CN113625162B - DC distribution network switching characteristic test system and method - Google Patents
DC distribution network switching characteristic test system and method Download PDFInfo
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Abstract
The invention discloses a system and a method for testing the switch characteristics of a direct current distribution network, wherein the testing system comprises a first local acquisition unit, a second local acquisition unit and a third local acquisition unit, wherein the first local acquisition unit is used for being connected with a mechanical switch branch in the direct current distribution network switch; the second on-site acquisition unit is used for being connected with a transfer branch in the direct current distribution network switch; the third on-site acquisition unit is used for being connected with the energy consumption branch in the direct current distribution network switch; the test host is connected with the first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit respectively and is also used for being connected with the electronic current transformer and the direct current switch control protection module in the direct current distribution network switch. According to the invention, the non-contact sensor such as the TMR (tunnel magnetic resistance) sensor or the open Hall is additionally arranged in the DC distribution network switch, so that a test system of the DC distribution network switch is built, the current step moment is used as the action completion moment of the switch, the turn-on and turn-off time sequence of a plurality of branches in the DC distribution network switch is tested, and a flexible and comprehensive test means is provided for the DC distribution network switch.
Description
Technical Field
The invention belongs to the technical field of direct current distribution network testing, and particularly relates to a direct current distribution network switch characteristic testing system and method.
Background
With the continuous development of power electronics technology, a direct current power distribution network is a main expression form of a future alternating current-direct current hybrid power network. The dc distribution network is compared with the ac distribution network, the dc distribution network provides a dc bus for the load, the dc load can be directly supplied by the dc bus, the ac load needs to be supplied by the inverter, and if the dc load proportion in the load is larger, the dc distribution will have a larger advantage.
The dc distribution network switch is a main technical bottleneck for developing a dc distribution network, and currently, the dc distribution network switch generally adopts a hybrid dc breaker, as shown in fig. 1, and includes a primary circuit and a secondary part. The primary circuit consists of a mechanical switch branch, a transfer branch and an energy consumption branch, and the secondary part consists of an electronic current transformer and a direct current switch control protection unit. And the electronic current transformer sends the current sampling value to a direct current switch control protector and a direct current distribution network control protector. The control action logic of the direct current switch is as follows: after receiving a switching-off instruction of the direct current switch control unit, the switching-off instruction is firstly closed by the transfer branch, then the mechanical switch branch is opened, the current is transferred to the transfer branch, then the transfer branch is turned off, the current is consumed to the energy consumption branch, and the whole process involves the matching relation of three direct currents. In the prior art, the test of the direct current distribution network switch can only measure the action time of the switch by observing the current change of the electronic current transformer, and no good test means are available for the whole action characteristic, action logic and working mode of the direct current distribution network switch.
Disclosure of Invention
Aiming at the problems, the invention provides a system and a method for testing the characteristics of a direct current distribution network switch, wherein non-contact sensors such as TMR (tunnel magnetic resistance) sensors or opening Hall sensors are additionally arranged on each branch in the direct current distribution network switch, the testing system of the direct current distribution network switch is built, the current step moment is used as the action completion moment of the switch, the switching-on and switching-off time sequence of a plurality of branches in the direct current distribution network switch is tested, and a flexible and comprehensive testing means is provided for the direct current distribution network switch.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
in a first aspect, the present invention provides a system for testing the switch characteristics of a dc distribution network, including:
the first on-site acquisition unit is used for being connected with a mechanical switch branch in the direct current distribution network switch;
the second on-site acquisition unit is used for being connected with a transfer branch in the direct current distribution network switch;
the third on-site acquisition unit is used for being connected with the energy consumption branch in the direct current distribution network switch;
the test host is connected with the first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit respectively and is also used for being connected with the electronic current transformer and the direct current switch control protection module in the direct current distribution network switch.
Optionally, the test host sends a trip command to a direct current switch control and protection module in the direct current distribution network switch based on a preset distribution network control and protection trip protocol, and records the departure time t of the trip command 0 ；
The first local acquisition unit, the second local acquisition unit and the third local acquisition unit acquire the current of the corresponding branch and send the current to the test host;
the testing host calculates the step moment of each branch based on the received current of each branch;
the test host computer calculates the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and the test host obtains the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer.
Optionally, the step time calculation process of each branch includes:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and the step final value I of each branch current is calculated 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
Optionally, the step time calculation process of the electronic current transformer includes:
at the time t of going out 0 Recording abrupt change time of current data sent by the electronic current transformer as a reference;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Performing cubic spline interpolation calculation on current data sent by an electronic current transformer, and calculating a step final value I of each branch current 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
Optionally, the cubic spline interpolation calculation formula is:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c).
