5. The following circuit is adapted from the CIGRE benchmark low voltage distribution system (Stavros Papathanassiou et al, 2005, "A Benchmark Low Voltage Microgrid Network"). For the five loads, assume the power factor is 0.7 lagging. The impedance of the 8 branches in Ohm are given as the follows. z(6,7)=30* (3.69+i1*0.094) + 70+ (0.284+i1*0.083); z (7,6)=z(6,7); z(1,7)= 30*(1.380+i1+0.082)+i1*1.6; z(7,1) = z(1,7); z(2,7)=3+30+ (0.497+i1+0.086)+i1+1.6; z(7,2)z(2,7); z(7,8)70* (0.284+i1*0.083);z(8,7)z(7,8); z(8,9)3+35 = (0.284+i1*0.083); z(9,8)z(8,9); z(4,9)30 = (3.690+i1+0.094) +i1*1.6;z(9,4) = z(4,9); z(5,9)=30+ (1.380+i1*0.083) +30* (0.284+i1*0.083) +i1+1.6; z(9,5)z(5,9); z(3,8)=30+ (1.380+i1*0.082)+i1*1.6; z(8,3) =z(3,8);%3D For example, Bus 6 and Bus 7 are connected by a 30 m line (per km impedance is 3.67 + j 0.094 Ohm) and a 70 m line (per km impedance is 0.284 + j 0.083 Ohm). Convert all loads to impedances. Form a 9 by 9 Ybus matrix (per unit) for this system. All DERs are assumed as pure current sources. Please design code and come up with the Ybus matrix • Leave only the five DER buss and reduce the network fro 9 buses to 5 buses. Give the 5 by 5 Ybus matrix. • If we view from Bus 1 and the entire micro-grid is viewed as an impedance, what is the impedance?

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