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The main purpose of this article is to introduce a different method to electrify 0.5 MVA micro-loads using energy loss confined in insulated shielding wires of a 500 kV transmission line. The mathematical model of the system along with the series tuning reactor, necessary for voltage regulation, is described. Digital simulations are used to identify the maximum induced voltage in the insulated wire and the power extracted from the system. Finally, a transient analysis was presented showing that the modifications did not affect transmission line performance or reliability.

This paper presents a comparison of secondary electric arcs behavior for reclosing applications. The main objective of the paper is to show the differences in secondary arcs during simulations, laboratory tests and real life events. These comparisons can help engineers develop adaptive reclosing algorithms and improve power system stability. A software arc model, a laboratory test result and field events' harmonic contents were analyzed. Although the harmonics may differ in each method, they all provide enough information to be used in the reclosing algorithms.

This study presents the results of single-phase auto reclosing technique tests, comparing the performance of traditional procedure and fast adaptive procedure. The last is based on the measurement of voltage harmonic content on the transmission line faulty phase terminals. The transmission system used was modelled on the real-time digital simulator with a distance relay and a quality meter to more realistically implement the reclosing techniques. The studied system was based on an actual Brazilian 500 kV transmission system. This study highlights the advantages of using the adaptive technique opposite to the use of traditional manoeuvre.

This paper presents a relay model based on a manufactured differential transformer relay, SEL-787, developed in a real-time digital simulator. The objective of this study was to develop the model and to compare its performance to the actual relay and to a generic built-in model. With the proposed model, it is possible to implement studies in real-time simulators not only with the physical relay under analysis, but also with the surrounding protection system. The use of many relays for a real-time simulation test can be very expensive and complex. This paper presents the possibility of using models, based on actual relays, in the surrounding areas to cover all possible protection problems. The proposed model presents a new modeling technique and the comparisons to the relay itself and to the built-in generic model were made not only in terms of algorithms but also in terms of response time. The model’s performance was studied for different situations that interfere with the relay daily operation and it presented good adherence to the actual relay. This could not be observed in the built-in real-time simulator model.

The purpose of this paper is to supply technical data for the proposed field energization of 500 kV transmission lines present in the Brazilian interconnected system, forming a line, henceforth called AC-Link, slightly over a half-wavelength in 60 Hz. The purpose of the test is to investigate overvoltages and currents that result from the energization of the AC-Link. This paper shows the results of simulations performed in ATP (Alternative Transients Program) when considering the occurrence of three-phase faults along the AC-Link during energization. The results obtained show that, in certain situations, the overvoltages and energies in the arresters may reach very high values and some specific mitigation procedure should be implemented.

This paper proposes an enhancement on the methodology commonly used for overvoltage analysis motivated by the excitation of electric network resonance points due to injection of harmonic currents by equipment with nonlinear characteristics. The improvement proposed comprehends inclusion of effects caused by nonlinear equipment into the frequency scan study, harmonic content survey, transformation of currents and/or voltages from phase to sequence domain, and application of the Windowed Fast Fourier Transform (FFT). This enhanced methodology was applied in the investigation and identification of unexpected resonant behavior causes observed in pre-operational electromagnetic transient studies for an autotransformer energization.

This study involves the application of Short Time Discrete Fourier Transform in order to obtain the harmonic content of voltage between the terminals of 647 artificially generated long electrical arcs. Non-confined tests were conducted on three 500 kV towers specially built inside a laboratory facility, in order to represent as close as possible actual transmission line conditions. The 1-s duration arcs were artificially generated along the 4 m insulator string of a 500 kV tower by imposing a sustained 60 Hz current. The arc voltage harmonic content can be used to identify the moment at which the arc is stabilized in the air and only after this instant measured data can be used to derive mathematical arc model. A statistical analysis of the results, considering only the period for which the arc is stabilized, enabled the establishment of the harmonic signature of the electric arcs for a large arc current amplitude range. From the results it can be stated that an accurate arc model should properly reproduce the presented harmonic content for any arc current level.

