HW 5 Praveen

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    EEE 579

    POWER TRANSMISSION AND DISTRIBUTION

    SPRING 2011

    Dr. GEORGE. G. KARADY

    HOMEWORK 5

    LIGHTNING PROTECTION

    SHIELDING PROTECTION

    BACK FLASHOVER

    Praveen Ramiah Subramanian

    ASU ID: 1202919089

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    1. Introduction:

    Lightning is a natural phenomenon occurring due to discharge from the atmosphere and is a major

    cause of damage to transmission line system. This is because of the fact that most transmission lines

    traverse through barren uninhabited expanses of land and are totally conducting. Hence due to the

    extreme heights of the transmission lines and the fact that lightning strikes the highest conducting point

    closest to it, there exists a high probability of the lightning strokes to strike transmission lines.

    When a lightning strikes a transmission line, it induces currents in the range of 150 to 400 kA, voltages

    of the order 106 kV and temperatures close to 50,000 F. Lightning striking transmission lines cannot be

    prevented. The transmission lines are hence designed with shield conductors. The most important

    application of these shield conductors is to ground the lightning induced currents and prevent the

    transmission tower structure, phase conductors and insulators from damage.

    The focus of this project is on designing a robust lightning protection system. It is to be noted that

    lightning striking a transmission line cannot be completely avoided. However, with a systematicanalysis, the probability of successful performance of the lightning protection scheme can be gauged.

    For this analysis, the following parameters need to be calculated:

    Shielding performance

    Back flashover rate

    Expected outage per 100 miles

    Based on the study, the effectiveness of the shielding and lightning protection scheme can be observed

    and steps can be taken if possible to solve potential problems.

    2. Transmission Line Overview:

    Project name : High Plains Express Project

    Point of origin : Gladstone, NM

    Point of termination : Boone, COLine length : 182 miles

    Voltage class : 500 kV AC

    3. Conductor and Tower Data:

    3.1. Phase Conductor Data:

    Conductor Code = ACSR Kiwi Conductor

    Number of conductors per bundle (p) = 2Distance between bundles (dbun) = 18 inches

    Cross Section = 2167 kcmil

    Conductor Diameter = 1.735 inches

    Core Diameter = 0.347 inches

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    Resistance at 60 Hz at 50C (R50) = 0.0511 /mile

    Geometric Mean Radius (GMRc) = 0.0570 ft

    Maximum Current Carrying Capacity = 1000 A

    Conductor Span = 1000 ft

    3.2. Ground Conductor Data:

    Shield Conductor Code = Aluminum CladAlumoweld 7

    Number of Shield Conductors = 2

    Distance between Shield Conductors = 47.536 ftDiameter of Shield Conductor (Dshl) = 0.545 inches

    Resistance at 75C (Rshl75) = 1.669 /mile

    Geometric Mean Radius (GMRshl) = 0.00296 ftGround Resistance (Rground) = 0.095 /mile

    3.3. Transmission Line Data:

    Figure 1: Transmission TowerDimensions3.4. Conductor Coordinates:

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    Figure 2: Conductor Coordinates

    Conductor Horizontal Coordinate Vertical Coordinate

    Phase A x0 = -Dc = -40 yo = H0 = 109

    Phase B x1 = 0 ft y1 = H0 = 109

    Phase C x2 = Dc = 40 y2 = H0 = 109

    Ground 1 X3 = -Dg / 2 = -23.75 y3 = Hg = 150

    Ground 2 X4 = Dg / 2 = 23.75 y4 = Hg = 150

    Table 1: Conductor Coordinates

    SECTION I : SHIELDING4. Ground Flashover Density:

    The ground flashover equations are used to calculate the number of lightning strokes per square

    kilometer per year (Ng) and can be found using either of the following:

    Number of thunderstorm days (TD)

    Ng = 0.04 x TD1.25

    Number of thunderstorm hours(TH)