Optionally, the first in-situ acquisition unit, the second in-situ acquisition unit, and the third in-situ acquisition unit are identical in structure, and each include: the non-contact sensor, the conditioning loop, the sampling module and the second optical fiber sending module are connected in sequence; the non-contact sensor is used for being arranged in a corresponding mechanical switch branch, a transfer branch or an energy consumption branch; the second optical fiber sending module is used for communicating with the test host.
Optionally, the test host includes an upper computer, a first optical fiber sending module and an optical fiber receiving module, where the upper computer is connected with the first optical fiber sending module and the optical fiber receiving module respectively.
In a second aspect, the present invention provides a method for testing the switch characteristics of a dc distribution network, including:
the test host is utilized to send a tripping command to a direct current switch control and protection module in the direct current distribution network switch based on a preset distribution network control and protection tripping protocol, and the departure time t of the tripping command is recorded 0 ；
The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are utilized to acquire currents of corresponding branches in a direct current distribution network switch, and the currents are sent to a test host;
calculating the step moment of each branch by using the test host based on the received current of each branch;
the testing host computer is used for calculating the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and obtaining the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer by using the test host.
Optionally, the step time calculation process of each branch includes:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and each branch current is calculatedIs a step end value I of (2) 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
Optionally, the step time calculation process of the electronic current transformer includes:
at the time t of going out 0 Recording abrupt change time of current data sent by the electronic current transformer as a reference;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Performing cubic spline interpolation calculation on current data sent by an electronic current transformer, and calculating a step final value I of each branch current 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
Optionally, the cubic spline interpolation calculation formula is:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c).
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a system and a method for testing the switching characteristics of a direct current distribution network, wherein a TMR sensor is adopted as a current sensor in the testing system, and an openable design is adopted, so that the response speed of current is not influenced by the installation position; the optical fiber transmission effectively solves the problems of pressure resistance and interference resistance in the test process; the original electronic current transformer is used as the overall current sample, and a current sensor is not required to be arranged at the line side; the sampling rate of the TMR sensor reaches 1MHz, and an interpolation algorithm is not needed, so that the calculated amount of a test system can be reduced; and performing cubic spline interpolation on the original electronic current transformer, eliminating quantization errors caused by the original sampling rate, and adapting to data of different sampling rates.
The invention has strong universality, takes the rising edge and the falling edge of the current as the logical time sequence basis of the switch action, adapts to the direct current distribution network switch test of any principle, can judge the switching process of the switch by only utilizing the current step characteristic, and is simple and practical.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings, in which:
fig. 1 is a schematic structural diagram of a dc distribution network switch in the prior art;
fig. 2 is a schematic structural diagram of a dc distribution network switch characteristic test system according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a dc distribution network switch characteristic test system and a dc distribution network switch according to an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The principle of application of the invention is described in detail below with reference to the accompanying drawings.
Example 1
The embodiment of the invention provides a system for testing the switch characteristics of a direct current distribution network, as shown in fig. 2, comprising:
the first in-situ acquisition unit (i.e. in-situ acquisition unit 1 in fig. 2) is used for being connected with a mechanical switch branch in the direct current distribution network switch in fig. 1;
the second in-situ acquisition unit (i.e. in-situ acquisition unit 2 in fig. 2) is used for being connected with the transfer branch in the direct current distribution network switch in fig. 1;
the third in-situ acquisition unit (i.e. in-situ acquisition unit 3 in fig. 2) is used for connecting with the energy consumption branch in the direct current distribution network switch in fig. 1;
the test host is connected with the first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit respectively and is also used for being connected with the electronic current transformer and the direct current switch control and protection module in the direct current distribution network switch in fig. 1. In a specific implementation manner of the embodiment of the present invention, the first in-situ acquisition unit, the second in-situ acquisition unit, and the third in-situ acquisition unit have the same structure, and each includes: the device comprises a non-contact sensor (TMR sensor), a conditioning loop, a sampling module and a second optical fiber transmitting module which are connected in sequence; the non-contact sensor is used for being arranged in a corresponding mechanical switch branch, a transfer branch or an energy consumption branch; the second optical fiber sending module is used for communicating with the test host. The test host comprises an upper computer, a first optical fiber sending module and an optical fiber receiving module, wherein the upper computer is respectively connected with the first optical fiber sending module and the optical fiber receiving module, and the optical fiber receiving module is connected with the second optical fiber sending module.
The test host sends a tripping command to a direct current switch control and protection module in the direct current distribution network switch based on a preset distribution network control and protection tripping protocol, and records the departure time t of the tripping command 0 The method comprises the steps of carrying out a first treatment on the surface of the Specifically, an upper computer in the test host sends tripping commands to a direct current switch control and protection module in a direct current distribution network switch sequentially through a CPU, an FPGA and a first optical fiber sending module based on a preset distribution network control and protection tripping protocol;
the first local acquisition unit, the second local acquisition unit and the third local acquisition unit acquire the current of the corresponding branch and send the current to the test host;
the testing host calculates the step moment of each branch based on the received current of each branch;
the test host computer calculates the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and the test host obtains the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer.
