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Chapter 7. Capacitance Calculations

# Chapter 7. Capacitance Calculations - 7 CAPACITANCE...

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237 7. CAPACITANCE CALCULATIONS Summary Lumped circuit models of transformers require that the capacitance of coil sections, consisting of one or more disks, as well as coil to coil capacitances be determined. In addition, special treatment of the disks at the high voltage end of a winding, such as the use of static rings to shape the voltage profile, modify the normal disk capacitance. These changed capacitances must also be determined for use in lumped circuit as well as traveling wave models which attempt to simulate transformer behavior under impulse conditions. We calculate these capacitances in this report, using an energy method. We also calculate the capacitance of a pair of winding disks containing wound-in-shields by means of a simple formula and by means of a detailed circuit model In addition, experiments were performed to check the formula under various conditions such as changing the number of shield turns and attaching the shield to the high voltage terminal at different points or letting it float. Unlike a static capacitance calculation, these capacitances depend on inductive effects. 7.1 INTRODUCTION Under impulse conditions, very fast voltage pulses are applied to a transformer. These contain high frequency components, eliciting capacitative effects which are absent at normal operating frequencies. Thus, in order to simulate the behavior of a transformer under impulse conditions, capacitances must be determined for use in circuit or traveling wave models [Mik78, Rud40]. Usually, the highest electrical stresses occur at the high voltage end of the winding so that modifications are sometimes made to the first few disks to meet voltage breakdown limits. These modifications commonly take the form of the addition of one or more static rings so that their effect on the disk capacitance must be determined. Other methods such the use of wound-in-shields or interleaving, although effective in increasing the disk capacitance (which is generally favorable), are not treated here. © 2002 by CRC Press

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CAPACITANCE CALCULATIONS 238 We employ an energy method to determine the capacitance or, in general, the capacitance matrix. This method is a generalization of the method used by Stein to determine the disk capacitance of a disk embedded in a winding of similar disks [Ste64]. It utilizes a continuum model of a disk so that disks having many turns are contemplated. We also compare capacitances determined in this manner with capacitances determined using a more conventional approach. The conventional method also works for helical windings, i.e. windings having one turn per disk, and so is useful in its own right. For completeness we also calculate coil-coil, coil-core, and coil-tank capacitances which are qualitatively similar. These are based on a cruder model and assume an infinitely long coil, ignoring end effects.
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Chapter 7. Capacitance Calculations - 7 CAPACITANCE...

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