Question

If a transmission line carries 100 MW at unity power factor, the reactive power is:

• A. 0 MVAR
• B. 50 MVAR
• C. 1000 MVAR
• D. 10 MVAR

Hint:

Power Factor Relationships:
1. Unity Power Factor (\(\cos\theta = 1\)): \(Q = 0\).
2. Zero Power Factor (\(\cos\theta = 0\)): \(P = 0\), and power is purely reactive.
Operating at or near unity power factor minimizes transmission losses and improves voltage stability.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the reactive power (\(Q\)) carried by a transmission line when it is delivering a specified active power (\(P\)) at a unity power factor (\(\text{pf} = 1.0\)).

Step 2: Key Formula or Approach:
In AC power systems, active power (\(P\)) and reactive power (\(Q\)) are related to the apparent power (\(S\)) and power factor angle (\(\theta\)) by:
\[ P = S \cos\theta \] \[ Q = S \sin\theta \] The relation between active and reactive power is:
\[ Q = P \cdot \tan\theta \] where \(\cos\theta\) is the power factor.

Step 3: Detailed Explanation:

• Identify the given parameters:
- Active power, \(P = 100\text{ MW}\).
- Power factor, \(\cos\theta = 1.0\).

• Find the power factor angle \(\theta\):
\[ \theta = \cos^{-1}(1.0) = 0^\circ \]
• Calculate the reactive power \(Q\):
\[ Q = P \cdot \tan(0^\circ) = 100 \times 0 = 0\text{ MVAR} \]
• This shows that at unity power factor, the current and voltage are in phase, meaning no reactive power is drawn or supplied by the load.

Step 4: Final Answer:
The reactive power is 0 MVAR.