Consider a power system with three identical generators. The transmission losses are negligible. One generator ($$G1$$) has a speed governor which maintains its speed constant at the rated value, while the other generators ($$G2$$ and $$G3$$) have governors with a droop of $$5$$%. If the load of the system is increased, then in steady state.

A power system consists of 2 areas (Area 1 and Area 2) connected by a single tie line (figure). It is required to carry out a load flow study on this system. While entering the network data, the tie-line data (connectivity and parameters) is inadvertently left out. If the load flow program is run with this incomplete data.

Two transposed $$3$$ phase lines run parallel to each other. The equation describing the voltage drop in both lines is given below.

Compute the self and mutual zero sequence impedances of this system i.e, compute $${Z_{011}},\,\,{Z_{012}},\,\,{Z_{021}},\,\,{Z_{022}}\,\,\,$$ in the following equations.
$$\Delta {V_{01}} = {Z_{011}}\,{{\rm I}_{01}} + {Z_{012}}\,{{\rm I}_{02}}$$
$$\Delta {V_{02}} = {Z_{021}}\,{{\rm I}_{01}} + {Z_{022}}\,{{\rm I}_{02}}\,\,$$ where $$\,\Delta {V_{01}},$$
$$\Delta {V_{02}},\,{{\rm I}_{01}},\,{{\rm I}_{02}}\,\,$$ are the zero sequence voltage drops and currents for the two lines respectively.

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is