JPH1019965A - Faulty point locating equipment - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable accurate location of a faulty point even when sampling of voltage/current data at each terminal of a multi-terminal transmission line is not synchronized. SOLUTION: Voltage/current data at each terminal of a multi-terminal transmission line are received by data receiving parts 1 and 2. Based on the voltage/ current data on a first circuit and those on a second circuit received by the data receiving parts 1 and 2, an SP(sampling timing) difference measuring part 3 measures a sampling timing difference Φ between them. Based on the sampling timing difference Φ measured by the SP difference measuring part 3, phase correction is executed in an SP difference correcting part 4 in regard to the voltage/current data on the first or second circuit with either the first or second circuit made a reference, and a location computation part 5 executes the computation of location of a faulty point on the basis of the voltage/current data made the reference and the voltage/current data corrected in the SP difference correcting part.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a fault point locating apparatus for performing fault point locating of a transmission line based on voltage / current data of each terminal of a multi-terminal transmission line.

[0002]

2. Description of the Related Art As a method of locating a fault on a transmission line,
Collect the voltage data and current data of each terminal of the transmission line,
In some cases, fault point location is performed based on the voltage data and the current data. As a fault point locating method of such a fault point locating device, there are a surge receiving method and a pulse radar method, and in recent years, an impedance measuring method has been applied. The surge receiving method and the pulse radar method require a signal coupling device to an expensive transmission line, while the impedance measuring method converts the voltage and current obtained by a voltage transformer or current transformer into digital data to obtain the impedance, It measures the distance to the accident point.
As the impedance method, a method of determining the voltage and current of one terminal (Japanese Patent Publication No. 58-29471) and a method of
A method that uses the voltage and current of the terminals ("Transmission line fault point locator"
Hoki, Kitani, 1957 Ohmsha).

Here, there is a method for realizing a one-terminal determination type impedance measurement method based on the following equation by utilizing that the vector sum current of the current data of each terminal of the transmission line is the fault current component itself. is there. FIG. 6 is a system diagram showing the principle. In FIG. 6, VA is the voltage at terminal A, and VB is B
The terminal voltage, VF, is the residual voltage at the fault point F,
In this case, it is well known that the following equations (1) and (2) hold.

VA = x · z · IA + VF (1) VF = IF · RF (2) VA: Voltage at A terminal IA: Current at A terminal z: Impedance value per unit line length of transmission line VF: Accident Point remaining voltage IF: fault current RF: fault point resistance x: distance from A terminal to fault point Here, if RF is a real resistance component, equation (3) is established.

Im ｛VA ・ IF *｝ = Im ｛x ・ z ・ IA ・ IF * + RF ・ IF｝ IF *｝ = Im ｛x ・ z ・ IA ・ IF *｝ (3) In this equation (3) , * Indicates a conjugate complex number, and Im ｛｝ indicates an imaginary part of ｛｝. Further, from Equation (3), the orientation value x is given by Equation (4).

X = Im ｛VA ・ IF *｝ / Im ｛z ・ IA ・ IF *｝ (4) If the voltage data and the current data of the opposite terminal can be used, the remaining voltage at the fault point is obtained from the equation (5). The orientation value x can be obtained by equation (6) without being affected by VF in principle.

VA = x · z · IA + VF VB = (L−x) · z · IB + VF (5) x = {VA−VB + L · z · IB} / z (IA + IB) (6) VB: B terminal IB: Current at terminal B L: Line length between terminals A and B When fault location is performed by the location method shown in equation (4) or (6), voltage data and current at the opposite terminal Data is needed.

It is one means to provide a dedicated communication line for the fault point locating device in order to obtain the voltage data and the current data of the opposite terminals. However, it is necessary to synchronize sampling between the opposite terminals. Further, there is a problem that the cost becomes very high. As a solution to this, for example, a configuration is conceivable in which a current differential relay provided as a transmission line protection relay is used as a data collection device to obtain voltage data and current data of its own terminal and the opposite terminal. With this configuration, the above problem is solved.

[0009]

However, in the case of a multi-terminal transmission line, current data of the other line is also required since the transmission is performed in consideration of the induction from the other line. For example, in the case of a parallel two-line transmission line, it is necessary to consider the amount of guidance from an adjacent line.

