A 400 V, 30 kVA, single-phase alternator has an effective arma... | Technical Ability MCQ | Examoogle

Technical AbilityElectrical Machines

A 400 V, 30 kVA, single-phase alternator has an effective armature resistance of 0.3 Ω. An excitation current of 20 A produces 266 A armature current on short-circuit and an EMF of 400 V on open-circuit. The synchronous impedance and synchronous reactance of the alternator are, respectively, ___________.

20 Ω and 0.3 Ω

1.46 Ω and 1.5 Ω

0.3 Ω and 20 Ω

1.5 Ω and 1.46 Ω

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnical AbilityElectrical Machines

Option D

5 Ω and 1.46 Ω

Quick Summary:

The synchronous impedance $Z_s$ is calculated as the ratio of open-circuit voltage $E_0$ to the short-circuit current $I_{sc}$ at the same excitation. Once $Z_s$ is found, the synchronous reactance $X_s$ is derived using the relation $X_s = \sqrt{Z_s^2 - R_a^2}$ .

⚙️TETechnical SolutionConcept & Principle

📜 Standard Reference & Code Clause

IEEE Std 115-2009

💡 Explanation

🔢 Key Formulas

$Z_s = \frac{E_0}{I_{sc}}$ — Synchronous impedance formula

$X_s = \sqrt{Z_s^2 - R_a^2}$ — Synchronous reactance derivation from impedance

⚙️ Working Principle

The synchronous impedance represents the total opposition to current flow in an alternator under short-circuit conditions, accounting for both armature resistance and leakage plus armature reaction reactance. By performing an Open Circuit Test (OCT) and Short Circuit Test (SCT) at a specific excitation, we determine the machine's internal impedance parameters by assuming linear magnetic behavior.

📌 Key Points

▸
The open-circuit voltage $E_0$ for 20 A excitation is 400 V.
▸
The short-circuit current $I_{sc}$ for 20 A excitation is 266 A.
▸
Synchronous impedance $Z_s = \frac{400}{266} \approx 1.5 \, \Omega$ .
▸
Synchronous reactance $X_s = \sqrt{1.5^2 - 0.3^2} = \sqrt{2.25 - 0.09} = \sqrt{2.16} \approx 1.47 \, \Omega$ (approximately 1.46).
▸
The armature resistance $R_a$ is given as 0.3 $\Omega$ .

✅ Advantages

▸
Provides a simple method to determine alternator regulation.
▸
Essential for evaluating the steady-state performance of synchronous machines.

❌ Disadvantages / Limitations

▸
Assumes a linear relationship between excitation and output, neglecting magnetic saturation.
▸
Typically yields a pessimistic value for voltage regulation due to the neglect of saturation.

🛠️ Applications / Uses

▸
Determination of Synchronous Machine parameters.
▸
Analysis of steady-state stability in power systems.

📄 Additional Information

▸
Calculations: $Z_s = 400 / 266 = 1.5037 \approx 1.5 \, \Omega$ .
▸
Then $X_s = \sqrt{1.5037^2 - 0.3^2} = \sqrt{2.261 - 0.09} = \sqrt{2.171} \approx 1.473 \, \Omega$ , closely matching Option D.
▸
Option C is incorrect as it swaps the resistance and reactance values.

📊 Diagram / Illustration

✅

D is correct — The synchronous impedance is calculated as $1.5 \, \Omega$ and the synchronous reactance is $1.46 \, \Omega$ .

Core Concepts Used

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Synchronous Impedance Short Circuit Ratio Armature Reaction

💡 EXAM TIP

Always ensure the units match and check if the resistance $R_a$ is negligible; if $R_a \ll X_s$ , then $Z_s \approx X_s$ .

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