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Power Quality and inductance
- 1. Power Quality Vis-à-Vis Inductance Gary Malhoit, P.E. February 23, 2017
- 2. Tall Tree and the Eye 2
- 3. Overview Inductance? Background and History Flux Linkage Wire Size and Coil Aspect Ratio PQ Applications Comments and Questions 3
- 4. History of Inductance Part 1 Last of the 3 fundamental circuit characteristics “Electro-dynamic capacity” (Lord Kelvin) “A bugaboo” (Sir William Preece) War of Currents (1880s-1890s) Lexicographer of inductance (Oliver Heaviside) Heaviside Condition: 4 𝑮 𝑪 = 𝑹 𝑳
- 5. History of Inductance Part 2 Oersted’s discovery (1820) Ampère’s Theory (1823) Ampère’s circuital law says a magnetic flux forms around or encircles a current (moving charges) carrying conductor Displacement Current (1886) (James Maxwell) 5
- 6. Ampère’s Circuital Law 6 - V=0 E - E V>0 Φ V=Velocity
- 7. Magnetic Flux & Current 7 Current flowing through a Conductor Lines of Flux 𝜱 ∝ 𝑰 Φ= 𝟏 𝑫 D Cylindrical
- 8. Inductance Defined 8 𝐋 = 𝜱 𝑰 = 𝐰𝐞𝐛𝐞𝐫 𝐚𝐦𝐩𝐞𝐫𝐞 = henry If Φ changes I changes
- 9. Internal & External Inductance 9 Conductor Internal Magnetic Field External Magnetic Field X
- 11. Induction: Faraday’s Law 11 𝐕 = −𝑵 𝒅𝜱 𝒅𝒕 ( 𝒘𝒆𝒃𝒆𝒓 𝒔𝒆𝒄𝒐𝒏𝒅 ) By one definition, a volt is induced via one loop (N=number of turns=1) of a coil exposed to a magnetic flux of one weber changing to zero in one second. AC 𝑺 . 𝑬. 𝒅𝒍 = − 𝒅 𝒅𝒕 𝒔 . 𝑩. 𝒅𝒔
- 12. Induction As a Function of Inductance 12 𝑽 = −𝑳 𝒅𝑰 𝒅𝒕 The minus sign indicates the induced voltage opposes prior conditions and is called Lenz Law
- 13. A First Definition of Flux Linkage 13 𝐋 = 𝐅𝐥𝐮𝐱 𝐋𝐢𝐧𝐤𝐚𝐠𝐞 𝑰 = 𝑵𝜱 𝑰
- 14. A First Definition of Flux Linkage 14
- 15. A Second Definition of Flux Linkage 15 𝐋 = 𝐅𝐥𝐮𝐱 𝐋𝐢𝐧𝐤𝐚𝐠𝐞 𝑰 = 𝑵𝑨𝜱 𝑰
- 16. A Second Definition of Flux Linkage 16
- 17. Inductance of a Straight Wire 17 Area Magnetic Flux Line Conductor Flux Linkage Current
- 18. Inductance of a Straight Wire (Edward Rosa 1907) 18 Biot-Savart 𝟏 𝑫 𝟐 A First Point I A Second PointL ∞ R Area of Flux Linkage Conductor
- 19. Formula: Inductance of a Straight Wire 19 𝐋 = 2𝒍(𝑳𝒏 2𝒍 𝑹 − 1 + 1 4 ) R= wire radius l= wire length L= inductance
- 20. Inductance & Wire Diameter 20
- 21. Wheeler’s formula 21 L = 𝒂2 𝒏2 9𝒂 + 10𝒃 a= coil radius n= number of turns b=coil length L= inductance
- 22. Inductance of a Coil of 200 Inches of Wire 22
- 23. Inductance of a Conductor (Rectangular Cross-Section) 23 𝐋 = 2𝒍(𝑳𝒏 2𝒍 𝒘 + 𝒉 + 0.5 + 0.2235( 𝒘 + 𝒉 𝒍 ) l= wire length w= width of wire b= height of wire L= inductance
- 24. Inductance of a Conductor (Rectangular vs. Round Cross- Section) 24
- 26. Mutual Inductance: Parallel Conductors Currents Same Direction 26
- 27. Mutual Inductance: Parallel Conductors Currents Opposite Directions 27
- 28. Mutual Inductance: Parallel Conductors Occupy Same Space 28
- 29. Inductance & Lead Length Spacing of Metal Oxide Varistors 29 Minimize Spacing * * Minimize Lead Length Load
- 31. Rogowski Coil & Immunity to External Magnetic Fields 31
- 32. Triplen Harmonics 32 Third Harmonics Overlaid Sum of Third Harmonics Phase A Phase B Phase C Third Harmonics Sum Third Harmonics Odd Sequence: 1 3 5 7 9 11 Third Harmonic: 3 3 3 3 3 3 Triplens: 3, 9, 15, 21, 27, 33
- 33. Zigzag Transformer & Mitigation of Third Harmonics 33 Opposing Fields Substantially Cancel Zero Sequence Current!
- 35. Ferrite Beads 35
- 36. Ferrite Beads 36 Ferrimagnetic (Louis Néel, 1970) Ferromagnetic
- 37. Ferrite Beads 37 IDC IAC Magnitude Frequency Low Pass 𝑿 𝑳=ωL ω Bias
Editor's Notes
- Two house keeping items before we start: If you would like a copy of this presentation, you can get a copy on Slide share. I uploaded this presentation a couple of days ago. Feel free to interrupt this discussion with your comments and questions at any time.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.
- 1. A sinusoid is the lowest common denominator of all periodic signals. 2. Also, in engineering sinusoids are a preferred tool because of Sinusoidal Fidelity. If you apply a sinusoid to a linear system the output is always a sinusoid no other waveform has that characteristic. 3. The atom is depicted as the basic unit in chemistry. For this discussion, the sinusoid is analogous and the basic unit for periodic waveforms. 4. Utilities such as SRP are know as voltage providers. It should be noted that the voltage at least from the generator is near perfect.