The number of chained lumped-circuits for the physical analogy of half-wavelength power transmission lines

Half-wavelength AC power transmission (HWACT) technology has the special advantage of point-to-point transmission, and hence is very attractive for long-distance (3000km for 50Hz or 2500km for 60 Hz) and large-capacity power transmission. In order to implement physical analogy of HWACT lines, in general, the equivalent lumped-circuits consisting of some chained π-type circuits or T-type circuits are used in laboratory. The number of the chained circuits is the most important aspects in the physical analogy of HWACT lines. In this paper, the voltage waveform along π-type equivalent circuit is analysed for different number of the chained circuits. Next, the relationship between the number of chained circuits and the wave frequencies is discussed based on the relative error of the cascaded matrix (relative to the transfer matrix). For 50Hz, 32 chained π-type circuits can ensure the relative error of the cascaded matrix is less than 3%. The greater frequency is, the more the number of chained circuits required to establish good equivalence between the lumped-circuits and the transmission line. These works are instructive for the physical analogy of HWACT lines.