Final answer:
The total complex power for the given symmetrical components of voltages and currents is approximately S_total ≈ -2.671 - 26.27j.
Step-by-step explanation:
The symmetrical components of voltages and currents are often denoted as V_0, V_1, V_2 and I_0, I_1, I_2 respectively. They are related to the positive, negative, and zero-sequence components in a power system.
The complex power (S) is given by the formula:
S = VI^*\
where V is the voltage and I^*\ is the complex conjugate of the current.
For each component, the complex power can be calculated, and the total complex power is the sum of the individual components.
Let's calculate for the zero-sequence component:
S_0 = V_0I_0^*\
S_0 = (14.59 cis 73.66^\circ) x (17.32 cis 156.3^\circ)^* \
Now, calculate the product and sum the results for each component:
S_1 = V_1I_1^* \
S_2 = V_2I_2^* \
Finally, the total complex power is given by:
S_total = S_0 + S_1 + S_2
Performing these calculations should give you the total complex power in the system. Be mindful of the angles and use the appropriate trigonometric functions when dealing with complex numbers in polar form.