Consider the flow of unbalanced currents in the symmetrical three-phase line section with neutral conductor as shown in Figure 8.24.

(a) Express the voltage drops across the line conductors given by \(V_{a a}, V_{b b}\), and \(V_{c c}\) in terms of line currents, self-impedances defined by \(Z_{\mathrm{S}}=Z_{\mathrm{aa}}+Z_{\mathrm{nn}}-2 Z_{\text {an }}\), and mutual impedances defined by \(Z_{\mathrm{m}}=Z_{\mathrm{ab}}+Z_{\mathrm{nn}}=2 Z_{\mathrm{an}}\).

(b) Show that the sequence components of the voltage drops between the ends of the line section can be written as \(V_{\text {aa}^{\prime} 0}=Z_{0} I_{\mathrm{a} 0}, V_{\mathrm{aa}^{\prime} 1}=Z_{1} I_{\mathrm{a} 1}\), and \(V_{\mathrm{aa}^{\prime} 2}=Z_{2} I_{\mathrm{a} 2}\), where \(Z_{0}=Z_{\mathrm{S}}+2 Z_{\mathrm{m}}=\) \(Z_{\text {aa }}+2 Z_{\text {ab }}+3 Z_{\text {nn }}-6 Z_{\text {an }}\) and \(Z_{1}=Z_{2}=Z_{\mathrm{S}}=Z_{\mathrm{m}}=Z_{\text {aa }}-Z_{\text {ab }}\).

Transcribed Image Text:

Van Von an a b. n Ia Zab Z0 Z5 Z Zrn Zan a' b' n' Veh 12 5 +