Journal of Reliable Power - SEL

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Without Underbuild With 50 Miles Underbuild R1 7.50 Ω 7.50 Ω X1 22.757 Ω 22.757 Ω R0 21.327 Ω 15.488 Ω X0 134.16 Ω 88.75 Ω Figure 3 shows a completed nomograph. Figure 3 Printout Miles 69 kV Nomograph Partial, Total, and No Underbuild 60 55 50 45 40 35 30 25 20 15 10 5 0 0 10 20 30 40 50 60 Actual Miles 10 Miles Underbuild No Underbuild 60 Miles Underbuild Completed Nomograph for 69 kV Line IV. IMPEDANCE-BASED FAULT LOCATION METHODS AND REQUIREMENTS Impedance-based methods require the following approach: 1. Measure the voltage and current phasors. 2. Extract the fundamental components. 3. Determine the phasors and fault type. 4. Apply impedance algorithm. One-ended impedance methods of fault location are a standard feature in most numerical relays. One-ended impedance methods use a simple algorithm, and communication channels and remote data are not required (except when a channel is required to bring the fault location estimate to an operator). Two-ended methods can be more accurate but require data from both terminals. Data must be captured from both ends before an algorithm can be applied. The most popular impedance-based fault location methods are discussed in this paper: • Simple reactance method (one-ended) • Takagi method (one-ended) • Modified Takagi method that corrects for source impedance angle differences (one-ended) • Two-ended negative-sequence method One-ended impedance-based fault locators calculate the fault location from the apparent impedance seen by looking into the line from one end. An example system one-line is shown in Figure 4. To locate all fault types, the phase-toground voltages and currents in each phase must be measured. (If only line-to-line voltages are available, it is possible to locate phase-to-phase faults; if the zero-sequence source impedance, Z 0 , is known, we can estimate the location for phase-to-ground faults). If the fault resistance is assumed to be zero, we can use one of the impedance calculations in Table 1 to estimate the fault location. Fault Type TABLE 1 SIMPLE IMPEDANCE EQUATIONS Positive-Sequence Impedance Equation (mZ 1L =) A–ground Va ( Ia + k • 3 • I0 ) B–ground Vb ( Ib + k • 3 • I0 ) C–ground V ( I + k • 3 • I ) a–b or a–b–g b–c or b–c–g c–a or c–a–g c c 0 a–b–c Any of the following: Vab I ab, Vbc I bc, Vca I ca Where: k is (Z 0L – Z 1L ) / 3Z 1L , Z 0L is the zero-sequence line impedance, Z 1L is the positive-sequence line impedance, m is the per unit distance to fault (for example: distance to fault in kilometers divided by the total line length in kilometers), is the zero-sequence current. I 0 S Z S Figure 4 VS VS I S m mZ L Z L V V V I S I R VR I F R F ab bc ca I I I 1-m ab bc ca (1-m)Z L One-Line Diagram and Circuit Representation of Line Fault The challenges for accuracy of one-ended fault location are well known and are described in several sources [1] [2] [3] [4]. To summarize, the following conditions can cause errors for one-ended impedance-based fault location methods: • Combined effect of fault resistance and load • Zero-sequence mutual coupling • Zero-sequence modeling errors • System nonhomogeneity • System infeeds − Remote or third terminal infeed − Tapped load with zero-sequence source • Inaccurate relay measurement, instrument transformer or line parameters. I R VR R Z R 16 | Journal of Reliable Power
A. Simple Reactance Method From Figure 4, the voltage drop from the S end of the line is: VS = m • Z1L • IS + R F • IF (1) For an A-phase to ground fault, Vs = V a−g and I S = Ia + k • 3• I0 The goal is to minimize the effect of the R F • IF term. The simple reactance method divides all terms by I S (I measured at the fault locator) and ignores the (R F •I F / I S ) term. To do this, save the imaginary part, and solve for m: ( ) Im V /I = Im(m • Z ) = m • X S S 1L 1L m = I m ⎛ VS ⎞ ⎜ ⎝ I ⎟ ⎠ X 1L Error is 0 if ∠ I = ∠ I or R = 0 S S F F B. Takagi Method—One-Ended Impedance Method With No Source Data The Takagi method requires prefault and fault data. It improves upon the simple reactance method [2] by reducing the effect of load flow and minimizing the effect of fault resistance. VS = m • Z 1L • I + R F • IF (3) Use Superposition current (I sup ) to find a term in phase with I F : Isup = I − Ipre I = Fault Current (4) I = Pre-fault Current pre Voltage drop from Bus S: VS = m • Z 1L • IS + R F • IF Multiply both sides of equation (1) by the complex conjugate of I sup (I