(Solved): Given is a three-phase generator that feeds an underground line as shown in Figure 1 left side. ...

Given is a three-phase generator that feeds an underground line as shown in Figure 1 left side. Figure 1 Three phase generator with overhead line (left) 2 pol short circuit (right) The grid is supplied symmetrically: \[ \underline{S}_{1}=S, \quad \underline{S}_{2}=S \cdot \underline{a}^{2}, \quad \underline{S}_{3}=S \cdot \underline{a}, \quad \underline{a}=e^{j 120^{\circ}} \] 1) Transform the circuit from Figure 1 (left) into its symmetrical components by drawing their equivalent circuits for the zero, positive and negative sequence. 2) What are the values for the supply voltages \( \underline{S}^{0}, \underline{S}^{+} \)and \( \underline{S}^{-} \)? 3) What are the open circuit voltages \( \underline{V}_{o c}^{0}, \underline{V}_{o c}^{+}, \underline{V}_{a c}^{-} \)of the equivalent circuits of 1)? 4) What are the internal impedances \( \underline{Z}^{0}, \underline{Z}^{+}, \underline{Z}^{-} \)of the equivalent circuits in regard to terminals 1, 2, 3 and \( M \) ? Now a short circuit between terminals 2 and 3 will be investigated - Figure 1 (right): 5) What are the short circuit conditions for \( \underline{I}_{1}, \underline{I}_{2}, \underline{I}_{3} \) and \( \underline{V}_{1 M}, \underline{V}_{2 M}, \underline{V}_{3 M} \) ? 6) What are the related short circuit conditions for the symmetrical components \( \underline{I}^{0}, \underline{I}^{+}, \underline{I}^{-} \)and \( \underline{V}^{0}, \underline{V}^{+}, \underline{V}^{-} ? \) 7) How must the equivalent circuits be connected to comply with the short circuit conditions derived in 6)? 8) Calculate the currents \( \underline{I}^{0}, \underline{I}^{+}, \underline{I}^{-} \)as a function of \( S \) by applying the equivalent circuits from 7). Hint: If you could not solve 3), assume \( \underline{V}_{o c}^{0}=\underline{S}^{0} ; \underline{V}_{o c}^{+}=\underline{S}^{+} ; \underline{V}_{o c}^{-}=\underline{S}^{-} \)and \( \underline{Z}^{0}=\underline{Z}^{+}=\underline{Z}^{-}=Z \) 9) What are the currents \( \underline{I}_{1}, \underline{I}_{2}, \underline{I}_{3} \) during the 2-pol short circuit? Hint: You can solve 5), 6), 7), 8) and 9) without solving the problems before.