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A 3-ф synchronous generator has a direct axis synchronous reactance of 0.8 pu and quadrature axis synchronous reactance of 0.5 pu. The generator is supplying full load at 0.8 pf lag at 1 pu terminal voltage. The power angle in degrees is _____.
  • a)
    540
  • b)
    17.10
  • c)
    90.90
  • d)
    7.120
Correct answer is option 'B'. Can you explain this answer?
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A 3-ф synchronous generator has a direct axis synchronous reactance ...
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A 3-ф synchronous generator has a direct axis synchronous reactance ...
Given data:
- Direct axis synchronous reactance (Xd) = 0.8 pu
- Quadrature axis synchronous reactance (Xq) = 0.5 pu
- Power factor (pf) = 0.8 lagging
- Terminal voltage (Vt) = 1 pu

Calculating power angle:
1. The power angle (δ) can be calculated using the formula:
\[ \delta = \cos^{-1} (pf) \]
2. Given that the power factor (pf) is 0.8 lagging, we can substitute the value in the formula:
\[ \delta = \cos^{-1} (0.8) = 36.87 degrees \]
3. However, the above value is the electrical power angle. The mechanical power angle (δm) is given by:
\[ \delta_m = \delta - \tan^{-1} \left( \frac{Xq}{Xd} \right) \]
4. Substituting the values of Xd, Xq, and δ in the formula:
\[ \delta_m = 36.87 - \tan^{-1} \left( \frac{0.5}{0.8} \right) \]
\[ \delta_m = 36.87 - 33.13 = 3.74 degrees \]

Therefore, the power angle in degrees is approximately 3.74 degrees.
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A 3-ф synchronous generator has a direct axis synchronous reactance of 0.8 pu and quadrature axis synchronous reactance of 0.5 pu. The generator is supplying full load at 0.8 pf lag at 1 pu terminal voltage. The power angle in degrees is _____.a)540b)17.10c)90.90d)7.120Correct answer is option 'B'. Can you explain this answer?
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