WO2025045350A1

WO2025045350A1 - Distance relay, method and device for determining a fault distance in a power transmission line

Info

Publication number: WO2025045350A1
Application number: PCT/EP2023/073593
Authority: WO
Inventors: Manuel GALLER; Lothar Fickert
Original assignee: Technische Universität Graz
Priority date: 2023-08-29
Filing date: 2023-08-29
Publication date: 2025-03-06

Abstract

A method and a measuring device for determining a fault distance (l_fault) in an electric power transmission line (2) from the measuring device (21) connected at a first location (X), and a distance relay (13) for distance protection, wherein the method comprises: - provide (24) a characteristic resistance (R') and inductance (L') of the power transmission line (2) having a line fault at a second location (Y); - measuring (29) a line voltage (u) and a line current (i) at each of a sequence of sampling times (t_k); - calculating (30), for each sampling time (t_k), a replica voltage (u_replica) from the line current (i), the characteristic resistance and inductance (R', L'), and a length (l) from said first to said second location (X, Y); and - determining (33) the fault distance (l_fault) from said length (l) and a ratio between the line voltages (u) and the replica voltages (u_replica).

Description

Distance Relay, Method and Device for Determining a Fault Distance in a Power Transmission Line

The present invention relates to a method for determining a fault distance of a line fault in an electric power transmis- sion line , in particular a power transmission line in an elec- tric power grid to which one or more power electronic genera- tion systems are connected, from a measuring device connected to the power transmission line at a f irst location . The inven- tion further relates to the measuring device performing steps of the method and a distance relay for distance protection of the electric power transmission line , which comprises the meas- uring device .

The individual power transmission lines in current elec- tric power grids are usually protected using - mostly several - dif ferent protection methods and devices . Examples for such methods and devices include overcurrent protection, dif feren- tial protection and distance protection . Neither overcurrent protection, in which the line current is measured and a circuit breaker is tripped when the measured current exceeds a current limit , nor dif ferential protection, in which the currents at both ends of a power transmission line are measured and a cir- cuit breaker is tripped in case of a dif ference between the two , determine the location of a fault in the power transmis- sion line , i . e . its distance from the protection device . In distance protection, the voltage and the current in the power transmission line are measured continuously and the respective complex-valued voltage phasors and current phasors and the im- pedance of the power transmission line are determined therefrom and from their fundamental frequency. From a comparison of the determined impedance and a predetermined, e.g. measured, stand- ard reference impedance of the power transmission line, the distance - and mostly also the direction - of a line fault is determined. Upon fault detection, the distance relay is config- ured to trip a usually integrated circuit breaker at different times depending on the determined fault distance, i.e. the dis- tance of the detected fault from the distance relay: The fur- ther the line fault is away, the later the distance relay trips, typically in the range between a few microseconds and a few seconds after fault detection. Hence, distance relays clos- er to the line fault trips earlier such that those further away will no longer have to trip and merely a smaller portion of the protected power grid, i.e. only one or a few power transmission lines, is/are selectively taken from the grid.

Different methods of this kind for determining the fault distance are known, e.g., from US 5325061 B, WO 2008/046451 Al, DE 102020 129 189 Al or CN 108110741 B.

However, the calculation of the phasors require substan- tial computing power and, particularly, an accurate determina- tion of the fundamental frequency and its phasing. In M. Galler et al. "Evaluation and Test of Distance Protection in Cellular Energy Systems by Power Hardware in the Loop Method", PESS + PELSS 2022, Power and Energy Student Summit, Kassel, Germany, 2022, pp . 1-6, it has been shown that the determination of the phasing of the fundamental frequency becomes increasingly dif- ficult in modern electric power grids because of the increasing number of power electronic generation systems, such as power electronic converters in solar or wind energy plants etc., that are connected to the power grid and provide only a low short circuit current and often produce a non-sinusoidal or even pul- sating voltage waveform in case of a line fault. When the de- termination of the phasing is inaccurate, the phasors and the impedance determination are substantially impaired such that the determination of the fault location becomes highly inaccu- rate or even impossible.

It is an object of the present invention to provide a method, a measuring device and a distance relay which facili- tate an efficient and accurate fault distance determination and a reliable distance protection in a power transmission line even if one or more power electronic generation systems are connected to the electric power grid.

