switchingovervoltages produced during line energization has beenanalyzed in [168].

Similar models can be used with other switching devices, for

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which a representation for both opening and closing operationscan be needed.

3.9 OTHER COMPONENTS

Capabilities currently available in most emtps make practicallypossible user-developed models of those components for whicha built-in model has not been implemented. In fact, this is thecase for some component models discussed above

* a transformer model for low-frequency transients based onthe principle of duality has not been implemented in anyemtp, the capabilities needed to develope such a modelhave been used in some papers [107]

* there is no built-in model for circuit breakers in mostemtps, but its representation can be made using branchesand control features, available in all emtps [160], [164]

* although there is a built-in surge arrester model implemented in all emtps, it is not adequate for lightning

studies; users have to improve this model by takingadvantage of other capabilities.

Semiconductors are usually represented as ideal switches in allswitching operations, although some transients programs allowusers to consider ignition voltages and holding currents. Aswith other components, capabilities available in some transientprograms can be used to develop more accurate representations[169], [170].

The list of components for which a built-in model is notavailable might also include instrument transformers [171] -[175], protective relays [176] - [181], fuses [182], [183]. Theimplementation of models for instrument transformers andsome types of relays in one emtp was presented in [178].

4. MODELING GUIDELINES

The following aspects are to be considered in digitalsimulations of electromagnetic transients [184] :

a) Very often only approximated or estimated values are usedfor some parameters whose influence on the representationof a component can be important or very important. Ingeneral, this happens with some basic parameters andfrequency-dependent parameters in simulations of fast andvery fast front transients. In addition, it is important totake into account that some parameters may change due toclimatic conditions or be dependent on maintenance.

b) In many overvoltages studies it is the maximum peakwhich is of interest. This maximum usually occurs during

the first oscillation after the transient phenomenon starts.Large differences in peak values are mainly due to a poorrepresentation of losses, while deviations in inductances orcapacitances will lead to time shifting of the peak but notto important differences between the maximum values.

c) The more components the system in study has, the higherthe probability of insufficient or wrong modeling. Inaddition, a very detailed representation of a system willrequire very long simulation time. Some experience willbe therefore needed to decide how detailed the systemshould be and choose the model for the most importantcomponents.

Presently there are several sources where it is possible toconsult modeling guidelines of power components for time-domain digital simulations :

1) One of the first document published on this subject wasthat produced by the CIGRE WG 33-02 [184]; it coversthe most important power components and proposes therepresentation of each component taking into account thefrequency range of the transient phenomena to besimulated.

2) Modeling guidelines can also be found in the documentsproduced by the IEEE Working Group on Modeling andAnalysis of System Transients Using Digital Programs.The group was created in 1991 and later split up into 6Task Forces. Following a different approach to that of theCIGRE WG, each TF was created to produce

documentation on a particular type of studies : Low FrequencyTransients, Switching Transients, Fast Front Transients, Very Fast Transients, Power Electronics,

Protection and Control. Up to date, several papers havebeen presented [185] - [190].

3) Currently, the IEC Working Group 28-04 is dealing withthe same subject. This WG started its tasks in 1996. Theaim is to produce a document on modeling guidelines fordigital calculation of overvoltages.

5. CONCLUSIONS

Time-domain simulations of electromagnetic transients usingdigital computers were started in early 1960's. Currently, mosttransients programs are based on the Dommel's scheme whichcombines the trapezoidal rule and the Bergeron's method.

Much work has been done to solve some of the main drawbacksand limitations of the original scheme, i.e solution of nonlinearnetworks, elimination of numerical oscillations. In addition, asignificant effort has been dedicated to the development of new

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models, specially frequency-dependent models for the mostimportant power components.

The development of the first tools was mainly motivated by thecalculation of overvoltages. Presently most emtps can be usedfor simulating a broad spectrum of transient phenomena inpower systems : subsynchronous resonance, power qualityanalysis, AC-DC links, FACTS and Custom Powertechnologies, electronically-controlled drives.

Due to the wide range of transient phenomena in powersystems and the complexity of many studies, modelingguidelines are needed to choose a correct representation of themost critical components of the system to be simulated. Severalworks have been published during the last decade aimed atproviding these guidelines. However, some work is still neededto solve important limitations, i.e. the representation of somecomponents is very complex, reliable data are not alwaysavailable.

6. REFERENCES

[1] H.W. Dommel, "Digital computer solution ofelectromagnetic transients in single- and multi-phasenetworks", IEEE Trans. on Power Apparatus andSystems, vol. 88, no. 2, pp. 734-741, April 1969.

[2] H.W. Dommel and W. Scott Meyer, "Computation ofElectromagnetic Transients", Proc. of IEEE, vol. 62,no. 7, pp. 983-993, July 1974.

[3] H.W. Dommel, "Techniques for analyzing electromag-netic transients", IEEE Computer Applications inPower, vol. 10, no. 3, pp. 18-21, July 1997.

[4] "Digital Simulation of Electrical TransientPhenomena", A. Phadke (ed.), IEEE Tutorial Course,Course Text 81 EHO173-5-PWR.

[5] H.W. Dommel, Electromagnetic Transients Program.Reference Manual (EMTP Theory Book), BonnevillePower Administration, Portland, 1986.

[6] J.A. Martinez-Velasco (Ed.), Computer Analysis ofElectric Power System Transients, IEEE Press, 1997.

[7] L.O. Barthold and G.K. Carter, "Digital traveling-wave solutions. 1 - Single-phase equivalents", AIEETrans., vol. 80, pt. III, pp. 812-820, December 1961.

[8] W. Frey and P. Althammmer, "The calculation oftransients on lines by means of a digital computer",Brown Boveri Rev., vol. 48, pp. 334-355, May/June1961.

[9] J.R. Carson, "Wave propagation in overhead wireswith ground return", Bell Syst. Tech. J., vol. 5, pp.539-554, 1926.

