CA1249337A - Line protection - Google Patents
Line protectionInfo
- Publication number
- CA1249337A CA1249337A CA000484063A CA484063A CA1249337A CA 1249337 A CA1249337 A CA 1249337A CA 000484063 A CA000484063 A CA 000484063A CA 484063 A CA484063 A CA 484063A CA 1249337 A CA1249337 A CA 1249337A
- Authority
- CA
- Canada
- Prior art keywords
- transmission line
- power transmission
- voltage
- voltages
- wave
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
- G01R31/085—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution lines, e.g. overhead
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
- H02H7/00—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions
- H02H7/26—Sectionalised protection of cable or line systems, e.g. for disconnecting a section on which a short-circuit, earth fault, or arc discharge has occured
- H02H7/265—Sectionalised protection of cable or line systems, e.g. for disconnecting a section on which a short-circuit, earth fault, or arc discharge has occured making use of travelling wave theory
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Locating Faults (AREA)
- Measurement Of Resistance Or Impedance (AREA)
- Emergency Protection Circuit Devices (AREA)
Abstract
ABSTRACT OF THE DISCLOSURE
A method and a device for distance protection and location of a fault point on a transmission line based on voltage waves emitted from a measuring point towards a fault point and corresponding waves reflected from a fault point, which are included in a travelling wave model of a transmission line. At certain regular intervals, a measurement is effected of the instantaneous values of the current and the voltage at an end point of the transmission line, for example at a station. Based on these measured values, and with the aid of the travelling wave model, it is possible to calculate the voltage at a number of control points along the transmission line.
If the line is energized and the calculated control voltages at two control points have different signs during a time longer than a time corresponding to normal phase difference between the two voltages, there is a fault on the line between these points. By interpolation, it is possible, based on the distance between the points in question and the calculated control voltages, to precisely locate the fault point in the case of a low resistance fault.
A method and a device for distance protection and location of a fault point on a transmission line based on voltage waves emitted from a measuring point towards a fault point and corresponding waves reflected from a fault point, which are included in a travelling wave model of a transmission line. At certain regular intervals, a measurement is effected of the instantaneous values of the current and the voltage at an end point of the transmission line, for example at a station. Based on these measured values, and with the aid of the travelling wave model, it is possible to calculate the voltage at a number of control points along the transmission line.
If the line is energized and the calculated control voltages at two control points have different signs during a time longer than a time corresponding to normal phase difference between the two voltages, there is a fault on the line between these points. By interpolation, it is possible, based on the distance between the points in question and the calculated control voltages, to precisely locate the fault point in the case of a low resistance fault.
Description
Technical Field The present invention relates to a method and a device for distance protection and locali~ation of a fault point on a transmissio~ line based on a model of the line according to the travelling wave theory. The invention comprises carrying out, at certain definite time intervals, a measurement of the instantaneous values of the currents and the voltages at the end point of the transmission line, for example at a station. Based on these measured values and with the aid of travelling wave theory, it is nowadays possible - as a result of the technical developments within the electronics and microprocessor field - to arrive at new solution concepts within the relay protection technique, and particularly for distance protection devices and fault location devices.
Prior Art There are several different methods for fault location on a transmission line. One such method is known from the Brithish patent application with publication number
Prior Art There are several different methods for fault location on a transmission line. One such method is known from the Brithish patent application with publication number
2,036,478. This describes a method in which a fault point is assumed and, while making simplified assumptions about the parameters of the network, the current and voltages of the fault point are determined. The determinations are repeated until the current and the voltage have the same phase, which means that the fault point has been located.
Another method is described in the Canadian patent applica-tion 436,546. This application describes a fault location on a section of a three-phase power line. After measurement of currents and voltages at one end of the section, the type of fault is first determined and thereafter certain - 2 _ ~ r~ 3?i~
parameters in an equation system are determined. This system describes the relationships between the complex values of the impedance of the section, the source impedances at the remote end and at the near end of the network, as~well as measured currents and voltages while eliminating the fault resistance, the pre-fault current, the zero sequence componen-ts, etc. The solution of the equation system provides the distance from the end point of the section to the fault point in question.
Certain aspec-ts of travelling wave theory have also been employed. For example, U.S. Patent 3,878,460 utilizes the principle in the case of directional wave detector. By studying the signs of the current and voltage waves, it can be determined whether there is a fault in the monitoring direction of the relay protection device towards the fault point. If this is the case, the current and voltage waves have opposite signs.
20 This invention relates to a line protection device based on a travelling wave model of a line, which permits fault location for both single-phase and multi-phase systems. The method permits a rapid, accurate and reliable determination of the distance to the fault. In addition, the invention relates to a device for carrying out the method.
According to the present invention, there is provided a method Eor the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line, comprising:
- periodically measuring the voltage and current at an end point of the power transmission line;
- de-termining the wave impedance and the wave - 2a - ~ 3~
attenuation factor of the power transmission line and the transit time of the travelling wave;
- periodically generating signals representative of the measured voltage and current;
- periodically storing the vol-tage and current signals;
- establishi.ng a number of control points spaced a like number of distances from said end point of the power transmission line along said power transmission line;
- calculating a control voltage (ul, u2...uj...un) at each of said number of control points along said power transmission line from the following formula:
uj(-t) = Dj/2 {uo(t - Tj) + Zio(t - Tj)~
-~ 1/2Dj ~uo(t + Tj) - Zio(t + Tj)~
where:
Dj = said attenuation factor of a wave travelling along said power transmission line;
Tj = the determined transit times of the travelling wave;
uO = the measured voltage at said end point oE said power transmission line;
io = the measured current at said end point of said power transmission line; and z = the determined wave impedance of said power transmission line;
- determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - 2b -- generating output signals representative of the fault locations to provide an indication thereof.
According to the present invention there is also provided a device for the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line from measured voltage and measured current at an end point of the power transmission line, the predetermined wave impedance of the power transmission line, the predetermined wave attenuation factor and transit time based on said travelling wave model of the power transmission line, comprising:
- means for periodically generating signals represent-ative of the measured voltage and current;
- means for periodically storing the voltage and current signals;
- means for calculating a control ~ul, u2...uj...un) at each of a number of predetermined control points spaced a like number of distances from said end point of the power transmission line along said power transmission line from the following formula:
uj(t) = Dj/2 ~uo(t - Tj) + Zio(t - Tj) 3 + 1/2 Dj ~uo(t - Tj) ~ zio( t + Tj) where:
Dj = said predetermined attenuation fac-tor of a wave travelling along said power transmission line;
Tj = said predetermined transit time of the travelling wave;
uO = the measured voltage at said end point of said power '~3 ?~
-- 2c -transmission line;
io = the measured current at said end of said power transmission line:
Z = said predetermined wave impedance of said power transmission line; and - means for determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - means for generating outpu-t signals representative of the fault locations to provide an indication thereof.
Brief Description of Drawings In the following the invention will be described with refer-ence to the accompanying drawings, in which:
Figure 1 shows graphically waves on a transmission line and 20examples of control voltages.
Figure 2 also shows graphically waves on a transmission line but with alternative control voltages.
Figure 3 shows a voltage distribution calculated with the aid of sampled measured current (io) and voltage 25(uO) values.
Figure 4 shows a grounded network with a voltage source connected to the R-phase.
Figure 5 shows a symmetrical three-phase network.
-Figure ~ shows an example of an analogue design of a protection device shown according to the invention.
Figure 7 shows a different example of an analogue design of a protection device according to the invention.
Figure 8 illustrates a detailed embodiment of a protection device according to the invention in analogue design.
Description of the Princi le of the Invention __ P
In summary the invention, which comprises a method and a device for distance protection and fault location, can be desc-ribed as follows:
The instantaneous value of current and voltage at the end pointof a transmission line is measured, and a certain number of measured values are stored for a certain period of time in a shift register. The shift register is consecutively updated, and the measured values are used to calculate, digitally or analogically, a number of control voltages related to different points along the length of the protected line. The voltage is related to the measuring point uO, calculated voltages are designated ul 7 u2 ... un, and the measured current is designated io. The voltages ul, u2 ... un are calculated with the aid of formulae derived from the travelling wave theory. This theory states that a wave emanating from the measuring point can be desi9nated uO = 1/2(uo + Z io) and the wave arriving at the measuring point can be designated uO = 1/2(uo - Z ~io)~ where Z designates the wave impedance. Somewhere along the transmiss-ion line, these waves can be designated uj+(t) = Djuo+(t-~ ) and u; (t) = uO (t+ ~)/Dj, respectively, where Dj is the ratio of attenuation of the wave and ~ is the transit time. If the transmission line is energized and the calculated control voltage u; = uj+ + u; is constantly zero, there is a fault at point j. Normally, a fault is located between two control points.
Characteristic of the control voltages at the points on either side of a fault point is that they have different signs. By interpolation an accurate fault localization can be performed.
The invention makes use of suitably chosen matrices for trans-formation of measured currents and voltages so that transport ~3~
in shift registers can be carried out in independent modes.
Equations The theory of travelling waves on transmission lines is described in several text books, inter alia in "Elektricitetslara" by E. Hallén, Uppsala, 1953. The so-called "telegrapher's equation", which is well-known in this connection and the designation of which indicates that the equation was previously used primarily in fields other than power transmission, states that if u = the voltage at a point on the transmission line i = the current at the same point x = the coordinate of length of the transmission line r = the resistance per unit of length l = the inductance per unit of length g = the conductance per unit of length c = the capacitance per unit of length then the following relationships apply:
_ ~u = ri + l ~St (1) _ ~i = gu + c ~t (2) In the practical application, which will be described here, it can be assumed that the transmission line is distortion_free.
