Circulating-current Losses Research Articles

Correction of the IEC formula for the eddy-current loss factor: The case of single-core cables in trefoil formation with metallic screens bonded and earthed at one end

The purpose of this paper is to propose and apply the correct formula for the eddy-current loss factor for the case of three single-core cables in trefoil formation with metallic screens and armourings bonded and earthed at one end. This metallic screen bonding design is contrasted to the design where metallic screens and armourings are bonded and earthed at both ends, that is, the eddy-current loss factor is contrasted to the circulating-current loss factor. Ampacity calculations are carried out for 12 different underground lines with power cables of the type Cu/XLPE/CTS/PVC/AWA/PVC 1/C 19/33 kV (BS 6622), assuming that the 33 kV cables are installed directly in the soil without drying out. The ampacity is calculated analytically in accordance with IEC 60287-1-1 and IEC 60287-2-1, and numerically in accordance with IEC TR 62095. The numerical calculations are carried out to verify the accuracy of the proposed formula using the finite element method (FEM) in COMSOL 4.3. A validation of the proposed formula is conducted based on the manufacturer's technical data for the considered cables. The calculated ampacity values determined the incompleteness of the current IEC formula for the eddy-current loss factor, and verified the accuracy of the proposed one.

Analysis of a Wide Voltage Hybrid Soft Switching Converter

A hybrid PWM converter is proposed and investigated to realize the benefits of wide zero-voltage switching (ZVS) operation, wide voltage input operation, and low circulating current for direct current (DC) wind power conversion and solar PV power conversion applications. Compared to the drawbacks of high freewheeling current and hard switching operation of active devices at the lagging-leg of conventional full bridge PWM converter, a three-leg PWM converter is studied to have wide input-voltage operation (120–600 V). For low input-voltage condition (120–270 V), two-leg full bridge converter with lower transformer turns ratio is activated to control load voltage. For high input-voltage case (270–600 V), PWM converter with higher transformer turns ratio is operated to regulate load voltage. The LLC resonant converter is connecting to the lagging-leg switches in order to achieve wide load range of soft switching turn-on operation. The high conduction losses at the freewheeling state on conventional full bridge converter are overcome by connecting the output voltage of resonant converter to the output rectified terminal of full bridge converter. Hence, a 5:1 (600–120 V) hybrid converter is realized to have less circulating current loss, wide input-voltage operation and wide soft switching characteristics. An 800 W prototype is set up and tested to validate the converter effectiveness.

Analyses of Circulating-current Loss in Armature Windings and In-plane Eddy-current Loss in Electrical Steel Sheets of Permanent-magnet Synchronous Machines

Analyses of Circulating-current Loss in Armature Windings and In-plane Eddy-current Loss in Electrical Steel Sheets of Permanent-magnet Synchronous Machines

Circulating-current loss in transformer windings

Circulating-current loss in stranded windings of transformers has always attracted the attention of transformer designers. Analytical formulae based on the axial leakage field have long been used by designers for the calculation of circulating-current loss. The authors discuss these analytical formulae and compares them with 2-D finite element method (FEM) analysis, highlighting the errors involved in calculations for different types of windings. The analytical formulae contain little information on multiple transposition schemes, for which the FEM technique by the authors. The paper clearly demonstrates that as the number of parallel conductors in the radial direction increases, analytical formulations should not be used, and in such cases, 2-D FEM is a better option for calculating circulating-current loss in different transposition schemes. The paper also analyses the circulating-current loss in the case of bunched conductors which are increasingly being used in power transformers. The work has helped to evolve comprehensive guidelines for transformer designers to estimate and control circulating-current loss in windings.