[10] W. Scott Meyer and H.W. Dommel, "Numerical

modeling of frequency dependent transmission-lineparameters in an electromagnetic transients program",IEEE Trans. on Power Apparatus and Systems, vol.93, no. 5, pp. 1401-1409, September/October 1974.

[11] H.W. Dommel, "Nonlinear and time-varying elementsin digital simulation of electromagnetic transients",IEEE Trans. on Power Apparatus and Systems, vol.90, no. 6, pp. 2561-2567, November/December 1971.

[12] H.W. Dommel, "Usefulness and limitations of multi-terminal reduced circuits", Proceedings of 11th PSCC,pp. 1155-1160, August 30 - September 3, 1993,Avignon (France).

[13] T. Noda, K. Yamamoto, N. Nagaoka and A. Ametani,"A predictor-corrector scheme for solving a nonlinearcircuit", Proceedings of IPST'97, pp. 5-10, June 22-26, 1997, Seattle.

[14] D.A. Woodford, A.M. Gole and R.Z. Menzies,"Digital simulation of dc links and ac machines", IEEETrans. on Power Apparatus and Systems, vol. 102, no.6, pp. 1616-1623, June 1983.

[15] W. Derek Humpage, Z-transform ElectromagneticTransient Analysis in High-Voltage Networks, PeterPeregrinus Ltd., London, 1982.

[16] M. Roitman and P.S.R. Diniz, "Power systemsimulation based on wave digital filters", IEEE Trans.on Power Delivery, vol. 11, no. 2, pp. 1098-1104,April 1996.

[17] J.P. Bickford, N. Mullineux and J.R. Reed,Computation of Power System Transients, PeterPeregrinus Ltd., London, 1976.

[18] M. D'Amore and M.S. Sarto, "A new efficientprocedure for the transient analysis of dissipativepower networks with nonlinear loads", IEEE Trans. onPower Delivery, vol. 11, no. 1, pp. 533-539, January1996.

[19] Y. Kang and J.D. Lavers, "Transient analysis ofelectric power systems : Reformulation and theoreticalbasis", IEEE Trans. on Power Systems, vol. 11, no. 2,pp. 754-760, May 1996.

[20] S.C. Tripathy, N.D. Rao and S. Elangovan,"Comparison of stability properties of numericalintegration methods for switching surges", IEEE Trans.on Power Apparatus and Systems, vol. 97, no. 6, pp.2318-2326, November/December 1978.

[21] A. Semlyen and F. de León, "Computation of electro-magnetic transients using dual or multiple time steps",IEEE Trans. on Power Systems, vol. 8, no. 3, pp.1274-1281, August 1993.

[22] F.L. Alvarado, R.H. Lasseter and J.J. Sanchez,"Testing of trapezoidal integration with damping forthe solution of power transient studies", IEEE Trans.on Power Apparatus and Systems, vol. 102, no. 12,

1-13

pp. 3783-3790, December 1983.[23] J.R. Marti and J. Lin, "Suppression of numerical

oscillations in the EMTP", IEEE Trans. on PowerSystems, vol. 4, no. 2, pp. 739-747, May 1989.

[24] J. Lin and J.R. Marti, "Implementation of the CDAprocedure in the EMTP", IEEE Trans. on PowerSystems, vol. 5, no. 2, pp. 394-402, May 1990.

[25] B. Kulicke, "Simulation program NETOMAC :Difference conductance method for continuous anddiscontinuous systems", Siemens Research andDevelopment Reports, vol. 10, no. 5, pp. 299-302,1981.

[26] T.L. Maguire and A.M. Gole, "Digital simulation offlexible topology power electronic apparatus in powersystems", IEEE Trans. on Power Delivery, vol 6, no.4, pp. 1831-1840, October 1991.

[27] P. Kuffel, K. Kent and G. Irwin, "The implementationand effectiveness of linear interpolation within digitalsimulation", Electrical Power and Energy Systems, vol.19, no. 4, pp. 221-228, May 1997.

[28] H.W. Dommel, A. Yan and S. Wei, "Harmonics fromtransformer saturation", IEEE Trans. on PowerSystems, vol. 1, no. 2, pp. 209-215, April 1986.

[29] X. Lombard, J. Masheredjian, S. Lefebvre and C.Kieny, "Implementation of a new harmonicinitialization method in EMTP", IEEE Trans. onPower Delivery, vol. 10, no. 3, pp.1343-1352, July1995.

[30] B.K. Perkins, J.R. Marti and H.W. Dommel,"Nonlinear elements in the EMTP : Steady-stateinitialization", IEEE Trans. on Power Systems, vol. 10,no. 2, pp. 593-601, May 1995.

[31] Q.Wang and J.R. Marti, "A waveform relaxationtechnique for steady state initialization of circuits withnonlinear elements and ideal diodes", IEEE Trans. onPower Delivery, vol. 11, no. 3, pp. 1437-1443, July1996.

[32] G. Murere, S. Lefebvre and X.D. Do, "A generalizedharmonic balance method for EMTP initialization",IEEE Trans. on Power Delivery, vol. 10, no. 3, pp.1353-1359, July 1995.

[33] W. Xu, J.R. Marti and H.W. Dommel, "A multiphaseharmonic load flow solution technique", IEEE Trans.on Power Systems, vol. 6, no. 1, pp. 174-182,February 1991.

[34] W. Xu, J.R. Marti and H.W. Dommel, "Harmonicanalysis of systems with static compensators", IEEETrans. on Power Systems, vol. 6, no. 1, pp. 183-190,February 1991.

[35] W. Xu, J.R. Marti and H.W. Dommel, "Asynchronous machine model for three-phase harmonicanalysis and EMTP initialization", IEEE Trans. on

Power Systems, vol. 6, no. 4, pp. 1530-1538,November 1991.