That is, the denominator (z ·
IA) part or (z · IB), z in equation (6)
The (IA + IB) part is expanded as shown in the following equation (7). Here, the case of an r-phase accident is shown.

(Z · I) r = zrr · Ir + zrs · Is + zrt · It + zrr ′ · Ir ′ + zrs ′ · Is ′ + zrt ′ · It ′ (7) z ′: Neighbor line mutual impedance I ′: Neighbor line current r , S, t: phase As can be seen from the equation (7), the calculation of the fault point location is usually performed in consideration of the guidance from the adjacent line in order to improve the accuracy.

As described above, for example, when the voltage data and the current data of each of the first line and the second line are obtained from the current differential relay of each of the first line and the second line,
Normally, since the current differential relay has a line-by-line device configuration, sampling synchronization is not established between the devices of the first line and the second line. Therefore, the voltage data and the current data cannot be directly supplied to the calculation of the fault point location.

An object of the present invention is to provide an accident point locating method using multi-terminal data even when sampling synchronization of voltage / current data obtained from a data collection device for each terminal of a multi-terminal transmission line is not established. It is to provide a point location device.

[0014]

According to a first aspect of the present invention, data of voltage and current at each terminal of a first line of a multi-terminal transmission line and voltage and current data at each terminal of a second line of a multi-terminal transmission line are collected. The sampling timing at the data collecting device is asynchronous between the first line and the second line, and the fault point locating device performs fault point locating based on the collected voltage / current data. A data receiving unit that obtains the voltage / current data of each terminal of the line and the second line, and sampling between them based on the voltage / current data of the first line and the voltage / current data obtained by the data receiving unit An SP difference measuring unit for measuring a timing difference; and a first time based on either the first line or the second line based on the sampling timing difference measured by the SP difference measuring unit. Alternatively, an SP difference correction unit for performing phase correction on the voltage / current data of the second line, and a location calculation for performing a fault point location calculation based on the reference current / voltage data and the voltage / current data corrected by the SP difference correction unit Part.

According to the first aspect of the present invention, the data receiving unit receives the voltage / current data of each terminal of the first line and the second line, and the SP difference measuring unit receives the first and second data received by the data receiving unit.
Based on the voltage / current data of the line and the voltage / current data of the second line, a sampling timing difference between them is measured. The SP difference correction unit performs phase correction on the voltage / current data of the first line or the second line based on either the first line or the second line based on the sampling timing difference measured by the SP difference measurement unit. Then, the orientation calculation unit calculates the fault location based on the current-voltage data as a reference and the voltage-current data corrected by the SP difference correction unit.

According to a second aspect of the present invention, in the first aspect of the present invention, there is provided an SP signal receiving unit for directly receiving a sampling timing signal of the first line and the second line or a signal synchronized with the signal from the data collection device, The SP difference measurement unit is S
The measurement of the sampling timing difference is performed based on the signal indicating the sampling timing of the first line and the second line received by the P signal receiving unit.

According to a second aspect of the present invention, in addition to the operation of the first aspect, the SP signal receiving unit directly outputs a sampling timing signal of the first line and the second line or a signal synchronized with the signal from the data collection device. Receive. Then, the SP difference measuring unit receives the first line and the second line received by the SP signal receiving unit.
The sampling timing difference is measured based on a signal indicating the sampling timing of the line.

According to a third aspect of the present invention, in the first aspect of the present invention, the data collection device collects voltage / current data at a fixed timing based on the sampling timing signal of its own device and performs data transmission. A reception timing measurement unit that measures the reception timing of the voltage / current data from the data collection device received by the data collection unit, and the SP difference measurement unit uses the data reception timing signal from the data collection device measured by the reception timing measurement unit. The measurement of the sampling timing difference is performed.

According to a third aspect of the present invention, in addition to the operation of the first aspect, the data collection device collects voltage / current data at a fixed timing based on its own sampling timing signal and transmits the data. The SP difference measurement unit measures the sampling timing difference based on the data reception timing signal from the data collection device measured by the reception timing measurement unit.

The invention according to claim 4 is the invention according to claims 1 to 3.
In the invention, the SP difference correction unit obtains a phase difference between the voltage data of the first line from the data collection device and the voltage data of the second line from the data collection device, and determines the sampling timing difference based on the phase difference. The measurement is performed.