In a first aspect of the invention, this object is achieved with a method as specified at the outset which com- prises: in a first phase: providing, to a processor of the measuring de- vice, a characteristic resistance and a characteristic in- ductance of the power transmission line having a line fault at a predetermined second location in the power transmission line; receiving the provided characteristic resistance and inductance in the processor; in a second phase: measuring, with the measuring device, a line voltage and a line current at each of a sequence of sam- pling times; calculating, in the processor for each sampling time of the sequence, a replica voltage from the line cur- rent measured at that sampling time, the received charac- teristic resistance and inductance, and a length of the power transmission line from said first to said second lo- cation; and in a third phase: determining, in the processor, the fault dis- tance from said length of the power transmission line and a ratio between the measured line voltages and the calcu- lated replica voltages.

By using the instantaneous values of the measured line voltage and line current according to this method the require- ment for calculating complex-valued phasors and the resulting inaccuracies in the determination of the fault distance in electric grids with power electronic generation systems can be avoided. Thus, the present method is computationally efficient and the determination of the fault distance, which identifies the length of the transmission line from the measuring device to the line fault, is accurate in any power grid, in particular in a power grid to which one or more power electronic genera- tion systems are connected, and even in individual energy cells that are not further connected to a larger power grid. More- over, the fault distance of different types of line faults, e.g. phase-to-phase or phase-to-ground faults, can be deter- mined reliably by providing respective characteristic re- sistances and inductances each for a corresponding line fault at the second location. It shall be noted that the occurrence of the line fault as such is usually detected by other means. The terms "characteristic resistance" and "characteristic in- ductance" denominate resistance and inductance values per length of the power transmission line, i.e. its resistance and inductance per metre, kilometre or the like.

In a preferred embodiment, said determining in the third phase is implemented by with:

Ifauit being the fault distance;

1 being the length of the power transmission line from said first to said second location; u(t) being the measured line voltage at the sampling time t ;

Urepiica(t)being the calculated replica voltage at the sampling time t; ti, t_z being the first and last sampling times t of the se- quence .

Using this integration, the fault distance can be deter- mined particularly efficiently and accurately.

In a favourable variant thereof, the first sampling time is chosen to be close to the occurrence of the line fault. Thereby, an accurate fault distance can be achieved faster and/or the determined value of the fault distance, when calcu- lated repeatedly, converges faster.

It is particularly advantageous when said second location is at the far end of the power transmission line when seen from the first location. This further increases the accuracy of the determination of the fault location.

In a beneficial embodiment, the first phase of the method is executed merely once. The characteristic resistance and in- ductance is usually known for a power transmission line that shall be protected. Alternatively, it can be measured or other- wise determined, e.g. by simulation or by experience using structural and environmental parameters of the power transmis- sion line, either in the measuring device or independently thereof, even before connecting the measuring device to the power transmission line.

Moreover, it is advantageous, when said determining in the third phase of the method is executed repeatedly in a manner interlaced with the second phase. Thereby, the calculation and determination steps can be concluded whenever a convergence of the determined fault distance to a fixed value is recognised. In a second aspect, the present invention provides for a measuring device for determining a fault distance of a line fault in an electric power transmission line, in particular a power transmission line in an electric power grid to which one or more power electronic generation systems are connected, wherein the measuring device is connectable to the power trans- mission line at a first location, comprises a processor and is configured to receive, in the processor, a characteristic re- sistance and a characteristic inductance of the power transmis- sion line having a line fault at a predetermined second loca- tion; measure a line voltage and a line current at each of a sequence of sampling times; calculate, in the processor for each sampling time of the sequence, a replica voltage from the line current measured at that sampling time, the received characteristic resistance and inductance, and a length of the power transmission line from said first to said second location; and determine, in the processor, the fault distance from said length of the power transmission line and a ratio between the measured line voltages and the calculated replica voltages.

With respect to advantages, embodiments and variants of the measuring device it is referred to the above explanations on the method.

In a third aspect, the present invention provides for a distance relay for distance protection of an electric power transmission line, in particular a power transmission line in an electric power grid to which one or more power electronic generation systems are connected, wherein the distance relay comprises a circuit breaker and the measuring device of the abovementioned type and is configured to trip the circuit breaker when a fault distance of a line fault is determined to fall below a predetermined threshold value for a predetermined time.

The invention shall now be described by means of an exem- plary embodiment thereof with reference to the enclosed draw- ings, in which:

Figs, la and lb show an electric power grid with an elec- tric power transmission line to which a measuring device and a distance relay according to the invention are connected (Fig. la) and the power transmission line in greater detail (Fig. lb), each in a schematic circuit diagram;

Fig. 2 shows a method for determining a fault distance ac- cording to the invention in a flow chart; and

Figs. 3a, 3b and 3c show line voltages (Fig. 3a) and line currents (Fig. 3b) measured with the measuring device of Fig. lb and a result of the method of Fig. 2 (Fig. 3c), each in a diagram over time.