[36] J.J. Allemong, R.J. Bennon and P.W. Selent,"Multiphase power flow solutions using EMTP andNewtons method", IEEE Trans. on Power Systems,vol. 8, no. 4, pp. 1455-1462, November 1993.

[37] L. Dube and H.W. Dommel, "Simulation of controlsystems in an electromagnetic transients program withTACS", Proc. of IEEE PICA, pp. 266-271, 1977.

[38] R. Lasseter and J. Zhou, "TACS enhancements for theElectromagnetic Transient Program", IEEE Trans. onPower Systems, vol. 9, no. 2, pp. 736-742, May 1994.

[39] L.X. Bui, S. Casoria, G. Morin and J. Reeve, "EMTPTACS-FORTRAN interface development for digitalcontrols modeling", IEEE Trans. on Power Systems,vol. 7, no. 1, pp. 314-319, February 1992.

[40] L. Dubé and I. Bonfanti, "MODELS : A newsimulation tool in the EMTP", European Transactionson Electrical Power Engineering, vol. 2, no. 1, pp.45-50, January/February 1992.

[41] A.E.A. Araujo, H.W. Dommel and J.R. Marti,"Simultaneous solution of power and controlequations", IEEE Trans. on Power Systems, vol. 8, no.4, pp. 1483-1489, November 1993.

[42] S. Lefebvre and J. Mahseredjian, "Improved controlsystems simulation in the EMTP throughcompensation", IEEE Trans. on Power Delivery, vol.10, no. 4, pp. 1654-1662, April 1995.

[43] X. Cao et al., "Suppression of numerical oscillationcaused by the EMTP-TACS interface using filterinterposition", IEEE Trans. on Power Delivery, vol.11, no. 4, pp. 2049-2055, October 1996.

[44] A. Budner, "Introduction of frequency-dependent lineparameters into an electromagnetic transientsprogram", IEEE Trans. on Power Apparatus andSystems, vol. 89, no. 1, pp. 88-97, January 1970.

[45] J.K. Snelson, "Propagation of travelling waves ontransmission lines - Frequency dependent parameters",IEEE Trans. on Power Apparatus and Systems, vol.91, no. 1, pp. 85-91, January/February 1972.

[46] P.C. Magnusson, "Traveling waves on multi-conductor open-wire lines. A numerical survey of theeffects of frequency dependence of modalcomposition", IEEE Trans. on Power Apparatus andSystems, vol. 92, no. 3, pp. 999-1008, May/June1973.

[47] R.G. Wesley and S. Selvavinayagamoorthy,"Approximate frequency-response values fortransmission line transient analysis", Proc. IEE, vol.121, no. 4, pp. 281-286, April 1974.

[48] A. Semlyen and A. Dabuleanu, "Fast and accurateswitching transient calculations on transmission lines

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with ground return using recursive convolutions",IEEE Trans. on Power Apparatus and Systems, vol.94, no. 2, pp. 561-571, March/April 1975.

[49] A. Ametani, "A highly efficient method for calculatingtransmission line transients", IEEE Trans. on PowerApparatus and Systems, vol. 95, no. 5, pp. 1545-1551,September/October 1976.

[50] A. Semlyen, "Contributions to the theory of calculationof electromagnetic transients on transmission lines withfrequency dependent parameters", IEEE Trans. onPower Apparatus and Systems, vol. 100, no. 2, pp.848-856, February 1981.

[51] J.F. Hauer, "State-space modeling of transmission linedynamics via nonlinear optimization", IEEE Trans. onPower Apparatus and Systems, vol. 100, no. 12, pp.4918-4924, December 1981.

[52] J.R. Marti, "Accurate modeling of frequency-dependent transmission lines in electromagnetictransient simulations", IEEE Trans. on PowerApparatus and Systems, vol. 101, no. 1, pp. 147-155,January 1982.

[53] L. Marti, "Low-order approximation of transmissionline parameters for frequency-dependent models",IEEE Trans. on Power Apparatus and Systems, vol.102, no. 11, pp. 3582-3589, November 1983.

[54] A. Oguz Soysal and A. Semlyen, "Reduced ordertransmission line modeling for improved efficiency inthe calculation of electromagnetic transients", IEEETrans. on Power Systems, vol. 9, no. 3, pp. 1494-1498, August 1994.

[55] J.R. Marti, H.W. Dommel, L. Marti and V.Brandwajn, "Approximate transformation matrices forunbalanced transmission lines", Proc. of the 9th PowerSystems Computer Conference, Cascais (Portugal),1987.

[56] M. D'Amore and M.S. Sarto, "Modelling of lossyground parameters in the EMTP for very-fast transientanalysis", Proceedings of IPST'97, pp. 49-54, June 22-26, 1997, Seattle.

[57] L.M. Wedepohl, H.V. Nguyen and G.D. Irwin,"Frequency-dependent transformation matrices foruntransposed transmission lines using Newton-Raphsonmethod", IEEE Trans. on Power Systems, vol. 11, no.3, pp. 1538-1546, August 1996.

[58] B. Gustavsen and A. Semlyen, "Simulation oftransmission line transients using vector fitting andmodal decomposition", IEEE Trans. on PowerDelivery, vol. 13, no. 2, pp. 605-614, April 1998.

[59] B. Gustavsen and A. Semlyen, "Calculation oftransmission line transients using polar decomposition",IEEE Trans. on Power Delivery, vol. 13, no. 3, pp.855-862, July 1998.

[60] R. Mahmutcehajic, S. Babic, R. Gacanovic and S.Carsimamovic, "Digital simulation of electromagneticwave propagation in a multiconductor transmissionsystem using the superposition principle and Hartleytransform", IEEE Trans. on Power Delivery, vol. 8,no. 3, pp. 1377-1385, July 1993.