Calculation of extra losses in shell form power transformer windings

Extra losses in shell-form power transformers are calculated. Some analytical methods are proposed for the calculation of eddy-current losses, circulating-current losses, and transpositions. Based on these methods a code has been written. Some calculation and test results are reported for a 13.333-MVA single-phase shell-form power transformer built for this study.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

AC Losses in Crossbonded and Bonded at Both Ends High Voltage Cables

An integral equation method for calculating eddy-current and circulating-current losses in low-resistance sheaths of the three-core cables in triangular formation has been developed. The theory takes into account the influence between eddy-currents and circulating-currents and can be applied to any system. The losses have been calculated for sheaths bonded at both ends and for cross-bonded or bonded only at one end. In addition the proximity effect between the cores and the sheaths has been considered. The method was then applied to loss estimation in sheaths and metallic cooling pipes surrounding the three-cable system in triangular configuration. Several practical important conclusions have been drawn and good agreement with other published calculated and measured results have been obtained

Circulating-current loss within Roebel-bar stator windings in hydroelectric alternators

Circulating currents are produced within stator windings of Roebel bars by endregion leakage fields, causing voltages to arise between the strands or subconductors. A method for calculating the endregion fields arising from both rotor and stator is given, and values of voltage for a simplified bar representation are obtained. The impedance of a Roebel bar to a circulating current is discussed, and values of circulating current are obtained for one machine. It is shown that the circulating currents in each bar are substantially independent of those in other bars, but that the reactance within each bar is of the same order as the resistance. The circulating-current loss is a small component of the total loss in the machine considered (10% of the stator I2R loss), but varies with the load and the power factor. Its significance is that two-thirds of it occurs in the top layer of the stator winding, increasing the temperature rise there by 13%. The theoretical analysis from which the above conclusions are drawn is confirmed by search-coil measuremnets which show an average agreement within 18%.

Survey of basic stray losses in squirrel-cage induction motors

A study of the literature reveals that there is still considerable confusion on various aspects of stray losses, particularly with regard to their definition and origin. Accordingly the theoretical information is presented in a rationalised and systematic way to obtain a fully comprehensive approach, based on classifying stray losses into two groups, namely those due to main flux variations (stray no-load losses) and those due to leakage fluxes (stray load losses). In this way three and six main basic types of stray losses can be recognised under the two headings, respectively. Having identified the physical origin of these stray losses, their effect on motor design parameters can be ascertained qualitatively, and available methods of quantitative calculation, which are mostly semiempirical, can then be judged.A critical appraisal of two synthetic test methods for stray load losses, the reverse-rotation and d.c./a.c.-short-circuit tests, is made in the light of basic theory, and the fundamental deficiencies of these tests, particularly the reverse-rotation test, are demonstrated theoretically and by tests carried out on a number of medium-to-large induction motors ranging from 400hp, 4pole, to 1700hp, 8pole. The importance of insulating squirrel cages to avoid circulating-current losses deduced theoretically is confirmed by experiment.Additionally, a direct investigation into squirrel-cage circulating-current losses on a 1500hp 4pole motor shows how such losses can be controlled by a suitable current-displacement rotor design; these additional losses being directly measurable at no load on this machine with open stator slots.Consideration is also given to the fact that modern, high-efficiency (particularly totally enclosed) machine designs cannot cater thermally for substantially increased losses, e.g. excessive stray losses of any kind. There is therefore already an overriding and definite safeguard that the declaration of efficiency to BS 269 is substantially correct, or, more specifically, that there cannot be any major error in the value of the declared losses. However, a modification of the fixed allowance for stray load losses is suggested.From the theoretical and practical investigations carried out, it is concluded that making a nominal allowance for stray load losses is at present the only reasonable and practicable method of declaring efficiency.

Stray-Current Losses in Stranded Windings of Transformers

Previous solutions of the stray loss problem in transformer windings have been made on the assumption that the winding turns contain only one conductor. In a stranded winding this solution represents only the eddy-current loss component of the total stray losses. A second loss component is caused by circulating currents flowing back and forth between the strands. This circulating-current loss depends upon the relative physical location of the strands throughout the winding. Considering various types of stranding, this paper gives equations and charts for the circulatingcurrent loss in a number of different coil constructions as well as for the eddy-current loss.

