# PD-Free Design of Insulation Systems: An Application to Laminated Busbars
## 1 Introduction  
The design of insulation systems for electrical and electronics components has been for decades a commodity: the same materials, same standards, and same technology were used when AC sinusoidal voltage was the generalized power supply. Insulation volume was not an issue, and, in fact, the insulation electric field was typically a few kV/mm in almost all applications (the main exceptions were high voltage, HV, cables, where the design field was going up to 10 kV/mm or more). This is changing progressively in industrial and electrified transportation applications, involving new and compelling research and development activity addressed to electrical insulating material engineering and insulation system design. Indeed, the resurgence of research and science in this field has started with the \"gift\" of progressive diffusion of power electronics supply, from low voltage, LV, to extra-high voltage, EHV, with solid-state components providing higher voltage as well as faster switching. Insulation premature failures have begun to occur with much higher probability than what was expected on the basis of previous field returns during the AC sinusoidal era. This, for example, happened for rotating machines fed by pulse-width modulation, PWM, especially at the time of transition from IGBT to MOSFET switching technologies. Research showed that the root of such an increased failure rate was the uneven and magnified field distribution due to voltage drops in the primary windingsand repetitive overvoltage. This was shown to reduce life and increase the risk of partial discharges, PDs, inception [1]. Life reduction can be caused by two types of accelerated aging: intrinsic and extrinsic aging. The former can be associated with overall aging due to electric field magnitude, which is typically described by life models [2; 3], and it is used to design insulation systems. The latter is due to the inception of extrinsic aging mechanisms, which further increase the aging rate, such as PD [4]. For the above case of rotating machines, the magnified electric field distribution and increased field amplitude due to repetitive overvoltage can cause directly accelerated intrinsic aging but especially extrinsic aging if the partial discharge inception voltage, PDIV, is exceeded. The risk of aging acceleration brought by the inception of PD in insulation systems could be then a major drive in their design. The new design concept should consist of developing an insulation system which must be free of PD in any part of it (including, thus, bulk and surface) and for all its operating life. In this case, an appropriate design, based on the accurate knowledge of electrical stresses and their time variation, would match specifications on life and failure probability [5]. One of the key aspects of the PD-free design is to go beyond approaches driven by the concepts of creepage distance and by the Paschen law, which are based on the assumption of uniform electric field distribution. This assumption, however, is often not satisfied in electric systems with complex geometries, such as transformers or laminated busbars, LBBs. A _non-uniform_ electric field distribution, indeed, can cause the PDIV to significantly deviate from predictions that assume a uniform field distribution. For example, in [6], deviations from the Paschen law were observed at the triple point between the conductor, solid dielectric insulation and air, and the reason was ultimately ascribed to the non-uniformity of the electric field in proximity of the junction (also, it must be reminded that the Paschen law was derived by discharge in air from metal electrodes, while here, we deal with solid insulation systems). Highly non-uniform electric fields were also observed in configurations where the field could be expected, as a first approximation, to be almost uniform. For example, this is the case of [7], where the breakdown voltage in the air gap between two spheres was computed by including a drift-diffusion equation to model the generation of electrons.