[61] A. Oguz Soysal and A. Semlyen, "State equationapproximation of transfer matrices and its applicationto the phase domain calculation of electromagnetictransients", IEEE Trans. on Power Systems, vol. 9, no.1, pp. 420-428, February 1994.

[62] B. Gustavsen, J. Sletbak and T. Henriksen,"Calculation of electromagnetic transients intransmission cables and lines taking frequencydependent effects accurately into account", IEEETrans. on Power Delivery, vol. 10, no. 2, pp.1076-1084, April 1995.

[63] T. Noda, N. Nagaoka and A. Ametani, "Phase domainmodeling of frequency-dependent transmission lines bymeans of an ARMA model", IEEE Trans. on PowerDelivery, vol. 11, no. 1, pp. 401-411, January 1996.

[64] T. Noda, N. Nagaoka and A. Ametani, "Furtherimprovements to a phase-domain ARMA line model interms of convolution, steady-state initialization, andstability", IEEE Trans. on Power Delivery, vol. 12,no. 3, 1327-1334, July 1997.

[65] F. Castellanos and J.R. Marti, "Full frequency-dependent phase-domain transmission line model", IEEE Trans. on Power Systems, vol. 12, no. 3, pp.1331-1339, August 1997.

[66] H.V. Nguyen, H.W. Dommel and J.R. Marti, "Directphase-domain modeling of frequency-dependentoverhead transmission lines", IEEE Trans. on PowerDelivery, vol. 12, no. 3, 1335-1342, July 1997.

[67] A. Morched, B. Gustavsen and M. Tartibi, "Auniversal model for accurate calculation ofelectromagnetic transients on overhead lines andunderground cables", Paper presented at the 1997IEEE PES Summer Meeting, July 20-24, 1997, Berlin.

[68] B. Gustavsen and A. Semlyen, "Combined phase andmodal domain calculation of transmission linetransients based on vector fitting", IEEE Trans. onPower Delivery, vol. 13, no. 2, pp. 596-604, April1998.

[69] M.T. Correia de Barros and M.E. Almeida,"Computation of electromagnetic transients onnonuniform transmission lines", IEEE Trans. on PowerDelivery, vol. 11, no. 2, pp. 1082- 1091, April 1996.

[70] H.V. Nguyen, H.W. Dommel and J.R. Marti,"Modeling of single-phase nonuniform transmissionlines in electromagnetic transient simulations", IEEETrans. on Power Delivery, vol. 12, no. 2, 916-921,

1-15

April 1997.[71] W.A. Chisholm, Y.L. Chow and K.D. Srivastava,

"Lightning surge response of transmission towers",IEEE Trans. on Power Apparatus and Systems, vol.102, no. 9, pp. 3232- 3242, September 1983.

[72] W.A. Chisholm and Y.L. Chow, "Travel time oftransmission towers", IEEE Trans. on PowerApparatus and Systems, vol. 104, no. 10, pp. 2922-2928, October 1985.

[73] M. Ishii et al., "Multistory transmission tower modelfor lightning surge analysis", IEEE Trans. on PowerDelivery, vol. 6, no. 3, pp. 1327-1335, July 1991.

[74] T. Yamada et al., "Experimental evaluation of a UHVtower model for lightning surge analysis", IEEE Trans.on Power Delivery, vol. 10, no. 1, pp. 393-402,January 1995.

[75] M.Mihailescu-Suliciu and I. Suliciu, "A rate typeconstitutive equation for the description of the coronaeffect", IEEE Trans. on Power Apparatus and Systems,vol. 100, no. 8, pp. 3681-3685, August 1981.

[76] X.-R. Li, O.P. Malik and Z.-D. Zhao, "A practicalmathematical model of corona for calculation oftransients on transmission lines", IEEE Trans. onPower Delivery, vol. 4, no. 2, pp. 1145-1152, April1989.

[77] M.A. Al-Tai et al., "The simulation of surge coronaon transmission lines", IEEE Trans. on PowerDelivery, vol. 4, no. 2, pp. 1360-1368, April 1989.

[78] X.-R. Li, O.P. Malik and Z.-D. Zhao, "Computationof transmission lines transients including coronaeffects", IEEE Trans. on Power Delivery, vol. 4, no.3, pp. 1816-1821, July 1989.

[79] C. de Jesus and M.T. Correia de Barros, "Modellingof corona dynamics for surge propagation studies",IEEE Trans. on Power Delivery, vol. 9, no. 3, pp.1564-1569, July 1994.

[80] K.C. Lee, "Non-linear corona models in anelectromagnetic transients program (EMTP)", IEEETrans. on Power Apparatus and Systems, vol. 102, no.9, pp. 2936-2942, September 1983.

[81] W.-G. Huang and A. Semlyen, "Computation ofelectro- magnetic transients on three-phase transmissionlines with corona and frequency dependentparameters", IEEE Trans. on Power Delivery, vol. 2,no. 3, pp. 887-898, July 1987.

[82] P. Sarma Maruvada, D.H. Nguyen and H.Hamadani-Zadeh, "Studies on modeling coronaattenuation of dynamic overvoltages", IEEE Trans. onPower Delivery, vol. 4, no. 2, pp. 1441-1449, April1989.

[83] S. Carneiro Jr. and J.R. Marti, "Evaluation of coronaand line models in electromagnetic transient

simulations", IEEE Trans. on Power Delivery, vol. 6,no. 1, pp. 334-342, January 1991.

[84] S. Carneiro Jr., H.W. Dommel, J.R. Marti and H.M.Barros, "An efficient procedure for the implementationof corona models in electromagnetic transientsprograms", IEEE Trans. on Power Delivery, vol. 9,no. 2, pp. 849-855, April 1994.

[85] J.R. Marti, F. Castellanos and N. Santiago, "Wide-band corona circuit model for transient simulations",IEEE Trans. on Power Systems, vol. 4, no. 2, pp.1003-1013, May 1995.