This means that rc = gl which permits a very simple solution of the equation systems (1) and (2). With the assumption according to equation (3), the voltage at a point j on the transmission line can be written as uj(t) = l~j+(t) + uj-(t) (4) where uj+(t) i5 a wave moving in the positive direction of the trans-mission line and Uj (t) is a wave moving in the negative direction.
Further, it is commonly known that the wave velocity v = ~ (5) and that the wave impedance, with the aid of which the curren-t wave can be expressed, is Z = ~ (6) In the same way as the voltage at a point j, the current at the same point j can be expressed in accordance with equation (4) as ij = ij+ + ij- (7) where the function dependence on t for simplicity has been omitted.
In addition, the following general equations apply ij+ =
ij = _ _i_ which enables the equation (4) to be expressed as uj(t) = 2uj+(t) - Zij(t) (10) or 20 uj(t) = 2uj-(t) + Zij(t) (11) When a wave rnoves along a line, an attenuation of the amplitude is obtained. When the wave has moved from x = 0 to x = dj, it has at the same time been attenuated by a factor ~ 2~3~
~i 6 Dj = e Z (12) Starting from the wave velocity according to equation (5), the transit time for the wave from x = 0 to x = dj will be ~j = dj ~ (13) The attenuation according to equation (12) and the transit time according to equation (13) permit uj+(t) and uj-(t) to be written as uj (t) = Dj uo+(t - ~j) (14) and lû uj (t) = D uO (t + ~-j) (15) where uO is the voltage related to the measuring point, From equations (10) and (11), uj+(t) and uj-(t) can also be written as uj+(t) = 1/2 Ej(t) + Zij(t~ (16) and uj-(t) = 1/2 ~uj(t) - Zij(t~ (17) With the aid of the measured values of uO and io~ the voltage at a point at the distance dj from the measurinq point as a function of the time t, i.e , uj(t), can now be calculated.
Parameters in the algorithm for uj(t) are, besides the time t, the attenuation Dj, the transit time ~ and the wave impedance Z according to equation (6). The solution is as follows u (t) = _i LuO(t-~j) ~ zio(t~~ + 2DJ Eo' ~ i~
Further, using equations (14) and (15), the equation (4) can 7 ~ 3~
be written as uj(t) = DjUo (t ~ ) + D o ( i (15) Graphic representation of the movements of the waves To gain a deeper understanding of the presented theory and thus also of the principle of this invention, we can study Figures 1, 2 and 3. On examining the movement of a wave along a transmission line, a time table can be set up. According to equations (5) and (13), the wave velocity is ~ ,i v = ~1c = ~t where, as mentioned, dj = the distance from the measuring point, for example at a station, to a certain point along the trans-mission line which has been given the serial number j. Since the velocity is constant, the graph for the movement of the wave is a straight line.
In Figure 1 the movement for a plurality of waves has been plotted graphically with the distance along the transmission line on the horizontal axis and the time along the vertical axis. The inclination of each line is determined by the wave velocity v.
Starting from time t = O, a number of waves passing the measur-ing point t = O in the positive direction have been displayed.
These are U5+, U4+ ... uO+ and u 1+- The time difference between their passage of the measuring point d = O is ~1- ~ ~ , where ~ = 2~ ?-3 = 3~~and so on. ~aves moving in a negative direc-tion, that is u 1 ~ uO , u1 ... U5 , have also been displayedon the graph.
Since the theory states that the voltage at a point, j, on the transmission line at a certain moment is the sun of the wave in the positive direction uj+ and the wave in the negative dir-ection Uj , at each meeting between a wave with a positive dir-ection of movement and a wave with a negative direction of move-ment, the voltage Uj can be calculated.
Different intersectional points between the u+-waves and the u -waves may be optionally studied. Figure 1 shows control voltages which are related to the same point of time. In Figure 2 it has been chosen to study control voltages related to a certain wave, U5 , in the negative direction. Also other alter-natives are possible.
In Figure 1 the calculated voltages u 1, uO, ul ... U5 serve to keep a check on the voltage that prevails at different points along the transmission line at a certain moment. The condition for u 1 -- u5 to correspond to actual voltages in the network is that there are no discontinuities between the measuring point, 0, and point j. For j = -1 this condition does not generally apply, since the point 0 lies at the beginning of the transmission line at a station of some kind. Thus, u 1 is a fictitious voltage which is used for detection and for distance determination.
Several sUch fic-titious voltages could also be conceived, for example u 5, which can be used for detecting a fault which lies behind the measuring point of the transmission line.
If a fault has occurred between, for example, points 3 and 4, U4 and U5 will also become purely fictitious voltages, which are still included in the pattern constituted by the control voltages and used by the logic unit of the protection device to determine the condition of the transmission line. The task of the fault detection logic unit is to identify the pattern formed by the control voltages during a sequence of times in order to determine whether a fault has occured and where the fault has occurred. Figure 3 indicates that the pattern may vary with time, but the voltage at the fault point f is constantly zero. Also, strictly mathematically it can be shown that the sign of fictitious voltages beyond a fault point has been changed.
When there is a fault point on the transmission line, this will normally lie between two control points, for example between the control points j and j+l.
Transformations_to and from independent modes The equations stated above apply to single-phase systems. Power lines normally consist of three or possibly more phases. It ~2~ 37 i5 well known that a symmetrical multi-phase system can be divi-ded into independent modes. In this way, by suitable transfor-mation, a symmetrical three-phase system can be divided into three single-phase systems which are independent of each other.
By applying the previously stated equations to the systems obtained by transformation, the travelling wave model can also be used for calculating the faults for multi-phase systems.
For fault analyses and for level sensing, it is often most suitable to use the phase and main voltages of the original multi-phase system. Therefore, an inverse transformation of the modal control voltages back to the original multi-phase system takes place.
Transformations of these kinds are known from a number of publi-cations of various kinds, for example Proceedings IEE 113 (1966):
6 (June) "Study of symmetrical and related components through the theory of linear vector spaces".
Since the utilization of such transformations is included as an integrated part of the method and the device to which this invention relates, a brief summary of the transformation metho-dology will be described.
Figure 4 shows an arbitrary network with connection terminalsR, S and T and a ground connection. If a voltage URA is connec-ted between terminal R and ground, as shown in the figure, a current IR will arise. This means that we can define the impedance URA
ZRR = IR (20) At the same time, as indicated in Figure 4, the voltages U5A
and UTA between terminal S and ground and between terminal T
and ground can be measured. This makes it possible to define mutual impedances as U A
ZSR = IR (21) U A
ZTR IR (22)
Another method is described in the Canadian patent applica-tion 436,546. This application describes a fault location on a section of a three-phase power line. After measurement of currents and voltages at one end of the section, the type of fault is first determined and thereafter certain - 2 _ ~ r~ 3?i~
parameters in an equation system are determined. This system describes the relationships between the complex values of the impedance of the section, the source impedances at the remote end and at the near end of the network, as~well as measured currents and voltages while eliminating the fault resistance, the pre-fault current, the zero sequence componen-ts, etc. The solution of the equation system provides the distance from the end point of the section to the fault point in question.
Certain aspec-ts of travelling wave theory have also been employed. For example, U.S. Patent 3,878,460 utilizes the principle in the case of directional wave detector. By studying the signs of the current and voltage waves, it can be determined whether there is a fault in the monitoring direction of the relay protection device towards the fault point. If this is the case, the current and voltage waves have opposite signs.
20 This invention relates to a line protection device based on a travelling wave model of a line, which permits fault location for both single-phase and multi-phase systems. The method permits a rapid, accurate and reliable determination of the distance to the fault. In addition, the invention relates to a device for carrying out the method.
According to the present invention, there is provided a method Eor the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line, comprising:
- periodically measuring the voltage and current at an end point of the power transmission line;
- de-termining the wave impedance and the wave - 2a - ~ 3~
attenuation factor of the power transmission line and the transit time of the travelling wave;
- periodically generating signals representative of the measured voltage and current;
- periodically storing the vol-tage and current signals;
- establishi.ng a number of control points spaced a like number of distances from said end point of the power transmission line along said power transmission line;
- calculating a control voltage (ul, u2...uj...un) at each of said number of control points along said power transmission line from the following formula:
uj(-t) = Dj/2 {uo(t - Tj) + Zio(t - Tj)~
-~ 1/2Dj ~uo(t + Tj) - Zio(t + Tj)~
where:
Dj = said attenuation factor of a wave travelling along said power transmission line;
Tj = the determined transit times of the travelling wave;
uO = the measured voltage at said end point oE said power transmission line;
io = the measured current at said end point of said power transmission line; and z = the determined wave impedance of said power transmission line;
- determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - 2b -- generating output signals representative of the fault locations to provide an indication thereof.
