METHOD, DEVICE AND SYSTEM FOR DETERMINING THE FAULT LOCATION OF A FAULT ON A LINE OF AN ELECTRICAL ENERGY SUPPLY NETWORK

Abstract

A fault location of a fault on a line of an electrical energy supply network is determined from measured current and voltage values at the first and second line ends. Highly accurate fault location with measured values from both line ends is provided even in the absence of temporal synchronization of the measurements at the line ends. Characteristics of first and second fictitious fault voltage values present at a fictitious fault location on the line are defined using the first and second current and voltage values. A fictitious fault location is determined for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values. The fictitious fault location is used as the actual fault location. We also describe a correspondingly configured device and a system for determining a fault location.

Claims

1. A method for determining the fault location of a fault on a line of an electrical energy supply network, the method comprising: measuring first current and voltage values at a first line end of the line; measuring second current and voltage values at a second line end of the line; defining a characteristic of first fictitious fault voltage values present at a fictitious fault location on the line using the first current and voltage values and a propagation model for traveling waves on the line; defining a characteristic of second fictitious fault voltage values present at a fictitious fault location on the line using the second current and voltage values and the propagation model for traveling waves on the line; determining a fictitious fault location of the type on the line for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values; and defining the fault location of the fault on the line, and thereby using the fictitious fault location as the fault location of the fault on the line.

2. The method according to claim 1, which comprises determining the fictitious fault location on the line for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values by way of an optimization method wherein the fictitious fault location is used as an optimization parameter of a target function of the optimization method.

3. The method according to claim 2, wherein the optimization method is an iterative optimization method.

4. The method according to claim 2, which comprises defining the fictitious fault location for which a minimum of the difference between the characteristic of the first fictitious fault voltage values and the characteristic of the second fictitious fault voltage values is present with the target function.

5. The method according to claim 2, which comprises defining the fictitious fault location for which a maximum of the product of the characteristic of the first fictitious fault voltage values and the complex-conjugate characteristic of the second fictitious fault voltage values is present with the target function.

6. The method according to claim 1, which comprises: subjecting the respective current and voltage values measured at the line ends to filtering, and forming first and second filtered current and voltage values which represent a selected frequency range of the measured current and voltage values; and defining the fictitious first and second fault voltage values using the first and second filtered current and voltage values.

7. The method according to claim 6, wherein the selected frequency range comprises high-frequency transient components or band-limited transient components of the measured current and voltage values.

8. The method according to claim 6, wherein the electrical energy supply network is a multiphase electrical energy supply network and the method comprises: in respect of the first and second filtered current and voltage values, performing a mathematical transformation to decouple individual phase components to thereby form first and second transformed current and voltage values; and defining the fictitious first and second fault voltage values using the first and second transformed current and voltage values.

9. The method according to claim 1, which comprises determining the fault location if a jump which exceeds a predefined threshold has been identified in the characteristic of the first current and voltage values or values derived therefrom and/or in the characteristic of the second current and voltage values or values derived therefrom.

10. The method according to claim 1, which comprises: determining the fault location with a device configured therefor; and outputting the fault location so determined with the device.

11. The method according to claim 1, which comprises: determining the fault location in each case by way of a respective device at each of the line ends; and outputting with the devices the fault locations determined by way of the devices.

12. A device for determining the fault location of a fault on a line of an electrical energy supply network, the device comprising: a processing device configured to receive first current and voltage values measured at a first line end of the line and second current and voltage values measured at a second line end of the line and, following the occurrence of a fault on the line, to determine the fault location of the fault using the first current and voltage values and the second current and voltage values, wherein: said processing device is configured to define a characteristic of first fictitious fault voltage values present at a fictitious fault location on the line using the first current and voltage values and a propagation model for traveling waves on the line; said processing device is configured to define a characteristic of second fictitious fault voltage values present at the fictitious fault location on the line using the second current and voltage values and the propagation model for traveling waves on the line; and said processing device is configured to determine a fictitious fault location of this type on the line for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values, and to indicate the determined fictitious fault location as the fault location of the fault on the line.

