Information processing apparatus, information processing method and information processing program

Abstract

To provide an information processing apparatus that can locate a fault point with high accuracy.SOLUTION: An information processing apparatus that locates a fault point when a fault has occurred in an electric power system comprises: a first acquisition unit that acquires a first measurement value of ground electrostatic capacitance of an electric power system; an estimation unit that estimates at least either one of a ground electrostatic capacitance of a zero-phase component or fault point resistance in each of distribution lines between a plurality of nodes provided in the electric power system on the basis of the first measurement value; and a location unit that locates a fault point on the basis of the estimation result of the estimation unit.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an information processing device, an information processing method, and an information processing program. [Background technology]

[0002] Patent Document 1 discloses a device that can easily measure the earth capacitance of a power distribution system without performing dangerous and time-consuming artificial earth fault tests. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 6-109784 Summary of the Invention [Problem to be solved by the invention]

[0004] When a ground fault occurs in a power system, the fault point is located using a support system, etc., but since the measured value of the power system's earth capacitance is not used to locate the fault point, it has been difficult to locate the fault point with high accuracy.

[0005] The present invention has been made in consideration of the above problems, and has an object to provide an information processing device, an information processing method, and an information processing program capable of locating a fault point with high accuracy. [Means for solving the problem]

[0006] One invention for achieving the above-mentioned object is an information processing device that locates a fault point when a fault occurs in an electric power system, the information processing device including: a first acquisition unit that acquires a first measurement value of the earth capacitance of the electric power system; an estimation unit that estimates at least one of the earth capacitance of the zero-phase component in each of the distribution lines between a plurality of nodes provided in the electric power system or the fault point resistance based on the first measurement value; and a location unit that locates the fault point based on the estimation result by the estimation unit.

[0007] Also, an information processing method in which an information processing device locates a fault point when a fault occurs in a power system includes the steps of: acquiring a first measured value of the earth capacitance of the power system; estimating at least one of the earth capacitance of the zero-phase component in each of the distribution lines between a plurality of nodes provided in the power system or the fault point resistance based on the first measured value; and locating the fault point based on the estimated result.

[0008] The present invention is also an information processing program for locating a fault point when a fault occurs in a power system, the information processing program causing a computer to realize a first acquisition unit that acquires a first measurement value of the earth capacitance of the power system, an estimation unit that estimates at least one of the earth capacitance of the zero-phase component in each of a plurality of distribution lines between a plurality of nodes provided in the power system or the fault point resistance based on the first measurement value, and a locating unit that locates the fault point based on the estimation result by the estimation unit. Other features of the present invention will become apparent from the description of this specification. Effect of the Invention

[0009] According to the present invention, it is possible to provide an information processing device capable of locating a fault point with high accuracy. [Brief description of the drawings]

[0010] [Figure 1] 1 is a diagram showing an example of a power system 1 in which an information processing device 2 locates a fault point. [Diagram 2] FIG. 1 is a diagram illustrating a node branch model. [Diagram 3] 4A and 4B are schematic diagrams showing a data structure and an example of node data; [Figure 4] 4 is a schematic diagram showing a data structure and an example of branch data; FIG. [Diagram 5] 4A and 4B are schematic diagrams showing a data structure and an example of measurement data. [Figure 6] FIG. 2 is a schematic diagram showing a data structure and an example of substation data. [Figure 7] 2 is a diagram illustrating a hardware configuration of an information processing device 2. FIG. [Figure 8] FIG. 2 is a diagram showing functional blocks of an information processing device 2. [Figure 9] 13 is a flowchart illustrating a first effective value method location process executed by the information processing device 2. [Figure 10] 10A and 10B are schematic diagrams showing a data structure and an example of converted measurement data. [Figure 11] 4 is a schematic diagram showing a data structure and an example of effective value analysis data; FIG. [Figure 12] 13 is a flowchart illustrating a second effective value method location process executed by the information processing device 2. [Figure 13] 13 is a flowchart illustrating a resonant frequency method location process executed by the information processing device 2. [Figure 14] 11A and 11B are diagrams illustrating a process of identifying a resonance frequency. [Figure 15] 4 is a schematic diagram showing a data structure and an example of resonance frequency data; FIG. [Figure 16] FIG. 13 is a diagram illustrating a resonance frequency analysis. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] =====First embodiment===== First, the first embodiment will be described.

[0012] <<Power system 1>> 1 is a diagram showing an example of a power system 1 in which an information processing device 2 described later locates a fault point P. The power system 1 includes a distribution substation 10, a distribution line 11, a circuit breaker 12, one or more measuring devices 13 installed at predetermined positions on the distribution line 11, automatic switches 14a and 14b installed at predetermined positions on the distribution line 11, and an earth capacitance measuring device 16.

[0013] [Distribution Substation 10] The distribution substation 10 transforms the voltage supplied from a transmission line (not shown) and outputs a voltage of 6.6 kV to the distribution line 11.

[0014] [Power distribution line 11] A plurality of distribution lines 11 are radially connected to the distribution substation 10, with the distribution substation 10 serving as an origin (sending node). Only one distribution line 11 is shown in Fig. 1. The distribution line 11 is a power line for supplying three-phase AC power having a-phase, b-phase, and c-phase.

[0015] [Circuit Breaker 12] The circuit breaker 12 is a device, such as a distribution circuit breaker or a feeder circuit breaker, that interrupts a current to protect the power system 1 when an accident, such as a short circuit or a ground fault, occurs in the power system 1. In the illustrated example, one circuit breaker 12 is installed for one distribution line 11.

[0016] [Measuring instrument 13] Measuring device 13 is a switch having a sensor capable of measuring measurement values ​​at a fixed period at the installed position (switch with sensor). The measurement values ​​of measuring device 13 include at least the voltage of distribution line 11 and the current flowing through distribution line 11 at the installation point of measuring device 13. The measurement values ​​of measuring device 13 are output to and stored in a database DB (described later).

[0017] [Automatic switch 14a, 14b] The automatic switches 14a and 14b are power devices that are installed on utility poles 15 and automatically open and close electric circuits. A plurality of pole-mounted transformers are connected between the automatic switch 14a and the automatic switch 14b, and power is supplied to each consumer. When a ground fault or the like occurs in the power system 1, the automatic switches 14a and 14b at both ends of a fault point P caused by the ground fault are automatically opened by the power distribution system 20, and a power outage occurs in the section between the opened automatic switches 14a and 14b. Hereinafter, the section that has been blacked out due to a ground fault is referred to as the "blacked out section SC." The blacked out section SC includes the fault point P. In this embodiment, a case where there are a plurality of pole-mounted transformers between the automatic switch 14a and the automatic switch 14b will be described, but there may be only one.