According to a fourth aspect of the present invention, in addition to the functions of the first to third aspects of the present invention, the SP difference correction unit includes a first line voltage data from the data collection device and a second line voltage from the data collection device. The difference of the sampling timing is measured based on the phase difference with the voltage data.

The invention according to claim 5 is the invention according to claims 1 to 4.
In the present invention, the SP difference correction unit corrects the sampling timing difference for the voltage / current data on the healthy line using the voltage / current data on the fault line as a synchronization reference.

According to the fifth aspect of the present invention, in addition to the functions of the first to fourth aspects, the SP difference correction unit uses the voltage / current data of the faulty line as a synchronization reference to obtain the voltage / current data of the healthy line. Is corrected for the sampling timing difference.

[0024]

Embodiments of the present invention will be described below. FIG. 1 is a block diagram showing a first embodiment of the present invention, and FIG. 2 is a system diagram showing an accident point locating apparatus according to the present invention applied to a multi-terminal transmission line. FIG. 2 shows a case of a parallel two-line transmission line that is a two-terminal transmission line, but the same applies to a multi-terminal transmission line of three or more terminals.
The parallel two-circuit transmission line is a multi-terminal transmission line in which the first line 1L and the second line 2L are to be located.

In FIG. 2, the first line 1 is connected to the A terminal side.
A current transformer 11A for detecting a current of 1L and a current transformer 12A for detecting a current of the second line 2L are provided, and a transformer 21A and a second line 2L for detecting a voltage of the first line 1L.
A transformer 22A for detecting the voltage of the power supply is provided. The current and voltage of the first line detected by the current transformer 11A and the transformer 21A are collected by the 1L data collection device 101A. Similarly, the current and voltage of the second line detected by the current transformer 12A and the transformer 22A are equal to those of the 2L data collection device 10A.
Collected at 2A.

On the other hand, the current transformer 11B for detecting the current of the first line 11L and the second
A current transformer 12B for detecting the current of L is provided, and a transformer 21B for detecting the voltage of the first line 1L and a transformer 22B for detecting the voltage of the second line 2L are provided.
The current and voltage of the first line detected by the current transformer 11B and the transformer 21B are collected by the 1L data collection device 101B. Similarly, the current and voltage of the second line detected by the current transformer 12B and the transformer 22B are collected by the 2L data collection device 102B.

Each of the 1L data collection devices 101A and 101 of the A terminal and the B terminal installed on the first line 1L side.
B is connected by a transmission system such as a microwave line via transmission interfaces 111A and 111B, and the data collection device 101A is configured to be able to acquire the voltage data and the current data of the terminal B which is the opposite terminal.
Similarly, on the second line 2L side, the 2L data collection devices 102A and 102B of the A terminal and the B terminal installed on the second line 2L side
The data collection device 102A is configured to be able to acquire the voltage data and the current data of the terminal B, which is the opposite terminal, by being connected by a transmission system such as a microwave line via 2A and 112B.

The fault point locating device 30 according to the present invention is connected to these data collecting devices 101A and 102A, and from there, the voltage data and current data of the first line 1L and the second line 2L of the A terminal, and the data data of the B terminal, respectively. 1st line 1L
And voltage data and current data of the second line 2L are obtained and the orientation calculation is performed. In this case, the data collection device 1
As 01 and 102, a protective relay device or an oscilloscope device connected to the opposite terminal via a transmission system is used.

Next, FIG. 1 is a block diagram showing a first embodiment of the present invention. In FIG. 1, the accident point locating device 30 is configured as follows. A of the first line 1L
The voltage data and the current data of the terminal and the B terminal are received by the 1L data receiving unit 1, and similarly, the voltage data and the current data of the A terminal and the B terminal of the second line 2L are received by the 2L data receiving unit 2. The received voltage data and current data (hereinafter referred to as voltage / current data) are input to the SP difference measurement unit 3. The SP difference measuring unit, based on the voltage / current data of the first line 1L and the voltage / current data of the second line 2L received by the 1L data receiving unit 1 and the 2L data receiving unit 2, uses a sampling timing difference (hereinafter, referred to as a sampling timing difference between them).と い う is measured.

