Tests Used to Determine Induction Motor Parameters

Because the induction motor equivalent circuit closely resembles that of a transformer, a similar set of standard tests is used to determine the machine’s electrical parameters.

Overview of Standard Test Procedures

1. DC Test

Used to determine the baseline Stator Resistance (R₁).

A variable DC voltage source is connected across two stator terminals. The voltage is adjusted until approximately the rated stator current flows, and the stator resistance is calculated using Ohm’s law: Rdc = Vdc / Idc.

2. No-Load Test

Evaluates Core Losses & Magnetising Branch (R_m & X_m)

The motor is energised at rated voltage and frequency while running freely without any mechanical load. Under this condition, the useful output power is zero, meaning almost all input power represents internal losses.

3. Locked-Rotor Test

Isolates Rotor & Stator Leakage Impedances.

The rotor is mechanically locked so it cannot rotate (Slip = 1). At reduced AC voltage, the parallel magnetising branch contributes minimally and can be neglected, leaving the combined stator and rotor leakage elements.

Test Mechanics & Per-Phase Conversions

Because DC applies equal current through all winding segments, the measured resistance must be converted to per-phase form based on configuration:

Star-Connected Stator: R₁ = Rdc / 2
Delta-Connected Stator: R₁ = 3Rdc / 2
No-Load Power Input: Pin ≈ Core Loss + Friction and Windage Loss
Locked-Rotor Series Impedance: Z_LR = R₁ + R₂ + j(X₁ + X₂)

Example Induction Motor Parameter Question

Machine Specifications: Three-phase, star-connected induction motor rated at 415 V, 50 Hz, with a rated winding current of 45 A.

Collected Test Data:
• D.C. Test: Applied phase-to-phase voltage of 25 V produced a current of 45 A.
• No-Load Test: Line voltage = 415 V, Line current = 7.5 A, Total 3-phase power = 600 W.
• Locked-Rotor Test: Line voltage = 70 V, Line current = 35 A, Total 3-phase power = 2750 W.

Step 1: Evaluation of the DC Test Data

                Idc = 45 A

                R = V / I = 25 / 35 = 0.71 Ω

                R₁ = 0.71 / 2 = 0.357 Ω

Step 2: Analysis of No-Load Test Parameters

Per-phase layout for the parallel excitation branch:

No-Load Parallel Equivalent Circuit Branch

                VL = 415 V , I = 7.5 A , P = 600 W

                θ = cos⁻¹( P / (√3 × VL × I) ) = cos⁻¹( 600 / (√3 × 415 × 7.5) )

                θ = 83.6°

Power Triangle and relationship to Current and Impedance:

Resolving components using Ohm’s Law (V_phase = 415 / √3 = 240 V):

                IRT = I × cos(θ) = 7.5 × cos(83.6°) = 0.836 A

                IXT = I × sin(θ) = 7.5 × sin(83.6°) = 7.45 A
                Rm = V / IRT = 240 / 0.836 = 287.1 Ω

                Xm = V / IXT = 240 / 7.45 = 32.2 Ω

Step 3: Evaluation of Locked-Rotor Impedances

Bypassing the excitation parameters gives the following series simplified configuration:

Locked Rotor Series Equivalent Circuit Layout

                Vp = 70 V / √3 = 40.4 V

                Z = V / I = 70 / 35 = 2.0 Ω

                θ = cos⁻¹( P / (√3 × VL × I) ) = cos⁻¹( 2750 / (√3 × 70 × 35) ) = 49.6°

                RT = Z × cos(θ) = 2.0 × cos(49.6°) = 1.30 Ω

                XT = Z × sin(θ) = 2.0 × sin(49.6°) = 1.52 Ω
                Isolating Rotor Resistance (R₂):

                RT = R₁ + R₂ = 1.30 Ω

                0.357 + R₂ = 1.30

                R₂ = 1.30 – 0.357 = 0.943 Ω
                Isolating Stator and Rotor Leakage Reactances (Assumed Equal):

                X₁ = X₂ = 1.52 / 2 = 0.76 Ω