[0018] [Earth capacitance measuring device 16] The earth capacitance measuring device 16 is a measuring device that is connected to the power system 1 and measures the earth capacitance and earth resistance of the sending node of the power system 1. The measured values ​​of the earth capacitance measuring device 16 are output to and stored in a database DB (described later).

[0019] [Power distribution system] The power distribution system 20 is a system that controls the power system 1. For example, when the power distribution system 20 detects a ground fault or the like based on the operation of a protective relay, the power distribution system 20 opens the automatic switches 14a, 14b so that a fault point P caused by the ground fault is included in the power outage section SC. The power distribution system 20 has a database DB and an information processing device 2.

[0020] In this embodiment, a case will be described in which the power distribution system 20 includes the database DB and the information processing device 2, but the database DB and the information processing device 2 may be provided in another system (for example, a cloud or the like).

[0021] Next, various data stored in the database DB will be described before describing the information processing device 2. The database DB pre-stores node data and branch data related to a node-branch model described later, measurement data, and substation data.

[0022] <Node Branch Model> FIG. 2 is a diagram for explaining the node branch model. In the node branch model, the electric power system 1 is modeled by using utility poles 15 as nodes and power distribution lines 11 between the nodes as branches. For the sake of convenience, the node with the node name "NOi (i is a natural number)" will be referred to as node N. i The node name is identification information for identifying each node N. For example, a node N with a node name of "NO1" is written as node N1. i For matters common to all of the above, the node number will be omitted and simply referred to as "node N" or "each node N." Additionally, the direction of the distribution line 11 toward the distribution substation 10 is defined as the "upstream side," and the direction away from the distribution substation 10 is defined as the "downstream side."

[0023] [node] In this embodiment, the node N is an aggregation unit managed on a utility pole (not shown) basis. Consumers such as loads and solar power generation facilities are connected to the node N via pole transformers. Power output from the distribution substation 10 to the distribution line 11 is supplied to the consumers via the node N.

[0024] In the example shown in FIG. 2, the node N n (n is a natural number) to node N of the automatic switch 14b n+5 The blackout section SC is the section between the power outage and the node N n+1 to node N n+4 Customers connected to the network will experience a power outage.

[0025] <node data> FIG. 3 is a schematic diagram showing a data structure and an example of node data. As shown in the figure, the node data has items of node name, type, load active power, and load reactive power. The type is the type of auxiliary equipment installed at the node N (electric pole 15). Examples of auxiliary equipment include a circuit breaker 12 (FCB), a measuring instrument 13, automatic switches 14a and 14b, or a pole transformer (not shown). The load active power is the active power (unit: kW (kilowatt)) of a load connected to the auxiliary equipment. The load reactive power is the reactive power (unit: kvar (kilovar)) of a load connected to the auxiliary equipment. The load active power and the load reactive power are calculated from the measured value of the measuring instrument 13 or the measured value of a smart meter or the like installed at each load (consumer).

[0026] The node data may include location information. The location information is information for identifying the location of the node N. The location information is a location on a map. The location on the map can be expressed by latitude and longitude.

[0027] <branch data> 4 is a schematic diagram showing a data structure and an example of the branch data. As shown in the figure, the branch data has items of substation side node name, end side node name, span length, positive sequence component, negative sequence component, and zero sequence component. The substation side node name is the node name of the node N provided on the upstream side of the branch. The end side node name is the node name of the node N provided on the downstream side of the branch. The span length is the span length (in meters (m)) of the distribution line 11 in the branch.

[0028] Although details will be described later, the information processing device 2 locates the fault point using voltage, current, and impedance expressed in a symmetrical coordinate system expressed by zero-phase, positive phase, and negative phase. The positive-phase components are the positive-phase resistance (R) (unit: Ω (ohm)), inductive reactance (ωL) (unit: Ω), and capacitive reactance of the capacitance to earth (1 / ωC) (unit: MΩ) expressed using the symmetrical coordinate system. The negative-phase components are the negative-phase resistance (R), inductive reactance (ωL), and capacitive reactance of the capacitance to earth (1 / ωC) expressed using the symmetrical coordinate system. The zero-phase components are the zero-phase resistance (R), inductive reactance (ωL), and capacitive reactance of the capacitance to earth (1 / ωC) expressed using the symmetrical coordinate system. The resistance (R), inductive reactance (ωL), and capacitive reactance (1 / ωC) of each phase are values ​​calculated in advance based on the geometric structure of the power system 1, such as the line-to-line distance (span length) of the distribution lines 11 and the height of the utility poles 15.

[0029] <Measurement data> FIG. 5 is a schematic diagram showing a data structure and an example of the measurement data. The measurement data is a measurement value measured by the measuring device 13 within a predetermined period in the past (for example, one week). The measurement data includes a measurement value D1 before a fault occurred in the power system 1 and a measurement value D2 after the fault. The measurement value of the measuring device 13 is used when the information processing device 2 locates the position of the fault point P. As shown in the figure, the measurement data has items of a measuring device ID, a measurement time, an a-phase voltage, an a-phase current, a b-phase voltage, a b-phase current, a c-phase voltage, and a c-phase current. The measuring device ID is identification information for identifying the measuring device 13. The measurement time is the date and time (year, month, day, hour, minute) when the measurement values ​​(a-phase voltage, a-phase current, b-phase voltage, b-phase current, c-phase voltage, and c-phase current) of the measuring device 13 were measured. The a-phase voltage is the voltage of the a-phase (unit: V (volts)). The a-phase current is the current (unit: A (amperes)) flowing through the a-phase. The b-phase voltage is the voltage of phase b. The b-phase current is the current flowing through phase b. The c-phase voltage is the voltage of phase c. The c-phase current is the current flowing through phase c.