Then, the SP difference correction unit 4 sets the first line 1L or the second line based on either the first line 1L or the second line 2L based on the SP difference で measured by the SP difference measurement unit 3. The phase correction is performed on the 2L voltage / current data.
FIG. 1 shows a case where the voltage / current data of the first line 1L is used as a synchronization reference. That is, a case is shown in which the sampling timing (hereinafter referred to as SP) of the voltage / current data of the second line 2L is phase-corrected to the SP of the first line 1L. The voltage / current data of the first line and the voltage / current data of the second line whose phase has been corrected are input to the location calculation unit 5, and the location calculation unit calculates the fault point based on the voltage / current data.

That is, the 1L data receiving section 1 receives the voltage / current data of all terminals of the first line 1L from the 1L data collection device 101. Similarly, the 2L data receiving unit 2 receives voltage / current data of all terminals of the second line 2L from the 2L data collection device 102. The SP difference measuring unit 3 receives the first line 1L received by the 1L data receiving unit 1 and the 2L data receiving unit 2.
Then, the SP difference 間 の between the first line 1L and the second line 2L is measured based on the voltage and current data of the second line 2L.

Thereafter, the SP difference correction unit 4 corrects the SP difference Ф measured by the SP difference measurement unit 3 with reference to the voltage / current data of either the first line 1L or the second line 2L. For example, when the SP difference correction is performed on the voltage / current data on the second line 2L with reference to the voltage / current data on the first line 1L, the correction is performed using the equations (8) and (9). be able to.

V2m = V2ncosφ− (√3V2n−2V2n−1) sinφ (8) i2m = i2ncosφ− (√3i2n−2i2n−1) sinφ (9) V2m, i2m: sample values of 2L voltage and current data m: Sampling time series equivalent to the 1L side n: Sampling time series of 2L data received from the data collection device In the orientation calculation unit 5, the voltage / current data (V1m, i1m) received by the 1L data reception unit 1, Using the voltage / current data (V2m, i2m) after the SP difference correction is performed by the SP difference correction unit 4 according to the equations (8) and (9), using the calculation formulas such as the formula (6) to the fault point To determine the distance.

As described above, in the first embodiment, the parallel 2
The voltage and current data of each terminal of the line transmission line are collected by the respective data collection devices 101 and 102. Then, the accident point locating device 30 receives the collected voltage / current data of each terminal of the first line 1L by the 1L data receiving unit 1, and similarly receives the voltage / current data of each terminal of the second line 2L by the 2L data receiving unit. 2 and the first data obtained by these data receiving units 1 and 2
The SP difference 間 の between the voltage / current data of each of the line 1L and the second line 2L is measured by the SP difference measuring unit 3. After that, SP
In the correction unit 4, the first line 1 measured by the SP difference measurement unit 3
Based on the SP difference 間 の between L and the second line 2L, the phase correction is performed on the voltage / current data obtained by the respective data receiving units 1 and 2 with reference to either the first line 1L or the second line 2L. Then, the orientation calculation unit 5 uses the voltage-current data as a reference and the voltage-current data of each terminal, in which the SP difference 間 の between the first line 1L and the second line 2L obtained by the SP difference correction unit 4 is corrected. Calculate the accident point location.

Therefore, even if the voltage / current data of the first line 1L and the voltage / current data of the second line 2L are dumped asynchronously, the calculation of the fault point can be properly performed.

Next, a second embodiment of the present invention is shown in FIG. The second embodiment differs from the first embodiment shown in FIG. 1 in that the 1L data collection device 111 and the 2L data collection device 112 directly transmit the first line and the second line from the 1L data collection device 112, respectively.
1LSP signal receiving units 61 and 2LS for receiving a line sampling timing signal or a signal synchronized with the signal
A P signal receiving unit 62 is provided, and the SP difference measuring unit 3
The SP difference Ф is measured based on the signals indicating the sampling timings of the first line and the second line received by the LSP signal receiving unit 61 and the 2L signal receiving unit 62.

In FIG. 3, the SP difference measuring section 3 has the SPs of the first line 1L and the second line 2L received by the 1 LSP signal receiving section 61 and the 2 LSP signal receiving section 62, respectively.
The SP difference Ф is measured directly from the signal. The SP difference correction unit 4 performs the phase correction using the SP difference Ф measured in this manner in the same manner as in the first embodiment. The content of the operation is
Since it is the same as the first embodiment, the description is omitted.

