Thermal Equivalent Current of Delta Connected or V Connected Three Phase Power Source for Multiple Intermittent Single Phase Loads

Abstract

Equation (8) shows the general expression of thermal equivalent current for a single phase source when many intermittent loads are connected. In the equation I₁, I₂……are currents, α₁, α₂. are duty cycles and φ₁, φ₂……are lagging power factor angles of individual loads.
The equation was deduced from equation (3) which shows the instantaneous source current, ε₁, ε₂……being unity or zero (See equ. (2).) whose probabilities of being unity are α₂, α₂…….
Equation (19) shows the result for A phase source of delta-connected three phase system of A, B, C with single phase intermittent loads.
The equation was deduced from (12), in which k_a, k_b, k_c are as defined in equ. (13), z_a, z_b, z_c being the internal impedance of source transformers.
Equation (20) shows the result when the current, duty cycle and power factor are equal in a given phase, n_A, n_B, n_C being the number of loads.
In the case of V-connection, where the C phase source transformer is disconnected, k_a, k_b, k_c in equ. (19) arc given by equ. (24).