This paper describes the statistical study of important factors that influences transient over voltages resulting from three-phase reclosing of shunt compensated transmission lines. These factors include the model used for transmission line representation and the influence of line transposition. Additionally, the over voltages reduction to proper levels depending on the type of control technique are illustrated and analyzed in statistical terms. The evaluation covers three shunt compensation degrees. The digital simulations were performed using the PSCAD/EMTDC software.

In the present paper the main results of the pre-operational studies related to the energization maneuver of a Half-Wavelength Transmission Line (AC-Link), are presented. The simulations were performed in PSCAD with actual Brazilian system data. Specifically the following studies were performed: electromagnetic transient studies of energization maneuver considering no fault and the occurrence of fault along the trunk; dynamic analysis of generator units that will energize the AC-Link; TRV on the circuit-breaker that will energize the trunk. The main conclusion is that the AC-Link energization experiment can be implemented without jeopardizing or causing time-life reduction of the equipment involved in the experiment, which comprises the generator unit that will energize the trunk, the step-up transformer, the arresters that will be kept during the experiments, as well as the circuit-breaker that will energize and then trip the AC-Link.

This paper presents the main results on the use of conventional protection hardware to protect a Half Wavelength Transmission Line, or shortly AC-Link, for possible occurrence of three-phase and single-phase fault during energization maneuver. Lines of these dimensions do not exist today, but in countries of continental size they could be an interesting alternative to HVDC transmission, since the AC-Link has less dependence on Power Electronics technology. The studies on performance and relay settings were implemented using the RTDS real-time simulator. It is important to note that the AC-Link protection for the energization maneuver can be performed with existing hardware on conventional relays.

Transmission lines with half wavelength properties have been studied since many years and are still of interest due to recent necessity of bulk power transmission from power generated by intermittent sources over long distances. Nowadays HVDC systems are used to this transmission application, however classical HVDC presents some restrictions. This paper presents a study of important properties of flexible distance AC link transmission system with half wavelength properties, like adequate voltage reactive power regulation. Electromagnetic transient study was implemented taking into account the strength of terminal power systems. All simulations are performed with PSCAD/EMTDC.

This paper presents the methodology and the main results of the optimization process to increase the transmission capacity of overhead lines of 500, 750 and 1000 kV by changing the geometry of the bundles using a new heuristic algorithm. The optimization process is done respecting the insulating distances, the maximum electric field at a height of 1.5 meters from the ground surface, the electric field balance in the conductors, and avoiding the generation of corona effect. Using this methodology it was possible to substantially increase the capacity of transmission lines using bundles with moderate dimensions, and having different geometries from previous authors.

This paper proposes a new control method to reduce overvoltages due to three-phase reclosing for shunt compensated transmission lines (TL). The method detects the first minimum voltage region of the beating across the circuit breakers after protection dead time and works independently of voltage zero crossing, reducing significantly the reclosure time. The controller was tested on a Real Time Digital Simulator (RTDS) and its performance was compared to the traditional preinsertion resistor approach and another existing control method.

The secondary arc extinction is the main concern in single-phase auto reclosure (SPAR) switching studies, since it dictates whether the reclosure will be successful or not. In this context, a function that describes the arc length variation over time (l(t)) is an important information not only for dynamic response but also for the analysis of transient arc processes. Given that purely electrotechnical approach only gives a profile of the curve l(t), the application of techniques based on image analysis has been considered for obtaining such function. In this paper, a new approach based on 3D-reconstruction and the tracking of an electrical arc is proposed for performing a computer-based evaluation of variations in its length. It was applied a three-dimensional active contour named 3D-snake that is geometrically represented by a B-spline, which evolves in 3D space. This new model is much less dependent on the determination of homologous points than the ad hoc approaches found in the literature for recovering 3D geometry of electrical discharges based on image analysis. In addition, the proposal presented is capable of tracking the evolution of the electrical discharge taking into account the time dependence between consecutive pairs of frames in two videos providing the required function l(t).

The energization of long transmission lines can cause high overvoltage stresses not only along the transmission line, but also in the rest of the network. The traditional method of limiting switching overvoltages to acceptable levels is the use of circuit breakers equipped with pre-insertion resistors. The present paper describes a study comparing this traditional method with two other alternatives for the limitation of switching overvoltages during line energization in an actual 500 kV transmission system: the use of metal oxide surge arresters at both line closing of circuit breaker poles. Digital simulations were made with PSCAD/EMTDC software and the degree of shunt compensation is considered as an independent parameter.