13. The device according to claim 12, wherein the device is an electrical protection device.

14. The device according to claim 12, wherein the device is a separate fault-localizing device.

15. A system for determining a fault location of a fault on a line of an electrical energy supply network, the system comprising: two devices each configured according to claim 12; and a communication connection interconnecting said two devices for exchanging data therebetween.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

[0059] FIG. 1 shows a schematic view of a line of an energy supply network with a system for determining a fault location;

[0060] FIG. 2 shows a representation of the electrical parameters of a line section x to explain the definition of a fault location according to the traveling wave principle;

[0061] FIG. 3 shows an example of a transmission characteristic of a filter for generating filtered current and voltage values;

[0062] FIG. 4 shows examples of characteristics of current and voltage measured values;

[0063] FIG. 5 shows examples of characteristics of filtered current and voltage values;

[0064] FIG. 6 shows examples of characteristics of transformed current and voltage values generated from the filtered current and voltage values;

[0065] FIG. 7 shows examples of characteristics of fault voltage values with synchronous measurements and a known fault location;

[0066] FIG. 8 shows examples of characteristics of fault voltage values with non-synchronous measurements and a known fault location;

[0067] FIG. 9 shows examples of characteristics of fault voltage values with non-synchronous measurements and a fictitious fault location which does not correspond to the actual fault location;

[0068] FIG. 10 shows examples of characteristics of fault voltage values with non-synchronous measurements and a fictitious fault location which corresponds to the actual fault location;

[0069] FIG. 11 shows examples of characteristics of target functions for fault location; and

[0070] FIG. 12 shows a schematic view of a flow diagram to explain an example embodiment of a method for fault location.

DETAILED DESCRIPTION OF THE INVENTION

[0071] Referring now to the figures of the drawing in detail and first, particularly, to FIG. 1 thereof, there is shown a schematic view of a system 10 for determining a fault location in an electrical energy supply network. For this purpose, FIG. 1 shows a simplified representation of an electrical line 11 of the energy supply network. The line is assumed to have the length l. The line 11 may be a single-phase or multiphase line.

[0072] The line 11 is delimited at its line ends 11a and 11b by power switches 12a, 12b and can be disconnected by the latter from the remaining energy supply network (not shown in detail in FIG. 1). Measuring points at which current and voltage measured values are recorded with current transformers 13a, 13b and voltage transformers 14a, 14b shown in FIG. 1 merely by way of example are furthermore present at the line ends 11a, 11b. The current transformers 13a, 13b and the voltage transformers 14a, 14b may be conventional or unconventional transformers. Current measured values i and voltage measured values u, which may be analog or digitized values, are output by the transformers on the secondary side.

[0073] Devices 15a, 15b for determining a fault location are connected to the current transformers 13a, 13b and the voltage transformers 14a, 14b at the respective line ends 11a, 11b. These devices 15a, 15b may, for example, be electrical protection devices which, as well as a fault location function, perform other protection and monitoring functions as well. For example, the protection devices may be distance protection devices, differential protection devices or overcurrent protection devices which monitor the operating state of the line 11 on the basis of the recorded current and voltage measured values and, in the event of a fault, transmit a shutdown signal T to their respective power switch 12a, 12b to cause the latter to open its switching contacts.

[0074] The devices 15a, 15b are configured, in the event of a fault on the line 11, to determine and output the fault location, i.e. the location on the line at which a fault (e.g. short circuit, earth fault) has occurred. To do this, they use the current and voltage measured values of their own line end and the respective other line end which have been recorded during the fault. For this purpose, the devices 15a, 15b are connected via a communication connection 16, which may be any given suitable wired or wireless communication connection. The devices 15a, 15b can exchange, inter alia, their current and voltage measured values via the communication connection 16 in order to determine the fault location.

[0075] The devices 15a, 15b carry out a fault location according to the traveling wave principle. This exploits the fact that, when a fault occurs, high-frequency transient signal components are produced in the current and in the voltage which propagate roughly at the speed of light in both directions on the line 11. This is drawn by way of example in FIG. 1. For this purpose, it is assumed that a fault has occurred at a fault location F. The traveling waves propagate as shown from the fault location F both in the direction of the first line end 11a and in the direction of the second line end 11b and can be measured there with the transformers and can be evaluated with the devices 15a, 15b in order to define the fault location. Seen from the first line end, the fault location F is located at a distance x, and, correspondingly from the perspective of the second line end, the fault location F is located at a distance I-x. As described in detail below, the devices evaluate the current and voltage measured values and output the fault location F, for example as a distance or percentage of the line length I.

[0076] The operator of the energy supply network can forward the determined fault location F to a maintenance team which can then visit the fault location and eliminate the cause of the fault. The most accurate possible determination of the fault location is required for this purpose. A procedure for the fault location is described below which, unlike previous traveling wave fault locations, does without temporally synchronized measured values from the line ends 11a, 11b.

