This paper presents the implementation of a thermal camera for the quantitative estimation of power losses in a high frequency planar transformer (100 kHz/ 5600 VA). The methodology is based on the observation of the transient temperature rise and determination of the power losses by means of curves representing the derivative of temperature as a function of power losses dissipated in the transformer. First, the thermal calibration characteristics had to be obtained from a simple experiment, where power losses are generated by DC current in the ferrite core and windings. Next, experimental investigations focused on the determination of the transformer power losses for a short circuit and no load, with a resistive load and with the rectifier as a load were carried out. Finally, to verify the obtained results, analytical calculations based on Dowell’s and modified Steinmetz’s equations were additionally made, which showed a good convergence. The proposed method is easy to implement and can be used as an alternative to the calorimetric method which is time-consuming and requires a complicated measurement setup.

The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.