[0030] <Substation data> 6 is a schematic diagram showing the data structure and an example of the substation data. As shown in the figure, the substation data has the following items: transformer capacity, transformer %Z, substation capacitance to ground, total substation length, and length of each feeder. The transformer capacity is the capacity (unit: MW (megawatts)) of the transformer installed in the distribution substation 10. The transformer %Z is the reactance component L of the percent impedance of the transformer installed in the distribution substation 10. T1 The substation capacitance to earth is the capacitance to earth of the power system 1 measured by the capacitance to earth measuring device 16 (unit: uF (microfarad)). The total substation length is the length of the entire distribution lines 11 connected to the distribution substation 10 (unit: km (kilometers)). The length of each feeder is the length of the distribution lines 11 of each feeder connected to the distribution substation 10 (unit: km). In the illustrated example, the length of each feeder includes the length of the first feeder, the length of the second feeder, the length of the third feeder, and the length of the fourth feeder. The substation data may include location information of the distribution substation 10.

[0031] <<Information processing device 2>> The information processing device 2 is a device that locates a fault point P when a fault occurs in the power system 1 due to an accident or the like. Hereinafter, the hardware configuration and functional blocks of the information processing device 2 will be described in that order.

[0032] <Hardware configuration of information processing device 2> 7 is a diagram illustrating a hardware configuration of the information processing device 2. The information processing device 2 is a computer having a CPU (Central Processing Unit) 21, a memory 22, an input unit 23, an output unit 24, a storage unit 25, a recording medium drive unit 26, and a network connection unit 27.

[0033] [CPU21] The CPU 21 executes information processing programs stored in the memory 22 or the storage unit 25 to realize various functions of the information processing device 2.

[0034] [Memory 22] The memory 22 is, for example, a RAM (Random-Access Memory) and is used as a temporary storage area for various programs, data, and the like.

[0035] [Input section 23] The input unit 23 is a device that accepts commands and data input by a user, and includes an input interface such as a keyboard and a touch sensor that detects a touch position on a touch panel display.

[0036] [Output section 24] The output unit 24 is, for example, a device such as a display or a printer.

[0037] [Storage section 25] The storage unit 25 is a non-transitory (eg, non-volatile) storage device that stores various data to be executed or processed by the CPU 21.

[0038] [Recording medium drive unit 26] The recording medium driving unit 26 reads various data such as information processing programs recorded on a recording medium such as an SD card, a DVD, or a CD-ROM, and stores the data in the storage unit 25.

[0039] [Network connection part 27] The network connection unit 27 exchanges various programs and data with other computers via the network.

[0040] <Function blocks of information processing device 2> 8 is a diagram showing functional blocks of the information processing device 2. The information processing device 2 includes a first acquisition unit 210, a second acquisition unit 211, an estimation unit 212, a location unit 213, and an output unit 214. The information processing device 2 realizes the functions of the first acquisition unit 210, the second acquisition unit 211, the estimation unit 212, the location unit 213, and the output unit 214 by the CPU 21 reading out a program stored in the storage unit 25 into the memory 22 and executing the program.

[0041] Each of these will be explained below, but first an overview will be given, and then each will be explained in detail later with specific examples using flow charts.

[0042] [First acquisition part 210] The first acquisition unit 210 acquires a measurement value D0 (corresponding to a "first measurement value") of the capacitance to earth at the sending node of the power system 1 from the database DB.

[0043] [Second acquisition part 211] The second acquisition unit 211 acquires, from the database DB, a measurement value D1 before the fault and a measurement value D2 after the fault (corresponding to a "second measurement value") measured by the sensor of the measuring device 13. The measurement values ​​here include the voltage of the distribution line 11 at the installation point of the measuring device 13 and the current flowing through the distribution line 11.

[0044] [Estimation section 212] The estimation unit 212 estimates at least one of the zero-phase component capacitance to earth or the fault point resistance in each of the distribution lines 11 (branches) between multiple nodes N provided in the power system 1, based on the measured value D0 of the capacitance to earth acquired by the first acquisition unit 210.

[0045] Specifically, the estimation unit 212 estimates the zero-phase-sequence component capacitance to earth in each of the distribution lines 11 (branches) between nodes N by calculating the zero-phase-sequence component capacitance to earth per unit length of the distribution line 11 of the power system 1 based on the measured value D0 of the capacitance to earth.

[0046] Alternatively, the estimation unit 212 estimates the capacitance to earth of the zero-phase component of each of the distribution lines 11 (branches) between nodes N based on the measured value D0 of the capacitance to earth, the capacitance to earth of the zero-phase component of the power system 1 calculated in advance from the structure of the power system 1, and the capacitance to earth of the zero-phase component of each of the distribution lines 11 (branches) between nodes N calculated in advance from the structure of the power system.

[0047] [Orientation section 213] When a fault occurs in the power system 1, the locating unit 213 locates the fault point P based on the estimation result by the estimating unit 212.

[0048] Specifically, the location unit 213 calculates a calculated value C corresponding to the post-fault measurement value D2 when one of the multiple nodes N provided in the power system 1 is assumed to be the fault point P, based on at least one of the estimated zero-phase component earth capacitance or the estimated fault point resistance, and locates the fault point P based on the calculated value C and the post-fault measurement value D2.

[0049] It should be noted that the "calculated value C corresponding to the measured value D2 after the fault" is the calculated value of the voltage of the distribution line 11 and the current flowing through the distribution line 11 at the installation point of the measuring instrument 13, and is a calculated value obtained by a calculation simulating a fault.

[0050] [Output section 214] The output unit 214 outputs the location result (for example, the fault point P) by the location unit 213.

[0051] <<Processing Executed by Information Processing Device 2>> The process executed by the information processing device 2 will be described with reference to a flowchart. Fig. 9 is a flowchart for explaining the first effective value method location process executed by the information processing device 2. Note that, although the following description will be given by taking as an example a case where a single-line ground fault occurs in the power system 1, the effective value method can locate the fault point P not only when a ground fault occurs but also when a short circuit occurs.

[0052] First, in step S101, the first acquisition unit 210 and the second acquisition unit 211 read input data (node ​​data, branch data, measurement data, and substation data) from the database DB. At this time, the first acquisition unit 210 acquires the substation earth capacitance (measured value D0 of the earth capacitance of the power system 1) from the substation data. In addition, the second acquisition unit 211 acquires a measured value D1 before the fault and a measured value D2 after the fault from the measurement data.

[0053] Next, in step S102, the estimation unit 212 performs a frequency analysis of the power system 1 based on the post-fault measurement value D2 (analyzes the waveform data). Specifically, the estimation unit 212 first calculates a zero-phase voltage V0, a ​​positive-phase voltage V1, and a negative-phase voltage V2 by the following formula (1).