[0077] A brief explanation of the principle of traveling wave fault location will first be given. For this purpose, a bilateral traveling wave fault location algorithm is explained, i.e. an algorithm which operates with measured values from both line ends 11a, 11b. A propagation model for traveling waves along the line 11 is used. The algorithm used in the method according to the invention furthermore does without time-synchronized measured values.

[0078] The theory of long lines is used to produce the algorithm concerned. This involves the model-based mapping of an electrical line in the form of distributed parameters. This is shown by way of example in FIG. 2.

[0079] FIG. 2 shows that the network parameters such as the inductance per unit length L.sub.0, capacitance per unit length C.sub.0, resistance per line length R.sub.0 and conductivity per unit length G.sub.0 are distributed along the line. On the basis of this line model, using Kirchhoff's laws for the section x of the line, the following equations are obtained for the voltage u and the current i:

[00001]$\begin{array}{cc}u\left(x+.Math..Math.x,t\right)=R_0.Math..Math..Math.x.Math.i\left(x+.Math..Math.x,t\right)+L_0.Math..Math..Math.x.Math.\frac{i\left(x+.Math..Math.x,t\right)}{t}+u\left(x,t\right)& \left(1\right)\\ i\left(x+.Math..Math.x,t\right)=G_0.Math..Math..Math.x.Math.u\left(x,t\right)+C_0.Math..Math..Math.x.Math.\frac{u\left(x,t\right)}{t}+i\left(x,t\right)& \left(2\right)\end{array}$

[0080] Through mathematical transformations, equations (1) and (2) can be converted into the following form:

[00002]$\begin{array}{cc}\frac{u\left(x,t\right)}{t}=R_0.Math.i\left(x,t\right)+L_0.Math.\frac{i\left(x,t\right)}{t}& \left(3\right)\\ \frac{i\left(x,t\right)}{x}=G_0.Math.u\left(x,t\right)+C_0.Math.\frac{u\left(x,t\right)}{t}& \left(4\right)\end{array}$

[0081] These equations (3) und (4) are partial differential equations of a homogeneous line and are normally referred to as telegraph equations. They can be generalized to apply to any given conductors.

[0082] By considering equations (3) and (4) in the Laplace domain, assuming x as a parameter, many effects occurring in the line can be interpreted substantially more simply:

[00003]$\begin{array}{cc}\frac{u\left(x,s\right)}{x}=R_0.Math.i\left(x,s\right)+{\mathrm{sL}}_0.Math.i\left(x,s\right)& \left(5\right)\\ \frac{i\left(x,s\right)}{x}=G_0.Math.u\left(x,s\right)+{\mathrm{sC}}_0.Math.u\left(x,s\right)& \left(6\right)\end{array}$

[0083] The derivation of equations (5) und (6) according to parameter x produces the following:

[00004]$\begin{array}{cc}\frac{{}^2.Math.u\left(x,s\right)}{x^2}=Z\left(s\right).Math.Y\left(s\right).Math.u\left(x,s\right)& \left(7\right)\\ \frac{{}^2.Math.i\left(x,s\right)}{x^2}=Y\left(s\right).Math.Z\left(s\right).Math.i\left(x,s\right)& \left(8\right)\end{array}$

[0084] Equations (7) and (8) can be solved separately using the differential equation theory for voltage and current:

U(x)=e.sup.(s)x.Math.A.sub.1+e.sup.(s)x.Math.A.sub.2 (9)

Z.sub.c(s).Math.I(x)=e.sup.(s)x.Math.A.sub.1e.sup.(s)x.Math.A.sub.2 (10)

[0085] In solving equations (9) und (10), it is possible to calculate the unknown parameters A.sub.1 and A.sub.2 from the initial conditions:

A.sub.1=1/2(U.sub.1(s)+Z.sub.c(s).Math.I.sub.1(s)) (11)

A.sub.2=1/2(U.sub.1(s)Z.sub.c(s).Math.I.sub.1(s)) (12)

[0086] wherein U.sub.1 and I.sub.1 represent the initial conditions at x=0. In addition, equations (9) and (10) contain a wave impedance Z.sub.c and the propagation constant , which can be calculated from the line parameters:

(s).sup.2=Z(s)Y(s) (13)

Z.sub.c(s)=(s).sup.1.Math.Z(s) (14)

[0087] Here, Z represents the line impedance and Y the shunt admittance of a section of the line. The values are indicated in each case in relation to length.

