The effects of eddy currents in transformer windings are considered, and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings. The method consists in dividing the winding into portions, calculating the d.c. resistances and d.c. leakage inductances of each of these portions, and then multiplying the d.c. values by appropriate factors to obtain the corresponding a.c. values. These a.c. values are then referred to, say, the primary winding and summed to give the total winding resistance and leakage inductance of the transformer. Formulas are derived and quoted for calculating the d.c. resistances and leakage inductances of the winding portions. Theoretical expressions are derived for the variation with frequency etc. of the factors by which the d.c. values must be multiplied to obtain the corresponding a.c. values. These expressions are presented in the form of graphs, permitting the factors to be read as required.

Effects of eddy currents in transformer windings

The classical one dimensional magnetic field and eddy current distribution ("proximity effect") within a series connected multiple layer coil is reexamined with regard to power losses withinthe windings. When the lengthand number of layers ina coilare fixed, the power dissipation within each layer can be minimized by choosing a specific radial thickness for each layer. Above or below this thickness, the losses within the winding increase. The conductor thickness which results in minimum dissipation depends on the relative position of the layer. When compared to a design having a constant thickness for each layer (chosen for minimum total dissipation), it is found that substantial savings in power consumption can be realized by employing a variable thickness of conductor. The one dimensional solution in cylindrical coordinates for the eddy current and skin effect in amultiple layer series connected coil is alsopresented. By solving the problem n cylindrical coordinates, the effect of curvature on the power consumption within each layer is apparent. This analysis should have application to the design of power transformers, armature windings, and inductors for power transmission lines.

Multiple Layer Series Connected Winding Design for Minimum Losses

The use of adjustable-speed drives requires transformers capable of withstanding high levels of harmonic currents under normal operating conditions. Experience has been that overheating problems are much more common with dry-type transformers than with liquid-filled transformers. Transformer insulation life is determined by the hot spot temperature but confirmation of hot spot temperature rise is one performance characteristic which is ignored in industry standards. This is especially important for transformers rated for nonsinusoidal load currents. The design of transformers for nonsinusoidal load currents should include an analysis of the eddy loss distribution in the windings and calculation of the hot spot temperature rise. Calculations and thermal tests giving only average winding temperature rises are not sufficient. Thermal tests with nonsinusoidal currents and measurements of hot spot temperature rises are extremely difficult on large transformers. The combination of testing and analysis may be the only economically practical approach. Analysis indicates that the dry type transformer hot spot temperature is very sensitive to the eddy loss magnitude and distribution. The Underwriters Laboratories Inc. (UL) K-factor rated dry type transformer and the recommended practices given in ANSI/IEEE C57.110 are reviewed. When purchasing transformers subject to nonsinusoidal load currents, considerations should be given to the manufacturer's development program and capability to calculate the eddy loss distribution and hot spot temperatures.

Transformer design and application considerations for nonsinusoidal load currents

IN any multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers. Eddy currents are set up in each layer in a direction to partly neutralize the magnetic intensities in the interior of the copper wire in each layer. As a result of the eddy-current losses in the copper, the effective resistance of the winding to the alternating current it carries may be many times its resistance to continuous currents.

Effective resistance to alternating currents of multilayer windings

Effective Resistance to Alternating Currents of Multilayer Windings

The object of the present paper is the discussion of the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron.

A. B. Field

Papers

Eddy Currents in Large Slot-Wound Conductors