Final answer:
The total complex power is 360 kW + j208 kvar. The power factor is 0.764. The supply current is 18.34 + j10.59 kA.
Step-by-step explanation:
To determine the total complex power, power factor, and supply current, we need to calculate the individual complex powers of the loads and then sum them up.
The inductive load has a power factor of 0.8, so its reactive power can be calculated as 660 kvar x 0.8 = 528 kvar. The complex power for the inductive load is then 60 kW + j528 kvar.
The capacitive load has a power factor of 0.8 and a power of 240 kW. The complex power for the capacitive load is 240 kW - j320 kvar.
The resistive load has a power of 60 kW and a power factor of 1 (since it is purely resistive). The complex power for the resistive load is 60 kW.
Now, we can calculate the total complex power by adding up the individual complex powers: (60 kW + j528 kvar) + (240 kW - j320 kvar) + 60 kW = 360 kW + j208 kvar.
The power factor can be calculated as the cosine of the angle between the real power and the total complex power, which is 360 kW in this case. The power factor is therefore 360 kW / sqrt((360 kW)^2 + (208 kvar)^2) = 0.764.
The supply current can be calculated using the formula I = S / (sqrt(3) x V), where S is the total complex power and V is the line-to-line voltage. Plugging in the values, we get I = (360 kW + j208 kvar) / (sqrt(3) x 11 kV) = 18.34 + j10.59 kA.