[0054]

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[0055] Here, E' a is the a-phase voltage after the fault, and E' b is the b-phase voltage after the fault, and E' c is the c-phase voltage after the fault. Also, a=cos120°+jsin120°.

[0056] Moreover, the estimation unit 212 calculates the zero-phase current I0, the positive-phase current I1, and the negative-phase current I2 by the following equation (2).

[0057]

number

[0058] Here, I' a is the a-phase current after the fault, and I' b is the b-phase current after the fault, and I' c is the c-phase current after the fault. The estimation unit 212 calculates the zero-phase voltage V0, the positive-phase voltage V1, the negative-phase voltage V2, the zero-phase current I0, the positive-phase current I1, and the negative-phase current I2 for each measurement time after the fault, and generates converted measurement data that represents the calculated voltages and currents in a time series.

[0059] <Measurement data after conversion> 10 is a schematic diagram showing a data structure and an example of the converted measurement data. As shown in the figure, the converted measurement data includes items such as a measuring device ID, a measurement time, a positive-phase voltage, a positive-phase current, a negative-phase voltage, a negative-phase current, a zero-phase voltage, and a zero-phase current.

[0060] Next, in step S103, the estimation unit 212 estimates the earth capacitance of the zero-phase-sequence component in each branch based on the substation earth capacitance by the following estimation method 1 or 2.

[0061] The capacitance to earth of the zero-phase component of each branch included in the branch data is a value calculated from the geometric structure of the power system 1, such as the line distance of the distribution lines 11 and the height of the utility poles 15. However, the actual capacitance to earth of the zero-phase component of each branch is affected by devices such as pole transformers, low-voltage distribution lines, houses and trees, weather conditions, etc., and an error of about two to three times occurs from the calculated value. Therefore, the error reduces the accuracy of estimating the state of the power system 1.

[0062] Here, the "state of the power system 1" specifically refers to the state of the node N i are the voltage of the power distribution line 11 and the current flowing through the power distribution line 11 at (1≦i≦M).

[0063] On the other hand, by using the capacitance to the earth of the power system 1 measured by the capacitance to the earth measurement device 16, it is possible to calculate the capacitance to the earth of the zero-phase component of each branch with high accuracy. This makes it possible to improve the accuracy of estimating the state of the power system 1.

[0064] [Estimation method 1] The estimation method 1 is a method of apportioning the zero-phase-sequence component capacitance to the ground based on the span length of each branch. In the estimation method 1, the estimation unit 212 first calculates the zero-phase-sequence component capacitance to the ground C per unit length (unit length) by the following equation (3): u0 Calculate.

[0065]

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[0066] Here, C0 is the zero-phase component of the substation capacitance to earth (the zero-phase component of the measured value D0 of the capacitance to earth of the power system 1 measured by the capacitance to earth measuring device 16).Σ is the total length of the substations.

[0067] Next, the estimation unit 212 calculates the zero-phase component capacitance to earth C per unit length. u0 Based on the span length of each branch included in the branch data, the zero-phase-sequence component capacitance to earth of each branch is calculated using the following equation (4).

[0068]

number

[0069] Here, C i0 is the capacitance to earth of the zero-phase component in the i-th branch. Also, l i is the span length in the i-th branch.

[0070] [Estimation method 2] Estimation method 2 is a method of apportioning the capacitance to the earth based on the magnitude of the capacitance to the earth of the zero-phase component of each branch, which is set in advance in the branch data. The capacitance to the earth of the zero-phase component of each branch, which is set in advance in the branch data, is a value calculated in advance from the geometric structure of the power system 1. In estimation method 2, first, the estimation unit 212 calculates the capacitance to the earth of the zero-phase component of the power system 1, C, calculated in advance from the geometric structure of the power system 1, using the following equation (5): 0__geometric Calculate.

[0071]

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[0072] Here, C fi0_geometric is the zero-sequence component earth capacitance of the i-th branch of the f-th feeder calculated from the geometric structure of the power system 1, which is preset in the branch data. F is the number of feeders in the power system 1. M is the number of nodes in the f-th feeder.

[0073] The zero-phase capacitance to earth of the power system 1 calculated here is C 0_geometric Since it includes errors due to the various factors mentioned above, it does not necessarily match the zero-phase component C0 of the substation capacitance to earth (measured value D0).

[0074] Next, the estimation unit 212 calculates the capacitance to earth of the zero-phase component in each branch by the following equation (6), and overwrites the branch data with the calculated capacitance (updates the branch data).

[0075]

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[0076] Here, C fi0 is the zero-sequence capacitance to earth of the ith branch of the fth feeder.

[0077] In this way, by modifying the parameters for estimating the state of the power system 1 (the capacitance to earth of the zero-phase component in each branch), the parameter error can be reduced and the accuracy of estimating the state of the power system 1 can be improved.

[0078] Next, in step S110, the location unit 213 estimates the pre-fault state of the power system 1 based on the equipment information (node ​​data, branch data, and substation data) of the power system 1 and the pre-fault measurement value D1.

[0079] Specifically, the location unit 213 determines whether a plurality of nodes N i The voltage and current values ​​at each of (1≦i≦M) are estimated.

[0080] Next, in step S111, the location unit 213 generates an impedance matrix Z. When the current injected into each of the multiple nodes N is I and the voltage of each of the multiple nodes N is V, the impedance Z is expressed by the following equation (7).

[0081]

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[0082] In the following description, the power system 1 has M nodes (nodes N1 to N M In this case, the voltage V is expressed by the following equation (8), the current I by the following equation (9), and the impedance Z by the following equation (10).

[0083]

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[0084]

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[0085]

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[0086] In other words, the voltage V and the current I are a matrix with M rows and 1 column, and the impedance Z is a matrix with M rows and M columns. Hereinafter, the impedance Z in equation (10) will be particularly referred to as the "impedance matrix Z."

[0087] In equation (8), the component V of the voltage V i (1≦i≦M) is node N i In addition, in equation (9), the component I of the current I i (1≦i≦M) is node N i is the injection current into the

[0088] In equation (10), the component Z of the impedance matrix Z ij (1≦i≠j≦M) is the node N i and node N j is the impedance between

[0089] In addition, in equation (10), the diagonal components Z of the impedance matrix Z ii is the node Ni This corresponds to the impedance of the entire power system 1 when the reference voltage is 1.

