There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Residual charges produced in previous partial discharges (PDs) are considered as one aspect of memory effects that affect subsequent discharge behavior. In this paper, we review past studies about memory effects induced by residual charges during successive PDs. At first, surface charge dynamics for cavity and needle-to-dielectric discharges are presented. Subsequently, three methods used to unravel the memory effects are described, e.g. conditional distribution, pulse sequence analysis (PSA) and chopped PD (CPD). Then effects of residual charges on PD inception, discharge propagation and collective behavior are summarized. In addition, contributions of residual charges to the transitions between discharge modes and discharge patterns are presented. At last, some problems relevant to the memory effects are discussed, followed by suggestions for future work.

Understanding Partial Discharge Behavior from the Memory Effect Induced by Residual Charges: A Review

The effect of DC bias on electrical tree growth and partial discharge (PD) characteristics in epoxy resin (Araldite LY® 5052/Aradur® HY 5052 supplied by Huntsman) is investigated using three waveforms: AC, AC with positive DC bias, and AC with negative DC bias. Needle-plane samples are used. Tree growth is shown to be accelerated by the combined effect of DC and 50 Hz AC, beyond the AC growth rate. Positive and negative DC biased tests result in 62% and 54% reductions in average time to breakdown, respectively. Different tree structures and stages of development are associated with different partial discharge characteristics, with thick dark tree branches associated with high PD magnitudes, whereas fine tree channel growth is linked with PD magnitudes below 1 pC. AC tests showed five distinct stages of tree growth compared to four stages seen in DC biased tests. In particular, trees growing in the ‘reverse direction’ from the planar to the point electrode, which is observed in the latter stages of AC tests, is not seen in the DC biased tests. It is concluded that for composite voltages, the AC component is the essential driver of tree growth but the DC component can accelerate propagation. AC noise may therefore compromise the reliability of insulation in HVDC networks.

/pdf/electrical-tree-growth-and-partial-discharge-in-epoxy-resin-h5jcsj6jpx.pdf

Electrical tree growth and partial discharge in epoxy resin under combined AC and DC voltage waveforms

Summary Dielectric polymers are ubiquitous as electrical insulation in electrical power systems and electronic devices. Electrical treeing is typically regarded as an irreversible degradation process of dielectric polymers subjected to high electric stresses, which significantly limits their lifespan and endangers the reliability of electronics and electrical power systems. Here, we report self-healing polymers consisting of microcapsules that are capable of completely restoring the dielectric properties as a direct response to electrical tree degradation. We design the microcapsules with a relatively higher dielectric constant than polymer matrix to guide the propagation of electrical trees. The electroluminescence generated in situ during electrical treeing of polymers triggers crosslinking of the healing agents released from the capsules to repair the electrically damaged areas under ambient conditions. Notably, the breakdown strength of the mended region is largely enhanced upon healing, which was initiated at different locations. The integration of autonomous healing capability into dielectric materials opens new avenues to smart polymers for electronics and energy applications.

https://www.cell.com/matter/pdf/S2590-2385(19)30348-0.pdf

Autonomous Self-Healing of Electrical Degradation in Dielectric Polymers Using In Situ Electroluminescence

Electrical tree growth is a precursor to dielectric breakdown in high voltage polymeric insulation. Partial discharge (PD) has a close relationship with electrical tree propagation and can be both used to understand the aging process, and as a diagnostic tool for asset management. In this paper it is shown that PD patterns change through the early stages of tree growth, and consideration of these changes gives insight into the processes of tree growth. Here, trees have been grown in epoxy resin in needle-plane geometries with 2 mm gaps, at 15 kV peak AC. The PD phase-resolved pattern can be regarded as a combination of the well-known turtle-like and wing-like PD patterns. As a tree extends its length, a wing-like pattern is seen and the maximum discharge magnitude has an almost linear relationship with the maximum length of the growing branch. Comparison of the energy released by discharges and the vaporization energy needed for tree growth supports the proposal that the wing-like pattern corresponds to PDs responsible for growth in length of the trees. Implications for mechanisms for tree growth are considered. Results suggest that asset managers may be able to use partial discharge analysis to distinguish different stages of tree growth, providing a valuable prognostic tool for optimising high voltage plant management and replacement.

Evolution of partial discharges during early tree propagation in epoxy resin

Electrical tree propagation is a precursor to dielectric failure in high voltage polymeric insulation. Tree growth has been widely studied under AC conditions, but its behavior under DC is not well understood. The aim of this work was to examine the importance of polarity and initiating defect size on DC tree propagation. Electrical tree propagation in epoxy resin under constant DC voltages of +60 kV and −60 kV was measured in samples with classical needle-plane electrodes, but with small initial trees (< 100 μm) incepted under lower AC voltages before the DC tests. Experimental results showed strong polarity dependence. In either polarity, the length of the initial AC tree had a major influence on the inception of the subsequent DC tree. The effect was attributed to the defect being influential if it is larger than the space charge injection region. As a consequence, there is a critical defect size that will accelerate failure of DC insulation dependent on space charge injection behavior of the polymer/electrode system in question — a critical finding for high voltage asset management.

DC electrical tree growth in epoxy resin and the influence of the size of inceptive AC trees

An electrical treeing process is presented which consists of two types of electrical tree structures that coexist in the same epoxy resin: these have been termed as ‘filamentary trees’ and ‘reverse trees’. In samples with needle-plane electrode geometries, a filamentary tree that consists of fine tree channels propagates from the needle electrode to the plane ground electrode under an applied AC voltage. It is observed that once the filamentary tree has crossed the insulation, trees then grow from the planar electrode towards the needle electrode as reverse trees, eventually leading to dielectric breakdown. The characteristics of the treeing processes have been obtained for a range of samples through optical observations. In addition, partial discharge (PD) activity associated with the growth of a reverse tree is thoroughly characterized. The prior existence of a filamentary tree is a prerequisite for the development of a reverse tree. PD does not appear to be a driving force for the growth of the filamentary trees, whereas high levels of PD are associated with the growth of a reverse tree. This distinction shows that aging can occur undetected by PD, but asset management of the more aggressive treeing stages can use PD analytics.

Hualong Zheng

Papers

Evolution of partial discharges during early tree propagation in epoxy resin

DC electrical tree growth in epoxy resin and the influence of the size of inceptive AC trees

Electrical treeing and reverse tree growth in an epoxy resin

Electrical tree growth and partial discharge in epoxy resin under combined AC and DC voltage waveforms

The influence of AC and DC voltages on electrical treeing in low density polyethylene