Fast and accurate two-dimensional modelling of high-current, high-voltage air-cored transformers

Abstract

This paper presents a detailed two-dimensional model for high-voltage air-cored pulse transformers of two quite different designs. A filamentary technique takes magnetic diffusion fully into account and enables the resistances and self and mutual inductances that are effective under fast transient conditions to be calculated. Very good agreement between calculated and measured results for typical transformers has been obtained in several cases, and the model is now regularly used in the design of compact high-power sources.

A 10 GW Tesla-Driven Blumlein Pulsed Power Generator

“…The filamentary technique has been developed and applied at Loughborough for a broad range of pulsed power applications, with the way that it is used to calculate the Tesla transformer parameters being detailed in [2]. As Fig.…”

“…For the single-turn primary winding, the number of filaments was progressively increased according to the procedure outlined in [2], until the resulting numerical simulation for self-inductance reached an asymptote (converged) i.e., for a further substantial increase the result changed by less than 0.1%. A convenient filamentary representation of the primary is using a matrix of 5 (radially distributed) by 200 filaments (axially distributed).…”

“…, where t is the time in microseconds for which the instantaneous voltage exceeds 60% of the peak applied voltage and A is the surface area of the electrode in cm 2 . Application of this formula, with t ≈ 0.4 µs, to the outer surface of the inner electrode, for which A ≈ 6540 cm 2 , predicts there is a 50% chance of breakdown at an electric stress of E b ≈ 360 kV/cm.…”

A Tesla-pulse forming line-plasma opening switch pulsed power generator

“…Tesla transformer Figure 1 shows the electrical arrangement of the overall Tesla-PFL-POS assembly. The detailed design of the Tesla transformer used the Loughborough 2D filamentary model, 5,6 which accounts for magnetic diffusion, skin and proximity effects, and even the influence of metallic components located in the vicinity, such as the PFL. The capacitance of the multiturn secondary winding was calculated using a two-step process.…”

“…1. This is a self-breaking high-voltage fast spark-gap, made from a pair of 60 mm diameter bead-blasted brass hemispheres with about 5 mm separation, securely mounted on polyethylene supports The switch operates in high-pressure SF 6 , has a linear voltage-pressure characteristic over the range used during the tests ͑i.e., 250 kV at 28 psi to 300 kV at 35 psi͒ and an excellent closing voltage reproducibility. Figure 5 shows the output voltage of the PFL during charging, together with the voltage and current delivered to a fixed low-inductance ͑approximately 55 nH͒ load, following FIG.…”