    Ng = 0.054 x TH1.1

    h

    Hc Hg

    Dc

    Dg

    X

    Y

    x0

    y0

    x4

    y4

    x1

    y1

    x2

    y2

    x3

    y3

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    The TD and TH are obtained from the Isokeraunic map showing the mean annual days and hours of

    thunderstorm activity. The transmission line under study is to be installed from New Mexico to

    Colorado. The TD and TH values for these areas are as follows:

    TD = 70

    Ng = 0.04 x (70)1.25

    = 8.1

    TH = 100

    Ng = 0.054 x (100)1.1

    = 8.6

    5. Electric Shadow:

    Average height of conductor is given by:

    hcond = hat_tower - (2/3)sag

    Average height of phase conductors

    yc1 = yc - (2/3)sagc= 109(2/3)41.26= 81.493 ft = 24.839 m

    Average height of ground conductorsyg1 = hat_g - (2/3)sagg

    = 150(2/3)21.36

    = 115.76 ft = 35.284 m

    The shadow is given by:

    W = b + (hcond)1.09

    Where,

    b is the breadth of the transmission line at its base in meters.

    b = 40 ft = 12.192 mW = 12.192 + (33.22)1.09

    = 57.73 m

    6. Shielding Angle:

    Shielding angle is given by:

    = tan-1 [ ( xg - xc ) / ( yg1 - yc1 ) ]

    Where,

    xg is the horizontal distance between the shield conductors and vertical axisyg is the vertical distance between the shield conductors and ground

    xc is the horizontal distance between the phase conductors and vertical axis

    yg is the vertical distance between the phase conductors and ground

    All the above values can be obtained from table 1.

    = tan-1 [ ( 23.75 - 40) / ( 115.76 - 81.493) ]

    = -25.369

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    Bundle radius with corona is given by:

    Rbundle_corona = rbund + rcorona= 0.753 m

    Surge impedance of phase conductor with corona is given by:

    = 348.184

    9. Minimum Stroke Current:

    The minimum stroke current that would be created by a lightning is given by:

    IL_min = 20.467 kA

    10. Strike Distance vs. Current Functions:

    The strike distance for both the phase conductors and shield conductors is given by the followingequation:

    The strike distance for the phase conductors to ground is:

    Sph_g = 71.151 m

    The distance for the shield conductors to ground is:

    Sshld_g = 233.436 ft

    Similarly, the strike distance to the ground is calculated by:

    Sg(IL_min) = 60.68.3 m = 199.092 ft

    11. Shielding Effectiveness:

    The shielding effectiveness is determined by plotting the strike circles for the phase conductors and the

    shield conductors.

    Zsurge_corona 60 ln 4yc

    rbundl_corona

    ln 4 yc

    rbund

    IL_min

    2 Vins

    Zsurge_corona

    Sc_g IL 10IL

    kA

    0.65

    m

    Sg IL if yc 40m 3. 6 1. 7 ln 43 ycm

    IL

    kA

    0.65

    5.5 ILkA

    0.65

    m

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    11.1. Phase Conductor Strike Circle:

    The phase conductor strike circle equation is:

    Sc_g IL 2

    x xc 2

    y yc1 2

    Lower part of the circle is represented by the equation:

    Upper part of the circle is represented by the equation:

    11.2. Shield Conductor Strike Circle:

    The phase conductor strike circle equation is also similar to the phase conductor equation. The lower

    part of the shield conductor strike circle is given by:

    Upper part of the circle is represented by the equation:

    Lower part of the circle is represented by the equation:

    yshield_lx IL yg1 Sc_g IL 2

    x xg 2

    11.3. Ground Strike Circle Equation:

    The ground strike circle equation is represented by the following equation:

    The circles are plotted for the value of IL_min obtained from section 9 previously. These plots wouldhelp obtain the unprotected area of the transmission line conductors. The parameters given as inputs to

    obtain the plots are:

    Distance along the x axis, in steps of 1 ft. Range [0 to 350].