According to the present invention there is also provided a device for the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line from measured voltage and measured current at an end point of the power transmission line, the predetermined wave impedance of the power transmission line, the predetermined wave attenuation factor and transit time based on said travelling wave model of the power transmission line, comprising:
- means for periodically generating signals represent-ative of the measured voltage and current;
- means for periodically storing the voltage and current signals;
- means for calculating a control ~ul, u2...uj...un) at each of a number of predetermined control points spaced a like number of distances from said end point of the power transmission line along said power transmission line from the following formula:
uj(t) = Dj/2 ~uo(t - Tj) + Zio(t - Tj) 3 + 1/2 Dj ~uo(t - Tj) ~ zio( t + Tj) where:
Dj = said predetermined attenuation fac-tor of a wave travelling along said power transmission line;
Tj = said predetermined transit time of the travelling wave;
uO = the measured voltage at said end point of said power '~3 ?~
-- 2c -transmission line;
io = the measured current at said end of said power transmission line:
Z = said predetermined wave impedance of said power transmission line; and - means for determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - means for generating outpu-t signals representative of the fault locations to provide an indication thereof.
Brief Description of Drawings In the following the invention will be described with refer-ence to the accompanying drawings, in which:
Figure 1 shows graphically waves on a transmission line and 20examples of control voltages.
Figure 2 also shows graphically waves on a transmission line but with alternative control voltages.
Figure 3 shows a voltage distribution calculated with the aid of sampled measured current (io) and voltage 25(uO) values.
Figure 4 shows a grounded network with a voltage source connected to the R-phase.
Figure 5 shows a symmetrical three-phase network.
-Figure ~ shows an example of an analogue design of a protection device shown according to the invention.
Figure 7 shows a different example of an analogue design of a protection device according to the invention.
Figure 8 illustrates a detailed embodiment of a protection device according to the invention in analogue design.
Description of the Princi le of the Invention __ P
In summary the invention, which comprises a method and a device for distance protection and fault location, can be desc-ribed as follows:
The instantaneous value of current and voltage at the end pointof a transmission line is measured, and a certain number of measured values are stored for a certain period of time in a shift register. The shift register is consecutively updated, and the measured values are used to calculate, digitally or analogically, a number of control voltages related to different points along the length of the protected line. The voltage is related to the measuring point uO, calculated voltages are designated ul 7 u2 ... un, and the measured current is designated io. The voltages ul, u2 ... un are calculated with the aid of formulae derived from the travelling wave theory. This theory states that a wave emanating from the measuring point can be desi9nated uO = 1/2(uo + Z io) and the wave arriving at the measuring point can be designated uO = 1/2(uo - Z ~io)~ where Z designates the wave impedance. Somewhere along the transmiss-ion line, these waves can be designated uj+(t) = Djuo+(t-~ ) and u; (t) = uO (t+ ~)/Dj, respectively, where Dj is the ratio of attenuation of the wave and ~ is the transit time. If the transmission line is energized and the calculated control voltage u; = uj+ + u; is constantly zero, there is a fault at point j. Normally, a fault is located between two control points.
Characteristic of the control voltages at the points on either side of a fault point is that they have different signs. By interpolation an accurate fault localization can be performed.
The invention makes use of suitably chosen matrices for trans-formation of measured currents and voltages so that transport ~3~
in shift registers can be carried out in independent modes.
Equations The theory of travelling waves on transmission lines is described in several text books, inter alia in "Elektricitetslara" by E. Hallén, Uppsala, 1953. The so-called "telegrapher's equation", which is well-known in this connection and the designation of which indicates that the equation was previously used primarily in fields other than power transmission, states that if u = the voltage at a point on the transmission line i = the current at the same point x = the coordinate of length of the transmission line r = the resistance per unit of length l = the inductance per unit of length g = the conductance per unit of length c = the capacitance per unit of length then the following relationships apply:
_ ~u = ri + l ~St (1) _ ~i = gu + c ~t (2) In the practical application, which will be described here, it can be assumed that the transmission line is distortion_free.
This means that rc = gl which permits a very simple solution of the equation systems (1) and (2). With the assumption according to equation (3), the voltage at a point j on the transmission line can be written as uj(t) = l~j+(t) + uj-(t) (4) where uj+(t) i5 a wave moving in the positive direction of the trans-mission line and Uj (t) is a wave moving in the negative direction.
Further, it is commonly known that the wave velocity v = ~ (5) and that the wave impedance, with the aid of which the curren-t wave can be expressed, is Z = ~ (6) In the same way as the voltage at a point j, the current at the same point j can be expressed in accordance with equation (4) as ij = ij+ + ij- (7) where the function dependence on t for simplicity has been omitted.
In addition, the following general equations apply ij+ =
ij = _ _i_ which enables the equation (4) to be expressed as uj(t) = 2uj+(t) - Zij(t) (10) or 20 uj(t) = 2uj-(t) + Zij(t) (11) When a wave rnoves along a line, an attenuation of the amplitude is obtained. When the wave has moved from x = 0 to x = dj, it has at the same time been attenuated by a factor ~ 2~3~
~i 6 Dj = e Z (12) Starting from the wave velocity according to equation (5), the transit time for the wave from x = 0 to x = dj will be ~j = dj ~ (13) The attenuation according to equation (12) and the transit time according to equation (13) permit uj+(t) and uj-(t) to be written as uj (t) = Dj uo+(t - ~j) (14) and lû uj (t) = D uO (t + ~-j) (15) where uO is the voltage related to the measuring point, From equations (10) and (11), uj+(t) and uj-(t) can also be written as uj+(t) = 1/2 Ej(t) + Zij(t~ (16) and uj-(t) = 1/2 ~uj(t) - Zij(t~ (17) With the aid of the measured values of uO and io~ the voltage at a point at the distance dj from the measurinq point as a function of the time t, i.e , uj(t), can now be calculated.
Parameters in the algorithm for uj(t) are, besides the time t, the attenuation Dj, the transit time ~ and the wave impedance Z according to equation (6). The solution is as follows u (t) = _i LuO(t-~j) ~ zio(t~~ + 2DJ Eo' ~ i~
Further, using equations (14) and (15), the equation (4) can 7 ~ 3~
be written as uj(t) = DjUo (t ~ ) + D o ( i (15) Graphic representation of the movements of the waves To gain a deeper understanding of the presented theory and thus also of the principle of this invention, we can study Figures 1, 2 and 3. On examining the movement of a wave along a transmission line, a time table can be set up. According to equations (5) and (13), the wave velocity is ~ ,i v = ~1c = ~t where, as mentioned, dj = the distance from the measuring point, for example at a station, to a certain point along the trans-mission line which has been given the serial number j. Since the velocity is constant, the graph for the movement of the wave is a straight line.
In Figure 1 the movement for a plurality of waves has been plotted graphically with the distance along the transmission line on the horizontal axis and the time along the vertical axis. The inclination of each line is determined by the wave velocity v.
Starting from time t = O, a number of waves passing the measur-ing point t = O in the positive direction have been displayed.
These are U5+, U4+ ... uO+ and u 1+- The time difference between their passage of the measuring point d = O is ~1- ~ ~ , where ~ = 2~ ?-3 = 3~~and so on. ~aves moving in a negative direc-tion, that is u 1 ~ uO , u1 ... U5 , have also been displayedon the graph.
Since the theory states that the voltage at a point, j, on the transmission line at a certain moment is the sun of the wave in the positive direction uj+ and the wave in the negative dir-ection Uj , at each meeting between a wave with a positive dir-ection of movement and a wave with a negative direction of move-ment, the voltage Uj can be calculated.
Different intersectional points between the u+-waves and the u -waves may be optionally studied. Figure 1 shows control voltages which are related to the same point of time. In Figure 2 it has been chosen to study control voltages related to a certain wave, U5 , in the negative direction. Also other alter-natives are possible.
In Figure 1 the calculated voltages u 1, uO, ul ... U5 serve to keep a check on the voltage that prevails at different points along the transmission line at a certain moment. The condition for u 1 -- u5 to correspond to actual voltages in the network is that there are no discontinuities between the measuring point, 0, and point j. For j = -1 this condition does not generally apply, since the point 0 lies at the beginning of the transmission line at a station of some kind. Thus, u 1 is a fictitious voltage which is used for detection and for distance determination.
Several sUch fic-titious voltages could also be conceived, for example u 5, which can be used for detecting a fault which lies behind the measuring point of the transmission line.
If a fault has occurred between, for example, points 3 and 4, U4 and U5 will also become purely fictitious voltages, which are still included in the pattern constituted by the control voltages and used by the logic unit of the protection device to determine the condition of the transmission line. The task of the fault detection logic unit is to identify the pattern formed by the control voltages during a sequence of times in order to determine whether a fault has occured and where the fault has occurred. Figure 3 indicates that the pattern may vary with time, but the voltage at the fault point f is constantly zero. Also, strictly mathematically it can be shown that the sign of fictitious voltages beyond a fault point has been changed.
When there is a fault point on the transmission line, this will normally lie between two control points, for example between the control points j and j+l.
Transformations_to and from independent modes The equations stated above apply to single-phase systems. Power lines normally consist of three or possibly more phases. It ~2~ 37 i5 well known that a symmetrical multi-phase system can be divi-ded into independent modes. In this way, by suitable transfor-mation, a symmetrical three-phase system can be divided into three single-phase systems which are independent of each other.
By applying the previously stated equations to the systems obtained by transformation, the travelling wave model can also be used for calculating the faults for multi-phase systems.
For fault analyses and for level sensing, it is often most suitable to use the phase and main voltages of the original multi-phase system. Therefore, an inverse transformation of the modal control voltages back to the original multi-phase system takes place.
Transformations of these kinds are known from a number of publi-cations of various kinds, for example Proceedings IEE 113 (1966):
6 (June) "Study of symmetrical and related components through the theory of linear vector spaces".
