Question

Slope of the tangent drawn on initial portion of O.C.C of synchronous generator is

• A. \( \text{Unsaturated synchronous resistance} \)
• B. \( \text{Saturated synchronous impedance} \)
• C. \( \text{Critical resistance} \)
• D. \( \text{Unsaturated synchronous impedance} \)

Hint:

- Initial linear portion of O.C.C. $\rightarrow$ Unsaturated state $\rightarrow$ Yields Unsaturated Synchronous Impedance. - Actual saturated portion of O.C.C. $\rightarrow$ Saturated state $\rightarrow$ Yields Saturated Synchronous Impedance.

Answer 1

The Correct Option is D

Concept: The Open Circuit Characteristic (O.C.C.) of a synchronous generator is a plot of the open-circuit terminal voltage ($V_{oc}$) versus the field excitation current ($I_f$) at rated synchronous speed.
• Initial Portion (Air-gap line): At low excitation currents, the magnetic core is completely unsaturated. The reluctance of the magnetic path is dominated by the air gap, which is constant. Hence, the initial portion of the O.C.C. is a straight line.
• Knee and Saturation Region: As excitation increases, the iron core begins to saturate, causing the curve to bend away from the straight line. Synchronous impedance ($Z_s$) is determined by taking the ratio of open-circuit voltage to short-circuit current ($I_{sc}$) at a specific field current: $$Z_s = \frac{V_{oc}}{I_{sc}}$$

Step 1: Define the initial straight-line section of the O.C.C.
The straight-line projection representing the initial unsaturated region is known as the Air-Gap Line. Along this line, magnetic saturation is completely absent. Any parameters calculated using the voltage values along this initial linear tangent represent the unsaturated properties of the synchronous machine.

Step 2: Relate the slope to synchronous parameters.
When we combine data from the initial portion of the O.C.C. with the linear Short Circuit Characteristic (S.C.C.), the ratio of the unsaturated open-circuit voltage to the short-circuit current yields a constant value known as the unsaturated synchronous impedance ($Z_{s(\text{unsat})}$): $$Z_{s(\text{unsat})} = \frac{V_{oc} \text{ (from air-gap line)}}{I_{sc}}$$ Because the initial portion of the O.C.C. tracks this unsaturated air-gap condition, its slope directly represents this unsaturated factor.

Step 3: Select the correct option.
Comparing with the available options:
• (1) Unsaturated synchronous resistance (Incorrect, resistance is a purely ohmic winding factor).
• (2) Saturated synchronous impedance (Incorrect, this occurs past the knee point).
• (3) Critical resistance (Incorrect, this relates to DC shunt generators).
• (4) Unsaturated synchronous impedance (Correct). Therefore, option (4) is correct.