Final answer:
To determine the secondary current magnitude referred to the primary of a three-phase star-connected transformer, one must utilize the apparent power formula along with the given transformer rating, load, and power-factor.
Step-by-step explanation:
The question refers to finding the secondary current magnitude in kA referred to the primary for a three-phase star-connected transformer with a rating of 12kV/275kV, 500MVA, that is delivering a load of 287MW at a power-factor of 0.73 lagging at rated output voltage.
To find the secondary current magnitude referred to the primary, we need to use the formula for apparent power (S) in a three-phase system: S = √3 × V_L × I_L, where V_L is the line-to-line voltage and I_L is the line current. Given that S = 500MVA for the transformer, and the primary voltage (V_L) is 12kV, we can solve for the primary current (I_p). Then we will need to find the real power (P), which is the product of the apparent power S, the power-factor (pf), and the cosine of the phase angle (cosφ).
The real power for our case is P = S × pf × cosφ = 500MVA × 0.73 × cos(acos(0.73)), which equals 287MW. With this value, we can solve for the secondary current referred to the primary (I'_s) by modifying the apparent power formula to include the real power, leading to I'_s = P / (√3 × V_p).