[0090] Next, in step S112, the location unit 213 executes a calculation to simulate the power system 1 when a predetermined fault condition is imposed on the power system 1, and calculates a calculated value C corresponding to the post-fault measurement value D2 acquired by the second acquisition unit 211 in step S101. At this time, the location unit 213 performs the calculation by imposing one of a plurality of predetermined fault conditions on the power system 1.

[0091] The fault condition is a node corresponding to the fault point P and a fault point resistance of the fault point P. Specifically, the "node corresponding to the fault point P" is the node N i (1≦i≦M). In addition, the "fault point resistance of the fault point P" is one of the multiple pre-set candidate values ​​of fault point resistance R fk (1≦k≦K) (k and K are natural numbers). Candidate value R fk may be K values ​​extracted from a range assumed to include the actual fault point resistance value of the fault point P.

[0092] In step S112, the location unit 213 determines the state of node N i Assuming that the fault point is P, the candidate value R fk to node N i The fault point resistance is assumed to be P. Hereinafter, the node N i is called the "simulated fault point", and the candidate value R fk is called the "simulated fault point resistance."

[0093] The calculations performed by location unit 213 in step S112 are described in detail below. The calculations performed by location unit 213 in step S112 specifically include a step of calculating the voltage and current at fault point P, and a step of calculating the voltage and current after the fault at the installation point of measuring device 13. The calculations are described in detail below.

[0094] [Step to calculate voltage and current at fault point P] First, the node N assumed to be the fault point P i As mentioned above, in this example, the type of fault that has occurred is a line-to-ground fault. In this case, the following formula is used to calculate the current and voltage.

[0095]

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[0096]

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[0097] As described above, the orientation unit 213 performs calculations using a symmetric coordinate system. Therefore, the components of the current I, voltage V, and impedance matrix Z are given superscripts to indicate that they are expressed using a symmetric coordinate system. The superscript "0" means zero phase, the superscript "1" means positive phase, and the superscript "2" means negative phase. The same applies in the following explanation.

[0098] In equations (11) and (12), "F" indicates after a fault. Also, the R in the denominator on the right side of equation (11) fk is one of multiple candidate values ​​of the fault point resistance of the fault point P.

[0099] Node N assumed to be fault point P i The voltage can be expressed by the following equations (13) to (15).

[0100]

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[0101]

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[0102]

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[0103] V on the right hand side of equation (14) i 1 is the node N i The positive-phase voltage before the fault, and the value estimated in step S110 can be substituted therein. The currents in equations (11) and (12) can be substituted into the currents on the right-hand sides of equations (13) to (15). The location unit 213 uses equations (11) to (15) to determine the node N assumed to be the fault point P. i Calculate the voltage.

[0104] [Step of calculating the voltage and current after a fault at the installation point of the measuring instrument 13] Next, the voltage and current after the fault at the installation point of the measuring instrument 13 are formulated. As described above, the installation point of the measuring instrument 13 is a position corresponding to any one of the multiple nodes, and the node is referred to as node N. k Let us assume that.

[0105] Node N corresponding to the installation point of the measuring instrument 13 k The voltage is calculated using the following equations (16) to (18) using equations (13) to (15) and Ohm's law.

[0106]

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[0107]

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[0108]

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[0109] Furthermore, a node N corresponding to the installation point of the measuring instrument 13 k The current is calculated using the following equations (19) to (21) using equations (16) to (18) and Ohm's law.

[0110]

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[0111]

number

[0112]

number

[0113] Here, each of the formulas (19) to (21) is k and node N k Node N adjacent to j The denominator of the right hand side of the second equal sign in each of equations (19) to (21) is the current between node N k and node N j is the impedance between

[0114] The location unit 213 can calculate the voltage and current (calculated value C) after a fault occurs at the installation point of the measuring device 13 using the formulas (16) to (21).

[0115] Next, in step S113, the location unit 213 detects the simulated fault point (node ​​N i ), simulated fault point resistance (candidate value R fk ), and the calculated value C are stored in the database DB in correspondence with each other.

[0116] The location unit 213 further calculates the calculated value C corresponding to the post-fault measurement value D2 for all fault conditions in the above-mentioned procedure, and stores the calculated value C in the database DB.

[0117] In other words, the location unit 213 calculates the calculated value C corresponding to the measured value D2 after the fault in this case at the node N i For each (1≦i≦M), multiple candidate fault point resistances R fk (1≦k≦K). That is, the location unit 213 performs the processes of S112 and S113 on the simulated fault point (node ​​N i(1≦i≦M)), the loop R1 is executed for each i and M by using multiple simulated fault point resistors R fk This is executed every (1≦k≦K) (loop R2). Therefore, the orientation unit 213 obtains M×K calculated values ​​C.

[0118] In addition, the preset candidate value R fk There is no particular limit to the number K. fk may be K values ​​extracted from a range assumed to include the actual fault point resistance value of the fault point P.

[0119] For example, it is sufficient to set K values ​​that equally divide the range assumed to include the value of the actual fault point resistance of the fault point P into K-1 values.

[0120] Next, in step S114, the location unit 213 locates the fault point P based on the similarity between the measured value D2 after the fault and the M×K calculated values ​​C calculated in step S112, and calculates the fault point resistance R f Among the multiple assumed fault conditions, the fault condition whose corresponding calculated value C is similar to the measured value D2 after the fault is considered to be closer to the state of the power system 1 after the fault. Using this, the locating unit 213 locates the fault point P while estimating the fault point resistance R f Estimate.

[0121] Specifically, the locating unit 213 uses an evaluation function indicating the degree of similarity to locate the fault point P. The evaluation function used is a function that changes according to the difference between the measured value and the calculated value C for the voltage and current of each phase in a symmetrical coordinate system expressed by the zero phase, the positive phase, and the negative phase.

[0122] In this embodiment, the orientation unit 213 uses an evaluation function F shown in the following equation (22).

[0123]

number

[0124]

number

[0125] p in equation (22) is a variable shown in equation (23), and the node N assumed to be the fault point P i and the candidate value R of the fault point resistance of the fault point P fk This is a summary of some of the above.

[0126] The evaluation function of equation (22) is a weighted sum obtained by multiplying the absolute value of the difference between the post-fault measurement value D2 and the calculated value C for the voltage of each phase in the symmetric coordinate system and the difference between the post-fault measurement value D2 and the calculated value C for the current of each phase by predetermined weights w1 to w6.