In a specific implementation manner of the embodiment of the present invention, the calculation process of the step moment of each branch includes:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and the step final value I of each branch current is calculated 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
In a specific implementation manner of the embodiment of the present invention, a step time calculation process of an electronic current transformer includes:
at the time t of going out 0 Recording abrupt change time of current data sent by the electronic current transformer as a reference;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Performing cubic spline interpolation calculation on current data sent by an electronic current transformer, and calculating a step final value I of each branch current 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
The cubic spline interpolation calculation formula is as follows:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 Is original asSampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c).
The following working process of the direct current distribution network switch characteristic test system in combination with an embodiment of the invention is specifically as follows:
(1) Before the test starts, the TMR sensor is arranged in the corresponding branch of the direct current distribution network switch, and the open-close type design is realized without moving the main loop of the direct current distribution network switch.
(2) The upper computer is provided with a communication protocol of the electronic current transformer and a tripping protocol of the direct current switch control and protection module (see figure 1).
(3) The primary circuit (see fig. 1) is charged and the current of each circuit is monitored for a proper condition.
(4) The upper computer sends out a tripping command, the test host sends out the tripping command to the direct current switch control and protection module according to the tripping protocol of the control or protection device of the direct current power distribution network, and records the departure time t of the tripping command 0 。
(5) And recording the current changes of the electronic current transformer and the three TMR sensors.
(6) And analyzing and calculating the recording data, and recording the mutation time of each current. The step initial value I of each branch current is obtained by a filtering algorithm by taking a 10ms data window 0 After the abrupt current is stable, the step final value I is obtained 1 . I is as follows 1 -I 0 The 90% value time of (2) is the switch operation completion time. In order to accurately obtain 90% of step moment, aiming at quantization error of discrete sampling value of optical fiber digital signal, generalized polynomial fitting is adopted to calculate step initial value I of digital sampling output 0 And a step end value I 1 Noise errors in the initial value and the influence of overshoot fluctuation in the initial stage of the step on the final value of the step are eliminated, and an accurate basis is provided for step amplitude calculation and 90% amplitude calculation in the later stage. Generalized polynomial fitting fits data to a polynomial function represented by the following equation:
wherein f i Output sequence for best polynomial fit, x i Is an input sequence, a j Is a polynomial coefficient and m is the polynomial order.
Obtaining an accurate step initial value I after curve fitting 0 And a step end value I 1 And 90% value I of the step 90 = (initial value of step I 0 And a step end value I 1 )*0.9。
The sampling rate of the TMR sensor is 1MHz, the time discrete error is 1us, interpolation calculation is not needed, and 90% step time t90 of the TMR sensor can be directly obtained. The sampling rate of the electronic current transformer is an uncertain value for the direct current distribution network switching system, so that the sampling value of the electronic current transformer is subjected to cubic spline interpolation calculation in order to obtain accurate 90% step time.
Wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c). Obtaining accurate step 90% time t after cubic spline interpolation calculation 90 。
(7) The time t0 for issuing the switch tripping command is taken as a time reference, and 90% of the time t90 of each branch current step is taken as a switch completion combined process time stamp. Thus obtaining the integral action time sequence of the direct current distribution network switch.
(8) Comparing the operation time sequence of each branch of the DC switch with the relevant standard, and verifying the correctness of the operation of the DC switch example 2
The embodiment of the invention provides a method for testing the switch characteristics of a direct current distribution network, which comprises the following steps:
configuration based on presetting by using test hostThe network control tripping protocol sends tripping command to the DC switch control module in the DC distribution network switch and records the starting time t of the tripping command 0 ；
The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are utilized to acquire currents of corresponding branches in a direct current distribution network switch, and the currents are sent to a test host;
calculating the step moment of each branch by using the test host based on the received current of each branch;
the testing host computer is used for calculating the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and obtaining the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer by using the test host.
In a specific implementation manner of the embodiment of the present invention, the calculation process of the step moment of each branch includes:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and the step final value I of each branch current is calculated 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
In a specific implementation manner of the embodiment of the present invention, a step time calculation process of an electronic current transformer includes:
at the time t of going out 0 Recording abrupt change time of current data sent by the electronic current transformer as a reference;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Three times of current data sent by the electronic current transformerSpline interpolation calculation is carried out to calculate the step final value I of each branch current 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
The cubic spline interpolation calculation formula is as follows:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c).
