Derivation and Scaling of AC Copper Loss in Thermal Modeling of Electrical Machines

Abstract

Accurate prediction of temperature-dependent ac winding loss effects is crucial in the design of electrical machinery. Average ac winding loss as a function of operating frequency is commonly characterized by the ratio of the equivalent ac and dc resistances (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> /R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> ). However, as the ac and dc components of the winding loss scale differently with temperature, a single value of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> /R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> derived for one temperature can be inadequate when used in thermal modeling. In this paper, methods of deriving the R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> /R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> ratio, together with scaling techniques of the ac winding loss accounting for thermal effects, are discussed. As an alternative to computationally intensive 3-D finite-element analysis, an experimental approach based on tests on full-scale stator assemblies is proposed. A previously proposed scaling technique of the ac winding loss is discussed and developed further. The proposed techniques of deriving the ac winding loss accounting for temperature variation are illustrated using both theoretical analysis and experimental data.