Class 09: Induction Motor Testing — No-Load, Blocked Rotor & DC Tests

Date: 21.07.2026 / 22.07.2026 | Instructor: Fariya Tabassum (FT Mam)
Source Scan Pages: P17_R, P18 (Left/Right), P19_L
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1. Overview and Purpose of Testing

The primary objective of induction motor testing is to experimentally determine the essential parameters of the per-phase equivalent circuit ($R_1,X_1,R_2,X_2,X_m,R_c$):

$$\text{Parameter Determination}⟶X_1,R_1,X_2,R_2,X_m$$

The Three Interdependent Tests
├── 1. No-Load Test (Open-Circuit Test)      ──> Core loss, friction/windage loss, X_m
├── 2. Blocked-Rotor Test (Short-Circuit)    ──> Equivalent leakage reactance (X_1 + X_2), (R_1 + R_2)
└── 3. DC Resistance Test                   ──> Stator per-phase winding resistance R_1

• Grid and Voltage Ratings:
  • Industrial and commercial 3-phase supply: $V_L=400\text{ V}$ (Line-to-Line).
  • Residential single-phase voltage: $V_p=\frac{V_L}{\sqrt{3}}=\frac{400}{\sqrt{3}}\approx 230\text{ V}$ (Phase-to-Neutral).

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2. No-Load (Open Circuit) Test

• Test Condition:
  • No mechanical load is coupled to the motor shaft ($\text{Load}=0$).
  • The rotor accelerates to near-synchronous speed ($N_r\approx N_s$).
  • Consequently, slip is extremely small / near zero: $$s\approx 0⟹\frac{R_2}{s}⟶\infty$$

Circuit Simplification:

• Since $\frac{R_2}{s}\approx \infty$, the parallel rotor branch acts virtually as an Open Circuit.
• Furthermore, $I_w\ll I_{\mu }$ (the wide air-gap requires a dominant magnetizing current).
• Therefore, the total input power measured by wattmeters comprises: $$\boxed{P_{NL}=3I_{NL}^2{R}_1+P_{core}+P_{w,f}}$$ (Stator copper loss + Core iron loss + Friction and windage losses).

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3. Blocked Rotor (Locked Rotor) Test

• Test Condition:
  • The rotor is mechanically clamped/locked so that it cannot rotate: $$N_r=0⟹s=\frac{N_s-0}{N_s}=1$$
  • A very low reduced voltage ($10-15\%$ of rated voltage) is applied to the stator to circulate rated full-load current.

Circuit Simplification:

• Since $s=1$, the effective rotor resistance is $\frac{R_2}{s}=R_2$ (which is very small).
• Due to the drastically reduced applied voltage, current through the parallel magnetizing branch ($X_m,R_c$) is negligible ($I_0\approx 0$).
• The entire network simplifies into a simple series circuit: $$Z_{BL}=\frac{V_{BL}/\sqrt{3}}{I_{BL}}$$ $$R_{BL}=R_1+R_2=\frac{P_{BL}}{3I_{BL}^2}$$ $$X_{BL}=X_1+X_2=\sqrt{Z_{BL}^2-R_{BL}^2}$$ (Typically divided equally: $X_1=X_2=0.5X_{BL}$).

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4. DC Stator Resistance Test

When DC is applied to an inductive coil, the inductive reactance drops to zero ($\omega =0⟹X_L=0$). The inductor behaves as a pure short circuit, leaving only the pure ohmic resistance effective:

$$R_{DC}=\frac{V_{DC}}{I_{DC}}$$ (Total DC resistance measured between any two line terminals).

Relation Between $R_{DC}$ and Per-Phase Stator Resistance ($R_1$):

1. For Wye / Star (Y) Connected Stator: Two phase windings are connected in series: $$R_{DC}=2R_1⟹\boxed{R_1(\text{wye})=\frac{R_{DC}}{2}}$$

2. For Delta ($\Delta$) Connected Stator: One phase winding is connected in parallel with the series combination of the other two phases: $$R_{DC}=R_1\parallel (R_1+R_1)=\frac{R_1\cdot 2R_1}{3R_1}=\frac{2}{3}{R}_1$$ $$⟹\boxed{R_1(\Delta )=1.5\cdot R_{DC}}$$

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