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This article presented two areas of research poignant to the progression of HTS power apparatus design: electromagnetic design and dielectric phenomena. To be accepted into service, HTS power apparatus must be economically competitive and technically viable, which includes the need for reliability. To maximize the potential savings of HTS power equipment, the view taken at Southampton has been to design apparatus to operate at LN2 temperatures, thus greatly reducing the refrigeration load, cost, and complexity. Several demonstrator projects have been undertaken, including the design, manufacture, and testing of a 10 kVA transformer demonstrating the performance of HTS tapes and the satisfactory use of electromagnetic models to calculate losses, a key design parameter. Strategies for controlling partial discharge and resulting damage to insulation include increasing the operating pressure or reducing temperature. This decision has an impact on refrigeration load and operational cost. Therefore, it will depend on the application. Future research effort is focused on solids for use at cryogenic temperatures, and the interaction of electric field and bubble dynamics affording a greater understanding or the performance of cryogenic dielectrics.