Starting currents of transformers : with special reference to transformers with silicon steel cores . agnetic material. Since the flux is not any longer proportional to the current, thecounter e. m. f. due to the inductance must be written AdB Ade where B = flux density and A = constant,instead of , di diL-r or X -r-dt L dd and equation (1) becomes e=Em3Xsmd = A^- + Ri (4) — £n„x d (cos 9) = AdB + Rid 0 dB = — ^d(cosO)— ^-idd (5) Under normal conditions, the resistance drop due to the magnetizingcurrent of a transformer is negligible, and dB = ^ d (cos 6)The normal maximum value of B is then o
Starting currents of transformers : with special reference to transformers with silicon steel cores . agnetic material. Since the flux is not any longer proportional to the current, thecounter e. m. f. due to the inductance must be written AdB Ade where B = flux density and A = constant,instead of , di diL-r or X -r-dt L dd and equation (1) becomes e=Em3Xsmd = A^- + Ri (4) — £n„x d (cos 9) = AdB + Rid 0 dB = — ^d(cosO)— ^-idd (5) Under normal conditions, the resistance drop due to the magnetizingcurrent of a transformer is negligible, and dB = ^ d (cos 6)The normal maximum value of B is then obtained by integrating dB IT from - to J, dB = B =— E max max cos 1 ^ = £m^xA 6 ILLINOIS ENGINEERING EXPERIMENT STATION .\^ = £maxand^=!^ (6) max Substituting (6) in (5) dB Bmd (cosd)— §®*Rid6 (7) max Since the relation between the magnetizing current and theresulting flux can not be expressed mathematically in any practicalequation, the magnetizing current necessary to produce the requiredflux according to the above equation can be determined only analyt-ically, as follows:. Fig. 1 Suppose Fig. 1 to represent the saturation curve of a transformerand the hysteresis loop for normal voltage and frequency. The hys-teresis loop shows what residual magnetism remains in the iron afterthe current has been removed, ob and od represent this residualmagnetism, depending upon whether the current has died down from apositive or a negative value. Suppose the circuit is closed when the impressed e. m. f. passesthrough 0 from negative to positive, i. e., 8 = 0, and that the residualmagnetism is ob. It is evident then that the change of flux to pro-duce the counter e. m. f. must start from b. If equation (7) be re-written in the form *£ = -£maxA(cos0) - p^Ri^e ......(8) max and small intervals of 6, say io°, be taken, the actual conditions canvery nearly be approached. Starting from b, the flux will follow acurve, such as the dashed curve between b and a, and will cont
Size: 2285px × 1094px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjecttheses, bookyear1912