[0127] The location unit 213 uses predetermined weights w1 to w6 set according to the type of fault. For example, if the type of fault is a ground fault, the weight w1 related to the zero-phase voltage and the weight w4 related to the zero-phase current may be set to 1, and the other weights may be set to 0. Alternatively, if the type of fault is not a ground fault, the weight w1 related to the zero-phase voltage and the weight w4 related to the zero-phase current may be set to 0, and the other weights may be set to 1.

[0128] The evaluation function is not limited to the example of formula (22). As another example, instead of the absolute value of the difference between the measured value D2 after the failure and the calculated value C in formula (22), another function that increases as the absolute value of the difference between the measured value D2 after the failure and the calculated value C increases may be used.

[0129] The location unit 213 calculates an evaluation value F(p) using an evaluation function for each of all fault conditions (combinations of simulated fault points and simulated fault point resistances), generates data for effective value analysis indicating the calculated evaluation values, and stores the generated data for effective value analysis in a database DB.

[0130] <Data for effective value analysis> 11 is a schematic diagram showing a data structure and an example of effective value analysis data. As shown in the figure, the effective value analysis data includes an evaluation value and a simulated fault point resistance (candidate value Rfk ) and the simulated fault point (node ​​N i The orientation unit 213 sorts the calculated evaluation values ​​in ascending order, for example, to generate effective value analysis data.

[0131] Next, in step S115, the output unit 214 selects the fault condition (simulated fault point (node ​​N i ) and simulated fault point resistance (candidate value R fk )) and extract the extracted simulated fault point (node ​​N i ) and simulated fault point resistance (candidate value R fk ) is the orientation result (fault point P and fault point resistance R f For example, in the data example shown in FIG. 11, the location unit 213 outputs the node N 100 The node name "NO100" is the fault point resistor R f Then, the RMS method location process ends.

[0132] As described above, the value of the earth capacitance of the zero-phase component in each branch can be obtained from the geometric structure of the power system 1, such as the line distance of the distribution line 11 and the height of the utility pole 15. However, in reality, due to the influence of devices such as transformers, the influence of low-voltage distribution lines, the influence of houses and trees, or the influence of weather conditions, an error of about two to three times occurs from the calculated earth capacitance. Therefore, due to this error, the location accuracy of the fault point P by the effective value location method is reduced. In contrast, in this embodiment, the information processing device 2 calculates the earth capacitance of the zero-phase component of each branch based on the earth capacitance (substation earth capacitance) of the power system 1 measured by the earth capacitance measuring device 16, and rewrites the branch data with the calculated value. This makes it possible to reduce the model error of the earth capacitance of the zero-phase component of the branch data in the node branch model, and therefore to improve the location accuracy of the fault point P by the effective value location method.

[0133] ===== Second embodiment ===== Next, a second embodiment will be described. In this embodiment, the information processing device 2 calculates the fault point resistance R f Calculate the calculated fault point resistance R f The second embodiment differs from the first embodiment in that the fault point P is located using the above. The hardware configuration and the functional configuration of the information processing device 2 are similar to those of the first embodiment, and therefore the description thereof will be omitted.

[0134] The location unit 213 in this embodiment calculates a calculated value C corresponding to a post-fault measurement value D2 when one of a plurality of nodes N provided in the power system 1 is assumed to be a fault point P, based on a fault point resistance estimated from a measurement value D0 of the earth capacitance, and locates the fault point P based on the calculated value C and the post-fault measurement value D2.

[0135] 12 is a flowchart for explaining the second effective value method location processing executed by the information processing device 2 in this embodiment. The processing of steps S201 to S203 of the second effective value method location processing in this embodiment is similar to the processing of steps S101 to S103 of the first effective value method location processing in the first embodiment, and therefore the description thereof will be omitted.

[0136] In this embodiment, following step S203, in step S204, the estimation unit 212 estimates the fault point resistance R f Estimate.

[0137] The zero-phase voltage V0 calculated by the above-mentioned formula (1) can be approximately calculated by the following formula (24) if the absolute value of the line impedance is sufficiently smaller than the earth resistance of the earth capacitance measuring device 16 (for example, about 10,000 Ω).

[0138]

number

[0139] Here, E is the line voltage of a healthy phase. A healthy phase is a phase in which no fault occurs in the power distribution line 11. Furthermore, ω is the angular frequency of the commercial power supply of the power system. Furthermore, R0 is the earth resistance of the earth capacitance measuring device 16. The earth resistance R0 is a value (e.g., approximately 10,000 Ω) that is set in advance in the earth capacitance measuring device 16. The database DB stores the angular frequency ω and the earth resistance R0 in advance.

[0140] The estimation unit 212 uses the zero-phase voltage V0 calculated by the above-mentioned equation (1) and the ground capacitance C0 of the zero-phase component of the power system 1 to calculate the fault point resistance R f Calculate.

[0141] In step S212, the location unit 213 calculates the fault point resistance R f is assumed to be the resistance of the fault point P to calculate the calculated value C. Therefore, in the second effective value method location process in this embodiment, the location unit 213 does not repeatedly execute the loop R2 of the first effective value method location process in the first embodiment shown in Fig. 9. Other processes of steps S210 to S215 of the second effective value method location process in this embodiment are similar to the processes of steps S110 to S115 of the first effective value method location process in the first embodiment, and therefore description thereof will be omitted.

[0142] In the first embodiment, the fault point resistance R f Since is unknown, the orientation unit 213 performs the first effective value method orientation process by i The calculated values ​​C of each of the K fault point resistances R f That is, in the first embodiment, the above-mentioned loop R2 needs to be repeated K times, which may take a long time for the calculation.

[0143] In contrast, in this embodiment, the location unit 213 calculates the fault point resistance R of the fault point P based on the measured value D0 of the ground capacitance of the power system 1. fTherefore, it is not necessary to repeatedly execute loop R2 in the second effective value method location process. Therefore, the calculation time in the second effective value method location process can be shortened. Specifically, in the first embodiment, M×K calculated values ​​C are calculated, whereas in this embodiment, M calculated values ​​C are calculated.

[0144] In addition, the fault point resistance R is calculated by using the zero-phase component capacitance C0 of power system 1. f By calculating the fault point resistance R f Since it is possible to calculate the above, the location accuracy of the fault point P can be improved.