Next, a third embodiment of the present invention is shown in FIG. The third embodiment is different from the first embodiment shown in FIG. 1 in that 1L for measuring reception timing when voltage / current data is received from the 1L data collection device 111 is measured.
A data reception timing measurement unit 71 and a 2L data reception timing measurement unit 72 that measures a 2L data reception timing that measures reception timing when voltage and current data are received from the 2L data collection device 112 are additionally provided. It is.

The 1L data collection device 111 and the 2L data collection device 112 respectively respond to their own SP signals.
Data is transmitted to the accident point locating device 30 at a predetermined timing. In this case, there is a difference between the transmission delay time in the data transmission between the 1L data collection device 111 and the accident location device 30, and the transmission delay time in the data transmission between the 2L data collection device and the accident location device 30. If not, the timing difference when the fault point locating device 30 receives the voltage / current data from the 1L data collection device 111 and the 2L data collection device 112, respectively, is 1L.
The SP difference between the data collection device 111 and the 2L data collection device 112 is Ф.

Utilizing this, the SP difference measuring unit 3 measures the voltage / current data from the first line 1L measured by the 1L data reception timing measuring unit 71 and the 2L data reception timing measuring unit 72. The data reception timing difference from the second line 2L voltage / current data is measured.
Thus, the SP difference Ф between the 1L data collection device 111 and the 2L data collection device 112 is obtained. The SP difference correction unit 4 performs the phase correction using the SP difference Ф measured in this manner in the same manner as in the first embodiment. The details of the calculation are the same as in the first embodiment, and a description thereof will be omitted.

Next, FIG. 5 is an explanatory diagram of the principle of measuring the SP difference Ф between the 1L data collection device 111 and the 2L data collection device 112. For example, when a current differential relay is considered as the data collection devices 111 and 112,
Normally, the digital relay samples analog input data every 30 electrical degrees and has a separate device configuration for each line. Sampling timing is asynchronous.

FIGS. 5A and 5B show a state in which the current differential relays of the 1L data collection device 111 and the 2L data collection device 112 sample the voltage at the same terminal. In this case, since the sampling timing is asynchronous between the 1L current differential relay and the 2L current differential relay, data is sampled at different timings. FIG. 5 (A), FIG.
In (B), the sampling timing difference between the 1L current differential relay and the 2L current differential relay indicates a state of φ.

In this state, when data is transmitted to the fault locating device, if the voltage data of the same terminal are the same, 1L, 2L
These voltage data transmitted from each of the L current differential relays represent exactly the same waveform.
Since the sampling timing is different between the 2L current differential relays, the fault point locating device 30 looks out of phase with the sampling timing difference Ф.

FIG. 5C shows this state. The SP difference measuring unit 3 of the accident point locating device 30 measures the SP difference by measuring the apparent phase difference 間 の between the voltages of the same terminal of 1L and 2L.

As described above, the data collection devices 111, 1
Accident point locating device 3 using voltage and current data from
0, each data collection device 1 of the multi-terminal transmission line
Even if the sampling timings of the sampling timings 11 and 112 are asynchronous, the sampling timing difference Ф is measured, and the difference Ф is corrected by the equation (8), so that the adjacent line compensation as shown in the equation (7) is also accurately performed. be able to. That is,
A highly accurate accident point location device 30 can be provided. in this case,
The calculation of the accident point location is performed by the equations (4) and (6).

Next, a fourth embodiment of the present invention will be described. In the above description, the SP difference correction unit 4 uses the voltage / current data on the faulty line side as a synchronization reference to set the first line 1L
Alternatively, the correction is performed in such a manner that the other is corrected based on the voltage / current data of one of the second lines 2L. In the fourth embodiment, the SP difference correction unit 4 converts the voltage / current data of the fault line into As a synchronization standard, SP difference correction is performed on data on the healthy line side.

For example, when the fault point locating calculation is performed using the formula (4) or (6), the voltage drop due to the transmission line impedance due to the current at the time of the fault is calculated as in formula (7). On the other hand, the SP difference correction is performed on the first line 1L or the second line 2
The correction is performed in such a manner that the other is corrected with reference to any one of the voltage / current data L, but the data on the corrected side is data containing a slight error due to a measurement error of the SP difference Ф or the like.