sup* ) and save the imaginary part. Then, solve for m: I m[VS • I sup* ] = m • I m (Z1L • IS • I sup* ) + R F • I m (IF • I sup* ) I m (VS • I sup* ) (5) m = I (Z • I • I ) m 1L S sup* The key to the success of the Takagi method is that the angle of I S is the same as the angle of I F . For an ideal homogeneous system, these angles are identical. As the angle between I S and I F increases, the error in the fault location estimate increases. (2) C. Modified Takagi—Zero-Sequence Current Method with Angle Correction Another method (modified Takagi) uses zero-sequence current (3 • I 0S ) for ground faults instead of the superposition current. Therefore, this method requires no prefault data. Modified Takagi also allows for angle correction. If the user knows the system source impedances, the zero-sequence current can be adjusted by angle T to improve the fault location estimate for a given line. * − jT ( ( ) ) − ( ) Im V S • 3• I 0S • e m = (6) I Z • I • 3• I • e * jT ( ) m 1L S 0S The angle T selected will be valid for one fault location along the line. Figure 5 shows how to calculate T. Z 0S Figure 5 known) 3•I RS mZ 0L T 3• I RS I F I F (1-m)Z 0L Zero-Sequence Current Angle Correction (if source impedances are IF Z0S + Z0L + Z0R = = A∠T 3• I (1− m) • Z + Z RS 0L 0R D. Two-Ended Negative-Sequence Impedance Method A relatively new method, introduced in 1999, uses negative-sequence quantities from all line terminals for the location of unbalanced faults. By using negative-sequence quantities, we negate the effect of prefault load and fault resistance, zero-sequence mutual impedance, and zerosequence infeed from transmission line taps. Precise fault type selection is not necessary. Data alignment is not required because the algorithm employed at each line end uses the following quantities from the remote terminal (which do not require phase alignment). • Magnitude of negative-sequence current, I2 • Calculated negative-sequence source impedance, Z ∠θ ° 2 2 Z 0R (7) Impedance-Based Fault Location Experience | 17
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Page 7 and 8: Both P and Q are two-input phase an
Page 9 and 10: TABLE 1: MHO ELEMENT POLARIZING CHO
Page 11 and 12: For an Aφ-ground fault on the syst
Page 13 and 14: The most onerous 3φ fault is one w
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Page 21 and 22: Figure 9 shows a screen capture of
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Page 25 and 26: IX. LAB TEST SETUP Several line fau
Page 27 and 28: APPENDIX The following are the rela
Page 29 and 30: The following shows the analog math
Page 31 and 32: Digital Communications for Power Sy
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Page 37 and 38: Noise from faults or other sources
Page 39 and 40: 80 60 40 20 R F 100 3 3 S 2 5 6 4 1
Page 41 and 42: 15. A POTT scheme implemented over
Page 43 and 44: Transmission Line Protection System
Page 45 and 46: One-Cycle Directional Element Figur
Page 47 and 48: element misoperation. Shunt reactor
Page 49 and 50: • SW2 is in Position 1 when there
Page 51 and 52: Complete reclosing relay supervisio
Page 53 and 54: IX. BIOGRAPHIES Armando Guzmán, P.
Page 55 and 56: 2 II. COMMON ZONE TIMING In June 20
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Page 61 and 62: 8 1_VA 1_VB 1_VC 2_VA 2_VB 2_VC 3_V
Page 63 and 64: 10 The phasors during the fault are
Page 65 and 66: 12 The prefault data from the backu
Page 67 and 68: 1 Adaptive Phase and Ground Quadril
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3 C. Short Line Applications A shor
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5 II. QUADRILATERAL DISTANCE ELEMEN
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7 For the purpose of implementing t
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9 The three-phase fault detection e
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11 Zone 1 distance elements should
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13 Fig. 24 shows the apparent resis
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15 B. Adaptive Resistance Element F
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17 Fig. 34 and Fig. 35 illustrate t
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Line Protection Bibliography Issue
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Hou, Daqing, and Jeff Roberts. “C
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©2010 Schweitzer Engineering Labor
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