Losses in Armored Single-Conductor Lead-Covered A-C. Cables

The losses occurring in single-conductor armored cables whose sheath and armor are bonded and grounded at more than one point are-besides the copper loss and the dielectric loss-the circulating-current losses in the sheath and in the armor, and the additional iron losses in an armor of magnetic material. The circulating-current losses are due to the currents induced in the sheath and armor circuits by the fluxes linking these circuits when these circuits are closed by the bonds or grounding connections. Since the losses obtained in such cables are widely variable, depending on the cable design, both designers and operating engineers desire to know the loss magnitudes obtained in different cases and to have an understanding of the factors tending to give low losses. In this paper the sheath and armor losses have been analyzed for a steel-wire armored cable, a copper-wire armored cable, a steel-tape armored cable, and a cable enclosed in an iron pipe, and have been compared with the losses occurring in a plain lead-covered cable without armor. The data used include test data and calculated values. It is shown that a steel-wire armored 350,000-circular mil single-conductor copper cable with sheath and armor short circuited by low-impedance bonds had a total loss (exclusive of dielectric losses), of 2.8 times the conductor loss, by test in a single-phase 60-cycle circuit at 4 ft. cable spacing, at 260 amperes. The corresponding loss in a similar cable without armor, with lead sheath short circuited, was 2.4 times the conductor loss.

Abridgment of losses in armored single-conductor lead-covered A-C. cables

Besides the copper loss and the dielectric loss, the losses occurring in single-conductor armored cables, whose sheath and armor are bonded and grounded at more than one point, are the circulating-current losses in the sheath and in the armor, and the additional iron losses in an armor of magnetic material. The circulating-current losses are due to the currents induced in the sheath and armor circuits by the fluxes linking these circuits when these circuits are closed by the bonds or grounding connections. The sheath and armor losses have been analyzed for a steel-wire armored cable, a copper-wire armored cable, a steel-tape armored cable, and a cable enclosed in an iron pipe, and have been compared with the losses occurring in a plain lead-covered cable without armor. The data used include test data and calculated values. It is shown that a steel-wire armored 350,000-cir. mil single-conductor cable with sheath and armor short-circuited by low-impedance bonds had a total loss (exclusive of dielectric losses), of 2.8 times the conductor loss, by test in a single-phase 60-cycle circuit at 4 ft. cable spacing, at 260 amperes. The corresponding loss in a similar cable without armor, with lead sheath short-circuited, was 2.4 times the conductor loss. Thus the steel-wire armored cable had an additional loss due to the armor of about 20 per cent. A steel-tape armor or an iron pipe surrounding a single-conductor cable usually introduces considerably higher losses. Under the same condition, a cable similar to the steel-wire armored one but having an armor of copper wires has a calculated total loss (exclusive of dielectric loss) of only 1.3 times the conductor loss, the armor current being 92 per cent of the conductor current. The reduction of losses due to diminished cable spacing in a single-phase circuit is shown. When the cable spacing is reduced from 10 ft. to 1 ft. the over-all losses for a steel-wire armored 350,000-cir. mil cable (exclusive of dielectric losses) are reduced about 8 per cent, while those for a similar cable with copper-wire armor drop only about 3 per cent. The relative total annual costs of a steel-wire armored cable and of a similar copper-armored cable, both cables having a conductor cross-section of 350,000 dr. mils, were compared. In view of the lower operating cost of the copper-armored cable, it was found to have a lower total annual cost than that of the steel-wire armored cable at load factors above 60 per cent, the steel-wire armor having the advantage economically at lower load factors.

Sheath losses in single-core cables for three-phase transmission

The controversy as to the calculation of sheath circulating-current losses is referred to, and single-phase tests are quoted to show which formulae agree best with actual measurements. Formulae for the circulating currents in three single-core cables with either horizontal or delta spacing are developed and experimental results are given to show how these agree with the values calculated from the formulas.