[0088] The following forms are thus obtained for equations (9) and (10):

U(x, s)=1/2e.sup.(s)x.Math.(U.sub.1(s)+Z.sub.c(s).Math.I.sub.1(s))+1/2e.sup.(s)x.Math.(U.sub.1(s)Z.sub.c(s).Math.I.sub.1(s)) (15)

Z.sub.c(s).Math.I(x,s)=1/2e.sup.(s)x.Math.(U.sub.1(s)+Z.sub.c(s).Math.I.sub.1(s))1/2e.sup.(s)x.Math.(U.sub.1(s)Z.sub.c(s).Math.I.sub.1(s)) (16)

[0089] Equations (15) and (16) represent a voltage-related or current-related propagation model for traveling waves along the line 11. The fault voltage at the initially unknown fault location F is considered for the traveling wave fault location described here. The relation described in equation (15) is used here.

[0090] This voltage equation (15) can be represented in the following form in the Laplace domain:

U(x, s)=U.sub.1(s)cos h(s)xZ.sub.c(s).Math.I.sub.1(s)sin h(s)x (17)

[0091] The transition to the frequency domain is effected by inserting s=j, where the angular frequency is represented as follows:

U(x, j)=U.sub.1(j)cos h(j)xZ.sub.c(j).Math.I.sub.1(j)sin h(j)(18)

[0092] This produces the analytical equation (18), which is satisfied for each occurring frequency f=/2. For this reason, the consideration can be limited to a selected frequency spectrum. The traveling wave fault location operates in a high-frequency range in which the information relating to the traveling wave propagation and the occurring reflections is significantly pronounced.

[0093] In this context, FIG. 3 shows the transmission function (amplitude and phase response) of an example of a filter by means of which the relevant frequencies are filtered from the characteristic of the current and voltage measured values for further analysis, wherein filtered current and voltage values are produced. An example of a passband of a suitable filter may be around 30 kHz to 400 kHz. In this range, conventional primary measuring transformers normally used in energy supply networks can transmit the signals with a quality sufficient for the fault location.

[0094] FIGS. 4 and 5 show by way of example how the filter impacts on the recorded current and voltage measured values. FIG. 4 shows an example of a characteristic of current and voltage measured values at a line end of a three-phase high-voltage line during a single-pole fault in phase A. The single-pole fault causes a rise in the current in the fault-affected phase A, whereas the voltage drops in phase A. Following the onset of the fault, the current and voltage signals contain high-frequency transients which are to be evaluated for the fault location.

[0095] The high-frequency transient components of the current and voltage measured values can be filtered out using a filter (for example a bandpass filter as described in connection with FIG. 2). This produces filtered current and voltage values as shown by way of example in FIG. 5. In considering the filtered current and voltage values, it should be noted that phases B and C that are unaffected by a fault have corresponding high-frequency patterns.

[0096] A fault at the fault location F of the line 11 (cf. FIG. 1) results in a division of the line 11 into two sections for which two voltage equations (19) and (20) can be obtained using equation (18):

U.sub.F,1(x,j)=U.sub.1(j)cos h(j)xZ.sub.c(j).Math.I.sub.1(j)sin h(j)x (19)

U.sub.F,2(lx, j)=U.sub.2(j)cos h(j)(lx)Z.sub.c(j).Math.I.sub.2(j)sin h(j)(lx) (20)

[0097] Here, I represents the line length, U.sub.F,1 the fault voltage at the fault location from the perspective of the first line end 11a and U.sub.F,2 the fault voltage at the fault location from the perspective of the second line end 11b. U.sub.1, U.sub.2 and I.sub.1, I.sub.2 represent the measured voltages and currents at both line ends. These two voltages are equal for the correct fault location at distance x (seen from the first line end) or I-x (seen from the second line end). This condition is used for the fault location.

[0098] The lines in energy supply networks normally comprise at least three phase conductors. It is thus necessary to present equations (18) or (19) and (20) set out above in the form of a matrix. An equation system of this type can be simplified by means of a modal or eigenvalue transformation. This enables the individual equations of the resulting equation system to be decoupled from one another and thus to be considered independently from one another. In addition, this transformation enables the equations already obtained to be considered in transformed components.

