阅读说明：本技术 直流配网开关特性测试系统及方法 (DC distribution network switch characteristic test system and method ) 是由 王晨清 高磊 罗飞 李鹏 孔祥平 杨毅 张弛 郑俊超 林金娇 于 2021-08-20 设计创作，主要内容包括：本发明公开了一种直流配网开关特性测试系统及方法,所述测试系统包括第一就地采集单元,用于与直流配网开关中的机械开关支路相连；第二就地采集单元,用于与直流配网开关中的转移支路相连；第三就地采集单元,用于与直流配网开关中的耗能支路相连；测试主机,分别所述第一就地采集单元、第二就地采集单元和第三就地采集单元相连,还用于与直流配网开关中电子式电流互感器和直流开关控保模块相连。本发明通过在直流配网开关内部加装非接触式传感器,如TMR(隧道磁阻式)传感器或开口霍尔,搭建直流配网开关的测试系统,采用电流阶跃时刻作为开关的动作完成时刻,测试直流配网开关内部多条支路的开断时序,为直流配网开关提供灵活且全面的测试手段。(The invention discloses a system and a method for testing the switch characteristics of a direct-current distribution network, wherein the test 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 a direct-current distribution network switch; the second local acquisition unit is used for being connected with a transfer branch in the direct-current distribution network switch; the third local acquisition unit is used for being connected with an energy consumption branch in the direct-current distribution network switch; and the test host is respectively connected with the first local acquisition unit, the second local acquisition unit and the third local acquisition unit and is also used for connecting an electronic current transformer and a direct current switch control protection module in the direct current distribution network switch. According to the invention, the non-contact sensor, such as a TMR (tunnel magneto-resistance) sensor or an open Hall sensor, 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 time is used as the action completion time of the switch, the on-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.)

1. The utility model provides a direct current distribution network switch characteristic test system which characterized in that includes:

the first local acquisition unit is used for being connected with a mechanical switch branch in the direct-current distribution network switch;

the second local acquisition unit is used for being connected with a transfer branch in the direct-current distribution network switch;

the third local acquisition unit is used for being connected with an energy consumption branch in the direct-current distribution network switch;

and the test host is respectively connected with the first local acquisition unit, the second local acquisition unit and the third local acquisition unit and is also used for connecting an electronic current transformer and a direct current switch control protection module in the direct current distribution network switch.

2. The direct current distribution network switch characteristic test system of claim 1, wherein: the test host sends a tripping command to a direct-current switch control protection module in the direct-current distribution network switch based on a preset distribution network control protection tripping protocol, and records the time t of the tripping command when the direct-current distribution network switch goes out₀；

The first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit acquire currents of corresponding branches and send the currents to the test host;

the test host calculates the step time of each branch circuit based on the received current of each branch circuit;

the test host also calculates the step time 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 acquires the action logic, the action time and the action time sequence of the direct current distribution network switch based on the step time of each branch and the electronic current transformer.

3. The system for testing the switching characteristics of the direct current distribution network according to claim 4, wherein the step time calculation process of each branch comprises:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

4. The system for testing the switching characteristics of the direct current distribution network according to claim 1, wherein the step moment calculation process of the electronic current transformer comprises:

at the moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

5. The system for testing the switching characteristics of the direct current distribution network according to claim 1, wherein the cubic spline interpolation calculation formula is as follows:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iSecond order derivation; y'_i+1Is y_i+1Second order derivation.

6. The system of 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 sequentially connected; the non-contact sensor is used for being installed 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.

7. The direct current distribution network switch characteristic test system of claim 1, wherein: 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.