The objective of this paper is to show an alternative methodology to calculate transmission-line parameters per unit length. With this methodology, the transmission-line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency-dependent transmission-line parameters by using Carson's and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency-dependent transmission-line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a two-phase and a three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulations results for a typical frequency spectrum of switching transients (10 Hz to 10 kHz).

Initially this paper shows the ground wire reduction process for generic multiphase transmission lines and after, the ground wire reduction process for a specific 440-kV three-phase overhead transmission line. Following this, the influence of the ground wire reduction process considering two situations is shown: first, considering frequency independence and second, when these parameters are considered as frequency dependent. This paper presents analytical results for generic multiphase transmission lines. For a specific 440-kV three-phase overhead transmission line, analytical and graphic results are shown considering real data for every frequency between 10 Hz and 1 MHz.

In the presented paper, it is shown how the utilization of a systematic three-phase fundamental frequency analysis and three-phase frequency scan can become helpful tools in an electromagnetic transient study. The present methodology was applied to a study of real transmission system expansion, and it allowed for the identification of some rather severe cases which would be very hard to discover through the ordinary transient study procedure.

The quality of electric power has been a constant topic of study, mainly because inherent problems to it can lead to great economic losses, especially in industrial processes. Among the various factors that affect power quality, those related to transients originating from capacitor bank (CB) switching in the primary distribution systems must be highlighted. In this work, the characteristics of transients resulting from the switching of utility CBs are analyzed, as well as factors that influence their intensities. The conditions under which these effects are mitigated can then be investigated. A circuit that represents a real distribution system, 13.8 kV, from Cia Paulista de Forca e Luz (CPFL—a Brazilian utility) was simulated through the software Alternative Transients Program ( atp ) for purposes of this study. Finally, a comparison with real-life data recorded at the distribution system was performed in order to validate the present simulation.

This paper describes the quasi-modes three-phase transmission line model, a new model to represent three-phase transmission lines in transient studies, with proper representation of the frequency dependence of longitudinal parameters. A unique transformation matrix—the Clarke matrix—is used for the entire frequency range. As this matrix is a real one. it can be modeled through ideal transformers. The circuit equations, which lead to the matrix modeling, are presented. This line model can be implemented in any digital program with R , L , C and transformer components.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with a cascade of π-circuit for each mode. A real transformation matrix is used for the entire frequency range and it is modeled through ideal transformers in a transient program like ATP, as described. An application of the methodology is presented for an actual 440 kV single three-phase transmission line where some transients results simulated in ATP are presented. The model is compared to two ATP line models, JMarti and Semlyen.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The model uses the exact modes, for ideally transposed lines, and "quasi-modes" for nontransposed lines. For the latter it is necessary to have a vertical symmetry plane. The frequency dependence is represented with synthetic circuits, with one /spl pi/-circuit for each mode. The transformation matrix used for the entire frequency range is the Clarke's one and as it is a real matrix it is modeled through ideal transformers. The model is described for three-phase lines and double three-phase lines. An application of the methodology is presented for a 440 kV single three-phase transmission line where it is made mode analysis, statistical energization and frequency scan analysis. The simulations are performed in EMTP with the proposed model and with a frequency dependent EMTP line model, the Semlyen one, supposing a transposed and nontransposed line.

Large hydroelectric power plants are planned or under construction on the Amazon basin, located in the north region of Brazil. However, the main load centers in Brazil are located on the southeast and northeast regions, far from these generation sites by 2500-3000 km. These projects bring new challenges for power system engineers in terms of designing and operating transmission lines for very large distances and capacity, creating the opportunity for innovative solutions. HVDC would be the natural solution but it is still expensive. Conventional AC transmission would be unfeasible due to the enormous need for reactive power compensation. Under this scenario, an alternative transmission technology comes to light, the half-wavelength AC transmission line. In this paper, three half-wavelength transmission corridors are studied for the interconnection of Belo Monte Power Plant, located on the State of Para, to the Brazilian interconnected system through Assis Substation, on the State of Sao Paulo, with a total distance of 2664km. Losses, voltage profile, level of reactive power compensation, solutions for the voltage control on both sending and receiving ends, insertion of loads or generation at intermediate points, are among the analyzed aspects for different loading and interchange scenarios.

