Asynchronous Motor Testing and Circle Diagram Analysis

Practice 17: Asynchronous Motor Circle Diagram Tests

Introduction to Indirect Motor Characterization

This practice involves the indirect determination of the characteristics of a three-phase asynchronous motor. This method provides results using considerably lower power than the rated motor power by following the model graph known as the circle diagram.

Practice Outline and Theoretical Basis

To determine the circle diagram, it is necessary to perform a load test and a short-circuit test. Additionally, knowledge of the stator resistance per phase (R₁) is required to separate the mechanical losses from the iron losses.

No-Load Test and Power Factor Determination

To perform the load test, the motor is applied its rated voltage and allowed to rotate freely (i.e., with no load). During this process, the current intensity (I₀) and power (P₀) are determined.

Using this data, the load power factor can be determined by the following relationship:
cos φ₀ = P₀ / (√3 · U · I₀)

Moreover, since the effective power is zero, all absorbed power results in losses in the form of:
P₀ = P_Fe + P_m + 3 · R₁ · I₀²

Where:

• P_Fe = Iron losses
• P_m = Mechanical and ventilation losses
• 3 · R₁ · I₀² = Copper losses in the stator

The losses in the rotor copper are negligible because the current (I₂) is only what is necessary for the motor to develop the torque required to overcome mechanical and ventilation losses.

Assuming the stator resistance per phase is known (determined in a preliminary step), the combination of mechanical and iron losses can be inferred as:
P_Fe + P_m = P₀ - 3 · R₁ · I₀²

Short-Circuit Test and Resistance Calculation

For the short-circuit test, the rotor is shorted to remain at rest. A reduced voltage (U_cc) is applied to circulate a current through the stator winding equal to the rated motor current (I₁). The measured power is the short-circuit power (P_cc).

The graphics will determine I_cc and the corresponding short-circuit power at nominal voltage. The short-circuit power factor is determined by the formula:
cos φ_cc = P_cc / (√3 · U · I_cc)

Where U is the nominal network voltage and I_cc is the short-circuit current. Additionally, from the short-circuit power, the short-circuit resistance may be established:
R_cc = P_cc / (3 · I_cc²)

Once all required values are obtained, the construction of the circle diagram will proceed.

Required Laboratory Equipment

• A DC voltage source
• A DC voltmeter and a DC ammeter
• A voltage-controlled three-phase AC source
• A three-phase asynchronous motor
• An AC voltmeter and an AC ammeter
• Two power meters (wattmeters)