[0099] By way of example, a simple symmetrical line having the following parameters for a rated frequency of 60 Hz will be considered below:

[00005]$\begin{array}{cc}Z=\left[\begin{array}{ccc}0.187+j.Math..Math.0.858& 0.098+j.Math..Math.0.3705& 0.098+j.Math..Math.0.Math..Math.\mathrm{.3705}\\ 0.098+j.Math..Math.0.3705& 0.187+j.Math..Math.0.858& 0.098+j.Math..Math.0.3705\\ 0.098+j.Math..Math.0.3705& 0.098+j.Math..Math.0.3705& 0.187+j.Math..Math.0.858\end{array}\right].Math.& \left(21\right)\\ Y=1.Math.e-5\left[\begin{array}{ccc}j.Math..Math.0.3& -j.Math..Math.0.036& -j.Math..Math.0.036\\ -j.Math..Math.0.036& j.Math..Math.0.3& -j.Math..Math.0.036\\ -j.Math..Math.0.036& -j.Math..Math.0.036& j.Math..Math.0.3\end{array}\right].Math.S& \left(22\right)\end{array}$

[0100] Here, Z represents the line impedance and Y the line admittance. The Clark transformation is used by way of example as the modal transformation for decoupling. This has a transformation matrix T as follows; this produces , and 0 components:

[00006]$\begin{array}{cc}T=\frac{2}{3}\left[\begin{array}{ccc}1& -0.5& -0.5\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ 0.5& 0.5& 0.5\end{array}\right]& \left(23\right)\end{array}$

[0101] The afore-mentioned matrices (21) and (22) can be transformed with the Clark transformation as follows:

[00007]$\begin{array}{cc}{Z}_{.Math..Math..Math..Math.0}={\mathrm{TZT}}^{-1}=\left[\begin{array}{ccc}0.0894+j.Math..Math.0.487& 0& 0\\ 0& 0.0894+j.Math..Math.0.487& 0\\ 0& 0& 0.383+j.Math..Math.1.599\end{array}\right].Math.& \left(24\right)\\ .Math.Y_{.Math..Math.0}={\mathrm{TYT}}^{-1}=1.Math.e^{-5}\left[\begin{array}{ccc}j.Math..Math.0.336& 0& 0\\ 0& j.Math..Math.0.336& 0\\ 0& 0& j.Math..Math.0.229\end{array}\right].Math.S& \left(25\right)\end{array}$

[0102] In conjunction with equations (13) and (14), this produces the three propagation constants (equation (26)) and wave impedances (equation (27)) which are to be considered:

[00008]$\begin{array}{cc}{}_{.Math..Math..Math..Math.0}=\left[\begin{array}{ccc}.Math.0.0001+j.Math..Math.0.00128& 0& 0\\ 0& 0.0001+j.Math..Math.0.00128& 0\\ 0& 0& 0.0002+j.Math..Math.0.0019\end{array}\right]& \left(26\right)\\ Z_{C.Math..Math.0}=1.Math.e+2\left[\begin{array}{ccc}3.821-j.Math..Math.0.3475& 0& 0\\ 0& 3.821-j.Math..Math.0.3475& 0\\ 0& 0& 8.411-j.Math..Math.0.994\end{array}\right].Math.& \left(27\right)\end{array}$

[0103] Through the analysis of the propagation constant , it is possible to infer which of the modal components has the highest speed, this being preferably used for the further analysis. In addition, the component which occurs to a sufficient extent in the signal must be evaluated. This depends heavily on the fault type. FIG. 6 shows the transformed current and voltage values produced from the filtered current and voltage values through transformation. These represent the actual traveling waves which are used for the fault location.

[0104] FIG. 6 shows that, in the example case of the single-pole fault in Phase A, the component does not occur. It is furthermore evident that the 0 component is substantially slower than the a component.

[0105] Assuming that the fault location is known, the voltage U.sub.F at the fault location can be inferred separately from both line ends 11a, 11b.

[0106] In conventional traveling wave fault location systems, the measured value recording takes place in a time-synchronized manner at both line ends 11a and 11b. The measured values are given a timestamp by means of which an exact allocation of the current and voltage measured values from both line ends can take place. A fault location can thus take place in a simple manner with synchronized measured value recording on the basis of equations (19) and (20). This case is shown by way of example in FIG. 7. It is evident that, at the correct fault location (distance x from the first line end 11k), the characteristic of the fault voltage values U.sub.F,1 defined with the measured values from the first line end 11a corresponds to the characteristic of the fault voltage values U.sub.F,2 defined with the measured values from the second line end 11b. For comparison, the lower diagram in FIG. 7 shows the characteristic of the fault voltage values U.sub.F which could be measured directly at the fault location. In the example shown in FIG. 7, all characteristics of the fault voltage values are positioned in the same measurement window. This is possible only through a highly accurate temporal synchronization.