    Strike circles y coordinates in ft, for phase conductors, shield conductors and ground conductors as a

    function of distance x. Range [0 to 120].

    ycond_l x IL Sc_g IL 2

    x xc 2

    ycond_u x IL yc Sc_g IL 2

    x xc 2

    yshield_l x IL yg Sc_g IL 2

    x xg 2

    yshield_u x IL yg Sc_g IL 2

    x xg 2

    yground x IL Sg IL

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    Figure 3: Strike Circles

    12. Calculation of Unprotected Area vs. Lightning Current:

    From the previously obtained strike circle curves, the y axis coordinates of the point of intersection of

    the shield strike circle and the ground strike circle is obtained an incorporated into the circle equation.

    This is eventually solved for the roots.

    Sc_g IL 2

    yc1 Sg IL 2 xc xint

    2

    Sc_g IL 2

    yc Sg IL 2 xc xint

    The two roots of the equation are positive and negative, are determined by:

    xint_ground_nIL xc Sc_g IL 2

    yc Sg IL 2

    xint_ground_pIL xc Sc_g IL 2

    yc Sg IL 2

    The coordinates at minimum current are:

    xint_ground_n(IL) = -53.447 m

    xint_ground_P(IL) = 77.831 m

    The initial assumed value for the negative root is x int_cg = 30 m. This value is utilized to obtain the true

    value of the negative value using the equation solver in MATHCAD.

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    Negative root:

    xint_cg_n(IL_min) = -54.371 m

    Similarly, the positive root is also solved for in the similar method.

    xint_cg_p(IL_min) = 73.808 m

    Unprotected area is calculated using the following formula:

    Xnot_prot_p IL xint_ground_p IL xint_cg_p IL

    xnot_prot_p(IL) = 4.023 m

    IL_min = 20.467 kA

    The maximum lightning current when the unprotected area becomes zero is obtained by solving for theroots of xnot_prot_p(IL).

    IL_max root Xnot_prot_p IL IL

    IL_max = 29.542 kA

    This variation of the lightning current can be plotted as follows:

    Figure 4: Variation of lightning current

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    13. Probability of Line Flashover:

    Ibase IL if IL 20kA 61.1kA 33.3kA

    IL if IL 20kA 1.33 0.605

    f IL 1

    2 IL IL

    kA

    e

    lnIL

    Ibase IL

    2 IL 2

    F(IL_min) = 6.264%

    P IL 1

    1IL

    Ifirst

    2.6

    Ifirst 25kA P(IL_min) = 62.719%

    Number of lightning strokes hitting the ground per year per 100 km2

    Ng_day = 8.099

    Number of flashovers per 100 km per year is:

    Xnot_prot_p(IL_min) = 4.023 m

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    SECTION II : BACK FLASHOVER

    14. Flashover Voltage across the gap and insulator:

    14.1 Flashover Voltage at 2 s:

    = 2 s

    Flashover voltage across the gap is given by:

    Vgap_2 s 0.4Lins

    m

    0.71dmin

    m

    2s

    s

    0.75

    M V

    = 5.88 MV

    Flashover voltage across the insulator is given by:

    Vins_2s 0.4Lins

    m

    0.71Lins

    m

    2s

    s

    0.75

    M V

    = 3.601 MV

    14.2 Flashover Voltage at 6 s:

    = 6 s

    Flashover voltage across the gap is given by:

    Vgap_6 s 0.4Lins

    m

    0.71dmin

    m

    6s

    s

    0.75

    M V

    = 3.563 MV

    Flashover voltage across the insulator is given by:

    Vins_6s 0.4Lins

    m

    0.71 Linsm

    6s

    s

    0.75

    M V

    = 2.563 MV

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    15. Surge Impedance Calculation:

    Vtop_2 Emax rcorona lnyc1

    rcorona

    Initial value of Emax is assumed

    Emax2 15 kVcm

    The rcorona2 value is found by solving for the roots of the above equation.

    rcorona2= 1.172 m

    The self impedance of the phase conductors with corona:

    Zshild_self 60 ln2.yg

    rCorona2

    ln2 yg

    rshild

    = 376.52

    Average distances:ds1_s2 = 2 xg = 14.489 m = 47.536 ft

    ds1_S2 xg2

    2 yg 2

    = 79.578 m

    Mutual surge impedance:

    Zshild_mutual 60 lnds1_S2

    dS1_S2

    = 102.201

    Surge impedance of shield conductors:

    Zshild

    Zshild_self Zshild_mutual

    2

    = 239.361

    16. Coupling Factor to each Phase:

    Zphase_self 60 ln2 yc

    rbund

    = 389.717

    da_1 xc xg 2

    yc yg 2

    = 8.09 m

    da_2 xc xg 2

    yc yg 2

    = 20.463 m

    Da_1 xc xg 2

    yc yg 2

    = 73.015 m

    Da_2 xc xg 2

    yc yg 2

    = 75.396 m

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    Za_1 60lnDa_1

    da_1

    = 132.022

    Za_2 60lnDa_2

    da_2

    = 78.247

    Ka_12

    Z

    a_1

    Z

    a_2

    Zshild_self Zshild_mutual

    = 43.919 %

    17. Tower Surge Impedance:

    rtower = 15 ft htower = 150 ft

    Ztower 60 ln 2 2.htower

    rtower

    1

    = 131.952

    Travel time is computed by:

    T

    htower

    0.85 300m

    s

    = 0.155 s

    top_crossarm 17.6ft

    0.85 300m

    s

    = 0.021 s

    span span

    300m

    s

    = 1.016 s

    Tower ground resistance:

    Rfoot_min 30 Rfoot_max 50

    Rground Rfoot_max

    23

    Rfoot_max

    = 23

    Intrinsin Circuit Impedance:

    Zto p

    Ztower

    Zshild

    2

    Ztower

    Zshild

    2

    = 62.759

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    19. Shield ConductorDamping Factor:

    r

    Rground Ztower

    Ztower Rground

    = -0.703

    s

    Zshild

    2Ztower

    Ztower

    Zshild

    2

    = -0.049

    st

    Ztower

    Zshild

    2

    Ztower

    Zshild

    2

    = 0.049

    ts

    Zshild

    2Ztower

    Ztower

    Zshild

    2

    = -0.049

    s

    2Zshild

    2

    Zshild

    2Ztower

    = 0.951

    20. Current Wave Plot:

    Tfront 2s Thalf 50s

    a 1kA

    Tfront

    = 500 A/s

    b1kA 0.5kA

    50s

    = 10 A/s

    The current wave is represented as:

    ILi t( ) if t Tfront a t a Tfront b t

    At 50 s, the current is found to be:ILi(50 s) = 500 A

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    Figure 5: Current Wave

    21. Tower Top Voltage:

    t 2s Vtop_0 t( ) ILi t( ) Ztop

    Vtop_0 t( ) 61.503 k

    1 r 0.297 T 0.155 s

    r s r2

    s 0.01 3 T 0.466 s

    r2 s2 r3 s2 3.491 10 4 5 T 0.777 s

    k 1 3

    rk 1

    sk 1

    rk

    sk 1

    0.257

    0.025

    -32.49410

    1 r Vtop_0 t 1 T 16.039 k

    Vground t k( ) if t k T 0kV Vtop_0 t k T rk 1 sk 1 rk sk 1

    Vground t k( )

    16.039

    1.448

    0.13

    kV

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    Vground_T t( )

    k

    Vground t k ( )V ground_T(t) = 17.617 kV

    The voltage equations obtained are plotted for the required time period.