[0145] =====Third embodiment===== Next, a third embodiment will be described. In the first and second embodiments, the information processing device 2 locates the fault point P by an effective value method, but in this embodiment, the information processing device 2 locates the fault point P by a resonant frequency method, which is different. The hardware configuration and the functional configuration of the information processing device 2 are the same as those of the first embodiment, so the description thereof will be omitted.

[0146] The location unit 213 in this embodiment identifies the resonant frequency of the power system 1 based on the results of frequency analysis of the power system 1 obtained using the post-fault measurement value D2, and locates the fault point P based on the identified resonant frequency and the estimated fault point resistance.

[0147] 13 is a flowchart for explaining the resonant frequency method location processing executed by the information processing device 2 in this embodiment. The processing of steps S301 to S302 of the resonant frequency method location processing in this embodiment is similar to the processing of steps S101 to S102 of the first effective value method location processing in the first embodiment, and therefore the description thereof will be omitted.

[0148] In this embodiment, following step S302, in step S303, the location unit 213 identifies a resonant frequency from the time-series waveform data of the zero-phase current.

[0149] Fig. 14 is a diagram for explaining the process of identifying the resonant frequency. In the illustrated graph 1010, the vertical axis is the zero-phase current and the horizontal axis is time, and represents the time-series waveform data of the zero-phase current. The location unit 213 performs a fast Fourier transform (FFT) on the waveform data of the zero-phase current shown in the graph 1010 as shown in the graph 1020. In the illustrated graph 1020, the vertical axis is the power spectrum and the horizontal axis is the frequency. The location unit 213 determines the frequency at which the power spectrum peaks (symbol 1021) among the frequencies exceeding a preset power spectrum threshold value α as the resonant frequency f0.

[0150] In this embodiment, the locating unit 213 specifies the resonance frequency based on the waveform data of the zero-phase current, but the method is not limited to this and the resonance frequency may be specified based on the waveform data of the zero-phase voltage. Also, the method of specifying the resonance frequency is not limited to the above, and may be based on the analysis results of frequency analysis (Fourier transform) performed based on the waveform data of the zero-phase current or the zero-phase voltage.

[0151] Next, in step S304, the estimation unit 212 estimates the fault point resistance R based on the substation ground capacitance (the measured value D0 of the ground capacitance of the power system 1). f Estimate the fault point resistance R f The estimation method is the same as in the second embodiment, and therefore the description thereof will be omitted.

[0152] Next, in step S305, the location unit 213 calculates the resonant frequency characteristic. Specifically, the location unit 213 calculates the resonant frequency characteristic based on the input data read in step S301 and the fault point resistance R f Using this, the resonance frequency f is calculated using the following equations (25) to (27).

[0153]

number

[0154]

number

[0155]

number

[0156] Here, R f is the fault point resistance, R u1 is the total resistance (positive sequence component) of the distribution line 11 where the fault occurred, and l fu is the distance from the distribution substation 10 to the fault point P, R T1 is the resistance (positive sequence component) of the transformer installed in the distribution substation 10, R u0 is the total resistance (zero-phase component) of the distribution line 11 where the fault occurred, L u1 is the total inductance (positive sequence component) of the distribution line 11 where the fault occurred, L T1 is the inductance (positive sequence component) of the transformer installed in the distribution substation 10, L u0 is the total inductance (zero-phase component) of the distribution line 11 where the fault occurs.

[0157] The location unit 213 is a distance l from the distribution substation 10 to the fault point P. fu Change each distance l fu For example, the location unit 213 calculates the resonant frequency f at each of the nodes N i The distance to each fu Then, for each node N i Calculate the resonant frequency f for each of these assuming them to be fault points P.

[0158] Next, in step S306, the location unit 213 calculates the fault point resistance R f , the distance l from the distribution substation 10 to the fault point P fu , and the calculated resonant frequency f are associated with each other and stored as resonant frequency data in the database DB.

[0159] <Resonant frequency data> FIG. 15 is a schematic diagram showing the data structure and an example of the resonant frequency data. The resonant frequency data is obtained by calculating the result of FFT and the fault point resistance R f and the distance l from distribution substation 10fu and resonance frequency f. The result of the FFT is the resonance frequency f0 ("1200" in the example shown in the figure) (unit: Hz (Hertz)) identified by frequency analysis in S303.

[0160] Next, in step S307, the locating unit 213 locates the fault point P by comparing the resonant frequency data with the resonant frequency f0 calculated in step S303.

[0161] 16 is a diagram for explaining the resonant frequency analysis. The resonant frequency data has characteristics as shown in a graph 1030. The vertical axis of the graph 1030 is the resonant frequency f, and the horizontal axis is the distance l from the distribution substation 10. fu The location unit 213 extracts the resonance frequency f that has the smallest difference from the resonance frequency f0 obtained in step S303 from the resonance frequency data, and calculates the distance l corresponding to the extracted resonance frequency f. fu Node N in i is located at the fault point P.

[0162] For example, in the data example shown in FIG. 15, the location unit 213 identifies the node N with the node name "NO102" at a distance "7.5" corresponding to the resonance frequency f "1205" that has the smallest difference from the resonance frequency f0 "1200". 102 is located at the fault point P.

[0163] Next, in step S308, the output unit 214 outputs the located fault point P as a location result. After that, this resonant frequency method location process ends.

[0164] According to the above-described procedure, the fault point resistance R f By calculating the fault point resistance R f Then, in the resonant frequency method, the calculated fault point resistance R fBy calculating the resonant frequency f using the above formula (27), the resonant frequency f can be calculated more accurately, thereby improving the accuracy of locating the fault point P. In addition, since the information processing device 2 substitutes the zero-phase component of the measurement value D0 of the earth capacitance measuring device 16 for C0 in the above formula (27), the resonant frequency f can be calculated more accurately. This improves the accuracy of locating the fault point P using the resonant frequency method.

[0165] =====Summary===== As described above, the information processing device 2 of the embodiment is an information processing device 2 that locates a fault point when a fault occurs in the power system 1, and includes a first acquisition unit 210 that acquires a first measurement value of the earth capacitance of the power system 1, an estimation unit 212 that estimates at least one of the earth capacitance of the zero-phase component in each of the distribution lines 11 between multiple nodes N provided in the power system 1 or the fault point resistance based on the first measurement value, and a location unit 213 that locates the fault point based on the estimation result by the estimation unit 212.

