System and method for determining location of phase-to-earth fault

1. A method for determining a distance of a phase-to-earth fault on a three-phase electric line of an electric network, the method comprising:

monitoring current and voltage quantities of the three-phase electric line at a measuring point;

detecting a phase-to-earth fault on the three-phase electric line and a faulted phase of the three-phase electric line;

determining a first estimate value for a distance between the measuring point and a point of fault on the basis of values of the monitored current and voltage quantities and a first equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the load of the electric line is located between the measuring point and the point of fault;

determining a second estimate value for the distance between the measuring point and the point of fault on the basis of values of the monitored current and voltage quantities and a second equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the point of fault is located between the measuring point and load of the electric line; and

selecting according to predetermined criteria one of the determined two estimate values as the distance between the measuring point and the point of fault.

2. The method of claim 1 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd · I F +s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s =per unit distance of equivalent load.

3. The method of claim 2 , wherein the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I f .

4. The method of claim 1 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd · I F +s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s=per unit distance of equivalent load.

5. The method of claim 4 , wherein the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I f .

6. The method of claim 1 , wherein the selection of one of the determined two estimate values as the distance d between the measuring point and the point of fault is performed according to the following criteria:

If s<de1<1, then d=de1, else d=de2

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

7. The method of claim 1 , wherein the selection of one of the determined two estimate values as the distance d between the measuring point and the point of fault is performed according to the following criteria:

If 0<de2< s, then d=de2, else d=de1

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

8. A computer readable medium storing computer program instructions which when executed by a computer program with the instructions causes the computer to carry out the following steps;

monitoring current and voltage quantities of the three-phase electric line at a measuring point;

detecting a phase-to-earth fault on the three-phase electric line and a faulted phase of the three-phase electric line;

determining a first estimate value for a distance between the measuring point and a point of fault on the basis of values of the monitored current and voltage quantities and a first equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the load of the electric line is located between the measuring point and the point of fault:

determining a second estimate value for the distance between the measuring point and the point of fault on the basis of values of the monitored current and voltage quantities and a second equation which relates the current and voltage quantities to the distance and is based on a fault loon model of the electric line, in which model the point of fault is located between the measuring point and load of the electric line; and

selecting according to predetermined criteria one of the determined two estimate values as the distance between the measuring point and the point of fault.

9. A system for determining a distance of a phase-to-earth fault on a three-phase electric line of an electric network, the system comprising:

means for monitoring current and voltage quantities of the three-phase electric line at a measuring point;

means for detecting a phase-to-earth fault on the three-phase electric line;

means for identifying a faulted phase of the three-phase electric line;

means for determining a first estimate value for a distance between the measuring point and a point of fault on the basis of values of the monitored current and voltage quantities and a first equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the load of the electric line is located between the measuring point and the point of fault;

means for determining a second estimate value for the distance between the measuring point and the point of fault on the basis of values of the monitored current and voltage quantities and a second equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the point of fault is located between the measuring point and load of the electric line; and

means for selecting, according to predetermined criteria, one of the determined two estimate values as the distance between the measuring point and the point of fault.

10. The system of claim 9 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd · I F +s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s=per unit distance of equivalent load.

11. A system as claimed in claim 10 , wherein in that the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I f .

12. The system of claim 9 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd · I F + s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s=per unit distance of equivalent load.

13. The system of claim 12 , wherein the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I f .

14. The system of claim 9 , wherein the means for selecting selects one of the determined two estimate values as the distance d between the measuring point and the point of fault according to the following criteria:

If s<de1<1, then d=de1, else d=de2

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

15. The system of claim 9 , wherein the means for selecting selects one of the determined two estimate values as the distance d between the measuring point and the point of fault according to the following criteria:

If 0<de2<s, then d=de2, else d=de1

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

16. An apparatus for determining a distance of a phase-to-earth fault on a three-phase electric line of an electric network, the apparatus comprising a processor to:

monitor current and voltage quantities of the three-phase electric line at a measuring point;

wherein the processor, in response to receiving an indication of a fault on the three-phase electric line and of a faulted phase of the three-phase electric line:

determines a first estimate value for a distance between the measuring point and a point of fault on the basis of values of the monitored current and voltage quantities and a first equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the load of the electric line is located between the measuring point and the point of fault;

determines a second estimate value for the distance between the measuring point and the point of fault on the basis of values of the monitored current and voltage quantities and a second equation which relates the current and voltage quantities to the distance and is based on a fault loop model of the electric line, in which model the point of fault is located between the measuring point and load of the electric line; and

selects, according to predetermined criteria, one of the determined two estimate values as the distance between the measuring point and the point of fault.

17. The apparatus of claim 16 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd I F +s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s=per unit distance of equivalent load.

18. The apparatus of claim 17 , wherein the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 +d· I 0Fd /2)+3 · Z F · I f .

19. The apparatus of claim 16 , wherein the first equation is:

U 0 + U 1 + U 2 =s· Z 1Fd · I 1 +( d−s )· Z 1Fd · I F +s· Z 2Fd · I 2 +( d−s )· Z 2Fd · I F +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I F

where

d=per unit fault distance from the measuring point to the fault point

U 0 =Zero sequence component voltage measured at the measuring point

U 1 =Positive sequence component voltage measured at the measuring point

U 2 =Negative sequence component voltage measured at the measuring point

Z 1Fd =Positive sequence impedance of the electric line per phase

Z 2Fd =Negative sequence impedance of the electric line per phase

Z 0Fd =Zero sequence impedance of the electric line per phase

Z F =Fault impedance

I 1 =Positive sequence component current measured at the measuring point

I F =Fault component current at the fault point

I 2 =Negative sequence component current measured at the measuring point

I 0 =Zero sequence component current measured at the measuring point

I 0Fd =Zero sequence component current of the electric line itself

s=per unit distance of equivalent load.

20. The apparatus of claim 19 , wherein the second equation is:

U 0 + U 1 + U 2 =d· Z 1Fd · I 1 +d· Z 2Fd · I 2 +d· Z 0Fd ·( I 0 + I 0Fd /2)+3 · Z F · I f .

21. The apparatus of claim 16 , wherein the apparatus selects one of the determined two estimate values as the distance d between the measuring point and the point of fault according to the following criteria:

If S<de1<1, then d=de1, else d=de2

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

22. The apparatus of claim 16 , wherein the apparatus selects one of the determined two estimate values as the distance d between the measuring point and the point of fault according to the following criteria:

If 0<de2<s, then d=de2, else d=de1

where

de1=the first estimate value for the distance between the measuring point and the point of fault determined on the basis of the first equation

de2=the second estimate value for the distance between the measuring point and the point of fault determined on the basis of the second equation

s=per unit distance of equivalent load.

23. The apparatus of claim 16 , wherein the apparatus is a protective relay.