Since the utilization of such transformations is included as an integrated part of the method and the device to which this invention relates, a brief summary of the transformation metho-dology will be described.
Figure 4 shows an arbitrary network with connection terminalsR, S and T and a ground connection. If a voltage URA is connec-ted between terminal R and ground, as shown in the figure, a current IR will arise. This means that we can define the impedance URA
ZRR = IR (20) At the same time, as indicated in Figure 4, the voltages U5A
and UTA between terminal S and ground and between terminal T
and ground can be measured. This makes it possible to define mutual impedances as U A
ZSR = IR (21) U A
ZTR IR (22)
3~.~
Now, if the voltage UR is removed and a voltage U5B is connec-ted to terminal S, this gives rise to a current I5, and in a corresponding manner a current IT is obtained when a voltage UTC is connected to terminal T. In the same way as for the R-phase, the impedances for S- and T-phases can now be defined:
ZSS l5 ZTS = l5 ZRS = 15 uTc uRc U5C (23) ZTT IT ZRT = IT ZST = IT
Now, if it is assumed that the currents IR, I5 and IT are sim-ultaneously applied to the respective terminals, according to the superposition theorem the following phase voltages are ob_ tained:
UR = URA + URB + URC
U5 = U5A + U B + U C (24) UT = UTA + UTB + UTC
By introducing the above-mentioned impedances, the equation system describing the network can be written as:
UR ~ ZRRIR ~ ZR5I5 + ZRTIT
5 Z5RIR + Z55I5 + ZSTIT (25) UT = ZTRIR + ZTSIS TT T
which in the matrix form can be written as R \ ~ZRR ZRS ZRT~~ IR \
U5 = ZSR Z55 ZST xI5 ¦ (26) ~UT ~ TR ZTS ZTT~IT /
or in reduced form 25 URST = ZRST x IRST (27) 3~
The equation system according to the above can? of course, be solved in conventional manner. In the same way as - in other technical fields - the calculations can be simplified by trans-formation of equation systems, for example, by Laplace trans-formation, from a time plane to a frequency plane, also in thiscase currents and voltages can be transformed so that, on certain conditions, simpler calculations and increased clarity can be achieved The transformation of the equation system (25) to modal or inde-pendent form implies that we are seeking an equation system Ua = Za x Ia Ub = Zb x Ib (28) Uc = Zc x Ic where it should be possible to express the parameters included in this system with the aid of the parameters in equation system (25). If such a transformation can be made, we will have obtained three systems which are independent of each other and then the movements of the shift register can be made separately.
The conditions and the method for performing such a transfor-mation will be clear from the following:
Let it first be assumed that IR, I5 and IT are replaced by alinear combination of three currents Ia, Ib and Ic which fulfil the following relationships IR = kRaIa + kRbIb + kRcI
25 IS = k5aIa ~ k5bIb + kScI (29) IT = kTaIa + kTbIb + kTcI
and in the matrix form it can be written as ~IR ~ ~kRa kRb kRc~ x ~Ia k5a ksb kSc 1 l b \ / ~kTa kTb kTc/ ~Ic~
12 -~r~
or in reduced form IRST = I(abc x Iabc (31' The same method can be applied to the voltages UR, U5 and UT
and in the matrix form there will be the following:
~UR~ ~]Ra lRb 1Rc ~ /Ua~
¦ U5 1 lSa lSb lScx ¦ Ub ¦ (32) T/ lTa lTb lTc~Uc/
or URST = Labc x Uabc (33) Equation systems (30) and (32) must have a solution. With matrix designations this means that there must be an inverse matrix (Kabc) s IabC = (Kabc) x IRST
and Uabc = (LabC) x URST
where the condition is that (Kabc) x (Kabc) and (Labc) x (Labc) = E
where E is a unit matrix.
Now, using equations (31) and (33) in equation (27), the result will be:
( abc) x Uabc = ZRST x (Kabc) x I b (36) ~o~3~
Multiplying both sides by (LabC) gives Uabc = (Labc) x ZR5Tx(Kabc) x Iabc (37) Assuming M = (LabC) x ZRST x (Kabc) (38) the following is obtained Uabc = M x Iabc On condition that M is given in the form of a diagonal matrix, that is, a matrix of the form ~Z O O \
10 M =¦ Zb l (40) ~ Z cJ
the equation system (39) can be written as Ua = Za x Ia Ub = Zb x Ib Uc = Zc x Ic that is, the desired equation system according to equation (28);
thus, three systems independent of each other.
With knowledge of Za~ Zb and Zc~ the network according to Figure
Now, if the voltage UR is removed and a voltage U5B is connec-ted to terminal S, this gives rise to a current I5, and in a corresponding manner a current IT is obtained when a voltage UTC is connected to terminal T. In the same way as for the R-phase, the impedances for S- and T-phases can now be defined:
ZSS l5 ZTS = l5 ZRS = 15 uTc uRc U5C (23) ZTT IT ZRT = IT ZST = IT
Now, if it is assumed that the currents IR, I5 and IT are sim-ultaneously applied to the respective terminals, according to the superposition theorem the following phase voltages are ob_ tained:
UR = URA + URB + URC
U5 = U5A + U B + U C (24) UT = UTA + UTB + UTC
By introducing the above-mentioned impedances, the equation system describing the network can be written as:
UR ~ ZRRIR ~ ZR5I5 + ZRTIT
5 Z5RIR + Z55I5 + ZSTIT (25) UT = ZTRIR + ZTSIS TT T
which in the matrix form can be written as R \ ~ZRR ZRS ZRT~~ IR \
U5 = ZSR Z55 ZST xI5 ¦ (26) ~UT ~ TR ZTS ZTT~IT /
or in reduced form 25 URST = ZRST x IRST (27) 3~
The equation system according to the above can? of course, be solved in conventional manner. In the same way as - in other technical fields - the calculations can be simplified by trans-formation of equation systems, for example, by Laplace trans-formation, from a time plane to a frequency plane, also in thiscase currents and voltages can be transformed so that, on certain conditions, simpler calculations and increased clarity can be achieved The transformation of the equation system (25) to modal or inde-pendent form implies that we are seeking an equation system Ua = Za x Ia Ub = Zb x Ib (28) Uc = Zc x Ic where it should be possible to express the parameters included in this system with the aid of the parameters in equation system (25). If such a transformation can be made, we will have obtained three systems which are independent of each other and then the movements of the shift register can be made separately.
The conditions and the method for performing such a transfor-mation will be clear from the following:
Let it first be assumed that IR, I5 and IT are replaced by alinear combination of three currents Ia, Ib and Ic which fulfil the following relationships IR = kRaIa + kRbIb + kRcI
25 IS = k5aIa ~ k5bIb + kScI (29) IT = kTaIa + kTbIb + kTcI
and in the matrix form it can be written as ~IR ~ ~kRa kRb kRc~ x ~Ia k5a ksb kSc 1 l b \ / ~kTa kTb kTc/ ~Ic~
12 -~r~
or in reduced form IRST = I(abc x Iabc (31' The same method can be applied to the voltages UR, U5 and UT
and in the matrix form there will be the following:
~UR~ ~]Ra lRb 1Rc ~ /Ua~
¦ U5 1 lSa lSb lScx ¦ Ub ¦ (32) T/ lTa lTb lTc~Uc/
or URST = Labc x Uabc (33) Equation systems (30) and (32) must have a solution. With matrix designations this means that there must be an inverse matrix (Kabc) s IabC = (Kabc) x IRST
and Uabc = (LabC) x URST
where the condition is that (Kabc) x (Kabc) and (Labc) x (Labc) = E
where E is a unit matrix.
Now, using equations (31) and (33) in equation (27), the result will be:
( abc) x Uabc = ZRST x (Kabc) x I b (36) ~o~3~
Multiplying both sides by (LabC) gives Uabc = (Labc) x ZR5Tx(Kabc) x Iabc (37) Assuming M = (LabC) x ZRST x (Kabc) (38) the following is obtained Uabc = M x Iabc On condition that M is given in the form of a diagonal matrix, that is, a matrix of the form ~Z O O \
10 M =¦ Zb l (40) ~ Z cJ
the equation system (39) can be written as Ua = Za x Ia Ub = Zb x Ib Uc = Zc x Ic that is, the desired equation system according to equation (28);
thus, three systems independent of each other.
With knowledge of Za~ Zb and Zc~ the network according to Figure
4 can be entirely controlled, and the voltages Ua, Ub and Uc and currents Ia, Ib and I can be calculated.
