To calculate the magnitude of the current at the generator terminals, we can use the following formula for apparent power ($S$):

$S = P + jQ$

where:

• $P = 50 \text{ MW}$ (real power)
• $Q = 50 \text{ MVAR}$ (reactive power)
• $S$ is the complex power in MVA.

Step 1: Calculate Apparent Power

The apparent power is the magnitude of the complex power $S$, which is given by:

$|S| = \sqrt{P^2 + Q^2}$

Substitute the given values for $P$ and $Q$:

$|S| = \sqrt{(50)^2 + (50)^2} = \sqrt{2500 + 2500} = \sqrt{5000} = 70.71 \text{ MVA}$

Step 2: Calculate Current Magnitude

Now, the magnitude of the current $I$ can be calculated using the formula for apparent power:

$|S| = \sqrt{3} \cdot V \cdot |I|$

where:

• $V = 13.8 \text{ kV} = 13,800 \text{ V}$ (line voltage)
• $|S| = 70.71 \text{ MVA}$
• $|I|$ is the current magnitude.

Rearranging for $|I|$:

$|I| = \frac{|S|}{\sqrt{3} \cdot V}$

Substitute the values:

$|I| = \frac{70.71 \times 10^6}{\sqrt{3} \times 13,800}$

Now let's calculate this:

$|I| = \frac{70.71 \times 10^6}{1.732 \times 13,800} = \frac{70.71 \times 10^6}{23,899.6} \approx 2,958.7 \text{ A}$

Final Answer:

The magnitude of the current at the generator terminals is approximately 2,958.7 A.

Would you like further details or have any questions?

Here are 5 related questions to explore this concept further:

1. How does reactive power affect the efficiency of a power system?
2. What are the differences between real, reactive, and apparent power?
3. How do changes in generator voltage affect the terminal current?
4. What is the power factor, and how can it be improved in this system?
5. How is the current distributed in a three-phase power system?

Tip: Always monitor the power factor in generators, as a low power factor can lead to inefficiencies and excessive current draw.