Parameter free identification of fault location in multi-terminal power transmission lines
A method and device can be used with a power transmission line. Pre-fault voltage and current phasors and during-fault voltage and current phasors for each of first, second, and third terminals are determined based on disturbance records. Using an assumed faulted section, values for a propagation constant of each section, a surge impedance of each section, and a fault location parameter are computed. The computing is based on simultaneously solving pre-fault and during-fault objective functions for the assumed faulted section with the computed pre-fault and during-fault voltage and current phasors. The pre-fault and during-fault objective functions are formulated based on equating junction voltages determined from two of the terminals, conservation of charge at the junction, and equating fault location voltages determined from one terminal and the junction. The values determined for the propagation constant, the surge impedance, and the fault location parameter can be compared with predefined criteria.
1. A method for use with a power transmission line having a first terminal, a second terminal, and a third terminal connected at a junction, wherein a first section connects the first terminal and the junction, a second section connects the second terminal and the junction, and a third section connects the third terminal and the junction, the method comprising:
obtaining synchronized disturbance records from each of the first, second, and third terminals after a fault has occurred in the power transmission line;
computing pre-fault voltage and current phasors and during-fault voltage and current phasors for each of the first, second, and third terminals based on the disturbance records;
using an assumed faulted section from among the first, second, and third sections, computing values for a propagation constant of each section, a surge impedance of each section, and a fault location parameter, wherein the computing is based on simultaneously solving a plurality of pre-fault objective functions and during-fault objective functions for the assumed faulted section with the computed pre-fault voltage and current phasors and during-fault voltage and current phasors, and wherein the pre-fault objective functions and during-fault objective functions are formulated based on equating junction voltages determined from two of the terminals, conservation of charge at the junction, and equating fault location voltages determined from one terminal and the junction; and
comparing the values determined for the propagation constant, the surge impedance, and the fault location parameter with predefined criteria.
2. The method as claimed in claim 1 , further comprising determining a faulted section, a fault location, and line parameters for each of the first, second, and third sections, based on the comparing.
3. The method as claimed in claim 1 , wherein the computing is based on simultaneously solving the plurality of pre-fault objective functions and during-fault objective functions for the assumed faulted section with the computed pre-fault voltage and current phasors, the during-fault voltage and current phasors, and lengths of each section.
4. The method as claimed in claim 1 , wherein the assumed faulted section is determined as being the faulted section when the values determined from the pre-fault objective functions and the during-fault objective functions for the assumed faulted section meet the predefined criteria, the predefined criteria comprising:
the fault location parameter has a value between zero and one;
a real part of the square of the propagation constant of each section is less than zero and the real part of the square of the surge impedance of each section is greater than zero; and
an imaginary part of the square of the propagation constant of each section is greater than zero and an imaginary part of the square of the surge impedance of each section is less than zero.
5. The method as claimed in claim 1 , wherein two of the sections have the same line parameters.
6. The method as claimed in claim 1 , wherein
the pre-fault objective functions comprise a set of pre-fault functions based on computation of voltage at the junction from each pair of terminals of the first, second, and third terminals, and a function based on conservation of charge at the junction; and
the during-fault objective functions for the assumed faulted section comprise a first set of during-fault functions based on computation of voltage at the junction from each pair of terminals excluding the terminal of the assumed faulted section, and a second set of during-fault functions based on computation of voltage at a fault point from the junction and the terminal of the assumed faulted section.
7. The method as claimed in claim 1 , wherein each of the pre-fault objective functions and the during-fault objective functions correspond to a function of a set of variables, the function being equal to zero, wherein the set of variables comprise the propagation constant of each section, the surge impedance of each section, and the fault location parameter.
8. The method as claimed in claim 1 , wherein simultaneously solving the pre-fault objective functions and the during-fault objective functions comprises applying a numerical analysis technique for determining the propagation constant of each section, the surge impedance of each section, and the fault location parameter.
9. The method as claimed in claim 1 , wherein the line parameters include resistance, conductance, and inductance of each section, and wherein the during-fault voltage and current phasors include at least two data sets.
10. A device for identifying a fault location in a power transmission line, the power transmission line having a plurality of terminals connected at one or more junctions, with at least a first terminal, a second terminal, and a third terminal connected at a junction, wherein a first section connects the first terminal and the junction, a second section connects the second terminal and the junction, and a third section connects the third terminal and the junction, the device comprising:
a phasor computation module configured to obtain synchronized disturbance records from each of the plurality of terminals after a fault has occurred in the power transmission line and compute pre-fault terminal voltage and current phasors and during-fault terminal voltage and current phasors; and
a fault location identification module configured to
compute, using an assumed faulted section from among the first, second, and third sections, values for propagation constant of each section, surge impedance of each section, and a fault location parameter, wherein the computation is based on simultaneously solving a plurality of pre-fault objective functions and during-fault objective functions for the assumed faulted section with the computed pre-fault voltage and current phasors, during-fault current and voltage phasors, and line lengths of each section, and wherein the pre-fault objective functions and during-fault objective functions are formulated based on equating junction voltages determined from two of the terminals, conservation of charge at the junction, and equating fault location voltages determined from one terminal and the junction;
compare the values determined for the propagation constant, the surge impedance, and the fault location parameter with predefined criteria; and
determine a faulted section, the fault location, and the parameters for each of the first, second, and third sections, based on the comparison.