    Figure 6: Voltage Plots

    Vtop_k t2 k Vtop_0 t2 2 k T rk

    sk 1 r

    k s

    k

    Vtop_k(t2,k) = -36.913 kV

    -2.97

    -0.227

    at the time of

    at the time of

    at the time of

    r r s 0.645 2 T 0.311 s4 T 0.622 s r

    2 s r

    2 s

    2 0.064

    6 T 0.932 s r3

    s2 r

    3 s

    3 6.269 103

    k 1 3 r

    ks

    k 1

    r

    ks

    k

    -0.645

    -0.064

    -3-6.26910

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    t3 0s 0.01s 10s

    Figure 7: Voltage at top of tower

    22. Reflected Voltage in Adjacent Towers:

    VTop_kt2 k if t2 2 k T 0kV Vtop_kt2 k

    VTop_k t2 k -36.913

    -2.97

    -0.227

    kV

    VT op t( ) Vtop_0 t( )

    k

    VTop_kt k ( )

    VT op t( ) 26.312 kV

    t 6s

    2 span 2.032 s

    Vref_1 t if t 2 span 0kV Vtop_0t 2 span st ts Vref_1 t 1.145 k

    VRef_6 s t VTop t Vref_1 t

    VRef_6s 6s 16.867 k

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    t. 0s 0.1s 5s

    Figure 8: Reflected voltage from adjacent towers

    23. Cross-arm Voltage:

    24. Insulator Voltage at Unit Current:

    Insulator voltage at 2 s:

    Vinsulator_2s Vcrossarm 2s Ka_12 VT op 2s = 13.579 kV

    Top Voltage at 6s:

    Vref_6s = 16.687 kV

    t4 2s

    Vcrossarm

    t4

    Vground_T

    t4

    T top_crossarm

    TV

    T opt4

    Vground_T

    t4

    VT op t4 Vground_T t4 8.695 k

    Vcrossarm t4 25.135 k

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    Insulator voltage at 6 s:

    Vinsulator_6s VRef_6s 6s 1 Ka_12 = 9.459 kV

    25. Critical Stroke Current:

    Flashover causing stroke current at 2 s:

    Istrok_2s

    Vgap_2s

    Vinsulator_2skA

    = 433.064 A

    Flashover causing stroke current at 6 s:

    Istrok_6s

    Vgap_6s

    Vinsulator_6skA

    = 376.88 A

    60 Hz stroke current component at 2 s:

    Effect of 60Hz voltage

    Istrok_2s_60Hz Istrok_2s

    Vgap_2s2 500 kV

    3sin 90 deg

    Vgap_2s

    = 463.129 kA

    60 Hz stroke current component at 6 s:

    Istrok_6 s_60Hz Istrok_6 s

    Vgap_6 s2 500 kV

    3sin 90 deg

    Vgap_6 s

    = 419.838 kA

    26. Probability of Line Flashover:

    Probability Function:

    P IL 1

    1

    IL

    Ifirst

    2.6

    Probability of flashover after 2 s:

    P(Istrok_2s_60Hz) = 0.051 %

    Probability of flashover after 6 s:

    P(Istrok_6s_60Hz) = 0.065 %

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    27. Number of Lightning Strokes:

    Average tower height yg1 = 35.284 m = 115.76 ft

    Estimated tower width b = 12.192 m = 40 ft

    Length = 100 km

    Widthb

    m

    yg1

    m

    1.09

    = 60.186

    Nline_d Ng_day Width = 492.554

    28. Number of Flashoers:

    Number of flashovers caused by shielding failure:

    Nshield = 4

    Nline = Nline_d - Nshield = 488.554

    29. Number of Back Flashovers per 100 km per year:

    Nback_2 s Nline P Istrok_2 s_60Hz = 0.247

    Nback_6 s Nline P Istrok_6 s_60Hz = 0.319

    Total number of flashovers per year per 100 km:

    Ntotal_line Nshild Nback_2 s Nback_6 s = 4.566

    30. Conclusion:

    The lightning protection of the proposed transmission line was designed in this module. The shieldingperformance was analyzed and is found to be a robust design. The shield conductors provide

    substantial protection to the transmission lines. The back flashover rate was also calculated and is

    found to be well within the limits. The expected outage rate is also computed and turns out to anacceptable value.