No-Load and Blocked-Rotor Tests

Chapter 64 gave the per-phase equivalent circuit: a series branch \(R_1 + jX_1\), a shunt branch \(R_c \parallel jX_m\), and the rotor branch \(R_2'/s + jX_2'\). Exactly as for the transformer in Part 3, we need two experiments that each make one part of the circuit dominate.

The stator resistance is measured first by applying a small DC voltage across two line terminals. For a star-connected stator the current passes through two phases in series:

The DC value is usually multiplied by 1.1–1.3 to allow for skin effect and for the higher operating temperature. Since no rotor current flows with DC excitation, this test tells us nothing about \(R_2'\).

The motor runs uncoupled at rated voltage and frequency. Two wattmeters (or a power analyser) record the total input \(P_0\), together with the line voltage \(V_0\) and line current \(I_0\).

• The input supplies only losses: stator copper loss \(3I_0^2R_1\), core loss \(P_\text{core}\), and friction and windage \(P_\text{fw}\). Rotor copper loss is negligible because \(s \approx 0\).

• The rotational loss is \(P_\text{rot} = P_0 - 3I_0^2R_1 = P_\text{core} + P_\text{fw}\).

• To split \(P_\text{rot}\), the test is repeated at decreasing voltage and \(P_\text{rot}\) is plotted against \(V^2\). The straight line extrapolated to \(V = 0\) gives \(P_\text{fw}\), which does not depend on voltage.

Because \(\cos\phi_0\) is very low (about 0.1–0.25), \(X_\text{NL} \approx Z_\text{NL}\) to a good approximation.

The rotor is locked and a reduced voltage is applied — just enough to circulate rated current, typically 10–25 % of rated voltage. Readings: \(V_\text{BR}\), \(I_\text{BR}\), \(P_\text{BR}\).

• Core loss is negligible because the voltage, and hence the flux, is low.

• The magnetising branch is bypassed by the low-impedance rotor branch, so the input is almost entirely copper loss.

• IEEE Std 112 recommends performing the test at 25 % of rated frequency, because a running motor sees rotor frequency \(sf\), only a few hertz. Testing at 50 Hz overstates \(R_2'\) through skin effect, especially in deep-bar and double-cage rotors (Chapter 70).

1. DC test → \(R_1\).

2. Blocked-rotor test → \(R_\text{eq}\) and \(X_\text{eq}\); then \(R_2' = R_\text{eq} - R_1\), and split \(X_\text{eq}\) using Table 65.1.

3. No-load test → \(X_m \approx X_\text{NL} - X_1\); the core-loss resistance follows from \(R_c = 3E_0^2/P_\text{core}\) if it is to be retained.

• No-load test (rated V, no load): gives rotational loss and \(X_1 + X_m\).

• Blocked-rotor test (reduced V, rated I): gives \(R_1 + R_2'\) and \(X_1 + X_2'\).

• DC test: gives \(R_1\), which separates \(R_2'\).

• Starting current scales linearly, and starting torque as the square, of the applied voltage.

1. P65.1 A 415 V, star-connected motor draws 10 A and 1500 W at no load. Its stator resistance is 0.6 Ω per phase. Find the rotational loss and no-load power factor.

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   \[P_\text{rot} = 1500 - 3(10)^2(0.6) = 1320~\text{W}, \qquad \cos\phi_0 = \frac{1500}{\sqrt{3}(415)(10)} = 0.209\]

2. P65.2 In a blocked-rotor test a star-connected motor took 80 V, 20 A, 1200 W. With \(R_1 = 0.4~\Omega\), find \(R_2'\) and \(X_1 = X_2'\).

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   \[Z = \frac{46.19}{20} = 2.309~\Omega,\; R_\text{eq} = \frac{1200}{1200} = 1.0~\Omega,\; X_\text{eq} = 2.082~\Omega\]

   Hence \(R_2' = 0.6~\Omega\) and \(X_1 = X_2' = 1.041~\Omega\).