[0166] According to this configuration, since the measured capacitance to ground of the power system 1 is used, the fault point can be located with high accuracy.

[0167] In addition, in the information processing device 2, the estimation unit 212 estimates the zero-phase-sequence component capacitance to earth in each of the distribution lines 11 between nodes N by calculating the zero-phase-sequence component capacitance to earth per unit length of the distribution lines 11 of the power system 1 based on the first measurement value.

[0168] According to such a configuration, the capacitance to earth of the zero-phase component in each of the distribution lines 11 (each branch) between the nodes N can be estimated more accurately with a simple calculation.

[0169] Furthermore, in the information processing device 2, the estimation unit 212 estimates the capacitance to earth of the zero-phase component of each of the distribution lines between the nodes N based on the first measurement value, the capacitance to earth of the zero-phase component of the power system 1 calculated in advance from the structure of the power system 1, and the capacitance to earth of the zero-phase component of each of the distribution lines 11 between the nodes N calculated in advance from the structure of the power system.

[0170] According to such a configuration, by utilizing the capacitance to earth of the zero-phase component of each of the distribution lines 11 between the nodes N, which is calculated in advance from the structure of the power system, it is possible to estimate the capacitance to earth of the zero-phase component of each of the distribution lines 11 (each branch) between the nodes N with higher accuracy.

[0171] The information processing device 2 also includes a second acquisition unit 211 that acquires second measurement values ​​including voltage and current after a fault from a measuring instrument 13 installed in the power system 1, and the location unit 213 calculates a calculation value corresponding to the second measurement value when one of a plurality of nodes N provided in the power system is assumed to be the fault point based on at least one of the estimated zero-phase component capacitance to earth or the estimated fault point resistance, and locates the fault point based on the calculated calculation value and the second measurement value.

[0172] According to this configuration, it is possible to improve the location accuracy by the effective value method.

[0173] The information processing device 2 also includes a second acquisition unit 211 that acquires second measurement values ​​including the voltage and current after the fault from a measuring instrument 13 installed in the power system 1, and a location unit 213 identifies the resonant frequency of the power system based on the result of frequency analysis of the power system 1 obtained using the second measurement values, and locates the fault point based on the identified resonant frequency and the estimated fault point resistance.

[0174] With this configuration, it is possible to improve the location accuracy using the resonance frequency method.

[0175] The above-mentioned embodiment is for the purpose of facilitating understanding of the present invention, and is not intended to limit the present invention. Furthermore, the present invention can be modified or improved without departing from the spirit of the present invention, and it goes without saying that the present invention includes equivalents thereof.

[0176] For example, the data stored in the above-mentioned database DB may be read by the CPU 21 via the recording medium drive unit 26, or may be obtained from an external computer or server via the network connection unit 27.

[0177] In addition, various data generated by each function of the information processing device 2, such as the above-mentioned converted measurement data, data for effective value analysis, or resonant frequency data, may be stored in the memory unit 25 by the CPU 21, may be written to a recording medium via the recording medium driving unit 26, may be stored as a structure on the memory 22, or may be output to the output unit 24 together with the positioning results. [Explanation of symbols]

[0178] power system 1 Distribution Substation 10 Power Lines 11 Circuit breaker 12 Measuring instrument 13 Automatic switch 14a, 14b Electric pole 15 Earth capacitance measuring device 16 Data processing device 2 CPU 21 Memory 22 Input section 23 Output section 24 Memory section 25 Recording medium drive unit 26 Network connection 27 First acquisition part 210 2nd acquisition part 211 Estimation part 212 Orientation section 213 Output section 214 Database DB

Claims

1. An information processing device that locates a fault point when a fault occurs in a power system, A first acquisition unit that acquires a first measured value of the ground capacitance of the power system; an estimation unit that estimates at least one of a zero-phase-sequence component capacitance to earth and a fault point resistance in each of a plurality of power distribution lines between a plurality of nodes provided in the power system based on the first measurement value; A location unit that locates the fault point based on the estimation result by the estimation unit; Including, Information processing device.

2. 2. The information processing device according to claim 1, The estimation unit is estimating a zero-phase-sequence capacitance to earth of each of the distribution lines between the nodes by calculating a zero-phase-sequence capacitance to earth per unit length of the distribution line of the power system based on the first measurement value; Information processing device.

3. 2. The information processing device according to claim 1, The estimation unit is estimating a capacitance to earth of a zero-phase component of each of the distribution lines between the nodes based on the first measurement value, a capacitance to earth of a zero-phase component of the power system calculated in advance from a structure of the power system, and a capacitance to earth of a zero-phase component of each of the distribution lines between the nodes calculated in advance from the structure of the power system; Information processing device.

4. 4. The information processing device according to claim 1, a second acquisition unit that acquires second measured values ​​including a voltage and a current after a fault from a sensor installed in the power system; The orientation unit includes: A calculation value corresponding to the second measurement value when any one of a plurality of nodes provided in the power system is assumed to be the fault point is calculated based on at least one of the estimated zero-phase component capacitance to earth or the estimated fault point resistance, and the fault point is located based on the calculated value and the second measurement value. Information processing device.

5. 2. The information processing device according to claim 1, a second acquisition unit that acquires second measured values ​​including a voltage and a current after a fault from a sensor installed in the power system; The locating unit identifies a resonant frequency of the power system based on a result of a frequency analysis of the power system obtained using the second measurement value, and locates the fault point based on the identified resonant frequency and the estimated fault point resistance. Information processing device.

6. An information processing method in which an information processing device locates a fault point when a fault occurs in a power system, comprising: obtaining a first measurement of capacitance to ground of the power system; estimating at least one of a zero-phase-sequence component capacitance to earth and a fault point resistance in each of a plurality of power distribution lines between a plurality of nodes in the power system based on the first measurement value; Locating the fault point based on the estimated result; Including, Information processing methods.

7. An information processing program for locating a fault point when a fault occurs in a power system, On the computer, A first acquisition unit that acquires a first measured value of the ground capacitance of the power system; an estimation unit that estimates at least one of a zero-phase-sequence component capacitance to earth and a fault point resistance in each of a plurality of power distribution lines between a plurality of nodes provided in the power system based on the first measurement value; A location unit that locates the fault point based on the estimation result by the estimation unit; To achieve this, Information processing program.

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