Starting from a symmetrical three-phase system, it can be shown that K = L and K 1 = L 1, respectively, ~t~ 3 that is, K x K 1 = K x L 1 = K-l x L = L x L~l = E
The matrices which are used in this connection are the so-called Clarke s matrices which, if the earlier matrix designa-tions are maintained, are constituted by / _ \
(Labe) = ~ _1 _1 ~ (41) 0 1 _1 1 Il ~ O\
Ibc ~ (42) 1 _1 _1 In a symmetrieal three-phase network, equation system (26) ean be written as ~UR \ ~ 1 Z2 Z3\ /IR~
U5 = ~ Z3 1 2 x I5 (43) \uT ~Z2 Z3 Zl ~IT
Equation (38) ean also be written as M = N x (KabC) that is, ( abe) x ZRST (45) 33~
With (L b ) 1 according to equation (41) arld ZRST according to equation (43), the following is obtained ~ ~ (Zl+z3+z2) ~ (Z2+z1+z3) ~ (Z3-~z2+zl) l N ~ ~ Zl ~ (Z3+z2) ~ Z2 ~ (Zl+Z3) ~ Z3 ~ ( 2+ 1) (46) ~ ~ (Z3-z2) ~ (Zl-Z3) ~ (Z2-Z
Now, in order for O O~
M = N x (KabC) = n Zb ~ (47) ZCJ
then it is presupposed that Z2 = Z3 (48) which, after certain intermediate calculations, gives Za = Zl + 2Z2 Zb Zl Z2 (49) Zc Zl Z2 Now, looking at a network according to Figure 5, it can be seen that Zl ZL + ZN (50) Z2 = Z3 = ZN (51) that is, after intermediate calculations Za = ZL + 3ZN
b L (52) Zc = Z.
3~
By measurement, UR, U5 and UT are known, and this provides a possibility of calculating, with the aid of equation (35), the transformed voltage vector U0' as Ua, Ub and Uc, that is, ~ ) (L )~1 ~ (53) With !<nowledge of Ua, Ub and Uc as well as Za~ Zb and Zc~ it is now possible to calculate Ia, Ib and Ic with the aid of IRo, I50 and ITo. When calculating in the respective independent a-, b- and c-systems, the paramters attenuation, transit time and wave impedance will be designated Dja~ ~ a' Za' Djb' ~ b~
Zb and Djc~ ~c and Zc' respectively. Phase quantities at the control point can be obtained again by transformation by K (or L), that is, ~UjR\
Uj = KUj' = l UiS
\ jT~
\ /
It is the phase quantities that are most suitable to study.
Single-phase faults are indicated by using UjR, Uj5 and UjT
individually, which also makes it possible to make phase selec-tions for single-phase tripping. For other types of fault, the respective main voltages are used, that is, UjR ~ UjS, Uj5 ~
~ UjT and UjT - UjR.
Embodiments The protaction device can be built in analog or digital tech-nique. Examples of embodiments in analog technique are shown in Figures 6 and 7.
In an embodiment according to Figure 6, transformation of in-coming phase voltages URST and phase currents IR5T into modal transformed quantities is carried out in the transformation units Ll and Kl with the matrices L and K , respectively.
In this embodiment a calculation is first carried out in the 3~
calculating unit A1 of U'0 = 1/2(U'o + Z I~o) and (55) U~0 = 1/2(U n - Z Io ), respectively, (56) which values are consecutively stored and updated in the shift registers 51 and S2. A shift register is present for each mode and each wave type, that is, both for voltage waves and current waves. In calculating unit A2 a calculation of uj'(t) in accordance with equation (19) takes place. The values of the modal voltages U , Ub and Uc at the selected points, thus obtained, are trans-formed in transformation unit K2, corresponding to the previouslydescribed matrix K, back to phase voltages UR, U5 and UT. These values for each selected point are then supplied to a fault detection logic unit FL for evaluation. From this unit a possible order for tripping via TR and printout of a fault report via FR is given.
Figure 7 is an embodiment showing the same units L1, K1, K2, FL, TR and FR as in Figure 6. In the shift registers 53 and 54 the transformed values of U0 and Io and possibly Io- Z
are conceived to be stored. In the calculating unit A3 the voltages Ua, Ub and Uc at the selected points are now calcula-ted in accordance with equation (18).
Example of embodiment usinq analoq technique Figure 8 illustrates a more detailed block diagram correspond-ing to Figure 7. Transformation of incoming phase voltages URST and phase currents IR5T to modal transformed voltages Ua, Ub and Uc and currents Ia, Ib and Ic takes place in the matrix units Lla, Llb, L1c and in Kla, Klb, K1c, respectively. As will be clear from Figure 8 only summing operational amplifiers are required both for the matrix treatment and other calculations.
The modal voltage values are supplied to a shift register 53a, 53b and S3c, and the modal current values are multiplied by the respective modal impedances, whereafter the voltage values are obtained and then supplied to shift registers 54a, 54b and 3~7 S4c.
If it is assumed that control vo:Ltages at n points along the transmission line are to be calculated, the shift register has to be able to store 2n measured values in each mode, correspond-
Starting from a symmetrical three-phase system, it can be shown that K = L and K 1 = L 1, respectively, ~t~ 3 that is, K x K 1 = K x L 1 = K-l x L = L x L~l = E
The matrices which are used in this connection are the so-called Clarke s matrices which, if the earlier matrix designa-tions are maintained, are constituted by / _ \
(Labe) = ~ _1 _1 ~ (41) 0 1 _1 1 Il ~ O\
Ibc ~ (42) 1 _1 _1 In a symmetrieal three-phase network, equation system (26) ean be written as ~UR \ ~ 1 Z2 Z3\ /IR~
U5 = ~ Z3 1 2 x I5 (43) \uT ~Z2 Z3 Zl ~IT
Equation (38) ean also be written as M = N x (KabC) that is, ( abe) x ZRST (45) 33~
With (L b ) 1 according to equation (41) arld ZRST according to equation (43), the following is obtained ~ ~ (Zl+z3+z2) ~ (Z2+z1+z3) ~ (Z3-~z2+zl) l N ~ ~ Zl ~ (Z3+z2) ~ Z2 ~ (Zl+Z3) ~ Z3 ~ ( 2+ 1) (46) ~ ~ (Z3-z2) ~ (Zl-Z3) ~ (Z2-Z
Now, in order for O O~
M = N x (KabC) = n Zb ~ (47) ZCJ
then it is presupposed that Z2 = Z3 (48) which, after certain intermediate calculations, gives Za = Zl + 2Z2 Zb Zl Z2 (49) Zc Zl Z2 Now, looking at a network according to Figure 5, it can be seen that Zl ZL + ZN (50) Z2 = Z3 = ZN (51) that is, after intermediate calculations Za = ZL + 3ZN
b L (52) Zc = Z.
3~
By measurement, UR, U5 and UT are known, and this provides a possibility of calculating, with the aid of equation (35), the transformed voltage vector U0' as Ua, Ub and Uc, that is, ~ ) (L )~1 ~ (53) With !<nowledge of Ua, Ub and Uc as well as Za~ Zb and Zc~ it is now possible to calculate Ia, Ib and Ic with the aid of IRo, I50 and ITo. When calculating in the respective independent a-, b- and c-systems, the paramters attenuation, transit time and wave impedance will be designated Dja~ ~ a' Za' Djb' ~ b~
Zb and Djc~ ~c and Zc' respectively. Phase quantities at the control point can be obtained again by transformation by K (or L), that is, ~UjR\
Uj = KUj' = l UiS
\ jT~
\ /
It is the phase quantities that are most suitable to study.
Single-phase faults are indicated by using UjR, Uj5 and UjT
individually, which also makes it possible to make phase selec-tions for single-phase tripping. For other types of fault, the respective main voltages are used, that is, UjR ~ UjS, Uj5 ~
~ UjT and UjT - UjR.
Embodiments The protaction device can be built in analog or digital tech-nique. Examples of embodiments in analog technique are shown in Figures 6 and 7.
In an embodiment according to Figure 6, transformation of in-coming phase voltages URST and phase currents IR5T into modal transformed quantities is carried out in the transformation units Ll and Kl with the matrices L and K , respectively.
In this embodiment a calculation is first carried out in the 3~
calculating unit A1 of U'0 = 1/2(U'o + Z I~o) and (55) U~0 = 1/2(U n - Z Io ), respectively, (56) which values are consecutively stored and updated in the shift registers 51 and S2. A shift register is present for each mode and each wave type, that is, both for voltage waves and current waves. In calculating unit A2 a calculation of uj'(t) in accordance with equation (19) takes place. The values of the modal voltages U , Ub and Uc at the selected points, thus obtained, are trans-formed in transformation unit K2, corresponding to the previouslydescribed matrix K, back to phase voltages UR, U5 and UT. These values for each selected point are then supplied to a fault detection logic unit FL for evaluation. From this unit a possible order for tripping via TR and printout of a fault report via FR is given.
Figure 7 is an embodiment showing the same units L1, K1, K2, FL, TR and FR as in Figure 6. In the shift registers 53 and 54 the transformed values of U0 and Io and possibly Io- Z
are conceived to be stored. In the calculating unit A3 the voltages Ua, Ub and Uc at the selected points are now calcula-ted in accordance with equation (18).
Example of embodiment usinq analoq technique Figure 8 illustrates a more detailed block diagram correspond-ing to Figure 7. Transformation of incoming phase voltages URST and phase currents IR5T to modal transformed voltages Ua, Ub and Uc and currents Ia, Ib and Ic takes place in the matrix units Lla, Llb, L1c and in Kla, Klb, K1c, respectively. As will be clear from Figure 8 only summing operational amplifiers are required both for the matrix treatment and other calculations.
The modal voltage values are supplied to a shift register 53a, 53b and S3c, and the modal current values are multiplied by the respective modal impedances, whereafter the voltage values are obtained and then supplied to shift registers 54a, 54b and 3~7 S4c.