Figs, la and lb exemplify an electric power grid 1 and an electric power transmission line 2 therein. The power grid 1 comprises, inter alia, a first busbar 3 to which a power elec- tronic generation system 4, e.g. a power electronic converter of a solar or wind energy plant, is connected via a transformer 5. The electric power grid 1 may, e.g., be single phase or (in this example) 3-phase. Likewise, the first busbar 3, the power electronic generation system 4, the transformer 5 and the elec- tric power transmission line 2 are single phase or 3-phase. Moreover, the electric power grid 1 may be of low-voltage type or (here) of medium- or high-voltage type, e.g., 3 kv, 6 kv, 10 kV, 15 kV, 20 kV, 30 kV, 110 kV, 220 kV, 380 kV, etc. and may have a different layout than in the present example.

The electric power grid 1 of the present example further comprises, at the far end of the power transmission line 2, a second busbar 6, to which a (here: large) electric supply power grid 7 is optionally connected. Both the first busbar 3 and the second busbar 6 are connected to a third busbar 8 via further electric power transmission lines 9 and 10. A further power electronic generation system 11 is connected to the third bus- bar 8 via a further transformer 12. At each end of each of the electric power transmission lines 2, 9, 10, e.g. close to or at each busbar 3, 6, 8, a respective protection device (here: a distance relay) 13, 14, 15, 16, 17, 18 may be (or in this exam- ple: is) connected. Moreover, there is a line fault 19, e.g. a ground fault or (in the present example) a 3-phase fault, in the power transmission line 2.

As shown in the example of Fig. lb, the distance relay 13 comprises a circuit breaker 20 and a measuring device 21. As symbolised by dashed lines, the distance relay 14 at the other end of the electric power transmission line 2 is optional. The line fault 19 in the power transmission line 2 occurred at a distance from the measuring device 21 (here likewise: from the distance relay 13), hereinafter referred to as the fault dis- tance Ifauit, which is smaller than the total length of the pow- er transmission line 2. The total length of the power transmis- sion line 2 is typically in the range of several kilometres or several tens of kilometres. In comparison therewith, a possible distance s between the distance relay 13 and the first busbar 3 is negligible in the present case.

Fig. 2 shows a method 22 for determining the fault dis- tance Ifauit of the line fault 19 in the electric power trans- mission line 2. To this end, the measuring device 21 is con- nected to the power transmission line 2 at a first location X. The method 22 comprises, in a first phase 23, step 24 of providing a characteristic resistance R' and a characteristic inductance L' of the power transmission line 2 having (e.g.: assuming) a line fault at a predetermined second location Y in the power transmission line 2. The terms "characteristic re- sistance" R' and "characteristic inductance" L' denominate such resistances and inductances that are related to length of the power transmission line, i.e. its resistance and inductance per metre, kilometre or the like. In said step 24, the characteris- tic resistance R' and inductance L' are provided to a processor 25 of the measuring device 21. Usually, the characteristic re- sistance R' and inductance L' is known for a power transmission line 2 to be protected. Alternatively, they may either be meas- ured with the assumed line fault applied or rather estimated on the basis of the structure and other parameters of the power transmission line 2 and its environment in consideration of the assumed line fault.

In the example of Fig. lb, the second location Y is at the far end of the power transmission line 2 when seen from the first location X, i.e. from the distance relay 13. In other cases, the second location Y may be chosen to be located else- where in the power transmission line 2. Moreover, the assumed line fault can be of any type, e.g. a ground fault or a 3-phase fault etc. Generally, the characteristic resistance R' and in- ductance L' are provided for each type of line fault separately for later comparison.

In the first phase 23, the method 22 further comprises step 26 of receiving the determined characteristic resistance R' and inductance L' in the processor 25 (Fig. lb) of the meas- uring device 21.

The first phase 23 may be performed by the measuring de- vice 21, by a different component of the distance relay 13 or by a separate device (not shown). Moreover, it may be executed periodically, repeatedly or merely once. At least for the first time, however, the first phase 23 of the method 22 is performed prior to a second and a third phase 27, 28 of the method 22 which shall now be described.

As illustrated in Figs. 3a and 3b, the second phase 27 of the method 22 is performed for a sequence of sampling times ti, t₂, ..., t_z, generally tk- In the second phase 27, the method 22 comprises measuring 29, with the measuring device 21, a line voltage u and a line current i, i.e. the instantaneous values of the line voltage u(tk) and the line current i(tk) at each sampling time tk of the sequence. The illustrations of Figs. 3a and 3b show 3-phase line voltages Ui, u₂, u₃ and line currents ii, i2, is, respectively. Depending on the number of phases of the power transmission line 2 the present method 22 is option- ally performed for each phase separately.