This paper proposes the use of three-phase twoports elements to obtain the sustained response of unbalanced electric power system. Representations of three-phase two-ports networks for various types of elements of the electrical power system are described. The methodology is applied to identify the optimum neutral reactor that minimizes the secondary arc current in a transmission system, thus enabling the single-phase auto-reclosing switching implementation.

The overvoltage phenomena due to three-phase reclosing of shunt compensated extra high voltage (EHV) transmission lines are analyzed and verified by PSCAD/EMTDC simulation. The study made in an actual 500 kV AC transmission system considers three alternatives in order to limit overvoltages during line reclosing: a developed synchronous switching method, the use of circuit breakers with pre-insertion resistors and the use of metal oxide surge arresters at both line ends. The developed synchronous switching method detects the first minimum region of the voltage beating across the circuit breakers after protection dead time and works independently of zero voltage crossing, reducing significantly the overvoltages and reclosure time. The study was realized taking the line length as an independent parameter.

This study involves the application of the Windowed Discrete Fourier Transform in order to obtain the harmonic content of the current and voltage between the terminals of 543 artificially generated electric arcs. This harmonic content can be used to identify the moment at which the arc is stabilized in the air. Using these data, the length variation results of 69 selected artificially generated arcs, obtained through the analysis of both visual records generated with two cameras and the first pseudo-harmonic voltage between the arcs terminals, are presented.

A new component transformation is proposed for six-phase systems, applicable for six-phase transmission lines studies, allowing its representation by two uncoupled three-phase lines. Cyclic transposition allows additional properties of the two three-phase groups that are presented. Transposed and nontransposed six-phase lines are analyzed, and the main characteristics of their natural modes are discussed in the frequency domain. An eigenvector normalization method for nontransposed lines that assures null modal conductance and, as a consequence, positive modal resistance, is proposed. Numeric results are presented in relation to an example line of 500 kV/sub rms/, phase to ground, with characteristic power of 5176 MW. >

In Brazil big blocks of energy will be transported through distances between 2500 and 3000 km to the strong network nodes. Among the AC transmission systems alternatives being analyzed the half-wave length transmission seems to be the natural solution as the lengths involved are around a half-wave length of a 60 Hz frequency system, as the Brazilian one. As there is no half-wave transmission system in operation in the world, there is a major sense of caution in order to be the first to construct and use this new AC-link. In order to give some support a field test with a set of existing similar 500 kV lines that could be connected in series was proposed to simulate the AC-link behavior under some controlled switching. The proposed AC-link test was simulated in PSCAD/EMTDC.

Brazilian electrical transmission system has radial sub-systems and not much meshed long EHV/HV lines, a profile that suggests single-phase auto-reclosure (SPAR) as usual procedure. Since year 2000, the national Electrical Energy Regulatory Agency (ANEEL) has required the use of SPAR in the design, construction and operation of new transmission lines. Analysis of SPAR success is basically related to secondary arc extinction in a reasonably short time. So, secondary arc modeling became an important issue on defining optimized solutions. In 2003, FURNAS, UFRJ and CEPEL - transmission utility, university and research center, respectively - started a research project related to secondary arc modeling. A test infra-structure was set up at CEPEL's high power laboratory, including an out door real 500 kV line piece, with three towers and two spans and necessary measuring devices (electrical parameters, visual - films - and wind records), where arcs have been generated and monitored. The main purpose of this research project is to obtain and validate a robust model of the primary and secondary arcs in a transmission line, allowing to investigate the interaction between the arc and the "network", at arc terminals, and the evaluation of SPAR procedure success (or not). This work presents: the basic aspects of the laboratorial work conception; some difficulties related to the accuracy quality of arc parameters evaluation, of some usual measurement and data processing procedures; the adopted solutions to overcome such difficulties. The results already obtained support the basic conception of a gray type arc model, developed previously, allowed the establishment of adequate research type procedures for measurements and data processing, supplied a huge amount of data for arc modeling, giving basis to obtain arc parameters in an important range of conditions. New results are still expected to complete the range of conditions covered by the research project.

