Patent AU-2003243099-A1 (AU)
Title: Fault location using measurements of current and voltage from one end of a line
Inventor: SAHA MURARI MOHAN
IPC: G01R31/08
Filed: 2003-06-18
Abstract: A method to locate a fault from one end of a section of a power line utilizing measurements of current, voltage and angles between the phases at a first end of said section. Symmetrical components of currents are calculated for the current and voltage measurement at the first end. A value of impedance is calculated for an extra link between the terminals with the impedance for the positive sequence equal to: <maths id="MATH-US-00001" num="1"> <MATH OVERFLOW="SCROLL"> <MROW> <MROW> <MO>(</MO> <MROW> <MSUB> <MUNDER> <MI>Z</MI> <MI>_</MI> </MUNDER> <MROW> <MROW> <MROW> <MN>1</MN> <MO>⁢</MO> <MSTYLE> <MTEXT> </MTEXT> </MSTYLE> <MO>⁢</MO> <MI>LB</MI> </MROW> <MO>&</MO> </MROW> <MO>⁢</MO> <MI>AB</MI> </MROW> </MSUB> <MO>=</MO> <MFRAC> <MROW> <MSUB> <MUNDER> <MI>Z</MI> <MI>_</MI> </MUNDER> <MROW> <MN>1</MN> <MO>⁢</MO> <MI>LB</MI> </MROW> </MSUB> <MO>⁢</MO> <MSUB> <MUNDER> <MI>Z</MI> <MI>_</MI> </MUNDER> <MROW> <MN>1</MN> <MO>⁢</MO> <MI>AB</MI> </MROW> </MSUB> </MROW> <MROW> <MSUB> <MUNDER> <MI>Z</MI> <MI>_</MI> </MUNDER> <MROW> <MN>1</MN> <MO>⁢</MO> <MI>LB</MI> </MROW> </MSUB> <MO>+</MO> <MSUB> <MUNDER> <MI>Z</MI> <MI>_</MI> </MUNDER> <MROW> <MN>1</MN> <MO>⁢</MO> <MI>AB</MI> </MROW> </MSUB> </MROW> </MFRAC> </MROW> <MO>)</MO> </MROW> <MO>⁢</MO> <MSTYLE> <MTEXT> </MTEXT> </MSTYLE> <MO>⁢</MO> <MI>where</MI> <MO>⁢</MO> <MSTYLE> <MTEXT>:</MTEXT> </MSTYLE> </MROW> </MATH> </MATHS> Z<SUB>1AB</SUB>=impedance for the positive sequence of the extra link, Z<SUB>1LA</SUB>=positive-sequence impedance of the healthy line. A compensation is determined for the shunt capacitance with the aid of an equation of the form: <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>2</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>(d<SUB>comp</SUB><SUB><SUB2>-</SUB2></SUB><SUB>1</SUB>)<SUP>2</SUP>+B<SUB>1</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>d<SUB>comp</SUB><SUB><SUB2>-</SUB2></SUB><SUB>1</SUB>+B<SUB>0</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>=0 where: <?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>2</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>=A<SUB>2</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>-A<SUB>2</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1 </SUP><?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>1</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>=A<SUB>1</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>-A<SUB>1</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1 </SUP><?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>0</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>=A<SUB>0</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>-A<SUB>0</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB><SUP>comp</SUP><SUP><SUB2>-</SUB2></SUP><SUP>1</SUP>. <?in-line-formulae description="In-line Formulae" end="tail"?> The zero-sequence current is determined from the healthy line of a section of parallel power lines. A distance to a fault is calculated for the parallel line section. The distance to the fault from the first end is calculated using a quadratic equation of the form: <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>2</SUB>d<SUP>2</SUP>+B<SUB>1</SUB>d+B<SUB>0</SUB>=0 where: <?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>2</SUB>=A<SUB>2</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>-A<SUB>2</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re </SUB><?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>1</SUB>=A<SUB>1</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>-A<SUB>1</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re </SUB><?in-line-formulae description="In-line Formulae" end="tail"?> <?in-line-formulae description="In-line Formulae" end="lead"?>B<SUB>0</SUB>=A<SUB>0</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>-A<SUB>0</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Im</SUB>A<SUB>00</SUB><SUB><SUB2>-</SUB2></SUB><SUB>Re</SUB>. <?in-line-formulae description="In-line Formulae" end="tail"?>