Calculate all of the impedances in the phase domain. Recall the phase domain has three components, A, B and C. In each component, there is a voltage drop, V, and a current, I. The impedance in the phase domain is given by Zij = Vi/Ij. In other words, to find the impedance for ij by dividing the voltage drop in component i by the current in component j. For example, the impedance for AC is Zac = Va/Ic. Calculate the impedances for all of the combinations AA, AB, AC, BA, BB, BC, CA, CB and CC.
Place the impedances into a three-by-three matrix of order A-B-C. That is, the first row designates the voltage drop for A, and the first column designates the current for A. For example, the impedance for AA should go in the cell located in the first row and first column, whereas the impedance for BC should go in the cell located in the second row and third column. Call this matrix Zabc.
Multiply the inverse of the phase domain to symmetrical component domain conversion matrix by Zabc. Recall that this inverse conversion matrix is given by three rows: [1 1 1], [1 a b], [1 b a] divided by three. In this matrix, “a” represents 120 degree phase shift and “b” represents a 240 degree phase shirt. Call this matrix Ainv. This step is, mathematically, Ainv * Zabc. Call this result I.
Multiply I by the phase domain to symmetrical component domain conversion matrix. Recall that this conversion matrix is given by the three rows [1 1 1], [1 b a], and [1 a b]. Call this matrix A. Thus, this step is the operation I * A. The result is the zero sequence impedance.