Asynchronous Induction Motors: Operation and Characteristics

Posted on Jan 5, 2025 in Geology

Asynchronous Induction Motor Equivalent Circuit

This document details the equivalent circuit of an asynchronous squirrel-cage induction motor. We will cover the tests and approximations used to determine the equivalent circuit parameters. The two main tests are the no-load test (open circuit) and the short-circuit test (rotor blocked).

A) No-Load Test (or Open Rotor Test)

This test consists of running the motor at no mechanical load, meaning the rotor is free. In this condition, the motor’s speed is very close to the synchronous speed. The primary voltage (_1n) is applied, and the absorbed power (P₀) and current (I₀) are measured. The following relationship holds:

P₀ = P_f + P_m + P_CU1

Where:

• P_f: Iron losses
• P_m: Mechanical losses
• P_CU1: Stator copper losses

To calculate P_CU1 (stator copper losses), we need to measure the resistance (R₁) of each phase of the stator. To determine P_f and P_m, we need to feed the motor with a variable voltage (U₁) and measure P₀, I₀, and U₁ at each step. From this, we can calculate:

P_f + P_m = P₀ – P_w = P₀ – m₁ * R₁ * I₀²

We can then obtain:

• cos(φ₀) = P₀ / (m₁ * U_1n * I₀)
• I_f = I₀ * cos(φ₀)
• I_μ = I₀ * sin(φ₀)
• R_f = U_1n / I_f
• X_μ = U_1n / I_μ

B) Short-Circuit Test

This test involves blocking the rotor, preventing it from rotating (n = 0, s = 1, R_c‘ = 0). A reduced voltage (U_1cc) is applied to the stator (starting from 0) until the absorbed current equals the nominal current (I_cc1 = I_1n). Then:

• cos(φ_cc) = P_cc / (m₁ * U_1cc * I_1n)
• R_cc = R₁ + R₂‘ = (U_1cc / I_1n) * cos(φ_cc)
• X_cc = X₁ + X₂‘ = (U_1cc / I_1n) * sin(φ_cc)

Equivalent Circuit of an Asynchronous Induction Motor

The equivalent circuit parameters (R₀, X₀, R_c‘) are defined as follows:

• R₀: Equivalent resistance in the no-load test per phase. It represents the fictitious resistance through which the current I_0f flows, dissipating the same amount of heat as the iron and mechanical losses in the real motor.
• X₀: Equivalent leakage reactance in the no-load test per phase. It is equal to the magnetizing reactance of the no-load motor.
• R_c‘ = R₂‘ * (1-s) / s: Equivalent load resistance per phase. It represents the fictitious resistance through which the current I_2f‘ flows, dissipating the same amount of heat as the energy produced in the real motor.

In a short circuit, s = 1, so R_c‘ = 0. At synchronism, s = 0, so R_c‘ = ∞.

Speed Regulation

There are several methods for speed regulation. Starting from the expression n = n_s * (1-s) = (60f / p) * (1-s), the speed depends on the slip, the number of poles, and the frequency.

Regulation by Varying the Number of Poles

Changing the number of poles changes the synchronous speed and consequently varies the rotor speed. This is only possible in motors with a squirrel-cage rotor, as this type of rotor automatically adapts to the number of poles in the stator. Each winding consists of two parts that can be connected in series or parallel, resulting in a reduction of the number of poles (half of the original) and increasing the rotor speed to double. This is a stepped regulation, suitable for applications like fans and elevators.

Regulation by Varying the Slip

We can vary the slip by changing the voltage applied to the motor, as the torque is affected (T = f(V²)). We can also vary the slip by changing the rotor resistance, but this causes significant losses due to the Joule effect in the regulation rheostat.

Regulation by Varying the Frequency

This is done using silicon rectifiers or thyristors. It is important to maintain a constant flow during frequency variation so that the torque is conserved and there is sufficient overload capacity.

Operating Principle and Equivalent Circuit of a Single-Phase Motor

Single-phase induction motors are commonly used in low-power applications (less than 1 hp), such as washing machines and fans. They are similar to three-phase motors but with only one stator winding powered by a single-phase supply. When current flows through the stator winding, it produces a rotating magnetic field in the air gap. This field induces currents in the rotor, and the interaction between the field and the rotor currents creates opposing torques, resulting in a zero initial net torque. Due to the absence of starting torque, these motors require an external torque greater than the resistant torque to start. Once started, the two opposing fields are no longer balanced, with one field being reinforced and the other diminished, producing a net torque that maintains rotation. The characteristic torque-slip curve will have two slip values: s_d = 1 – n / n₁ = s and s_i = 1 + n / n₁ = 2 – s.

Equivalent Circuit: Similar to two single-phase motors with their rotors coupled and stators connected in series (with opposite spin fields).

Double-Cage Squirrel-Cage Motor

This type of asynchronous motor utilizes the phenomenon of current displacement in the rotor winding to improve starting characteristics. The stator is conventional, while the rotor has two squirrel cages. The outer cage (near the air gap) has high resistance and low reactance, while the inner cage has low resistance and high reactance. During startup, the rotor frequency is equal to the stator frequency, and the reactances are higher than the resistances. The current flows mainly through the cage with lower reactance, which is the outer cage. At nominal speed, the rotor frequency is negligible, so the resistances prevail, and the current flows through the cage with lower resistance, which is the inner cage. This way, we achieve high torque at startup (due to high R) and good efficiency at nominal speed (due to low R).

Disadvantage: When these motors operate at half load, there will be currents in both circuits, leading to high losses due to the Joule effect.

Applications: Cranes, elevators, fans, centrifugal pumps.