Torque speed characteristics of Squirrel cage & Slip ring induction motors
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This video describes the Torque - Slip / Torque- Speed Characteristics of three phase squirrel cage induction motor and slip ring induction motor- also describes the Condition for the maximum torque - Pullout torque and Pullout torque equation
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Functions and Performance Requirements
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Types of Excitation Systems
Control and Protection Functions
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Torque speed characteristics of Squirrel cage & Slip ring induction motors
- 1. TORQUE- SPEED CHARACTERISTICS OF SQUIRREL CAGE & SLIP RING IM (OR) TORQUE- SLIP CHARACTERISTICS OF SQUIRREL CAGE & SLIP RING IM Basic Torque Equation of DC motor 𝐓 = 𝐤 ∗ ∅ ∗ 𝐈 Basic Torque Equation of AC motor 𝐓 = 𝐤 ∗ ∅ ∗ 𝐈 * cos Power in DC Circuit V* I Power in AC Circuit V* I * cos Torque - Multiplication of 2 magnetic fluxes Power – Multiplication of Voltage and Current
- 2. Torque Equation of AC Induction Motor 𝐓 = 𝐊 ∗ ∅ ∗ 𝐄 𝟐 𝐙 𝟐 ∗ 𝐑 𝟐 𝐙 𝟐 𝐓 = 𝐤 ∗ ∅ ∗ 𝐈 𝟐* cos 𝐓 = 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 𝐙 𝟐 𝟐 𝐓 = 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 + 𝐗 𝟐 𝟐 𝐓 = 𝐊 ∗ ∅ ∗ 𝐒 𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 + ( ሻ𝐒 𝐗 𝟐 𝟐 Slip speed (SNs) = Ns- N 𝐈 𝟐 = 𝐄 𝟐 𝐙 𝟐 ; 𝐂𝐨𝐬𝛗 = 𝐑 𝟐 𝐙 𝟐 𝒁 𝟐 = 𝑹 𝟐 𝟐 + 𝑿 𝟐 𝟐
- 3. 𝐓 ∝ 𝐊 ∗ ∅ ∗ 𝐒 𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 𝐓 = 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 + ( ሻ𝐒𝐗 𝟐 𝟐 𝐓 ∝ 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ൫ ሻ𝐒𝐗 𝟐 𝟐 𝐓 ∝ 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 𝐒 ∗ 𝐗 𝟐 𝟐 SLIP TORQUE 01 0 Ns SPEED Low SlipHigh Slip LOW SLIP REGION HIGH SLIP REGION Min speed N= 0 @ which slip S = 1 Max speed N= Ns @ which slip S = 0 Starting Torque Critical Slip Pull out Torque (𝐒𝐗 𝟐ሻ 𝟐 ≪ 𝐑 𝟐 𝟐 (𝐒𝐗 𝟐ሻ 𝟐 ≫ 𝐑 𝟐 𝟐 General Torque Equation
- 4. Slip ring Induction Motor (or) Torque –Speed characteristics of Slip ring Induction motor Decreasing Increasing 𝐓 ∝ 𝟏 𝑹 𝐓 ∝ 𝐑
- 5. What is the Condition for Maximum Torque? 𝐝𝐓 𝐝𝐒 = 𝟎 𝐝 𝐝𝐬 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 + ( ሻ𝐒𝐗 𝟐 𝟐 = 𝟎 ൯( 𝐑 𝟐 𝟐 + ሻ𝐒𝐗 𝟐 𝟐 ∗ (𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐ሻ − 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ (𝟐𝐒𝐗 𝟐 𝟐 𝑹 𝟐 𝟐 + 𝑺 𝟐 𝑿 𝟐 𝟐 𝟐 = 𝟎 V U’ U V’ 𝐕 𝟐 _
- 6. 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 𝟑 + 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 ∗ 𝐒 𝟐 𝐗 𝟐 𝟐 − 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ 𝟐𝐒𝐗 𝟐 𝟐 = 𝟎 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 (𝐑 𝟐 𝟐 + 𝐒 𝟐 𝐗 𝟐 𝟐 − 𝟐𝐒 𝟐 𝐗 𝟐 𝟐 ሻ = 𝟎 𝐑 𝟐 𝟐 − 𝐒 𝟐 𝐗 𝟐 𝟐 = 𝟎 𝐒 𝟐 = 𝐑 𝟐 𝟐 𝐗 𝟐 𝟐 𝐒 = 𝐑 𝟐 𝐗 𝟐 CRITICAL SLIP = 𝐑 𝟐 𝐗 𝟐 ൯( 𝐑 𝟐 𝟐 + ሻ𝐒𝐗 𝟐 𝟐 ∗ (𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐ሻ − 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ (𝟐𝐒𝐗 𝟐 𝟐 𝑹 𝟐 𝟐 + 𝑺 𝟐 𝑿 𝟐 𝟐 𝟐 = 𝟎
- 7. 𝐓 = 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 𝐑 𝟐 𝟐 + ( ሻ𝐒𝐗 𝟐 𝟐 𝐓(𝐦𝐚𝐱ሻ = 𝐊 ∗ ∅ ∗ 𝐑2 𝐗2 𝐄2 ∗ 𝐑2 𝐑2 2 + 𝐑2 2 𝐗2 2 ∗ 𝐗2 2 𝐓(𝐦𝐚𝐱ሻ = 𝐊 ∗ ∅ ∗ 𝐄2 ∗ 𝐑2 2 2𝐑2 2 ∗ 𝑿2 𝐓 𝐦𝐚𝐱 𝐨𝐫 𝐩𝐮𝐥𝐥𝐨𝐮𝐭 𝐭𝐨𝐫𝐪𝐮𝐞 = 𝐊 ∗ ∅ ∗ 𝐄 𝟐 𝟐 𝑿 𝟐 PULL OUT TORQUE EQUATION (Irrespective of rotor resistance 𝐑 𝟐)