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T-17b: Blocked Rotor Test

Section: B | Priority: 🟠 HIGH | Exam Frequency: 4/7 years Sources: Theraja Ch-35 (Art. 35.6-35.8), VK Mehta Ch-8, Slides L-05

Why This Topic Matters

The blocked rotor test is always tested together with the no-load test. The pair appeared in 4 out of 7 papers. The blocked rotor test determines the series impedance ($R_{01}$, $X_{01}$) of the equivalent circuit. A standalone SC test numerical (given $V_{sc}$, $I_{sc}$, $P_{sc}$, find $R_2^{\prime }$, $X_1$, $X_2^{\prime }$) appeared in 2023 Q7(b) for 4 marks.

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📝 Key Definitions

Blocked Rotor Test (Locked Rotor Test): "The rotor is held stationary (locked) so that it cannot rotate. A reduced voltage (10-15% of rated) is applied to the stator so that rated full-load current flows. Since the voltage is low, core losses are negligible and the input power is essentially the full-load copper loss." — Theraja, Art. 35.6

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Test Setup and Procedure

1. Lock the rotor mechanically so it cannot rotate ($s=1$).
2. Apply reduced voltage to the stator until rated full-load current flows.
3. Measure: line voltage $V_{sc}$, line current $I_{sc}$, total 3-phase input power $P_{sc}$.

What happens at blocked rotor:

• $s=1$, so $R_2/s=R_2$ (small value). The rotor branch draws heavy current.
• At low voltage (10-15% of rated), the shunt branch current is negligible.
• All input power is copper loss: $P_{sc}=P_{Cu,s}+P_{Cu,r}$.

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Parameters from Blocked Rotor Test

Equivalent impedance referred to stator (per phase):

$$Z_{01}=\frac{V_{sc}/\sqrt{3}}{I_{sc}}\text{(star connection)}$$

$$R_{01}=\frac{P_{sc}}{3I_{sc}^2}$$

$$X_{01}=\sqrt{Z_{01}^2-R_{01}^2}$$

Separating stator and rotor parameters:

$$R_2^{\prime }=R_{01}-R_1$$

where $R_1$ is from the DC resistance test.

$$X_1=X_2^{\prime }=\frac{X_{01}}{2}$$

(Assuming equal leakage reactances on stator and rotor sides.)

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DC Resistance Test (for $R_1$)

Apply DC voltage between two stator terminals. Measure $V_{DC}$ and $I_{DC}$.

$$R_{DC}=V_{DC}/I_{DC}$$

For star connection: $R_1=R_{DC}/2$ (two phases in series)

For delta connection: $R_1=1.5\times R_{DC}$ (parallel-series combination)

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Worked Example (PYQ 2023)

2023 Q7(b): Star-connected IM, SC test: $V=75$ V, $I=38$ A, $P=4$ kW. $R_1=0.5\Omega$/phase. Find $R_2^{\prime }$, $X_1$, $X_2^{\prime }$.

Per-phase voltage: $V_{sc,\varphi }=75/\sqrt{3}=43.30$ V

$$Z_{01}=\frac{43.30}{38}=\boxed{1.140\Omega }$$

$$R_{01}=\frac{4000}{3\times 38^2}=\frac{4000}{4332}=\boxed{0.923\Omega }$$

$$X_{01}=\sqrt{1.140^2-0.923^2}=\sqrt{1.300-0.852}=\sqrt{0.448}=\boxed{0.669\Omega }$$

$$R_2^{\prime }=R_{01}-R_1=0.923-0.5=\boxed{0.423\Omega }$$

$$X_1=X_2^{\prime }=X_{01}/2=0.669/2=\boxed{0.335\Omega }$$

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🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the no-load and blocked rotor tests. Determine equivalent circuit parameters.

Appeared: 2023 Q7(a), 2024 Q7(a) — (9 marks)

Full Answer:

See T-17a: No-Load Test for the no-load test portion.

Blocked-Rotor Test:

Rotor mechanically locked ($s=1$). Reduced voltage (10-15% of rated) applied until rated current flows. At low voltage, core loss is negligible. Input power = full-load copper loss.

Measurements: $V_{sc}$ (line voltage), $I_{sc}$ (line current), $P_{sc}$ (3-phase power).

Parameters:

$$Z_{01}=\frac{V_{sc}/\sqrt{3}}{I_{sc}},R_{01}=\frac{P_{sc}}{3I_{sc}^2},X_{01}=\sqrt{Z_{01}^2-R_{01}^2}$$

Split: $R_2^{\prime }=R_{01}-R_1$, and $X_1=X_2^{\prime }=X_{01}/2$.

DC Test for $R_1$: Apply DC between two stator terminals. Star: $R_1=R_{DC}/2$. Delta: $R_1=1.5R_{DC}$.

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🎯 Q2: SC test numerical: $V=75$ V, $I=38$ A, $P=4$ kW, $R_1=0.5\Omega$. Find $R_2^{\prime }$, $X_1$, $X_2^{\prime }$.

Appeared: 2023 Q7(b) — (4 marks)

Full Answer:

See Worked Example above. Results: $R_2^{\prime }=0.423\Omega$, $X_1=X_2^{\prime }=0.335\Omega$.

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Exam Variants

Year	Question	Marks	Type
2019 Q7(a)	Describe blocked rotor test	4	Theory
2023 Q7(a)	Explain NL + BR tests	9	Theory + formulas
2023 Q7(b)	SC test numerical	4	Numerical
2024 Q7(a)	NL + BR tests + parameters	9	Theory + formulas

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⚡ Exam Tips & Common Mistakes

1. Don't forget $\sqrt{3}$. For star connection: $V_{\varphi }=V_L/\sqrt{3}$. For delta: $V_{\varphi }=V_L$.
2. $R_{01}$ includes BOTH stator and rotor resistance. $R_2^{\prime }=R_{01}-R_1$.
3. The assumption $X_1=X_2^{\prime }$ is standard unless told otherwise. State it explicitly.
4. Blocked rotor test is analogous to SC test of transformer. Same formulas, same logic.
5. Power formula uses LINE current: $R_{01}=P_{sc}/(3I_{sc}^2)$ where $I_{sc}$ is the LINE current (which equals phase current for star).

🔗 Related Topics

• T-17a: No-Load Test — Always paired
• T-14: IM Equivalent Circuit — The circuit being determined
• T-18: Circle Diagram — Uses BR test data as input

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