Here, when the voltage drop calculation of the equation (7) is performed on the data after performing the SP difference correction, the current value is generally smaller than that of the healthy circuit side when compared for each phase. The accident line is larger. For this reason, the calculation result shows that the influence on the faulty line side is greater than the influence on the healthy line (adjacent line) side. In other words, when performing the SP difference correction, it is better to use the data on the accident line side as a reference (7).
The voltage drop calculated by the formula can be obtained with higher accuracy, and as a result, the positioning accuracy can be improved. Therefore, the SP difference correction unit 4 performs the SP difference correction on the data on the healthy circuit side using the voltage / current data on the faulty circuit side as a synchronization reference. Thereby, the accuracy of the orientation calculation is improved.

[0049]

As described above, according to the present invention,
After correcting the sampling phase difference between unsynchronized sampling data obtained from each data collection device of a multi-terminal transmission line, it is used for orientation calculation, so accident point location for collecting data of all terminals This eliminates the need for a dedicated communication line for the device, and enables high-precision orientation without being affected by the resistance of the accident point in principle.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a first embodiment of the present invention.

FIG. 2 is a system configuration diagram in which the accident point locating device of the present invention is applied to a multi-terminal transmission line.

FIG. 3 is a block diagram showing a second embodiment of the present invention.

FIG. 4 is a block diagram showing a third embodiment of the present invention.

FIG. 5 is an explanatory diagram illustrating a principle of measuring a sampling timing difference in an SP difference measuring unit according to the present invention.

FIG. 6 is an explanatory diagram of fault point location on a transmission line.

[Explanation of symbols]

 Reference Signs List 1 1L data receiving section 2 2L data receiving section 3 SP difference measuring section 4 SP difference correcting section 5 Orientation calculating section 61, 62 SP signal receiving section 71, 72 Receiving timing measuring section 11, 12 Current transformer 21, 22 Transformer 1L 1st line 2L 2nd line 101 1L data collection device 102 2L data collection device 111, 112 Transmission interface

Claims (5)

[Claims] 1. A data collection device collects voltage / current data at each terminal of a first line of a multi-terminal transmission line and voltage / current data at each terminal of a second line of the multi-terminal transmission line. Sampling timing is asynchronous between the first line and the second line, and in the fault point locating device that performs fault point locating based on the collected voltage / current data, each of the first line and the second line A data receiving unit for obtaining voltage / current data of a terminal, and an SP for measuring a sampling timing difference between the data based on the voltage / current data of the first line and the voltage / current data of the second line obtained by the data receiving unit A difference measurement unit based on either the first line or the second line based on the sampling timing difference measured by the SP difference measurement unit; An SP difference correction unit for performing phase correction on the voltage / current data of the first line or the second line, and an accident point location based on the reference current / voltage data and the voltage / current data corrected by the SP difference correction unit. And a location calculation unit for performing the calculation of (1). 2. An SP signal receiving unit for directly receiving a sampling timing signal of the first line and the second line or a signal synchronized with the signal from the data collection device, and the SP difference measuring unit includes: The accident point locating device according to claim 1, wherein the measurement of the sampling timing difference is performed based on a signal indicating the sampling timing of the first line and the second line received by a signal receiving unit. 3. The data collection device collects voltage / current data at a fixed timing based on its own sampling timing signal and performs data transmission. The data collection device receives the data from the data collection device received by the data reception unit. A reception timing measurement unit for measuring reception timing of the voltage / current data, wherein the SP difference measurement unit measures the sampling timing difference based on a data reception timing signal from the data collection device measured by the reception timing measurement unit; 2. The method according to claim 1, wherein
Accident point locating device described in. 4. The SP difference correction unit calculates a phase difference between voltage data of a first line from the data collection device and voltage data of a second line from the data collection device, and based on the phase difference. 4. The fault point locating apparatus according to claim 1, wherein the measurement of the sampling timing difference is performed. 5. The system according to claim 1, wherein the SP difference correction unit corrects the sampling timing difference with respect to the voltage / current data on the healthy line side based on the voltage / current data on the fault line side as a synchronization reference. The accident point location device according to any one of claims 1 to 4.