Comparison of Models

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The specifications of the set-down transformer selected for comparison have: power 192 VA; primary voltage 230 V; secondary voltag 24 V; power factor 0.8; ambient temperature 40°C; copper density 8800 kg.m^-3; iron density 7800 kg.m^-3; resistivity of copper 1.6.10^-8 Ω .m; coefficient of variation of the resistivity of copper 3.8.10^-3 °K^-1; coefficient of heat transfer by convection 10 W.m^-2°K^-1; thermal conductivity of insulating material 0.15 W.m^-1K^-1. One configuration is chosen with design variables: a = 15 mm ; b = 45 mm ; c = 30 mm ; d = 30 mm ; n₁ = 800 ; S₁ = 0.42 mm² ; S₂ = 3.67 mm² . The μr(B) curve of relative permeability of ferromagnetic material used for both analytical and 3D FEA models is the following figure.

                   

The results of both models with a selected configuration are presented in table I. 3D FE model is more accurate but requires a great amount of time because of the magneto-thermal coupling. The results of the analytical model are rather close to those of 3D FEA. The weakest points of the analytical model are the assumption of uniform temperature in copper and iron, and the computation of the leakage inductances.

Table I - Comparison of Analytical and FEA Models