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Topics
ImpedanceBased ReactanceMethod TakagiMethod ModificationstoTakagiMethod TWS&Double‐EndedNegativeSequence
Radial Line
Apply a fault “m” distance down a radial line
“m” is a percentage of the line. For example if the fault is 25% from Bus S then (1‐m) yields 75%, for a total line impedance, ZL ,of 100%
V/I = mZL (sometimes)
Using ohms law the fault locator at S can calculate the impedance, (mZL), that the voltage V is being dropped across for three‐phase bolted faults.
V/I Calculation
The equivalent circuit with respect to Bus S clearly shows that the measured voltage V is being dropped across the portion of the transmission line to the fault point.
(m)ZL = V/I (Ohms)
(V/I)ZL
m = (%)
Fault Location = m (Line Length) (miles)
Simplified V/I with some R
Let Is = 10∠0°A, XL = 10Ω, & RF = 5Ω VLINE = 10∠0°(10∠90°) = 100∠90°V VF = 10∠0° (5∠0°) = 50∠0°V Vs = VLINE + VF = 112∠63°V Distance = VS/IS = 11∠63° ΩmZL ≠ Distance
Is
Vs = VLINE + VF
VF
VLINE
XL
RF
Distance
V/I Limitations
Using ohms law directly as fault locator is impractical for a variety of reasons. Some of these include:
Only works on three‐phase faults Only works on radial lines Only works on bolted faults Impacted by Load
Simple Reactance Method
Transmissions line impedance, Z, is typically dominated by the reactive component, X.
Fault impedance is typically dominated by the resistive component, R.
Fault Resistance & Reactance Method
Lets look at the radial example with fault resistance again.
The forward voltage drop measured by the fault locator is Vs = mZL(Is) + Is(RF)
Minimize the Effect of RF using Reactance
Divide by the measured current Is
Retain only the imaginary component of each quantity
Reactance Method with Remote Source
No longer is the system radial
The current flowing through RF is now the sum of the local source, Is, and the remote source, IR
Same Reactance Technique: Now with IR
Write the forward voltage drop equation,
Divide by Is to calculate a measured Impedance,
Take the imaginary component of each term to mitigate fault resistance,
Homogenous System & Reactance
If you have a homogenous system then both IS and IR will have the same angle and the imaginary part of (If/Is)Rf is zero.
ӨӨ
Is
IRIf = IS+IR
Ө
Non‐Homogenous System & Reactance
IS and IR will not have the same angle and the imaginary part of (If/Is)Rf will show up in the fault location calculation as an error term.
lS
lR
α β
lf
δ
Simple Reactance Summary
The simple reactance method was an improvement over the straight Ohms Law calculation but it still has some drawbacks:
Impacted by Load Non‐homogenous systems introduce error in fault resistance term
Takagi Method
In 1979 Toshio Takagi and Yukinari Yamakoshi filed for a U.S. Patent for a new single‐ended fault locating method.
In 1982 Takagi, et al. deliver their paper.
T. Takagi, Y. Yamakoshi, M. Yamaura, R. Kondow, T. Matsushima, “Development of a New Type Fault Locator Using the One‐Terminal Voltage and Current Data”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS‐101, No. 8, August 1982.
Superposition
The key to the Takagi method is the idea of superposition
+
Load Pure Fault Network
Composite Fault Network
Takagi Local & Remote Current
Composite Fault Network Pure Fault Network
Voltage equation for the left‐hand side Voltage equation for the right‐hand side
Both equations equal VF. Set the Left side equal to the right side
No Fault Current in Load Circuit
If = I’f because there is no fault branch current in the pure load state
+
Load Pure Fault Network
Composite Fault Network
Forward Voltage Drop & Takagi
From the previous fault location algorithmswe developed the forward voltage drop equation with respect to fault locator:
Plug‐in our new equation for the fault branch current, If: +
=
Pause for Error
β will be zero if the numerator and denominator have the same phase angle, (homogeneous system)
If there is load flow on the system γ will be non‐zero but if the magnitude of fault duty is much greater than load, the angle γ will approach zero.