[86] H.M. Barros, S. Carneiro Jr. and R.M. Azevedo, "Anefficient recursive scheme for the simulation ofovervoltages on multiphase systems under corona",IEEE Trans. on Power Delivery, vol. 10, no. 3, pp.1443-1452, July 1995.

[87] A. Ametani, "A general formulation of impedance andadmittance of cables", IEEE Trans. on PowerApparatus and Systems, vol. 99, no. 3, pp. 902-910,May/June 1980.

[88] L.A. Wedepohl and D.J. Wilcox, "Transient analysisof underground power-transmission systems", Proc.IEE, vol. 120, no. 2, pp. 253-260, February 1973.

[89] G.W. Brown and R.G. Rocamora, "Surge propagationin three-phase pipe type cables. Part I - Unsaturatedpipe", IEEE Trans. on Power Apparatus and Systems,vol. 95, no. 1, pp. 88-95, January/February 1976.

[90] L. Marti, "Simulation of transients in undergroundcables with frequency-dependent modal transformationmatrices", IEEE Trans. on Power Delivery, vol. 3, no.3, pp. 1099-1110, July 1988.

[91] A. Ametani, "Wave propagation characteristics ofcables", IEEE Trans. on Power Apparatus andSystems, vol. 99, no. 2, pp. 499-505, April 1980.

[92] N. Nagaoka and A. Ametani, "Transient calculationson crossbonded cables", IEEE Trans. on PowerApparatus and Systems, vol. 102, no. 4, pp. 779-787,April 1983.

[93] B. Gustavsen and J. Sletbak, "Transient sheathovervoltages in armoured power cables", IEEE Trans.on Power Delivery, vol. 11, no. 3, pp. 1594-1600,July 1996.

[94] R.J. Meredith, "EMTP modeling of electromagnetictransients in multi-mode coaxial cables by finitesections", IEEE Trans. on Power Delivery, vol. 12,no. 1, pp. 489-496, January 1997.

[95] V. Brandwajn, H.W. Dommel and I.I. Dommel,"Matrix representation of three-phase n-windingtransformers for steady-state and transient studies",IEEE Trans. on Power Apparatus and Systems, vol.101, no. 6, pp. 1369-1378, June 1982.

[96] W.L.A. Neves and H.W. Dommel, "On modeling iron

1-16

core nonlinearities", IEEE Trans. on Power Systems,vol. 8, no. 2, pp. 417-425, May 1993.

[97] W.L.A. Neves and H.W. Dommel, "Saturation curvesof delta-connected transformers from measurements",IEEE Trans. on Power Delivery, vol. 10, no. 3, pp.1432-1437, July 1995.

[98] M. Vakilian and R.C. Degeneff, "A method formodeling nonlinear core characteristics of transformerduring transients", IEEE Trans. on Power Delivery,vol. 9, no. 4, pp. 1916-1925, October 1994.

[99] S.N. Talukdar and J.R. Bailey, "Hysteresis models forsystem studies", IEEE Trans. on Power Apparatus andSystems, vol. 95, no. 4, pp. 1429-1434, July/August1976.

[100] E.P. Dick and W.Watson, "Transformer models fortransient studies based on field measurement", IEEETrans. on Power Apparatus and Systems, vol. 100, no.1, pp. 401-419, January 1981.

[101] J.G. Frame, N. Mohan and T.H. Liu, "Hysteresismodeling in an electro-magnetic transients program",IEEE Trans. on Power Apparatus and Systems, vol.101, no. 9, pp. 3403-3412, September 1982.

[102] F. de León and A. Semlyen, "Simple representation ofdynamic hysteresis losses in power transformers",IEEE Trans. on Power Delivery, vol. 10, no. 1, pp.315-321, January 1995.

[103] J. Avila-Rosales and F.L. Alvarado, "Nonlinearfrequency dependent transformer model forelectromagnetic transient studies in power systems",IEEE Trans. on Power Apparatus and Systems, vol.101, no. 11, pp. 4281-4288, November 1982.

[104] J. Avila-Rosales and A. Semlyen, "Iron core modelingfor electrical transients", IEEE Trans. on PowerApparatus and Systems, vol. 104, no. 11, pp. 3189-3194, November 1985.

[105] E.J. Tarasiewicz, A.S. Morched, A. Narang and E.P.Dick, "Frequency dependent eddy current models fornonlinear iron cores", IEEE Trans. on Power Systems,vol. 8, no. 2, pp. 588-597, May 1993.

[106] F. de León and A. Semlyen, "Detailed modeling ofeddy current effects for transformer transients", IEEETrans. on Power Delivery, vol. 9, no. 2, pp. 1143-1150, April 1994.

[107] C.M. Arturi, "Transient simulation and analysis of athree-phase five-limb step-up transformer following anout-of-phase synchronization", IEEE Trans. on PowerDelivery, vol. 6, no. 1, pp. 196-207, January 1991.

[108] A. Narang and R. H. Brierley, "Topology basedmagnetic model for steady-state and transient studiesfor three-phase core type transformers", IEEE Trans.on Power Systems, vol. 9, no. 3, pp. 1337-1349,August 1994.

[109] X. Chen and S.S. Venkata, "A three-phase three-winding core-type transformer model for low-frequencytransient studies", IEEE Trans. on Power Delivery,vol. 12, no. 3, 775-782, April 1997.

[110] B.A. Mork, "Five-legged wound-core transformermodel: Derivation, parameters, implementation, andevaluation", Paper PE-414-PWRD-0-12-1997,presented at the 1998 IEEE PES Winter Meeting,February 1-5, 1998, Tampa.

[111] D.L. Stuehm, B.A. Mork and D.D. Mairs, "Five-legged core transformer equivalent circuit", IEEETrans. on Power Delivery, vol. 4, no. 3, pp.1786-1793, July 1989.