[0107] If no time synchronization of the measured value recording is available, the shape of the curves will not change if the fault location is known, but rather their temporal allocation; this is illustrated by way of example in FIG. 8. The measurement windows 80a, 80b with corresponding characteristics of the fault voltage values are visually highlighted in FIG. 8 in the characteristics of the fault voltage U.sub.F,1, U.sub.F,2 defined from the line ends 11a and 11b. For comparison, the lower diagram in FIG. 8 also shows the characteristic of the fault voltage values U.sub.F which could be measured directly at the fault location. The accordingly corresponding measurement window 80c is visually highlighted in this characteristic also. It is evident that the characteristics contained in the measurement windows 80a, 80b, 80c occur temporally shifted in relation to one another, but have virtually identical patterns.

[0108] However, virtually identical patterns of this type can only be defined for the actual fault location; outside the actual fault location, significantly different patterns occur for the characteristics of the fault voltage values U.sub.F,1, U.sub.F,2 . This is shown by way of example in FIG. 9, in which the fault voltage characteristics U.sub.F,1, U.sub.F,2 are shown for a fictitious fault location which does not correspond to the actual fault location. It is clearly evident in FIG. 9 that the fault voltage characteristics U.sub.F,1, U.sub.F,2 defined from both line ends 11a, 11b have no corresponding patterns inside and outside the measurement windows selected for the analysis in FIG. 8. For comparison, the lower diagram in FIG. 8 also shows the characteristic of the fault voltage values U.sub.F which could be measured directly at the actual fault location. Nor is there any evidence of correspondence between this characteristic U.sub.F and the two fault voltage characteristics U.sub.F,1, U.sub.F,2.

[0109] This finding that there is only one pattern for an actual fault location which can be calculated from both line ends and produces identical patterns in the respective fault voltage characteristics U.sub.F,1, U.sub.F,2 is exploited below for the fault location definition. Consequently, a fault location must be found for which the fault voltage values defined from both line ends 11a, 11b correspond to one another sufficiently closely. This problem can be solved for an existing measured value synchronization by simply equalizing the two equations (19) and (20) to obtain the distance x which indicates the correct fault location.

[0110] However, in the absence of temporal synchronization of the measured value recording, the required pattern recognition is rendered more difficult.

[0111] In order to nevertheless be able to carry out a determination of the actual fault location, the finding that a shift in the calculated fault voltage characteristics U.sub.F,1, U.sub.F,2 in each case by the propagation time of the traveling wave, i.e. the time that the traveling wave requires from the actual fault location to the respective line end 11a, 11b is exploited, results in the achievement of the same time basis.

[0112] In the time domain, the shift terms resulting for both line ends would be expressed as follows:

[00009]$\begin{array}{cc}{u}_{F,1}\left(t-\frac{x}{v_{\mathrm{mod}.Math..Math.e}}\right)& \left(28\right)\end{array}$

for the first line end 11a, and

[00010]$\begin{array}{cc}{u}_{F,2}\left(t-\frac{l-x}{v_{\mathrm{mod}.Math..Math.e}}\right)& \left(29\right)\end{array}$

for the second line end 11b. Here, v.sub.mode is the speed of a respectively selected mode; l is the line length.

[0113] In the frequency domain, the corresponding following shift terms are obtained herefrom:

U.sub.F,1(x,j)e.sup.(k)x (30)

for the first line end 11a, and

U.sub.F,2(x, j)e.sup.(j)(lx) (31)

for the second line end 11b. In the frequency domain, the temporal shift is reflected in the multiplication by the complex exponential function.

[0114] If the respective shift term (30) and (31) is transferred to equations (19) and (20), this produces the following equations for the fault voltage characteristics U.sub.F,1 , U.sub.F,2:

U.sub.F,1(x,j)e.sup.(j)x=U.sub.1(j)e.sup.(j)x cosh(j)x Z.sub.c(j).Math.I.sub.1(j)e.sup.(j)x sin h(j)x (32)

U.sub.F,2(lx, j)e.sup.(j)(lx)=U.sub.2(j)e.sup.(j)(lx) cosh(j)(lx)Z.sub.c(j).Math.I.sub.2(j)e.sup.(j)(lx) sin h(j)(lx) (33)

[0115] The result of this temporal shift is shown by way of example in FIG. 10 for a known actual fault location; here, all of the voltage curves and measurement windows have been converted by the shift to the same time basis. For comparison, the lower diagram in FIG. 10 also shows the characteristic of the fault voltage values U.sub.F which could be measured directly at the actual fault location.

