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
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
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!
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.