[112] X. Chen, "A three-phase multi-legged transformermodel in ATP using the directly-formed inverseinductance matrix", IEEE Trans. on Power Delivery,vol. 11, no. 3, pp. 1554-1562, July 1996.

[113] R.C. Degeneff, "A general method for determiningresonances in transformer windings", IEEE Trans. onPower Apparatus and Systems, vol. 96, no. 2,March/April 1977.

[114] R.C. Degeneff, "A method for constructing terminalmodels for single-phase n-winding transformers",Paper No. A 78 539-9, 1978 IEEE PES SummerMeeting, July 16-21, Los Angeles.

[115] A. Morched, L. Marti and J. Ottevangers, "A highfrequency transformer model for the EMTP", IEEETrans. on Power Delivery, vol. 8, no. 3, pp. 1615-1626, July 1993.

[116] P.T.M. Vaessen, "Transformer model for highfrequencies", IEEE Trans. on Power Delivery, vol. 3,no. 4, pp. 1761-1768, October 1988.

[117] V. Woivre, J.P. Artaud, A Ahmad and N. Burais,"Transient overvoltage study and model for shell-typepower transformers", IEEE Trans. on Power Delivery,vol. 8, no. 1, pp. 212-222, January 1993.

[118] A. Oguz Soysal, "A method for wide frequency rangemodeling of power transformers and rotatingmachines", IEEE Trans. on Power Delivery, vol. 8,no. 4, pp. 1802-1810, October 1993.

[119] S. Chimklai and J.R. Marti, "Simplified three-phasetransformer model for electromagnetic transientstudies", IEEE Trans. on Power Delivery, vol. 10, no.3, pp. 1316-1324, July 1995.

[120] G.B. Gharehpetian, H. Mohseni and K. Moller,"Hybrid modelling of inhomogeneus transformerwindings for very fast transient overvoltage studies",IEEE Trans. on Power Delivery, vol. 13, no. 1, pp.157-163, January 1998.

[121] R.C. Degeneff, M.R. Gutierrez and P.J. McKenny,"A method for constructing reduced order transformermodels for system studies from detailed lumped

1-17

parameter models", IEEE Trans. on Power Delivery,vol. 7, no. 2, pp. 649-655, April 1992.

[122] M. Gutierrez, R.C. Degeneff, P.J. McKennny andJ.M. Schneider, "Linear, lumped parametertransformer model reduction technique", IEEE Trans.on Power Delivery, vol. 10, no. 2, pp. 853-861, April1995.

[123] R.C. Degeneff, M.R. Gutierrez and M. Vakilian,"Nonlinear, lumped parameter transformer modelreduction technique", IEEE Trans. on Power Delivery,vol. 10, no. 2, pp. 862-868, April 1995.

[124] R.J. Galarza, J.H. Chow and R.C. Degeneff,"Transformer model reduction using time andfrequency domain sensitivity techniques", IEEE Trans.on Power Delivery, vol. 10, no. 2, pp. 1052-1059,April 1995.

[125] D.N. Ewart, "Digital computer simulation model of asteel-core transformer", IEEE Trans. on PowerDelivery, vol. 1, no. 3, pp. 174-183, July 1986.

[126] D. Dolinar, J. Pihler and B. Grcar, "Dynamic modelof a three-phase power transformer", IEEE Trans. onPower Delivery, vol. 8, no. 4, pp. 1811-1819, October1993.

[127] F. de León and A. Semlyen, "Complete transformermodel for electromagnetic transients", IEEE Trans. onPower Delivery, vol. 9, no. 1, pp. 231-239, January1994.

[128] B.C. Papadias et al., "Three phase transformermodelling for fast electromagnetic transient studies",IEEE Trans. on Power Delivery, vol. 9, no. 2, pp.1151-1159, April 1994.

[129] P. Bastard, P. Bertrand and M. Meunier, "Atransformer model for winding fault studies", IEEETrans. on Power Delivery, vol. 9, no. 2, pp. 690-699,April 1994.

[130] D.P. Carroll et al., "A dynamic surge arrester modelfor use in power system transient studies", IEEETrans. on Power Apparatus and Systems, vol. 91, no.3, pp. 1057-1066, May/June 1972.

[131] C. Dang, T.M. Parnell and P.J. Price, "The responseof metal oxide surge arresters to steep fronted currentimpulses", IEEE Trans. on Power Delivery, vol. 1, no.1, pp. 157-163, January 1986.

[132] W. Schmidt et al., "Behaviour of MO-surge-arresterblocks to fast transients", IEEE Trans. on PowerDelivery, vol. 4, no. 1, pp. 292-300, January 1989.

[133] IEEE Working Group on Surge Arrester Modeling,"Modeling of metal oxide surge arresters", IEEETrans. on Power Delivery, vol. 7, no. 1, pp. 302-309,January 1992.

[134] I. Kim et al., "Study of ZnO arrester model for steepfront wave", IEEE Trans. on Power Delivery, vol. 11,

no. 2, pp. 834-841, April 1996.[135] IEEE Working Group of Surge Protective Devices

Committee, "Modeling of current-limiting surgearresters", IEEE Trans. on Power Apparatus andSystems, vol. 100, no. 8, pp. 4033-4040, August 1981.

[136] D. L. Goldsworthy, "A linearized model for MOV-protected series capacitors", IEEE Trans. on PowerSystems, vol. 2, no. 4, pp. 953-958, November 1987.

[137] J.R. Lucas and P.G. McLaren, "A computationallyefficient MOV model for series compensation studies",IEEE Trans. on Power Delivery, vol. 6, no. 4, pp.1491-1497, October 1991.

[138] A.S. Morched and V. Brandwajn, "Transmissionnetwork equivalents for electromagnetic transientsstudies", IEEE Trans. on Power Apparatus andSystems, vol. 102, no. 9, pp. 2984- 2994, September1983.