[0116] However, since the actual fault location is initially unknown, the value for x which provides the closest correspondence of the two fault voltage characteristics U.sub.F,1, U.sub.F,2 must be found.

[0117] In other words, on the one hand, the characteristic of the fault voltage values U.sub.F,1 according to equation (32) must first be defined for a first fictitious or assumed fault location and, on the other hand, the characteristic of the fault voltage values U.sub.F,2 according to equation (33) must first be defined for the same fictitious or assumed fault location. If the two characteristics correspond to one another, the first fictitious fault location would correspond to the actual fault location. If no correspondence exists, the same procedure must be carried out for a second fictitious fault location. The procedure is continued until a correspondence of the two fault voltage characteristics U.sub.F,1, U.sub.F,2 is identified for a fictitious fault location; this fictitious fault location then corresponds to the actual fault location.

[0118] Such a manual search for the fault location is comparatively costly; furthermore, the characteristics of the fault voltage values U.sub.F,1, U.sub.F,2 cannot normally be expected to be exactly identical in reality due to measurement and calculation inaccuracies and the line parameters that are used.

[0119] The procedure described above can therefore be advantageously replaced with a mathematical optimization method in which a target function is defined with which the closest correspondence of the two fault voltage characteristics can be determined depending on the fault location. The distance x of the fault location from the first line end 11a can be used as a parameter for the target function. The following therefore applies to the actual fault location:

(U.sub.F,1(x,j)e.sup.(j)xU.sub.F,2(lx, j)e.sup.(j)(lx))0 (34)

[0120] Different target functions can be defined in order to satisfy the condition of equation (34). A possible target function ZF.sub.1, in which a minimization takes place for the optimization, is indicated below by equation (35):

[00011]$\begin{array}{cc}{\mathrm{ZF}}_1=\min .Math.{}_{}.Math.{\left(U_{F,1}\left(x,j.Math..Math.\right).Math.e^{-\left(j.Math..Math.\right).Math.x}-U_{F,2}\left(l-x,j.Math..Math.\right).Math.e^{-\left(j.Math..Math.\right).Math.\left(l-x\right)}\right)}^2& \left(35\right)\end{array}$

[0121] The characteristic of the target function ZF.sub.1 is shown by way of example in the upper diagram in FIG. 11 for the case of a single-pole fault with a distance x=60 km from the first line end 11a. In this case, the line length is assumed to be 150 km, resulting in a minimum 110a in the diagram for a distance of the fault location from the first line end 11a of x=60 km from the second line end 11b of (l-x)=90 km.

[0122] Another possible target function ZF.sub.2, in which a maximization takes place for the optimization, is indicated below by equation (36):

[00012]$\begin{array}{cc}{\mathrm{ZF}}_2=\max .Math.{}_{}.Math.\left(U_{F,1}\left(x,j.Math..Math.\right).Math.e^{-\left(j.Math..Math.\right).Math.x}.Math.{\left(U_{F,2}\left(l-x,j.Math..Math.\right).Math.e^{-\left(j.Math..Math.\right).Math.\left(l-x\right)}\right)}^{*}\right)& \left(36\right)\end{array}$

[0123] The complex-conjugate expression is designated by the asterisk *. The characteristic of the target function ZF.sub.2 is shown by way of example in the lower diagram in FIG. 11 similarly for the case of a single-pole fault with a distance x=60 km from the first line end 11a. The diagram shows a maximum 110b for a distance of the fault location from the first line end 11a of x=60 km and from the second line end 11b of (l-x)=90 km.

[0124] Equations (35) and (36) represent examples of target functions which must be subjected to a minimization or maximization process. This can be achieved, for example, by a mathematical iterative method. The minimization or maximization process can be carried out in both the frequency domain and the time domain, wherein the calculation of the fault voltage characteristics preferably takes place in the frequency domain. Since digital devices such as the devices 15a, 15b normally operate with discrete values, the methods can be adapted according to this requirement.

[0125] FIG. 12 finally shows a schematic flow diagram of an exemplary embodiment of a method for determining a fault location. The method steps above the dotted line take place in the device 15a at the first line end 11a, while those below the dotted line take place in the device 15b at the second line end 11b (cf. FIG. 1).