In the second phase 27, the method 22 further comprises calculating 30, in the processor 25 for each sampling time tk of the sequence, a replica voltage u_repii_ca(tk) - of. equation (4) further down - from the line current i(tk) measured at that sampling time tk, the received characteristic resistance R' and inductance L' and the length 1 of the power transmission line 2 from said first to said second location X, Y which, in the pre- sent example, conforms to the total length of the power trans- mission line 2. It is understood, that the sampling time tk may be either periodical or merely repeating, such that the second phase 27 of the method 22 is likewise performed periodically or repeatedly as symbolised by a loop 31 in Fig. 2.

The third phase 28 of the method 22 is performed only once or repeatedly, in particular periodically, e.g. in a manner in- terlaced with the second phase 27, as symbolised by the arrow 32 in Fig. 2. In the third phase 28, the method 22 comprises step 33 of determining, in the processor 25, the fault distance Ifauit from said length 1 of the power transmission line 2 and a ratio between the measured line voltages u and the calculated replica voltages u_repii_ca . In the example of Fig. 3c, an exemplary result of step 33 is illustrated. Therein, the fault distance Ifauit is determined in an interlaced manner for every sampling time tk and gradual- ly converges towards a constant final value (here: the correct value If*).

The method 22 encompasses different ways of performing the determination of the fault distance Ifauit in step 33. In a time-discrete approach as exemplified above, the determination step 33 may, e.g., be performed according to:

with: k indicating the k^th sampling time tk of the sequence; u(tk) being the measured line voltage u at the k^th sampling time t_k;

Urepiica(tk)being the calculated replica voltage u_repii_ca at the k^th sampling time tk,- and

At being the time difference between consecutive sam- pling times t_k of the sequence.

It is understood, that when the sampling times tk are not periodical, the time difference At, typically in the range of milliseconds or fractions thereof, e.g. 1/10 or 1/100 of a mil- lisecond, is not constant. Otherwise equation (1) one can be simplified to:

When in this embodiment a continuous-time approach is tak- en, on the other hand, the processor 25 may be configured to determine the fault distance lf_auit by

with: u(t) being the measured line voltage sampled at the (here: continuous) sampling time t;

Urepiica(t)being the calculated replica voltage at the (here: same continuous) sampling time t; ti, t_z being the first and last sampling times t, i.e. the beginning and the end, of the sequence.

Therein, the first sampling time ti may be chosen to be close to or coinciding with the occurrence of the line fault 19, as illustrated in Figs. 3a and 3b, in that the abovemen- tioned sequence of sampling times only starts at this sampling time, even if the measuring device 21 measures the line voltage u and line current I in an ongoing manner. In this case, step 30 of calculating the replica voltage u_repii_ca is performed for the first time at this first sampling time ti. Similarly, the last sampling time t_z of the sequence may be chosen. To this end, the processor 25 may optionally check whether or not the fault distance Ifauit determined in step 33 converges suffi- ciently towards a constant final value If*, and if so, choose the respective sampling time as the last sampling time t_z of the sequence to be included in the determination step 33.

It shall now be explicated how equation (3) can be de- duced. In the continuous-time approach, the replica voltage Urepiica is calculated according to equation (4)

with:

R', L' being the characteristic resistance R' and inductance L' of the power transmission line 2.

Accordingly, it can be assumed that the measured line voltage u in case of a line fault 19 is equation (5)

Introducing the difference between the two, equation (6)

and a fictitious power equivalent p(t)

equation (7) and deriving therefrom a fictitious energy equivalent E

equation (9)

leads to a solution for the fault distance Ifauit according to equation (10)

which is the same as equation (3).

Returning to Fig. lb, the distance relay 13, which com- prises the circuit breaker 20 and the measuring device 21, is configured to trip the circuit breaker 20 when the fault dis- tance Ifauit of the line fault 19 is determined to fall below a predetermined threshold value for a predetermined time. Differ- ent threshold values may be predetermined for different times as known in the art for common distance relays.

The invention is not restricted to the specific embodi- ments described in detail herein, but encompasses all variants, modifications and combinations thereof that fall within the scope of the appended claims.