[139] M. Kizilcay, "Low-order network equivalents forelectromagnetic transients studies", EuropeanTransactions on Electrical Power Engineering, vol. 3,no. 2, pp. 123-129, March/April 1993.

[140] A. Abur and H. Singh, "Time domain of externalsystems for electromagnetic transients programs",IEEE Trans. on Power Systems, vol. 8, no. 2, pp.671-679, May 1993.

[141] A.S. Morched, J.H. Ottevangers and L. Marti,"Multi-port frequency dependent network equivalentsfor the EMTP", IEEE Trans. on Power Delivery, vol.8, no. 3, pp. 1402-1412, July 1993.

[142] H. Singh and A. Abur, "Multiport equivalencing ofexternal systems for simulation of switchingtransients", IEEE Trans. on Power Delivery, vol. 10,no. 1, pp. 374-382, January 1995.

[143] V. Brandwajn and H.W. Dommel, "A new method forinterfacing generator models with an electromagnetictransients program", Proc. of IEEE PICA, pp.260-265, 1977.

[144] G. Gross and M.C. Hall, "Synchronous machine andtorsional dynamics simulation in the computation ofelectromagnetic transients", IEEE Trans. on PowerApparatus and Systems, vol. 97, no. 4, pp. 1074-1086,July/August 1978.

[145] V. Brandwajn, "Representation of magnetic saturationin the synchronous machine model in anelectromagnetic transients program", IEEE Trans. onPower Apparatus and Systems, vol. 99, no. 5, pp.1996-2002, September/October 1980.

[146] H.K. Lauw and W. Scott Meyer, "Universal machinemodeling for the representation of rotating machineryin an electromagnetic transients program", IEEE Trans.on Power Apparatus and Systems, vol. 101, no. 6, pp.1342-1352, June 1982.

1-18

[147] H.K. Lauw, "Interfacing for universal multi-machinesystem modeling in an electromagnetic transientsprogram", IEEE Trans. on Power Apparatus andSystems, vol. 104, no. 9, pp. 2367-2373, September1985.

[148] J.R. Marti and K.W. Louie, "A phase-domainsynchronous generator model including saturationeffects", IEEE Trans. on Power Systems, vol. 12, no.1, pp. 222-229, February 1997.

[149] A.M. Gole, R.W. Menzies, H.M. Turanli and D.A.Woodford, "Improved interfacing of electrical machinemodels to electromagnetic transients programs", IEEETrans. on Power Apparatus and Systems, vol. 103, no.9, pp. 2446-2451, September 1984.

[150] P.G. McLaren and M.H. Abdel-Rahman, "Modelingof large AC motor coils for steep-fronted surgestudies", IEEE Trans. on Industry Applications, vol.24, no. 3, pp. 422-426, May/June 1988.

[151] J.L. Guardado and K.J. Cornick, "A computer modelfor calculating steep-fronted surge distribution inmachine windings", IEEE Trans. on EnergyConversion, vol. 4, no. 1, 95-101, March 1989.

[152] A. Narang, B.K. Gupta, E.P. Dick and D.K. Sharma,"Measurement and analysis of surge distribution inmotor stator windings", IEEE Trans. on EnergyConversion, vol. 4, no. 1, 126-134, March 1989.

[153] N.J. Bacalao, P. de Arizon and R.O. Sánchez, "Amodel for the synchronous machine using frequencyresponse measurements", IEEE Trans. on PowerSystems, vol. 10, no. 1, pp. 457-464, February 1995.

[154] A. Domijan and Y. Yin, "Single-phase inductionmachine simulation using the ElectromagneticTransients Program : Theory and test cases", IEEETrans. on Energy Conversion, vol. 9, no. 3, pp.535-542, September 1994.

[155] H. Knudsen, "Extended Park's transformation for2x3-phase synchronous machine and converter phasormodel with representation of harmonics", IEEE Trans.on Energy Conversion, vol. 10, no. 1, pp. 126-132,March 1995.

[156] R. Hung and H.W. Dommel, "Synchronous machinemodels for simulation of induction motor transients",IEEE Trans. on Power Systems, vol. 11, no. 2, pp.833-838, May 1996.

[157] CIGRE Working Group 13.01, "Practical applicationof arc physics in circuit breakers. Survey of calculationmethods and application guide", Electra, no. 118, pp.64-79, 1988.

[158] CIGRE Working Group 13.01, "Applications of blackbox modelling to circuit breakers", Electra, no. 149,pp. 40-71, August 1993.

[159] EPRI Report EL-4651, "Electromagnetic Transients

Program (EMTP) Workbook II", 1989.[160] J.A. Martinez-Velasco, "Circuit breaker representation

for TRV calculations", EEUG Meeting 1995,Hannover, November 13-15, 1995.

[161] V. Phaniraj and A.G. Phadke, "Modeling of circuitbreakers in the electromagnetic transients program",IEEE Trans. on Power Systems, vol. 3, no. 2, pp.799-805, May 1988.

[162] L. van der Sluis, W.R. Rutgers and C.G.A. Koreman,"A physical arc model for the simulation of currentzero behaviour of high-voltage circuit breakers", IEEETrans. on Power Delivery, vol. 7, no. 2, pp.1016-1022, April 1992.

[163] Z. Ma et al., "An investigation of transient overvoltagegeneration when switching high voltage shunt reactorsby SF6 circuit breaker", IEEE Trans. on PowerDelivery, vol. 13, no. 2, pp. 472-479, April 1998.

[164] J.A. Martinez-Velasco, "Modelling of circuit breakerusing the type-94 component", EEUG Meeting 1995,Hannover, November 13-15, 1995.

[165] J. Mahseredjian, M. Landry and B. Khodabakhchian,"The new EMTP breaker arc model", Proceedings ofIPST'97, pp. 245-249, June 22-26, 1997, Seattle.

