Sequence Impedance Research Articles

Skin Effect in Multiple and Polyphase Conductors

The modal theory of current flow, previously successful in predicting skin-effect behavior of single isolated conductors, is generalized to apply to any number of parallel conductors arbitrarily arranged in space and excited electrically by arbitrary currents. The distribution of current density within each conductor is found in terms of a summation of the modal functions, and the terminal parameters of the system of conductors are given as an impedance matrix relating the total conductor currents to the voltage drops in the various conductors. Sequence impedances, losses, and other electrical properties are then calculable from the basic impedance matrix.

Analysis of T-T Connections of Two Single-Phase Transformers

The T-T connected transformer is a connection of two single-phase transformers which will yield the same phasor relation as a standard 3-phase transformer. However, because of the unsymmetrical nature of the T-T connected transformer, undesirable negative and zero-sequence voltages may be introduced into the electric system. Fortunately, these voltages are quite small for a properly designed T-T connected transformer under normal load. A method for determining the induced negative-and zero-sequence voltages (or currents) by utilizing the interconnected sequence impedance circuit for the T-T connected transformer is presented.

Unbalanced Converter Operation

The results of a digital computer investigation of the effects of unbalanced alternating voltages on converter operation is described. The problem is approached from the standpoint of symmetrical components and an exact analysis has been carried out for an arbitrary ratio of positive and negative sequence voltages. Variation of the grid control firing angle has been considered permitting a full range of rectifier and inverter performance. Effect of the magnitude of commutating reactance is also investigated. With the analysis of the data obtained from the exact representation indicated, it is possible to obtain the sequence impedances. It should be noted that these sequence impedances are a mathematical simplification and are not made of physically realizable R, L, or C, components.

Equivalent Sequence Impedance of Converter During Unbalanced Fault

Equivalent Sequence Impedance of Converter During Unbalanced Fault

The Phase Sequence Impedance of Pipe-Type Cables

The positive or negative phase sequence impedance of a pipe-type cable may be calculated by conventional formulas, suitably modified to include the effect of magnetic properties of the pipe. Calculation of the zero phase sequence impedance, however, is considerably more complicated, involving not only the permeability of the steel pipe, which depends upon the zero phase sequence current, but also the resistance of the shield skid wire assemblies. Formulas and curves are presented by which the zero phase sequence impedance may be determined for any particular case.

Digital Calculation of Sequence Impedances and Fault Currents for Radial Primary Distribution Circuits

Digital Calculation of Sequence Impedances and Fault Currents for Radial Primary Distribution Circuits

Sequence impedances of transformer connections

IN THE GENERAL APPLICATION of the method of symmetrical components to the solution of 3-phase problems, 3-phase circuits are resolved into three singlephase circuits, one for each of the sequences, positive, negative, and zero.

A New Method for Determining Sequence Impedances of Small Synchronous Machines [includes discussion

A New Method for Determining Sequence Impedances of Small Synchronous Machines [includes discussion

Sequence Impedances of Symmetrical 3-Phase Transformer Connections [includes discussion

Sequence Impedances of Symmetrical 3-Phase Transformer Connections [includes discussion

Split-Winding Starting of 3-Phase Motors

In this paper there is presented a new method of normal voltage reduced current starting for induction motors. The scheme consists in connecting one phase of a 3-phase winding in series during the starting period only, the other phases having circuits in parallel. When full speed is attained, the series connected winding is opened momentarily, and then put back on the line in parallel. This gives the advantages of reduced current without any current surge on reclosing, no external impedance, and a low cost of control. It provides about half torque with two-thirds average current, as compared to full voltage starting; it gives a smooth torque curve on the Y connection, and only a small one-third speed torque dip on delta connection; and it allows about 50 per cent greater stalled time than on full voltage. Although this type of connection will draw unbalanced line currents, this appears unimportant. In most cases there will be other machines on the line to act as phase balancers and absorb the relatively small negative sequence current. Formulas are given for currents and torque with and without external impedances. Formulas are in terms of voltage and forward, backward, and zero phase sequence impedances.

