Three-Phase Induction Motor Performance and Braking

Three-Phase Asynchronous Motor Performance

Consider a three-phase asynchronous motor with the following nominal characteristics: 220/380 V at 50 Hz. Iron and mechanical losses are negligible. The resistance and reactance values are R_st = R'_rot = 1.5 Ω and X_st = X'_rot = 2 Ω.

Determining Yield at 1400 RPM

To determine the yield for an operating system with a speed of 1400 RPM:

• Synchronous Speed: N₁ = 60 · f / p = 1500 RPM.
• Slip Calculation: On the other hand, (1500 - 1450) / 1500 = 0.06.
• Total Impedance: Z_T = (1.5 + 1.5 / 0.06) + j4 = 26.80 at an angle of 8.58°.
• Current: I = (380 / √3) / Z_T = 8.18 with a -8.58° angle.
• Input Power (P₁): m₁ · V₁ · I₁ · cos φ = (3 · 380 / √3) · 8.18 · cos(-8.58°) = 5323.65 W.
• Mechanical Power (P₄/P_mi): m₁ · R'₂ · (1 / s - 1) · I² = 4717.32 W.
• Efficiency: η = P₄ / P₁ = 0.88.

Induction Motor Performance Calculation

A three-phase induction motor of 5152 W, 6 poles, and 50 Hz is connected to a 230 V network. The network absorbs 7.2 kVA with a lagging power factor of 0.844 at full load. Calculate the engine performance:

• Useful Power (P_u): 5152 W.
• Input Power (P₁): 7200 · 0.844.
• Yield: The yield is equal to P_u / P₁ = 84.78%.

Wound Rotor Motor Speed Calculation

A four-pole asynchronous motor with a wound rotor has the following equivalent circuit parameters per phase: R_st = R'_rot = 0.1 Ω and X_st = X'_rot = 0.5 Ω. Neglect the parallel paths and mechanical losses. The engine is connected in a triangle (delta) configuration and the line voltage is 380 V at 50 Hz.

Calculating Rotor Speed for 86 kW Output

• Synchronous Speed: N₁ = 60 · f / p = 1500 RPM.
• Slip: s = (s₁ - s) / s₁.
• Mechanical Power: Given that P_mi = 86 kW.
• Current (I'₂): I'₂ = I₁ = (380 / √3) ∠ 0° / (0.1 + 0.1 / s).
• Calculation: As P_mi = m₁ · R'₂ · (1 / s - 1) · (I'₂)², substitute the values and calculate S.

Methods of Braking Induction Motors

There are three primary methods for producing the braking of induction motors:

• Regenerative Braking (Energy Recovery): This method makes the engine functional during the braking phase at speeds above the synchronism. In this case, the slip becomes negative. As deduced from the torque-speed characteristic, the sign of the torque is reversed, but it keeps the sense of movement.
• Plugging (Counter-current Braking): When an asynchronous motor reverses the connection of two phases, the motor becomes fed by a system of reverse sequence voltages. This is immediately translated into a reversal of the direction of rotation of the field in the gap. Thus, there is a reversal of the synchronous speed from +ω₁ to -ω₁ and the torque-speed curve.
• Dynamic Braking by Direct Current Injection: This method involves creating a fixed air gap magnetic field in space by feeding direct current into the stator windings.