In this paper transmission line transposition is analyzed focusing electromagnetic transient phenomena in the range up to 10 kHz. Line transposition is implemented to decrease phase unbalances at fundamental frequency. The transposition section must be much lower than 1/4 of wave-length, which means, for 60 Hz, much lower than 1250 km. normally a 100-km section is used. For fundamental frequency it is then correct to consider the line as an ideally transposed line. In the present paper it will be analyzed the error of treating transmission line as ideally transposed for all frequency ranges, specifically when dealing with switching transients up to 10 kHz. A theoretical analysis is performed identifying the unbalances between the phases considering the transmission line ideally transposed and considering transmission line with actual transposition sections. The frequency dependence of transmission line parameters was properly represented.

In this article a more accurate representation of soil behavior for transient studies is presented. The proposed model takes into account the earth conductivity and permittivity frequency dependence, which normally is not considered. One of the aspects covered in the paper is the importance of properly considering the earth's electromagnetic behavior when calculating transmission line parameters. For an actual 440 kV three-phase transmission line, the soil behavior is represented through a unique real value of conductance ( the normal approach) and through the proposed model.

This paper presents some guidelines for verifying the accuracy of a frequency dependent transmission line model in a time domain simulation program, such as EMTP. The guidelines are described for our quasi-mode transmission line model, which is applied to an actual 440 kV single three-phase transmission line model, using ATP.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. An application of the methodology is presented for an actual 440 kV single three-phase transmission line where some transient results simulated in ATP are presented. The model is compared to two ATP line models, JMarti and Semlyen.

The quality of electric power has been a constant topic of study, mainly because inherent problems to it can bring great economic losses, mainly in industrial processes. Among the various factors that affect power quality, those related to the transients originated from capacitor bank switching in the primary distribution systems must be highlighted. In this work, the characteristics of the transients resulting from the switching of the utility capacitor banks are analyzed, as well as factors that influence their intensities. The conditions under which these effects am mitigated can then be investigated. In addition, a spectral analysis of the current and voltage waves is made. This procedure can reveal the harmonic component, which can affect the operation of control and protection equipment, as well as sensitive loads of the industry. A circuit that represents a real distribution system, 13.8 kV, from CPFL (Cia Paulista de Forca e Luz-a Brazilian utility) was simulated through the software ATP (Alternative Transients Program) for purposes of this study.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The model uses the exact modes, for ideally transposed lines, and "quasi-modes" for nontransposed lines with a vertical symmetry plane. The frequency dependence is represented with synthetic circuits, with a cascade of /spl pi/-circuit for each mode. A real transformation matrix is used for the entire frequency range and it is modeled through ideal transformers. The model is described for three-phase lines, double three-phase lines and DC lines. An application of the methodology is presented for a 440 kV single three-phase transmission line where some transients results simulated in EMTP are presented.

This article presents a new model to represent multiphase transmission lines including the frequency dependence of longitudinal parameters. The model uses exact modes, for ideally transposed lines, and "quasi-modes" for nontransposed lines with a vertical symmetry plane. The line is represented through a cascade of /spl pi/-circuits, with one /spl pi/-circuit for each mode. The transformation matrix used is real and is modeled with ideal transformers. The model is described for three-phase lines, DC lines and double three-phase lines. An EMTP implementation of a 440 kV three-phase transmission line is performed to illustrate the model and a comparison with a frequency dependent EMTP line Semlyen model is made.

This paper presents a new model to represent three-phase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with a cascade of /spl pi/-circuits for each mode. The transformation matrix used for the entire frequency range is the Clarke one. The exact eigenvectors of the nontransposed line are analyzed in the frequency domain for some earth resistivity and compared to Clarke components.

A three-phase transformer model for the calculation of electromagnetic transients for differential protection studies is presented. The ATP-EMTP was chosen as a computer tool for modeling the following situations: internal faults; transformer energization and removal of external faults. An application of the methodology is exemplified for a 138/13.8 kV-25 MVA transformer, where some transient results are presented.