[166] J. Kosmac and P. Zunko, "A statistical vacuum circuitbreaker model for simulation of transientsovervoltages", IEEE Trans. on Power Delivery, vol.10, no. 1, pp. 294-300, January 1995.

[167] M.T. Glinkowski, M.R. Gutierrez and D. Braun,"Voltage escalation and reignition behavior of vacuumcircuit breakers during load shedding", IEEE Trans. onPower Delivery, vol. 12, no. 1, pp. 219-226, January1997.

[168] D.A. Woodford and L.M. Wedepohl, "Impact ofcircuit breaker pre-strike on transmission lineenergization transients", Proceedings of IPST'97, pp.250-253, June 22-26, 1997, Seattle.

[169] J.A. Martinez-Velasco, R. Abdo and G. Capolino,"Advanced representation of power semiconductorsusing the EMTP", Proceedings of IPST'95, pp. 505-510, September 3-7, 1995, Lisbon.

[170] C. Wong, "EMTP modeling of IGBT dynamicperformance for power dissipation estimation", IEEETrans. on Industry Applications, vol. 33, no. 1, pp.64-71, January/February 1997.

[171] J. Lucas et al., "Improved simulation models forcurrent and voltage transformers in relay studies",IEEE Trans. on Power Delivery, vol. 7, no. 1, pp.152-159, January 1992.

[172] M. Kezunovic et al., "Digital models of couplingcapacitor voltage transformers for protective relaytransient studies", IEEE Trans. on Power Delivery,vol. 7, no. 4, pp. 1927-1935, October 1992.

1-19

[173] M. Kezunovic et al., "Experimental evaluations ofEMTP-based current transformer models for protectiverelay transient study", IEEE Trans. on Power Delivery,vol. 9, no. 1, pp. 405-413, January 1994.

[174] M. Kezunovic et al., "A new method for the CCVTperformance analysis using field measurements, signalprocessing and EMTP modeling", IEEE Trans. onPower Delivery, vol. 9, no. 4, pp. 1907-1915, October1994.

[175] M.R. Iravani et al., "Digital time-domain investigationof transient behaviour of coupling capacitor voltagetransformer", IEEE Trans. on Power Delivery, vol. 13,no. 2, pp. 622-629, April 1998.

[176] A. Domijan and M.V. Emami, "State space relaymodeling and simulation using the ElectromagneticTransients Program and its Transient Analysis ofControl Systems capability", IEEE Trans. on EnergyConversion, vol. 5, no. 4, pp. 697-702, December1990.

[177] R.E. Wilson and J.M. Nordstrom, "EMTP transientmodeling of a distance relay and a comparison withEMTP laboratory testing", IEEE Trans. on PowerDelivery, vol. 8, no. 3, pp. 984-992, July 1993.

[178] A.K.S. Chaudhary, K.S. Tam and A.G. Phadke,"Protection system representation in theelectromagnetic transients program", IEEE Trans. onPower Delivery, vol. 9, no. 2, pp. 700-711, April1994.

[179] M.T. Glinkowski and J. Esztergalyos, "Transientmodeling of electromechanical relays. Part I :Armature type overcurrent relays", IEEE Trans. onPower Delivery, vol. 11, no. 2, pp. 763-770, April1996.

[180] M.T. Glinkowski and J. Esztergalyos, "Transientmodeling of electromechanical relays. Part II : PlungerType 50 relays", IEEE Trans. on Power Delivery, vol.11, no. 2, pp. 771-782, April 1996.

[181] J.A. Martinez-Velasco and L. Kojovic, "ATP modelingof electromechanical relays", Proceedings of IPST'97,pp. 446-451, June 22-26, 1997, Seattle.

[182] A. Petit, G. St-Jean and G. Fecteau, "Empirical modelof a current-limiting fuse using EMTP", IEEE Trans.on Power Delivery, vol. 4, no. 1, pp. 335-341,January 1989.

[183] L. Kojovic and S. Hassler, "Application of currentlimiting fuses in distribution systems for improvedpower quality and protection", IEEE Trans. on PowerDelivery, vol. 12, no. 2, 791-800, April 1997.

[184] CIGRE Working Group 02 (SC 33), "Guidelines forRepresentation of Network Elements when CalculatingTransients", 1990.

[185] IEEE Task Force on Slow Transients (M.R. Iravani,

Chairman), "Modeling and Analysis Guidelines forslow transients. Part I : Torsional Oscillations;Transient Torques; Turbine blade vibrations; Fast bustransfer", IEEE Trans. on Power Delivery, vol. 10,no. 4, pp. 1950-1955, October 1995.

[186] IEEE Task Force on Slow Transients (M.R. Iravani,Chairman), "Modeling and Analysis Guidelines forslow transients. Part II : Controller Interactions;Harmonic Interactions", IEEE Trans. on PowerDelivery, vol. 11, no. 3, pp. 1672-1677, July 1995.

[187] IEEE Task Force on Slow Transients (M.R. Iravani,Chairman), "Modeling And Anlysis Guidelines forslow transients - Part III : The study of ferroreso-nance", 1998 IEEE Summer Power Meeting, July 12-16, San Diego.

[188] IEEE TF on Fast Front Transients (A.Imece,Chairman), "Modeling guidelines for fast transients",IEEE Trans. on Power Delivery, vol. 11, no. 1,January 1996.

[189] IEEE TF on Very Fast Transients (D. Povh,Chairman), "Modeling and analysis guidelines for veryfast transients", IEEE Trans. on Power Delivery, vol.11, no. 4, October 1996.

[190] IEEE Task Force on Power Electronics (L. Tang,Chairman), "Guidelines for modeling power electronicsin electric power engineering applications", IEEETrans. on Power Delivery, vol. 12, no. 1, pp.505-514, January 1997.