If it is assumed that control vo:Ltages at n points along the transmission line are to be calculated, the shift register has to be able to store 2n measured values in each mode, correspond-
5 ing to measurements at times t ~ ~n~ t - ~ 1 ... t - `~, t, t + ~ ... t + ~r'l+l~ t + ~ . The stored values, related to a certain time t, are now used to calculate the control voltages at this time and the calculations take place according to equation (18). Figure 8 shows how the calculation at point n-1 may be performed. The calculation part A3n 1 is thus that part of A3 in Figure 7 which calculates the voltage at point n-1. Corre-sponding ca]culation parts exist for each control point. These parts are supplied with input values in the same way as A3n 1 from the arrows at n, n-2, etc., shown in the Figure.
The calculation part A3n 1 gives measured values corresponding to (Ua)n-l~ (Ub)n-l and (Uc)n 1- The corresponding U b values for the other control points are available in similar manner.
As mentioned previously, however, it is more convenient to deter-mine the parameters of a fault on the basis of the phase quan-tities in question. Converting to phase quantities is effected,as previously described, by inverse transformation of the cal-culated control voltages. In Figure 8 this inverse transfor-mation is described for the control voltages (U ) 1~ (Ub) and (Uc)n 1 with the transformation module K2n 1' corresponding to the previously described matrix according to equation (42).
Also in this case, the transformation can be carried out by using summing amplifiers only. After the transformation, the control voltage at point n-1 is now accessible in the form of respective phase voltages (UR)n_1~ (U5)n-l and (UT)n-l The calculated voltages Ua, Ub and Uc for the other control points are transformed in matrix blocks corresponding to K2n 1 into phase quantities (not shown), which means that the fault detection logic unit FL has access to all the phase voltages at all the control points.
Now, if the control voltages at two consecutive points j and 3~
k, that is, uj(t) and uk(t~, constantly have different signs, the conclusion can be drawn that there is a fault between j and k. It is obvious that it is desired to keep the number of control points as low as possible. Problems with the fault location may then arise in those cases where a fault lies near j and when Uj is near zero. A suitable comparison method is the following Uj ~ ~ Uj Uj_1 ~ ~uk uj ~uk U j ~ Uk+l In order quickly to obtain a fault indication, the value of the voltages u 1~ uO and un is of great value.
If the fault location logic has determined that two consecutive control points j and k are respectively situated on either side of a fault, the value of the control voltages u; and uk can be utilized for determining the position of the fault point.
If the point j lies at the distance dj from the measuring station, and if the distance between the control points is S(k-;), the 2n formula for calculating the distance from the measuring station to the fault point df will be :
~ (k-j) u df dj ~ uj - uk (57) This is an interpolation method, and for greater accuracy other interpolation methods may be needed.
If the source impedance is smaller than the line impedance, the current at the measuring point will be greater in the case of a near-end line fault than in the case of a busbar fault which is behind the measuring point. The result is that the calculated voltage un will be of large magnitude in the case of a near-end fault, whereas in the case of a busbar fault, un can never be greater than the operating voltage.
~2~3~
The voltage u = 1/2 ~Dnzio(t ~ ~n) ~ Dn n~
can be approximated to Un = Z/2 [iU(t ~ ~~n) ~ io(t + ~ ~
Thus, the value of voltage u will be greater if the current change is larger.
In the foregoing, only the methods for the fault location logic have been describedO Devices for carrying out the method can be constructed in many different ways which, however, are trivial and known per se and therefore not described in this specifica-tion.
The distance measuring relay protection device, which has been described above, can be supplemented with a directional wave detector.
The calculation part A3n 1 gives measured values corresponding to (Ua)n-l~ (Ub)n-l and (Uc)n 1- The corresponding U b values for the other control points are available in similar manner.
As mentioned previously, however, it is more convenient to deter-mine the parameters of a fault on the basis of the phase quan-tities in question. Converting to phase quantities is effected,as previously described, by inverse transformation of the cal-culated control voltages. In Figure 8 this inverse transfor-mation is described for the control voltages (U ) 1~ (Ub) and (Uc)n 1 with the transformation module K2n 1' corresponding to the previously described matrix according to equation (42).
Also in this case, the transformation can be carried out by using summing amplifiers only. After the transformation, the control voltage at point n-1 is now accessible in the form of respective phase voltages (UR)n_1~ (U5)n-l and (UT)n-l The calculated voltages Ua, Ub and Uc for the other control points are transformed in matrix blocks corresponding to K2n 1 into phase quantities (not shown), which means that the fault detection logic unit FL has access to all the phase voltages at all the control points.
Now, if the control voltages at two consecutive points j and 3~
k, that is, uj(t) and uk(t~, constantly have different signs, the conclusion can be drawn that there is a fault between j and k. It is obvious that it is desired to keep the number of control points as low as possible. Problems with the fault location may then arise in those cases where a fault lies near j and when Uj is near zero. A suitable comparison method is the following Uj ~ ~ Uj Uj_1 ~ ~uk uj ~uk U j ~ Uk+l In order quickly to obtain a fault indication, the value of the voltages u 1~ uO and un is of great value.
If the fault location logic has determined that two consecutive control points j and k are respectively situated on either side of a fault, the value of the control voltages u; and uk can be utilized for determining the position of the fault point.
If the point j lies at the distance dj from the measuring station, and if the distance between the control points is S(k-;), the 2n formula for calculating the distance from the measuring station to the fault point df will be :
~ (k-j) u df dj ~ uj - uk (57) This is an interpolation method, and for greater accuracy other interpolation methods may be needed.
If the source impedance is smaller than the line impedance, the current at the measuring point will be greater in the case of a near-end line fault than in the case of a busbar fault which is behind the measuring point. The result is that the calculated voltage un will be of large magnitude in the case of a near-end fault, whereas in the case of a busbar fault, un can never be greater than the operating voltage.
~2~3~
The voltage u = 1/2 ~Dnzio(t ~ ~n) ~ Dn n~
can be approximated to Un = Z/2 [iU(t ~ ~~n) ~ io(t + ~ ~
Thus, the value of voltage u will be greater if the current change is larger.
In the foregoing, only the methods for the fault location logic have been describedO Devices for carrying out the method can be constructed in many different ways which, however, are trivial and known per se and therefore not described in this specifica-tion.
The distance measuring relay protection device, which has been described above, can be supplemented with a directional wave detector.
Claims (12)
1. A method for the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line, comprising:
- periodically measuring the voltage and current at an end point of the power transmission line;
- determining the wave impedance and the wave attenuation factor of the power transmission line and the transit time of the travelling wave;
- periodically generating signals representative of the measured voltage and current;
- periodically storing the voltage and current signals;
- establishing a number of control points spaced a like number of distances from said end point of the power transmission line along said power transmission line;
- calculating a control voltage (u1, u2...uj...un) at each of said number of control points along said power transmission line from the following formula:
where:
Dj = said attenuation factor of a wave travelling along said power transmission line;
Tj = the determined transit times of the travelling wave;
u0 = the measured voltage at said end point of said power transmission line;
i0 = the measured current at said end point of said power transmission line; and Z = the determined wave impedance of said power transmission line;
- determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - generating output signals representative of the fault locations to provide an indication thereof.
- periodically measuring the voltage and current at an end point of the power transmission line;
- determining the wave impedance and the wave attenuation factor of the power transmission line and the transit time of the travelling wave;
- periodically generating signals representative of the measured voltage and current;
- periodically storing the voltage and current signals;
- establishing a number of control points spaced a like number of distances from said end point of the power transmission line along said power transmission line;
- calculating a control voltage (u1, u2...uj...un) at each of said number of control points along said power transmission line from the following formula:
where:
Dj = said attenuation factor of a wave travelling along said power transmission line;
Tj = the determined transit times of the travelling wave;
u0 = the measured voltage at said end point of said power transmission line;
i0 = the measured current at said end point of said power transmission line; and Z = the determined wave impedance of said power transmission line;
- determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - generating output signals representative of the fault locations to provide an indication thereof.
2. A method as claimed in claim 1, in which faults are located by monitoring the control voltages at two consecutive control points constantly having different signs, determining faults on the power transmission line as being located between any such two points from the following formula:
df = dj + .delta. (u - j)uj/uj - uk where df is the distance from the end point of said power transmission line; dj is the distance from the end point of said power transmission line to one of said control points having a different sign; (u - j) is the distance between the control points having different signs; and uj and uk are the control voltages having respective different signs.
df = dj + .delta. (u - j)uj/uj - uk where df is the distance from the end point of said power transmission line; dj is the distance from the end point of said power transmission line to one of said control points having a different sign; (u - j) is the distance between the control points having different signs; and uj and uk are the control voltages having respective different signs.
3. A method according to claim 2, in which for an at least three-phase system, the measured current and voltage values are transformed to independent modal values, the independent modal values are stored and the control voltages are calculated using the stored independent modal values.
4. A method according to claim 3, in which the modally calculated voltages are transformed by inverse transformation to respective phase voltages.
5. A method according to claim 1, in which in calculating the control voltages use is made of current and voltage values measured at the times t + ?k and t - ?k, where ?k is the transit time of a wave on the transmission line from the measuring point to the control point k, with k assuming values from 0 to n.
6. A method according to claim 2, in which in calculating the control voltages use is made of current and voltage values measured att the time t + ?k and t - ?k, where ?k is the transit time of a wave on the transmission line from the measuring point to the control point k, with k assuming values from 0 to n.
7. A method according to claim 1, in which for an at least three-phase system, the measured current and voltage values are transformed to independent modal values, the independent modal values are stored, and the control voltages are calculated using the stored independent modal values.
8. A method according to claim 7, in which the modally calculated voltages are transformed by inverse transformation to respective phase voltages.
