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1 EECE421 Power System Analysis aChapter 3: Transmission Line Serial Impedance

aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

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Page 1: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

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EECE421 Power System Analysis 

Chapter 3: Transmission Line Serial Impedance

ckim
Typewritten Text
www.mwftr.com
Page 2: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Conductor Types

CopperAluminum

SolidStrands

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Page 3: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Conductor Types

CopperAluminum

SolidStrands

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Page 4: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Conductor Types ‐ ACSR

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Page 5: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.2 Resistance

Diameter: mil = 10‐3 in = 1/1000 [in]

Area: cmil [circular mil]= (π/4)*mil2

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Page 6: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.2 Resistance

Diameter: mil = 10-3

in = 1/1000 [in]

Area: cmil [circular mil] = (π/4)*mil2

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Page 7: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.2 Resistance

Conductivity: Area (A): m^2 for SI  cmil for US

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Page 8: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.2 ResistanceTemperature Dependency

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Page 9: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.2 Resistance

Skin Effect

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Page 10: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Ex 3.1 (on All Aluminum Marigold stranded conductor)

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Page 11: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Ex 3.1 (on All Aluminum Marigold stranded conductor)

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Page 12: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

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3.3 Field Theory and Inductance

Changing flux Induced voltage Circuit property (Inductance L)

Page 13: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.4 Definition of Inductance2 fundamental equations:(1) Change of flux linkage 

induced voltage(2) Change in current  the amount of voltage induction

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Page 14: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.4 Definition of Inductance2 fundamental equations:(1) Change of flux linkage 

induced voltage(2) Change in current  the amount of voltage induction

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Page 15: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.4 Definition of InductanceUnder linear relationship of current (i) and flux linkage (τ)

Phasor

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Page 16: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.4 Definition of InductancePhasor

Mutual Inductance

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Page 17: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal fluxFlux Linkage (“effective flux”): flux liking a number of coils or coil turns (in our discussion here) flux linking to a portion of (or  full) the current in the conductor

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Page 18: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal flux

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Page 19: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal flux

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Page 20: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal flux

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Page 21: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal fluxFlux Linkage (dψ)

Flux linkage for the current inside the conductor

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Page 22: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.5 Inductance of a conductor due to internal flux

Inductance due to internal flux (Lint)

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Page 23: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.6 Flux Linkage between 2 external points 

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Page 24: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.6 Flux Linkage between 2 external points 

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Page 25: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

Current flows are forward and reverse (or return)r: conductor radiusD: Distance between the conductors (center to center)

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Page 26: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

Current flows are forward and reverse (or return)d1: a point between conductor 1 and 2d2: a point along the length of the conductor diameter

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Page 27: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

Current flows are forward and reverse (or return)d1: a point between conductor 1 and 2d2: a point along the length of the conductor diameter

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Page 28: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

Current flows are forward and reverse (or return)d1: a point between conductor 1 and 2d2: a point along the length of the conductor diameter

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Page 29: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

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Page 30: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.7 Inductance of a Single Phase 2‐wire Line 

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Page 31: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.8 Flux Linkage of one conductor in a group 

P: a point in the spaceFlux linkage between a conductor to the point P due to the current I1

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Page 32: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.8 Flux Linkage of one conductor in a group 

P: a point in the spaceFlux linkage between a conductor to the point P due to the current I2

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Page 33: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.8 Flux Linkage of one conductor in a group 

P: a point in the spaceFlux linkage between a conductor to the point P due to the current I2

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Page 34: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.8 Flux Linkage of one conductor in a group 

P: a point in the spaceFlux linkage between a conductor to the point P due to the current I2

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Page 35: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.9 Inductance of Composite‐Conductor Lines 

Stranded conductorComposite Conductor: 2 or more elements or strandsWe assume that composite conductors share the current equally

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Page 36: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.9 Inductance of Composite‐Conductor Lines 

We assume that composite conductors share the current equallyLet’s pick the filament aI/nI/m

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Page 37: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.9 Inductance of Composite‐Conductor Lines 

We assume that composite conductors share the current equallyLet’s pick the filament aI/nI/m

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Page 38: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.9 Inductance of Composite‐Conductor Lines 

The filaments are in parallelInductance then must be divided by the number of elementsUsing Log A + Log B = Log (AB)

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Page 39: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

3.9 Inductance of Composite‐Conductor Lines 

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Page 40: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

Ex 3.2 Inductance Calculation

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Page 41: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

GMD calculation between X and Y sides

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Page 42: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

GMR calculation for X side  Lx Calculation

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Page 43: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

GMR calculation for Y side  Ly Calculation

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Page 44: aChapter 3: Transmission Line Serial Impedance GMR calculation for X side ÆLx Calculation 42 GMR calculation for Y side ÆLy Calculation 43 L = Lx + Ly 44 Title Microsoft PowerPoint

L = Lx + Ly

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