Claims

Claims :

1. A method for determining a fault distance (Ifauit) of a line fault (19) in an electric power transmission line (2), in particular a power transmission line (2) in an electric pow- er grid (1) to which one or more power electronic generation systems (4, 11) are connected, from a measuring device (21) connected to the power transmission line (2) at a first loca- tion (X), comprising: in a first phase (23): providing (24), to a processor (25) of the meas- uring device (21), a characteristic resistance (R¹) and a characteristic inductance (L¹) of the power transmission line (2) having a line fault at a predetermined second lo- cation (Y) in the power transmission line (2); receiving (26) the provided characteristic re- sistance and inductance (R¹, L') in the processor (25); in a second phase (27): measuring (29), with the measuring device (21), a line voltage (u) and a line current (i) at each of a se- quence of sampling times (tk); calculating (30), in the processor (25) for each sampling time (tk) of the sequence, a replica voltage (u_repii_ca) from the line current (i) measured at that sam- pling time (tk), the received characteristic resistance and inductance (R¹, L¹ ), and a length (1) of the power transmission line (2) from said first to said second loca- tion (X, Y); and in a third phase (28): determining (33), in the processor (25), the fault distance (Ifauit) from said length (1) of the power transmission line (2) and a ratio between the measured line voltages (u) and the calculated replica voltages (Ureplica)■

2. The method according to claim 1, wherein said deter- mining (33) in the third phase (28) is implemented by

with:

Ifauit being the fault distance (Ifauit);

1 being the length (1) of the power transmission line

(2) from said first to said second location (X, Y); u(t) being the measured line voltage (u) at the sampling time (t);

Urepiica(t)being the calculated replica voltage (u_repii_ca) at the sampling time (t); ti, t_z being the first and last sampling times (t) of the sequence .

3. The method according to claim 2, wherein the first sampling time (ti) is chosen to be close to the occurrence of the line fault (19).

4. The method according to any one of claims 1 to 3, wherein said second location (Y) is at the far end of the power transmission line (2) when seen from the first location (X).

5. The method according to any one of claims 1 to 4, wherein the first phase (23) of the method (22) is executed merely once.

6. The method according to any one of claims 1 to 5, wherein said determining (33) in the third phase (28) of the method (22) is executed repeatedly in a manner interlaced with the second phase (27).

7. A measuring device for determining a fault distance (Ifauit) of a line fault (19) in an electric power transmission line (2), in particular a power transmission line (2) in an electric power grid (1) to which one or more power electronic generation systems (4, 11) are connected, the measuring device (21) being connectable to the power transmission line (2) at a first location (X), characterised in that the measuring device (21) comprises a processor (25) and is configured to receive (26), in the processor (25), a characteristic resistance (R¹) and a characteristic inductance (L¹) of the power transmission line (2) having a line fault at a predeter- mined second location (Y); measure (29) a line voltage (u) and a line current (i) at each of a sequence of sampling times (tk); calculate (30), in the processor (25) for each sam- pling time (tk) of the sequence, a replica voltage (u_repii_ca) from the line current (i) measured at that sampling time (tk), the received characteristic resistance and inductance (R¹, L¹ ), and a length (1) of the power transmission line (2) from said first to said second location (X, Y); and determine (33), in the processor (25), the fault dis- tance (Ifauit) from said length (1) of the power transmission line (2) and a ratio between the measured line voltages (u) and the calculated replica voltages (u_repii_ca).

8. The measuring device according to claim 7, character- ised in that the processor (25) is configured to determine the fault distance (Ifauit) by

with:

Ifauit being the fault distance (Ifauit);

1 being the length (1) of the power transmission line

9. The measuring device according to claim 8, character- ised in that the processor (25) is configured to choose the first sampling time (ti) to be close to the occurrence of the line fault (19).

10. The measuring device according to any one of claims 7 to 9, characterised in that said second location (Y) is at the far end of the power transmission line (2) when seen from the first location (X).

11. The measuring device according to any one of claims 7 to 10, characterised in that the processor (25) is configured to determine (33) the fault distance (Ifauit) repeatedly in a manner interlaced with the measuring (29) of the line voltages (u) and the line currents (i) and the calculating (30) of the replica voltages (u_repii_ca).

12. A distance relay for distance protection of an elec- tric power transmission line (2), in particular a power trans- mission line (2) in an electric power grid (1) to which one or more power electronic generation systems (4, 11) are connected, wherein the distance relay (13) comprises a circuit breaker (20), characterised in that the distance relay (13) further comprises a measuring device (21) according to any one of claims 7 to 11 and is configured to trip the circuit breaker (20) when a fault distance (Ifauit) of a line fault (19) is de- termined to fall below a predetermined threshold value for a predetermined time.