A new distance ground relay

DISTANCE-TYPE relays have been used successfully for many years to protect against phase faults on transmission lines. However, distance relays to protect against ground faults in the same satisfactory manner as for phase faults have not been generally available. The chief reason for the delay in producing these is that a ground fault is much more involved than a phase-to-phase fault so that the simple use of line-to-ground voltage and line current does not produce the right answer. The error is caused by the fact that the zero-sequence-line impedance is not equal to the positive sequence impedance, therefore distance response is varied by changes in the distribution of the positive, negative, and zero sequence currents caused by changes in system connections outside the protected line section.

Fault Location and Relay Performance Analysis by Automatic Oscillographs

The purpose of this paper is to describe a method developed for determining the location of ground faults on an extensive 140-kv grounded neutral transmission system. This method applies particularly to ground faults in a network of two or more parallel lines and is based on a comparison of the magnitude of ground currents in the faulted circuit and in the unfaulted circuits. Since the relative distribution of ground fault current in a network depends only on the zero sequence impedance of the system, an analysis of ground faults by comparison is independent of generation, fault resistance, or whether one or two phases are involved to ground. The paper also describes the use of ground fault current curves in determining the critical conditions for relay selectivity and summarizes the results of five years of satisfactory experience with automatic oscillographs used in the analysis of faults and relay operations on the system.

Fault location and relay performance analysis by automatic oscillographs

The purpose of this paper is to describe a method developed for determining the location of ground faults on an extensive 140-kv grounded neutral transmission system. This method applies particularly to ground faults in a network of two or more parallel lines and is based on a comparison of the magnitude of ground currents in the faulted circuit and in the unfaulted circuits. Since the relative distribution of ground fault current in a network depends only on the zero sequence impedance of the system, an analysis of ground faults by comparison is independent of generation, fault resistance, or whether one or two phases are involved to ground. The paper also describes the use of ground fault current curves in determining the critical conditions for relay selectivity and summarizes the results of five years of satisfactory experience with automatic oscillographs used in the analysis of faults and relay operations on the system.

Impedance Measurements on Underground Cables

To eliminate uncertainties arising from assumed constants involved in the calculation of sequence impedances, hield measurements of 60 cycle positive and zero sequence impedances of 2 sizes of 3-conductor underground power cable were made on the 27 kv system of a large eastern metropolitan company; the results are reported in this paper. While the principal results are applicable only to the particular system involved, they show that without the support of the experimental data the calculation of zero sequence impedance of feeder circuits in a system of this kind can be at best only roughly approximate.

Relation between Neutral Impedances and Zero Phase Sequence Impedance Viewed from the Point of Fault

Relation between Neutral Impedances and Zero Phase Sequence Impedance Viewed from the Point of Fault

Damper Windings for Water-Wheel Generators

The severity of unsymmetrical system faults is affected by the negative sequence impedance of the connected machines. These impedances in turn depend largely upon the character of damper windings. The paper discusses the effect of amortisseur or damper windings upon both the real and reactive components of the negative sequence impedance. Machines without damper windings possess the highest negative sequence reactance and from this viewpoint are the most desirable, but machines with high-resistance damper windings possess the highest negative sequence resistance. Calculations show that combining the effect of resistance and reactance, the high-resistance damper is more desirable. In the event of system oscillations low-resistance copper damper windings produce the greatest damping of the mechanical movement. However, this effect is unimportant during and following a system fault except in the exceptional, rather rare case in which the system is so constituted that pull-out takes place as a result of compound oscillations following a disturbance. Consideration is also given to a special type of double deck damper winding.

On the Method of Measurement of Zero and Negatlve Phase Sequence Impedance of the Three Phase Alternator

On the Method of Measurement of Zero and Negatlve Phase Sequence Impedance of the Three Phase Alternator