9. A device for the detection and location of faults on a power transmission line in at least one phase distribution system based on a travelling wave model of the power transmission line from measured voltage and measured current at an end point of the power transmission line, the predetermined wave impedance of the power transmission line, the predetermined wave attenuation factor and transit time based on said travelling wave model of the power transmis-sion line, comprising:
- means for periodically generating signals represent-ative of the measured voltage and current;
- means for periodically storing the voltage and current signals;
- means for calculating a control (u1, u2...uj...un) at each of a number of predetermined control points spaced a like number of distances from said end point of the power transmission line along said power transmission line from the following formula:
uj(t) = Dj/2 {uO(t - Tj) +ZiO(t - Tj)}
+ 1/2 Dj {uO(t - Tj) - ZiO(t + Tj)}
where:
Dj = said predetermined attenuation factor of a wave travelling along said power transmission line;
Tj = said predetermined transit time of the travelling wave;
uO = the measured voltage at said end point of said power transmission line;
iO = the measured current at said end of said power transmission line:
Z - said predetermined wave impedance of said power transmission line; and - means for determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - means for generating output signals representative of the fault locations to provide an indication thereof.
- means for periodically generating signals represent-ative of the measured voltage and current;
- means for periodically storing the voltage and current signals;
- means for calculating a control (u1, u2...uj...un) at each of a number of predetermined control points spaced a like number of distances from said end point of the power transmission line along said power transmission line from the following formula:
uj(t) = Dj/2 {uO(t - Tj) +ZiO(t - Tj)}
+ 1/2 Dj {uO(t - Tj) - ZiO(t + Tj)}
where:
Dj = said predetermined attenuation factor of a wave travelling along said power transmission line;
Tj = said predetermined transit time of the travelling wave;
uO = the measured voltage at said end point of said power transmission line;
iO = the measured current at said end of said power transmission line:
Z - said predetermined wave impedance of said power transmission line; and - means for determining faults as those locations on said power transmission line where the associated calculated control voltage is constantly zero; and - means for generating output signals representative of the fault locations to provide an indication thereof.
10. A device according to claim 9, wherein said means for receiving the measured voltage and current information are means for transforming the voltage and current information to modal quantities and said means for storing are shift registers for storing said modal quantities for both current and voltage, and further comprising means for transforming said calculated control voltages to phase voltages, and fault detection logic circuitry responsive to said phase voltages for determining whether a fault exists and for determining the distance to a fault from the point at which said voltages and currents are measured.
11. A device according to claim 10, in which the fault detection logic unit is constructed as an analog unit.
12. A device according to claim 10, in which the fault detection logic unit is constructed as a digital unit.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| SE8403226A SE442920B (en) | 1984-06-15 | 1984-06-15 | METHOD AND DEVICE FOR DETECTION AND LOCATION OF A FAILURE ON A POWER CORD |
| SE8403226-7 | 1984-06-15 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1249337A true CA1249337A (en) | 1989-01-24 |
Family
ID=20356252
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000484063A Expired CA1249337A (en) | 1984-06-15 | 1985-06-14 | Line protection |
Country Status (6)
| Country | Link |
|---|---|
| US (1) | US4719580A (en) |
| EP (1) | EP0164711B1 (en) |
| JP (1) | JPS6111673A (en) |
| CA (1) | CA1249337A (en) |
| DE (1) | DE3584856D1 (en) |
| SE (1) | SE442920B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113655339A (en) * | 2021-08-20 | 2021-11-16 | 许继集团有限公司 | Fault positioning method and device for direct-current transmission line protection system |
Families Citing this family (56)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SE451102B (en) * | 1985-12-20 | 1987-08-31 | Asea Ab | PROCEDURE FOR DETECTING HOGRESISTIVE EARTH ERROR ON A POWER PIPE LOCATED BETWEEN TWO STATIONS AND THE DEVICE FOR IMPLEMENTATION OF THE PRESENT PROCEDURE |
| SE449796B (en) * | 1985-12-20 | 1987-05-18 | Asea Ab | PROCEDURE AND DEVICE FOR LOCATION OF ERRORS ON A POWER CORD |
| SE452533B (en) * | 1986-04-08 | 1987-11-30 | Asea Ab | PROCEDURE FOR DIRECTIONAL DETECTION OF ERRORS ON A POWER CONTROL AND DEVICE FOR IMPLEMENTATION OF THE ABOVE PROCEDURE |
| SE459059B (en) * | 1987-09-16 | 1989-05-29 | Asea Ab | PROTECT FOR HIGH-RESISTANT EARTH ERRORS |
| SE459706B (en) * | 1987-11-12 | 1989-07-24 | Asea Ab | LAENGSDIFFERENTIALSKYDD |
| SE466366B (en) * | 1990-06-29 | 1992-02-03 | Asea Brown Boveri | PROCEDURE AND DEVICE MAKES COMMON LOCATION IN THE MULTI-TERMINAL |
| US5206595A (en) * | 1991-09-10 | 1993-04-27 | Electric Power Research Institute | Advanced cable fault location |
| US5506789A (en) * | 1993-10-15 | 1996-04-09 | The Texas A & M University System | Load extraction fault detection system |
| US5659453A (en) * | 1993-10-15 | 1997-08-19 | Texas A&M University | Arc burst pattern analysis fault detection system |
| US5550751A (en) * | 1993-10-15 | 1996-08-27 | The Texas A & M University System | Expert system for detecting high impedance faults |
| US5485093A (en) * | 1993-10-15 | 1996-01-16 | The Texas A & M University System | Randomness fault detection system |
| US5600526A (en) * | 1993-10-15 | 1997-02-04 | The Texas A & M University System | Load analysis system for fault detection |
| US5578931A (en) * | 1993-10-15 | 1996-11-26 | The Texas A & M University System | ARC spectral analysis system |
| US5512832A (en) * | 1993-10-15 | 1996-04-30 | The Texas A & M University System | Energy analysis fault detection system |
| US5729144A (en) * | 1996-12-02 | 1998-03-17 | Cummins; Kenneth L. | Systems and methods for determining location of a fault on an electric utility power distribution system |
| US5773980A (en) * | 1997-01-30 | 1998-06-30 | Abb Power T&D Company, Inc. | One-terminal fault location system that corrects for fault resistance effects |
| GB2345810B (en) * | 1999-01-13 | 2003-07-23 | Alstom Uk Ltd | Fault-detection apparatus |
| US6476613B2 (en) * | 2000-12-20 | 2002-11-05 | Abb Ab | Method of fault location in parallel transmission lines with series compensation |
| US6988042B2 (en) * | 2003-11-25 | 2006-01-17 | Myongji University | Method for detecting line-to-line fault location in power network |
| US7299143B2 (en) * | 2005-05-13 | 2007-11-20 | Abb Technology Ag | Method and apparatus for improving operational reliability during a loss of a phase voltage |
| US8089372B2 (en) * | 2005-06-02 | 2012-01-03 | Siemens Aktiengesellschaft | Method for transmission of data for controlling an HVDC transmission installation |
| US7286963B2 (en) * | 2005-12-30 | 2007-10-23 | Abb Technology Ltd. | Method and device for fault location on three terminal power line |
| US8315827B2 (en) * | 2009-02-26 | 2012-11-20 | Southern California Edison | Fault region location system |
| BRPI0901107A2 (en) * | 2009-03-05 | 2010-01-19 | Reason Tecnologia S A | Method and mechanism for identification, registration and storage of traveling wavefronts in electrical energy systems |
| MX2014003271A (en) | 2011-10-12 | 2014-04-10 | Schweitzer Engineering Lab Inc | Fault location using traveling waves. |
| CN103891077A (en) * | 2011-11-01 | 2014-06-25 | Abb技术有限公司 | Travelling-wave based fault protection of high-voltage transmission lines |
| CN102946090B (en) * | 2012-10-29 | 2015-06-03 | 中国电力科学研究院 | Power transmission line protection realizing method based on multi-dimensional information |
| CN102967803B (en) * | 2012-12-13 | 2015-05-06 | 山东理工大学 | Fault positioning method of power distribution network based on D type traveling wave principle |
| US9588168B2 (en) | 2013-09-16 | 2017-03-07 | Schweitzer Engineering Laboratories, Inc. | Fault location using traveling waves |
| US8990036B1 (en) | 2013-09-16 | 2015-03-24 | Schweitzer Engineering Laboratories, Inc. | Power line parameter adjustment and fault location using traveling waves |
| CN105021950B (en) * | 2014-04-18 | 2019-01-08 | 国家电网公司 | Feeder line fault localization method, apparatus and system |
| US9594112B2 (en) | 2014-09-16 | 2017-03-14 | Schweitzer Engineering Laboratories, Inc. | Fault detection in electric power delivery systems using underreach, directional, and traveling wave elements |
| US9509399B2 (en) | 2015-02-13 | 2016-11-29 | Schweitzer Engineering Laboratories, Inc. | Transmission line protection using traveling waves in optical ground wire fiber |