This paper presents a new model to represent three-phase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The transformation matrix used for the entire frequency range is the Clarke one. It is described how to model the transformation matrix using ideal transformers. This line model can be implemented in any digital program with R, L, C and transformer components.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with a cascade of /spl pi/-circuits for each mode. The transformation matrix used for the entire frequency range is the Clarke one. The model is described for three-phase lines. The exact eigenvector of the non-transposed line is analyzed in the frequency domain for some earth resistivity and compared to Clarke components.

This article presents a model to represent double three-phase transmission lines, including the frequency dependence of longitudinal parameters, achieved through phase/mode transformation. The proposed model uses a single real transformation matrix for the entire frequency range, 10 Hz to 10 kHz. The model includes the frequency dependence in digital programs, such as ATP and MICROTRAN, using ideal transformers. This model is applied to three types of line transposition and nontransposed line, called the quasi-mode transmission line model. It is employed for an actual double three-phase transmission line in MICROTRAN program. Some transient simulations are performed, such as energization and fault analysis.

In this article the quasi-modes model is used to observe the influence, in electromagnetic transient phenomena, of considering a more accurate representation of soil, taking into account the earth conductivity and permittivity frequency dependence. For an actual 440 kV three-phase transmission line the soil behavior is represented through a unique real value of conductance and through a more accurate model, considering its electromagnetic behavior.

This article presents a model to represent double three-phase transmission lines, including the frequency dependence of longitudinal parameters. For this, frequency dependence modeling is carried out on the mode domain. A single real transformation matrix is used for the entire frequency range (up to 10 kHz). This transformation matrix is obtained from the geometrical properties of the line and is based on Clarke transformation. One of the interesting aspects of this paper is the analysis of the natural modes of the double circuit line. The transposition of the line was supposed ideal, which resulted in five equal modes and one different mode. Afterwards the line was assumed transposed as if it were a six-phase transmission line. Following this, each circuit was considered ideally transposed and there was a coupling term between the circuits. Finally the line was assumed to be nontransposed. The analysis of all this mode behavior produces a very interesting conclusion, such as: the similitude of some modes, and the possibility of working with a real transformation matrix obtained from the geometrical properties of the line as is carried out in our quasi-mode model. Finally the model is employed for an application of double three-phase transmission line using a Microtran program.

In this paper the quasi-modes transmission line model is used to observe the influence of considering a more accurate representation of the earth conductivity and permittivity. For an actual 440 kV three-phase transmission line the soil behavior is represented through a unique real value of conductance and through a more accurate model, considering its electromagnetic behavior.

A paper representation of soil behaviour for transient studies is presented. Such representation is more accurate than the most common procedures of engineering practice and, in several conditions, lead to results with important differences. The proposed model takes into account the earth's conductivity and permittivity frequency dependence, which normally are not considered. One of the aspects covered in the paper is the importance of properly considering the earth's electromagnetic behaviour when calculating transmission line parameters. Some comparisons are presented for an actual 440 kV three-phase transmission line in which the soil behaviour is represented through a unique real value of conductance (the normal approach) and through the proposed model.

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with one n-circuit for each mode. The transformation matrix used for the entire frequency range is the Clarke one and as it is a real matrix it is modeled through ideal transformers. The model is described for three-phase lines. An application of the methodology is presented for a 440 kV single three-phase transmission line. The simulations are performed in EMTP. This line model can be implemented in any digital program with R, L, C and transformer components.

The objective of this paper is to show an alternative methodology to calculate transmission line parameters per unit length. With this methodology the transmission line parameters can be obtained starting from the phase currents and voltages in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson's and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, it is shown a new procedure to calculate frequency dependent transmission line parameters directly from currents and voltages of the line that is already built. Then, this procedure is applied in a two-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared.

The main aim of this article is to apply the modal analysis to double three-phase transmission lines, modeling the frequency dependence of the line parameters. For the typically important frequency range of switching electromagnetic transients, from 10 Hz to 10 kHz, the proposed model uses a single real transformation matrix. The model presents a transmission line frequency dependence model in digital programs, such as ATP, EMTP, EMTDC and MICROTRAN. Some results of presented model are given, for an actual double three-phase transmission line, obtained using the program Microtran.