Power Quality and inductance
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Transcript of Power Quality and inductance
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Power Quality Vis-à-Vis
Inductance Gary Malhoit, P.E.
February 23, 2017
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Tall Tree and the Eye
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Overview Inductance? Background and History Flux Linkage Wire Size and Coil Aspect Ratio PQ Applications Comments and Questions
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History of InductancePart 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:
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𝑮𝑪=
𝑹𝑳
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History of InductancePart 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)
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Ampère’s Circuital Law
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-
V=0
E
-
E
V>0 Φ
V=Velocity
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Magnetic Flux & Current
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Current flowing through a Conductor
Lines of Flux
𝜱∝ 𝑰Φ=
DCylindrical
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Inductance Defined
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= henry
If Φ changes I changes
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Internal & External Inductance
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Conductor
Internal Magnetic Field
External Magnetic Field
X
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Induction
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-
E
>0 ΦV=Velocity
Φ
Time
InductionInductionNo Induction
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Induction:Faraday’s Law
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( )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=− 𝒅𝒅𝒕∬𝒔
.
𝑩 .𝒅𝒔
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Induction As a Function of Inductance
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𝑽=−𝑳 𝒅𝑰𝒅𝒕
The minus sign indicates the induced voltage opposesprior conditions and is called Lenz Law
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A First Definition of Flux Linkage
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𝐋=𝐅𝐥𝐮𝐱 𝐋𝐢𝐧𝐤𝐚𝐠𝐞
𝑰 =𝑵𝜱𝑰
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A First Definition of Flux Linkage
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A Second Definition of Flux Linkage
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A Second Definition of Flux Linkage
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Inductance of a Straight Wire
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Area
Magnetic Flux Line
Conductor
Flux Linkage
Current
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Inductance of a Straight Wire (Edward Rosa 1907)
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Biot-Savart 𝟏𝑫𝟐
A First Point
IA Second PointL
∞R
Area of Flux Linkage
Conductor
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Formula: Inductance of a Straight Wire
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𝐋=2 𝒍(𝑳𝒏 2 𝒍𝑹 −1+ 14 )
R= wire radiusl= wire lengthL= inductance
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Inductance & Wire Diameter
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Wheeler’s formula
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L= 𝒂2𝒏29𝒂+10𝒃
a= coil radiusn= number of turnsb=coil lengthL= inductance
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Inductance of a Coil of 200 Inches of Wire
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Inductance of a Conductor
(Rectangular Cross-Section)
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𝐋=2 𝒍¿l= wire lengthw= width of wireb= height of wireL= inductance
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Inductance of a Conductor
(Rectangular vs. Round Cross-Section)
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Rectangular Cross-Section
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Mutual Inductance: Parallel Conductors
Currents Same Direction
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Mutual Inductance: Parallel ConductorsCurrents Opposite
Directions
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Mutual Inductance: Parallel
Conductors Occupy Same Space
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Inductance & Lead Length Spacing of Metal
Oxide Varistors
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Minimize Spacing
*
* Minimize Lead Length
Load
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Rogowski Coil
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Coaxial Return
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Rogowski Coil & Immunity
to External Magnetic Fields
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Triplen Harmonics
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Third HarmonicsOverlaid
Sum of ThirdHarmonics
Phase APhase BPhase C
Third HarmonicsSum Third Harmonics
Odd Sequence: 1 3 5 7 9 11Third Harmonic: 3 3 3 3 3 3
Triplens: 3, 9, 15, 21, 27, 33
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Zigzag Transformer & Mitigation of Third
Harmonics
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Opposing FieldsSubstantially CancelZero Sequence Current!
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Common Mode Signals
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Ferrite Beads
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Ferrite Beads
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Ferrimagnetic (Louis Néel, 1970)
Ferromagnetic
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Ferrite Beads
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IDC IAC
Mag
nitu
de
Frequency
Low Pass
=ωL
ω
Bias
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Questions & Comments
38