Takagi Distance
If we:Multiply by the complex conjugate of I’s, Take the imaginary part of the equation to eliminate fault resistance, Assume the system is totally homogeneous, and finally Solve for m
We will get the following equation:
Zero & Negative Sequence Takagi
The Takagi can use the zero sequence term for ground faults, eliminating the need for pre‐fault data
The negative sequence can also be used
Mutual Coupling
There is magnetic coupling between phases on a current carrying transmission line, Zm.
Mutual Coupling
Apply a bolted fault some length m down the line.
A voltage is induced in each phase through the mutual coupling. Here Zm is written explicitly as Zab and Zac.
Voltage Equation
The forward voltage drop equation for the faulted phase is
Adding & Subtracting the same quantity 0
Gatheringterms
Voltage Equation Cont’d
Recognize that Ia+Ib+Ic is the residual or zero sequence current
Zm is a difficult quantity to handle directly. Through the use of Symmetrical Component theory it can be shown that:
Solving for Zs in the ZL0 equation and plugging this into the ZL1 equation yields a Zm that is equal to:
Va and the mysterious k
Va isnowexpressedintermsofpositiveandzerosequencelineparameterswhichcanbeloadedintoarelayassettings
FactoroutmZL1,(thedistancetothefault)
Definektomaketheequationprettier
Two Terminal Methods
More accurate than single‐ended methods
Minimizes/Eliminates effects of Fault Resistance Loading Line Charging Current
More overhead. Data must be gathered or shared from multiple locations
Traveling Wave
A fault will cause a transient to propagate along the line as a wave
The wave is a composite of frequencies with a fast rising front and slower decaying tail
The waves travel at near the speed of light and eventually decay
By time tagging the wave fronts as they cross both terminals a very precise fault location can be calculated
Wave Propagation
The waves leave the disturbed area traveling at the velocity of propagation which is a little less than the speed of light
Negative Sequence Quadratic
In 1999 Demetrios A. Tziouvaras, Jeff Roberts, and Gabriel Benmouyal of SEL introduced a new double‐ended technique that uses the negative sequence quantities from both terminals to fault locate.
D.A. Tziouvaras, J.B. Roberts, G. Benmouyal, “New Multi‐Ended Fault Location Design For Two‐ or Three‐Terminal Lines,” presented at CIGRE Conference, 1999, http://www.selinc.com/techpprs/6089.pdf.
Double Ended Negative Sequence
By using the negative sequence methodology proposed by SEL the following sources of error are mitigated:
Prefault load Zero sequence mutual coupling Zero sequence infeed from line taps Fault Resistance
References
T. Takagi, Y. Yamakoshi, M. Yamaura, R. Kondow, and T. Matsushima, “Development of a New Type Fault Locator Using the One‐Terminal Voltage and Current Data,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS‐101, No. 8, August 1982.
W. A. Elmore, “Zero Sequence Mutual Effects on Ground Distance Relays and Fault Locators,” Proceedings of the 19th Annual Western Protective Relay Conference, Spokane, WA, October 1992.
E. O. Schweitzer III, “Evaluation and Development of Transmission Line Fault Locating Techniques Which Use Sinusoidal Steady‐State Information,” Proceedings of the 9th Annual Western Protective Relay Conference, Spokane, WA, October 1982.
K. Zimmerman, and D. Costello, “Impedance‐Based Fault Location Experience,” Proceedingsofthe31stWestern Protective Relay Conference, Spokane, WA, October 2004.
J. Glover, M Sarma, and T. Overbye, “Power System Analysis and Design,” Global Engineering, 2008.
W. Stevenson, and J. Grainger, “Power System Analysis,” McGraw‐Hill Series in Electrical and Computer Engineering, 1994
Hewlett Packard, “Traveling Wave Fault Location in Power Transmission Systems,” Application Note 1285