No Load Test Induction Motor Equivalent Circuit: Setup and Measurement Guide

The no-load test on an induction motor is the definitive bench and field method to extract the magnetizing branch parameters—core loss resistance (R_c) and magnetizing reactance (X_m)—for the per-phase equivalent circuit. By running the motor completely uncoupled from any mechanical load at rated voltage and frequency, the slip approaches zero (s ≈ 0). This effectively opens the rotor branch, forcing almost all input current through the magnetizing branch and allowing us to isolate core losses from copper losses.

Unlike a simple continuity check, deriving the exact no load test induction motor equivalent circuit parameters requires precise wattage measurements at very low power factors. Below is the exact procedure, meter configuration, and mathematical framework to get it right on the first attempt.

Meter Setup, Probe Placement, and CAT Safety

Meter Setup Block

To capture the true real power (Watts) at the motor's notoriously low no-load power factor (typically 0.10 to 0.20), a standard digital multimeter (DMM) is insufficient. You need a true-RMS power analyzer or a 3-phase wattmeter.

• Power Analyzer (e.g., Fluke 1735 or Yokogawa WT500): Set the dial/software mode to 3-Phase 3-Wire (or 3-Wattmeter method if neutral is available). Set the voltage range manually to 600V and current range to 20A to prevent auto-ranging delays during motor startup.
• Digital Multimeter (e.g., Fluke 87V): Set dial to AC Voltage (V~). Insert leads into COM and V/Ω jacks. Set to Auto-range. This is used strictly to verify bus voltage at the peckerhead before and during the test.

Probe Placement

1. Current Probes: Clamp the flexible Rogowski coils or CTs around the motor feeder conductors (T1, T2, T3) inside the terminal box. Ensure the directional arrow on each clamp points toward the motor windings.
2. Voltage Probes: Connect the voltage leads directly to the motor terminal studs (L1-L2, L2-L3, L3-L1). Never measure voltage back at the MCC or breaker panel for this test; feeder voltage drop will skew your R_c calculations.

Expected Readings and Equivalent Circuit Mapping

Before crunching the math, you need to know if your raw data makes physical sense. A good reading numerically means the no-load current (I_nl) falls between 20% and 30% of the motor's Full Load Current (FLC), and the real power (P_nl) is dominated by core and friction losses rather than copper losses.

The table below provides baseline expectations for a standard 5 HP, 460V, 60Hz, 4-pole (1800 RPM nominal) TEFC induction motor. Refer to the Electrical4U no-load test theory guide for deeper mathematical proofs of these parameters.

Deriving R_c and X_m from the Test Data

Once you have your stable readings (allow the motor to run uncoupled for at least 15 minutes to stabilize bearing friction and windage losses), you can map the data to the per-phase equivalent circuit. According to DOE motor efficiency guidelines, accurately separating these losses is critical for predicting motor performance under variable frequency drive (VFD) operation.

Worked Numeric Example

Assume our 5 HP motor yields the following stable test data:

• V_line = 460V
• I_nl = 2.2A (per phase)
• P_{nl_total} = 210W
• R₁ = 1.2Ω (measured previously via DC test, corrected to AC operating temperature)

Step 1: Calculate Per-Phase Voltage and Power
V_phase = V_line / √3 = 460 / 1.732 = 265.6V
P_{nl_phase} = 210W / 3 = 70W

Step 2: Subtract Stator Copper Loss
The wattmeter reads total input power, which includes stator I²R heating. We must subtract this to find the true core and rotational losses.
P_{stator_cu} = I_nl² × R₁ = (2.2)² × 1.2 = 4.84 × 1.2 = 5.8W per phase
P_core+fw = P_{nl_phase} - P_{stator_cu} = 70 - 5.8 = 64.2W per phase

Note: In a rigorous lab setting (IEEE 112), you would perform a variable-voltage no-load test to graphically separate friction/windage (P_fw) from core loss. For standard field equivalent circuit extraction, we often lump P_fw into the core loss branch, treating the 64.2W as the total shunt branch power dissipation.

Step 3: Calculate Core Loss Resistance (R_c)
R_c represents the resistance that would dissipate the core loss as heat.
R_c = V_phase² / P_core+fw = (265.6)² / 64.2 = 70,543 / 64.2 = 1,098 Ω

Step 4: Calculate Magnetizing Reactance (X_m)
First, find the total no-load impedance (Z_nl) and resistance (R_nl):
Z_nl = V_phase / I_nl = 265.6 / 2.2 = 120.7 Ω
R_nl = P_{nl_phase} / I_nl² = 70 / 4.84 = 14.46 Ω
X_nl = √(Z_nl² - R_nl²) = √(14568 - 209) = 119.8 Ω

Because X_nl is the series combination of stator leakage reactance (X₁) and magnetizing reactance (X_m), you must subtract X₁ (derived from a blocked-rotor test). If X₁ is known to be 4.5 Ω:
X_m = X_nl - X₁ = 119.8 - 4.5 = 115.3 Ω

Measurement Mistakes That Yield Misleading Readings

When your calculated R_c or X_m values look physically impossible (e.g., an X_m lower than X₁), the error is almost always in the measurement setup, not the motor. Avoid these common pitfalls:

1. Failing to Fully Uncouple the Mechanical Load

The entire mathematical premise of the no-load test relies on slip being zero (s ≈ 0), which opens the rotor branch in the equivalent circuit. If you leave a 'freewheeling' pump, gearbox, or even a tight V-belt connected, the motor experiences mechanical drag. Slip increases, current begins flowing through the rotor resistance branch (R₂/s), and your wattmeter reads rotor copper loss as if it were core loss. This will result in a drastically underestimated R_c.

2. Using a Standard DMM for Wattage at Low Power Factors

At no-load, an induction motor acts almost like a pure inductor, with a power factor often dropping below 0.15. Standard multimeters and cheap clamp meters calculate power by simply multiplying V_rms × I_rms, assuming a power factor of 1.0. This will give you Apparent Power (VA), not Real Power (W). If you use Apparent Power in the R_c formula, your calculated core loss will be 5 to 10 times higher than reality. You must use a meter capable of true phase-angle wattage measurement. Refer to Fluke's motor testing instrumentation guide for verified power analyzer setups.

3. Ignoring Stator Copper Loss (I²R)

While 5.8W of stator copper loss seems negligible compared to 210W of total input power in a 5 HP motor, the math changes drastically in fractional horsepower or high-efficiency motors where core losses are exceptionally low. Failing to subtract the stator I²R loss from the total measured wattage artificially inflates the core loss, yielding an equivalent circuit that predicts excessive heating under load.

4. Measuring Voltage at the Breaker Instead of the Peckerhead

If you measure 460V at the MCC breaker, but the feeder cables are undersized or run over a long distance, the actual voltage at the motor terminal box might only be 445V. Because core loss is proportional to the square of the voltage (V²/R_c), a 3% error in voltage measurement translates to a ~6% error in your calculated core loss and R_c value. Always place your voltage probes directly on the motor terminal studs.