8. A method for testing the switch characteristic of a direct current distribution network is characterized by comprising the following steps:

sending a tripping command to a direct current switch control protection module in a direct current distribution network switch by using a test host based on a preset distribution network control protection tripping protocol, and recording the exit time t of the tripping command₀；

The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are used for acquiring the current of corresponding branches in a direct-current distribution network switch and sending the current to a test host;

calculating the step time of each branch circuit based on the received current of each branch circuit by using the test host;

calculating the step time of the electronic current transformer by using the test host based on the received current data sent by the electronic current transformer in the direct current distribution network switch;

and obtaining the action logic, the action time and the action time sequence of the direct current distribution network switch by using the test host based on the step time of each branch and the electronic current transformer.

9. The method for testing the switching characteristics of the direct current distribution network according to claim 8, wherein the step time calculation process of each branch comprises the following steps:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

10. The method for testing the switching characteristics of the direct current distribution network according to claim 8, wherein the step moment calculation process of the electronic current transformer comprises the following steps:

at the moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

11. The method for testing the switching characteristics of the direct-current distribution network according to claim 10, wherein the cubic spline interpolation calculation formula is as follows:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a).

Technical Field

The invention belongs to the technical field of direct-current distribution network testing, and particularly relates to a system and a method for testing the switching characteristics of a direct-current distribution network.

Background

With the continuous development of power electronic technology, a direct current power distribution network is a main expression form of a future alternating current and direct current hybrid power grid. Compared with an alternating-current distribution network, the direct-current distribution network provides a direct-current bus for loads, the direct-current loads can be directly supplied with power by the direct-current bus, the alternating-current loads need to be supplied with power after passing through inverter equipment, and if the proportion of the direct-current loads in the loads is large, the direct-current distribution network has great advantages.

The dc distribution network switch is a major technical bottleneck in the development of the dc distribution network, and at present, 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 is composed of a mechanical switch branch, a transfer branch and an energy consumption branch, and the secondary circuit is composed of an electronic current transformer and a direct current switch control protection unit. The electronic current transformer sends a current sampling value to the direct current switch control protector and the direct current distribution network control protector. The control logic of the direct current switch is as follows: after a switching-off instruction of the direct current switch control unit is received, the transfer branch is closed firstly, then the mechanical switch branch is opened, current is transferred into the transfer branch, then the transfer branch is turned off, the current is consumed into the energy consumption branch, and the whole process relates to the matching relation of three direct currents. In the prior art, the test of the DC distribution network switch only depends on observing the current change of the electronic current transformer to measure the action time of the switch, and no good test means exists for the overall action characteristic, action logic and working mode of the DC distribution network switch.

Disclosure of Invention

Aiming at the problems, the invention provides a system and a method for testing the switch characteristics of a direct-current distribution network.

In order to achieve the technical purpose and achieve the technical effects, the invention is realized by the following technical scheme:

in a first aspect, the present invention provides a system for testing a switching characteristic of a dc distribution network, including:

the first local acquisition unit is used for being connected with a mechanical switch branch in the direct-current distribution network switch;

the second local acquisition unit is used for being connected with a transfer branch in the direct-current distribution network switch;

the third local acquisition unit is used for being connected with an energy consumption branch in the direct-current distribution network switch;

and the test host is respectively connected with the first local acquisition unit, the second local acquisition unit and the third local acquisition unit and is also used for connecting an electronic current transformer and a direct current switch control protection module in the direct current distribution network switch.

Optionally, the test host sends a trip command to the dc switch protection module in the dc distribution network switch based on a preset distribution network protection trip protocol, and records the time t of the trip command when the test host leaves the gate₀；

The first on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit acquire currents of corresponding branches and send the currents to the test host;

the test host calculates the step time of each branch circuit based on the received current of each branch circuit;

the test host also calculates the step time 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 acquires the action logic, the action time and the action time sequence of the direct current distribution network switch based on the step time of each branch and the electronic current transformer.

Optionally, the step time calculation process of each branch includes:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Optionally, the step time calculation process of the electronic current transformer includes:

at the moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Optionally, the cubic spline interpolation calculation formula is:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a).