| EP3093674B1 (en) * | 2015-05-14 | 2021-10-20 | General Electric Technology GmbH | Improvements in or relating to direct current distance protection schemes |
| US10090664B2 (en) | 2015-09-18 | 2018-10-02 | Schweitzer Engineering Laboratories, Inc. | Time-domain directional line protection of electric power delivery systems |
| WO2017049224A1 (en) | 2015-09-18 | 2017-03-23 | Schweitzer Engineering Laboratories, Inc. | Time-domain line protection of electric power delivery systems |
| WO2017066205A1 (en) | 2015-10-12 | 2017-04-20 | Schweitzer Engineering Laboratories, Inc. | Traveling wave directional element |
| US10564247B2 (en) | 2015-10-13 | 2020-02-18 | Schweitzer Engineering Laboratories, Inc. | Testing system for traveling wave fault detectors |
| EP3363087A4 (en) | 2015-10-13 | 2019-06-26 | Schweitzer Engineering Laboratories, Inc. | Testing system for traveling wave fault detectors |
| US10180451B2 (en) | 2015-10-13 | 2019-01-15 | Schweitzer Engineering Laboratories, Inc. | Electric power system monitoring using high-frequency signals |
| EP3362807A4 (en) | 2015-10-14 | 2019-06-26 | Schweitzer Engineering Laboratories, Inc. | High-frequency electric power system signal processing system |
| CN105244861B (en) * | 2015-10-23 | 2018-04-10 | 清华大学 | The guard method of transmission line of electricity and the protection device of transmission line of electricity |
| EP3469385A1 (en) | 2016-06-13 | 2019-04-17 | Schweitzer Engineering Laboratories, Inc. | Overcurrent element in time domain |
| EP3469674A1 (en) | 2016-06-14 | 2019-04-17 | Schweitzer Engineering Laboratories, Inc. | Phase selection for traveling wave fault detection systems |
| US10236675B2 (en) | 2016-07-26 | 2019-03-19 | Schweitzer Engineering Laboratories, Inc. | Fault detection and protection during steady state using traveling waves |
| US10295585B2 (en) | 2016-11-11 | 2019-05-21 | Schweitzer Engineering Laboratories, Inc. | Traveling wave based single end fault location |
| US10585133B2 (en) | 2016-11-11 | 2020-03-10 | Schweitzer Engineering Laboratories, Inc. | Electric power fault protection device using single-ended traveling wave fault location estimation |
| US11280834B2 (en) | 2018-08-30 | 2022-03-22 | Schweitzer Engineering Laboratories, Inc. | Detection of low-energy events in an electric power system |
| US10677834B2 (en) | 2018-09-14 | 2020-06-09 | Schweitzer Engineering Laboratories, Inc. | Distance protection of electric power delivery systems using time domain and frequency domain |
| US10641815B2 (en) | 2018-09-27 | 2020-05-05 | Schweitzer Engineering Laboratories, Inc. | Secure distance protection of electric power delivery systems under transient conditions |
| CN109470987B (en) * | 2018-09-30 | 2021-04-09 | 昆明理工大学 | T-connection power transmission line single-ended traveling wave distance measurement method based on section matching algorithm |
| US11067617B2 (en) | 2018-10-08 | 2021-07-20 | Schweitzer Engineering Laboratories, Inc. | Single-end traveling wave fault location using line-mounted device |
| CN109212384B (en) * | 2018-10-31 | 2019-07-19 | 海南电网有限责任公司电力科学研究院 | A kind of power transmission line fault locating method based on traveling wave amplitude attenuation theory |
| CN110888014B (en) * | 2019-10-15 | 2022-04-19 | 国电南瑞科技股份有限公司 | Line protection traveling wave distance measurement method and device |
| EP3968034A1 (en) | 2020-09-15 | 2022-03-16 | Hitachi Energy Switzerland AG | Method and device for estimating source impedances across one or more transmission lines |
| CN112782528B (en) * | 2020-12-31 | 2023-07-18 | 西安理工大学 | Power distribution network fault section positioning method by utilizing PMU |
Family Cites Families (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE1219585B (en) * | 1961-12-20 | 1966-06-23 | Siemens Ag | Arrangement for determining faults or inhomogeneities in electrical lines |
| DE2004848A1 (en) * | 1970-02-03 | 1971-08-19 | Siemens Ag | Circuit arrangement for determining errors or inhomogeneity points on electrical lines or cables |
| SE368092B (en) * | 1972-11-06 | 1974-06-17 | Asea Ab | |
| CH565468A5 (en) * | 1973-01-31 | 1975-08-15 | Bbc Brown Boveri & Cie | |
| CH610154A5 (en) * | 1975-04-28 | 1979-03-30 | Bbc Brown Boveri & Cie | |
| CH609181A5 (en) * | 1975-06-12 | 1979-02-15 | Bbc Brown Boveri & Cie | |
| FR2334116A2 (en) * | 1975-12-03 | 1977-07-01 | Metraplan Spa | METHOD AND DEVICE FOR LOCATING FAULTS IN SAFETY LINES FOR SKI LIFTS |
| JPS5829471B2 (en) * | 1978-10-30 | 1983-06-22 | 東京電力株式会社 | Accident point determination method |
| JPS5830554B2 (en) * | 1978-11-13 | 1983-06-29 | 東京電力株式会社 | Fault point location method for power line fault detection and power line protection |
| FR2494853A1 (en) * | 1980-11-25 | 1982-05-28 | Enertec | METHOD FOR DETERMINING THE DIRECTION OF THE ORIGIN OF A DISTURBANCE AFFECTING AN ELEMENT OF AN ELECTRIC POWER TRANSMISSION NETWORK |
| IN157698B (en) * | 1981-04-03 | 1986-05-17 | Gen Electric | |
| DE3115200A1 (en) * | 1981-04-15 | 1983-02-03 | Philips Kommunikations Industrie AG, 8500 Nürnberg | METHOD FOR MEASURING PULSE RUNNING TIMES, ERROR LOCATIONS AND DAMPING ON CABLES AND FOCUS |
| SE433405B (en) * | 1982-09-14 | 1984-05-21 | Asea Ab | PROCEDURE AND DEVICE FOR LOCATING A FAILURE ON A THREE-PHASE POWER CORD |
| DE3235239A1 (en) * | 1982-09-23 | 1984-03-29 | Siemens AG, 1000 Berlin und 8000 München | Method for locating faults on a line |
| US4471294A (en) * | 1982-10-29 | 1984-09-11 | The United States Of America As Represented By The Secretary Of The Army | Electrical conduit defect location |
-
1984
- 1984-06-15 SE SE8403226A patent/SE442920B/en not_active IP Right Cessation
-
1985
- 1985-06-08 DE DE8585107101T patent/DE3584856D1/en not_active Expired - Fee Related
- 1985-06-08 EP EP85107101A patent/EP0164711B1/en not_active Expired - Lifetime
- 1985-06-12 US US06/743,930 patent/US4719580A/en not_active Expired - Lifetime
- 1985-06-14 JP JP60128440A patent/JPS6111673A/en active Pending
- 1985-06-14 CA CA000484063A patent/CA1249337A/en not_active Expired
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113655339A (en) * | 2021-08-20 | 2021-11-16 | 许继集团有限公司 | Fault positioning method and device for direct-current transmission line protection system |
Also Published As
| Publication number | Publication date |
|---|---|
| SE8403226D0 (en) | 1984-06-15 |
| SE8403226L (en) | 1985-12-16 |
| DE3584856D1 (en) | 1992-01-23 |
| EP0164711B1 (en) | 1991-12-11 |
| SE442920B (en) | 1986-02-03 |
| JPS6111673A (en) | 1986-01-20 |
| US4719580A (en) | 1988-01-12 |
| EP0164711A3 (en) | 1987-04-08 |
| EP0164711A2 (en) | 1985-12-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA1249337A (en) | Line protection | |
| Das et al. | A fault locator for radial subtransmission and distribution lines | |
| EP0244649B1 (en) | Method and device for protecting a power tramsmission line | |
| US4731689A (en) | Directional detection in connection with faults in a power supply network | |
| US6934654B2 (en) | System and method for exact compensation of fundamental phasors | |
| Saha et al. | A new accurate fault locating algorithm for series compensated lines | |
| US4148087A (en) | Distance relay for electric power transmission lines | |
| US6397156B1 (en) | Impedance measurement system for power system transmission lines | |
| Girgis et al. | Fault location techniques for radial and loop transmission systems using digital fault recorded data | |
| Breingan et al. | The laboratory investigation of a digital system for the protection of transmission lines | |
| Schweitzer III | Evaluation and development of transmission line fault-locating techniques which use sinusoidal steady-state information | |
| WO2007032697A1 (en) | A method for fault location in electric power lines | |
| US20030098683A1 (en) | Apparatus and method for the measurement and monitoring of electrical power generation and transmission | |
| GB2036478A (en) | Method for locating a fault point on a transmission line | |
| Yalla | A digital multifunction protective relay | |
| US4261038A (en) | Protection of electrical power supply systems | |
| McLaren et al. | Enhanced double circuit line protection | |
| US4333151A (en) | Method for protecting an electric power system and digital protective system | |
| US4641088A (en) | Root mean square measuring device for negative sequence current | |
| CA2170536C (en) | Method and device for measuring and recreating the load current in a power network in connection with the occurrence of faults | |
| US5399974A (en) | Fault current filter | |
| Kawady et al. | Investigation of practical problems for digital fault location algorithms based on EMTP simulation | |
| US5796630A (en) | Protective relay system provided with difference and addition filters | |
| KR100425417B1 (en) | Method for detecting line to line fault location for power systems | |
| Phadke et al. | A Microcomputer Based Ultra-High-Speed Dostance Relay: Field Tests |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| MKEX | Expiry |