11. The device as claimed in claim 10 , wherein each of the pre-fault objective functions and the during-fault objective functions correspond to a function of a set of variables, the function being equal to zero, wherein the set of variables comprise the propagation constant of each section, the surge impedance of each section, and the fault location parameter, and wherein to simultaneously solve the pre-fault functions and the during-fault functions, the fault location identification module is configured to apply a numerical analysis technique to determine the propagation constant of each section, the surge impedance of each section, and the fault location parameter.
12. The device as claimed in claim 10 , wherein the assumed faulted section is determined as being the faulted section when the values determined from the pre-fault objective functions and the during-fault objective functions for the assumed faulted section meet the predefined criteria, the predefined criteria comprise:
the fault location parameter has a value between zero and one;
a real part of the square of the propagation constant of each section is less than zero and the real part of the square of the surge impedance of each section is greater than zero; and
an imaginary part of the square of the propagation constant of each section is greater than zero and an imaginary part of the square of the surge impedance of each section is less than zero.
13. A device for use with a power transmission line having a first terminal, a second terminal, and a third terminal connected at a junction, wherein a first section connects the first terminal and the junction, a second section connects the second terminal and the junction, and a third section connects the third terminal and the junction, the device comprising:
a processor; and
a non-transitory memory coupled to the processor, the memory storing computer code that, when executed by the processor, causes the processor to:
compute pre-fault voltage and current phasors and during-fault voltage and current phasors for each of the first, second, and third terminals based on synchronized disturbance records obtained from each of the first, second, and third terminals after a fault has occurred in the power transmission line;
compute, using an assumed faulted section from among the first, second, and third sections, values for a propagation constant of each section, a surge impedance of each section, and a fault location parameter, wherein the computation is based on simultaneously solving a plurality of pre-fault objective functions and during-fault objective functions for the assumed faulted section with the computed pre-fault voltage and current phasors and during-fault voltage and current phasors, and wherein the pre-fault objective functions and during-fault objective functions are formulated based on equating junction voltages determined from two of the terminals, conservation of charge at the junction, and equating fault location voltages determined from one terminal and the junction; and
compare the values determined for the propagation constant, the surge impedance, and the fault location parameter with predefined criteria.
14. The device as claimed in claim 13 , wherein the computer code further causes the processor to determine a faulted section, a fault location, and line parameters for each of the first, second, and third sections, based on the comparison.
15. The device as claimed in claim 14 , wherein the line parameters include resistance, conductance, and inductance of each section, and wherein the during-fault voltage and current phasors include at least two data sets.
16. The device as claimed in claim 13 , wherein the computer code further causes the processor to compute the propagation constant of each section, the surge impedance of each section, and the fault location parameter by on simultaneously solving the plurality of pre-fault objective functions and during-fault objective functions for the assumed faulted section with the computed pre-fault voltage and current phasors, the during-fault voltage and current phasors, and lengths of each section.
17. The device as claimed in claim 13 , wherein the assumed faulted section is determined as being the faulted section when the values determined from the pre-fault objective functions and the during-fault objective functions for the assumed faulted section meet the predefined criteria, the predefined criteria comprising:
the fault location parameter has a value between zero and one;
a real part of the square of the propagation constant of each section is less than zero and the real part of the square of the surge impedance of each section is greater than zero; and
an imaginary part of the square of the propagation constant of each section is greater than zero and an imaginary part of the square of the surge impedance of each section is less than zero.
18. The device as claimed in claim 13 , wherein
the pre-fault objective functions comprise a set pre-fault of functions based on computation of voltage at the junction from each pair of terminals of the first, second, and third terminals, and a function based on conservation of charge at the junction; and
the during-fault objective functions for the assumed faulted section comprise a first set of during-fault functions based on computation of voltage at the junction from each pair of terminals excluding the terminal of the assumed faulted section, and a second set of during-fault functions based on computation of voltage at a fault point from the junction and the terminal of the assumed faulted section.
19. The device as claimed in claim 13 , wherein each of the pre-fault objective functions and the during-fault objective functions correspond to a function of a set of variables, the function being equal to zero, wherein the set of variables comprise the propagation constant of each section, the surge impedance of each section, and the fault location parameter.
20. The device as claimed in claim 13 , wherein the computer code further causes the processor to compute the propagation constant of each section, the surge impedance of each section, and the fault location parameter by on simultaneously solving the pre-fault objective functions and the during-fault objective functions by applying a numerical analysis technique for determining the propagation constant of each section, the surge impedance of each section, and the fault location parameter.
21. A power transmission system comprising:
the device as claimed in claim 13 ; and
a power transmission line having the first terminal, the second terminal, and the third terminal connected at the junction, wherein the first section connects the first terminal and the junction, the second section connects the second terminal and the junction, and the third section connects the third terminal and the junction.
22. The system as claimed in claim 21 , wherein two of the sections have the same line parameters.