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. The utility model provides a DC distribution network switching characteristic test system which characterized in that includes:
the first on-site acquisition unit is used for being connected with a mechanical switch branch in the direct current distribution network switch;
the second on-site acquisition unit is used for being connected with a transfer branch in the direct current distribution network switch;
the third on-site acquisition unit is used for being connected with the energy consumption branch in the direct current distribution network switch;
the test host is respectively connected with the first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit and is also connected with the electronic current transformer and the direct current switch control protection module in the direct current distribution network switch;
the test host sends a tripping command to a direct current switch control and protection module in the direct current distribution network switch based on a preset distribution network control and protection tripping protocol, and records the departure time t of the tripping command 0 ；
The first local acquisition unit, the second local acquisition unit and the third local acquisition unit acquire the current of the corresponding branch and send the current to the test host;
the testing host calculates the step moment of each branch based on the received current of each branch;
the test host computer calculates the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and the test host obtains the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer.
2. The system for testing the switching characteristics of a direct current distribution network according to claim 1, wherein the step time calculation process of each branch circuit comprises:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and the step final value I of each branch current is calculated 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of each branch.
3. The system for testing the switching characteristics of a direct current distribution network according to claim 1, wherein the step time calculation process of the electronic current transformer comprises:
at the time t of going out 0 Recording electronic current each other as referenceAbrupt change time of current data sent by the sensor;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Performing cubic spline interpolation calculation on current data sent by the electronic current transformer, and calculating a step final value I of the current data sent by the electronic current transformer 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of the electronic current transformer.
4. A system for testing the switching characteristics of a dc distribution network according to claim 3, wherein the cubic spline interpolation calculation formula is:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second order derivative of (2); y' i+1 Is y i+1 Is a second order derivative of (c).
5. The system for testing the switch characteristics of a direct current distribution network according to claim 1, wherein the first local acquisition unit, the second local acquisition unit and the third local acquisition unit have the same structure, and each of them comprises: the non-contact sensor, the conditioning loop, the sampling module and the second optical fiber sending module are connected in sequence; the non-contact sensor is used for being arranged in a corresponding mechanical switch branch, a transfer branch or an energy consumption branch; the second optical fiber sending module is used for communicating with the test host.
6. The system for testing the switching characteristics of a direct current distribution network according to claim 1, wherein: the test host comprises an upper computer, a first optical fiber sending module and an optical fiber receiving module, and the upper computer is respectively connected with the first optical fiber sending module and the optical fiber receiving module.
7. A direct current distribution network switching characteristic test method based on the direct current distribution network switching characteristic test system according to claim 1, characterized by comprising:
the test host is utilized to send a tripping command to a direct current switch control and protection module in the direct current distribution network switch based on a preset distribution network control and protection tripping protocol, and the departure time t of the tripping command is recorded 0 ；
The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are utilized to acquire currents of corresponding branches in a direct current distribution network switch, and the currents are sent to a test host;
calculating the step moment of each branch by using the test host based on the received current of each branch;
the testing host computer is used for calculating the step moment of the electronic current transformer based on the received current data sent by the electronic current transformer in the direct current distribution network switch;
and obtaining the action logic, action time and action time sequence of the direct current distribution network switch based on the step moments of each branch and the electronic current transformer by using the test host.
8. The method for testing the switching characteristics of a direct current distribution network according to claim 7, wherein the step time calculation process of each branch circuit comprises the steps of:
at the time t of going out 0 Recording abrupt change time of each branch current as a reference;
the step initial value I of each branch current is obtained by utilizing a data window through a filtering algorithm 0 ；
Polynomial fitting is carried out on each branch current, and the step final value I of each branch current is calculated 1 ；
Based on the step initial value I 0 And a step end value I 1 Calculate each branchIs a step time of (a).
9. The method for testing the switch characteristics of the direct current distribution network according to claim 7, wherein the step time calculation process of the electronic current transformer comprises the following steps:
at the time t of going out 0 Recording abrupt change time of current data sent by the electronic current transformer as a reference;
the step initial value I of the current data sent by the electronic current transformer is obtained by utilizing a data window through a filtering algorithm 0 ；
Performing cubic spline interpolation calculation on current data sent by the electronic current transformer, and calculating a step final value I of the current data sent by the electronic current transformer 1 ；
Based on the step initial value I 0 And a step end value I 1 And calculating the step moment of the electronic current transformer.
10. The method for testing the switching characteristics of a direct current distribution network according to claim 9, wherein the cubic spline interpolation calculation formula is:
wherein x is i And x i+1 All are original sampling points, y i For the original sampling point x i Corresponding sample value, y i+1 For the original sampling point x i+1 Corresponding sampling value, x is interpolation point, y is interpolation amount, y' i Is y i Is a second derivative of (2); y' i+1 Is y i+1 Is a second derivative of (c).
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