[0126] The local currents and voltages are measured in each case with the devices 15a, 15b at both line ends in steps 120a and 120b and corresponding current and voltage measured values are produced. These measured values are present as sampling values of the current and voltage signals of the line 11. An example of the recorded current and voltage measured values is shown in FIG. 4.

[0127] So that only the high-frequency transient components (traveling waves) of the respective current and voltage measured values are recorded, a filtering (e.g. by a bandpass filter) takes place in each case in steps 121a and 121b. Through the selection of the cut-off frequencies, e.g. of the bandpass filter, the method can be adapted to the characteristics of the transformers 13a, 13b and 14a, 14b. If these transformers provide only a medium bandwidth, e.g. up to 10 kHz only, the filters must limit the bandwidth of the signals to the bandwidth of the transformers. Depending on the phase error of the transformers used, a slightly lower measurement accuracy can then be expected. If the transformers can provide a higher bandwidth, e.g. up to 500 kHz, the filters should be dimensioned accordingly.

[0128] In steps 121a, 121b, filtered current and voltage values are generated, as shown by way of example in FIG. 5. An example of a transmission characteristic of a suitable filter is shown in FIG. 3.

[0129] In steps 122a and 122b , the respective traveling waves are treated in each case by means of a transformation (e.g. Clarke transformation), e.g. in order to decouple the phase-related components. Transformed current and voltage values are generated, as shown by way of example in FIG. 6.

[0130] In order to start the fault location method or to position the measurement window correctly for the evaluation only if required, i.e. in the event of a fault, a transient jump, which is used e.g. as a trigger for the measurement window positioning, can furthermore be determined in each case for each side in steps 123a and 123b. The length of the measurement window should preferably be at least twice the propagation time of the traveling wave in the selected modal component. The jump detection can take place in relation to the transformed or filtered current and voltage values or in relation to the original current and voltage measured values.

[0131] A transfer of the transformed current and voltage values into the frequency domain takes place in steps 124a and 124b. This is preferably performed by means of Fast Fourier Transform (FFT) or Discrete Fourier Transform (DFT).

[0132] As indicated by the arrows between the blocks of steps 124a and 124b, the resulting values are exchanged in the frequency range between the devices 15a and 15b (cf. FIG. 1). This is performed via the communication connection 16.

[0133] With their own values and the values from the respective other line end, the devices 15a and 15b then perform a fault location search by means of optimization of a target function, as described above, in steps 125a and 125b. The target function can be processed, for example, in steps 125 and 125b according to equations (35) or (36). As described above, a fictitious fault location is sought for which the target function has a minimum or a maximum. This fictitious fault location is then accepted as the actual fault location.

[0134] The determined fault location is then output in step 126. According to FIG. 12, this takes place in a joint output step. Instead, a separate output can also be performed by each of the two devices 15a and 15b.

[0135] The devices 15a and 15b normally have a processing device in which steps 120a/b to 126 are carried out. This may be e.g. a microprocessor which accesses corresponding device software which is located in a memory of the respective device. Alternatively, it may also be a processing module with hardware-defined programming, for example, an ASIC or FPGA.

[0136] FIGS. 1 and 12 have shown a system for determining a fault location in which the fault location is determined with two devices 15a and 15b which are located in each case at one line end 11a or 11b. Instead, a central device can also be provided, to which the current and voltage measured values from the line ends are fed.

[0137] Once more to briefly summarize, the invention relates to a method for determining the fault location F of a fault on a line 11 of an electrical energy supply network, in which first current and voltage values are measured at a first line end 11a of the line 11, second current and voltage values are measured at a second line end 11b of the line 11, and the fault location F of said fault is defined using the first and second current and voltage values following the occurrence of a fault on the line 11.

[0138] In order to be able to perform a fault location with measured values from both line ends with high accuracy even in the absence of temporal synchronization of the measurements at the line ends, it is proposed that a characteristic of first fictitious fault voltage values present at a fictitious fault location on the line 11 is defined using the first current and voltage values, a characteristic of second fictitious fault voltage values present at a fictitious fault location on the line 11 is defined using the second current and voltage values, a fictitious fault location of this type on the line 11 is determined for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values, and the determined fictitious fault location is used as the fault location F of the fault on the line 11.

[0139] Although the invention has been illustrated and described in detail above through preferred example embodiments, the invention is not restricted to the disclosed examples, and other variations can be derived herefrom by the person skilled in the art without exceeding the protective scope of the following patent claims.