2 Analysis of heat transfer in a single-phase transformer

Assignment 2 2-6Initialization― Cooling conditions― Magnetic: B -> p fe― Electric: J k,ρ 0 -> p cuFind temperature― Coil hot-spot ϑ max― Coil average ϑ aveTarget― |ϑ target - ϑ max|≤0.05― iter ≥ max_iterResult visualization― Temperature plot (bmp)― Electric loading (txt)Obtain new values― ρ= ρ 0(1+α(ϑ ave-ϑ 0))― p cu=0.5 ρ (J k+1) 2 Kf― iter=iter+1Obtain current density― if ϑ target - ϑ max < - 40then J k+1=J k x 0.5― if ϑ target - ϑ max > 40then J k+1=J k x 2― elseJ k+1=J k W(ϑ target - ϑ max)Figure 2.2 Iterative hot-spot computation loop. Flowchart of the iterative current density computation in wherethe target hot spot temperature of the coil is estimated. The hot-spot temperature is obtained from aline that is defined through the cross-section of a winding. The weight factor W is chosen so that theconverging process is as well as fast as stabile. This flowchart does not indicate the solution when corelosses only give the target temperature or moreThe thermal models: EC model and FE model― Are two dimensional (2D), which means that heat transport along z axis and the heatgenerated in/dissipated from the end turns are neglected― Has the height of the transformer lamination stack equal to one meter (per unit of meter)― Assume the same loss density in the primary and the secondary windings― Assume naturally cooled sides h=20 W/Km 2 and ambient temperature of 40 0 C2.2 Geometry parameterizationThe geometric model was formulated so that transformer length and insulation thickness togetherwith proportion factors will define the whole geometry. Additional parameters, such as proportionfactors specify the geometric proportions between the different parts of the transformer.― Ks (variable) – proportion between the slot length and core limb length― Kw (=0.5) – proportions between primary and secondary windingThe length of the leg in the magnetic core is expressed by using the relative slot length k s and thelength needed to form a one electromagnetic pole. For the single-phase core and shell type oftransformers the number of poles N p =2.ll( − k )trc= 1s( 2.1 )NpSimilarly the length of the slot is formulated according to the length of a single electromagnetic poleand the relative slot length.AAV0090 Electrical Drives - project, TTU, 2008