Optionally, the first on-site acquisition unit, the second on-site acquisition unit and the third on-site 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 sequentially connected; the non-contact sensor is used for being installed 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 comprises an upper computer, a first optical fiber sending module and an optical fiber receiving module, and 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 a switching characteristic of a dc distribution network, including:

sending a tripping command to a direct current switch control protection module in a direct current distribution network switch by using a test host based on a preset distribution network control protection tripping protocol, and recording the exit time t of the tripping command₀；

The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are used for acquiring the current of corresponding branches in a direct-current distribution network switch and sending the current to a test host;

calculating the step time of each branch circuit based on the received current of each branch circuit by using the test host;

calculating the step time of the electronic current transformer by using the test host based on the received current data sent by the electronic current transformer in the direct current distribution network switch;

and obtaining the action logic, the action time and the action time sequence of the direct current distribution network switch by using the test host based on the step time of each branch and the electronic current transformer.

Optionally, the step time calculation process of each branch includes:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Optionally, the step time calculation process of the electronic current transformer includes:

at the moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Optionally, the cubic spline interpolation calculation formula is:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a).

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 the testing system adopts a TMR sensor as a current sensor, adopts an openable design, and has no influence on the response speed of current due to the installation position; the problems of voltage resistance and interference resistance in the test process are effectively solved through optical fiber transmission; the original electronic current transformer is used as the total current for sampling, and a current sensor does not need to be arranged on the line side; the TMR sensor sampling rate reaches 1MHz, and an interpolation algorithm is not needed, so that the calculated amount of a test system can be reduced; cubic spline interpolation is carried out on the original electronic current transformer, quantization errors caused by the original sampling rate are eliminated, and the method can be self-adapted to data with different sampling rates.

The method has strong universality, takes the rising edge and the falling edge of the current as the logical time sequence basis of the switch action, is suitable for the test of the DC distribution network switch of any principle, can judge the switch on-off process only by utilizing the current step characteristic, and is simple and practical.

Drawings

In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the present disclosure taken in conjunction with the accompanying 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 testing system according to an embodiment of the present invention;

fig. 3 is a schematic structural diagram of a dc distribution network switch characteristic testing system and a dc distribution network switch according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of the invention.

The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.

Example 1

The embodiment of the invention provides a system for testing the switching characteristics of a direct-current distribution network, which comprises the following components:

a first local acquisition unit (i.e. local acquisition unit 1 in fig. 2) for connecting to a mechanical switch branch in the dc distribution network switch in fig. 1;

a second local acquisition unit (i.e. local acquisition unit 2 in fig. 2) for connecting to the transfer branch in the dc distribution network switch in fig. 1;

a third local acquisition unit (i.e. local acquisition unit 3 in fig. 2) for connecting to the energy consuming branch in the dc distribution network switch in fig. 1;

and the test host is connected with the first local acquisition unit, the second local acquisition unit and the third local acquisition unit respectively and is also used for connecting an electronic current transformer and a direct current switch control protection module in the direct current distribution network switch in the figure 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 of the first in-situ acquisition unit, the second in-situ acquisition unit and the third in-situ acquisition unit includes: the system comprises a non-contact sensor (TMR sensor), a conditioning loop, a sampling module and a second optical fiber sending module which are connected in sequence; the non-contact sensor is used for being installed 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 protection module in the direct-current distribution network switch based on a preset distribution network control protection tripping protocol, and records the time t of the tripping command when the direct-current distribution network switch goes out₀(ii) a Specifically, an upper computer in the test host sends a tripping command 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 on-site acquisition unit, the second on-site acquisition unit and the third on-site acquisition unit acquire currents of corresponding branches and send the currents to the test host;

the test host calculates the step time of each branch circuit based on the received current of each branch circuit;

the test host also calculates the step time 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 acquires the action logic, the action time and the action time sequence of the direct current distribution network switch based on the step time of each branch and the electronic current transformer.

In a specific implementation manner of the embodiment of the present invention, the step time calculation process of each branch includes:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time 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 moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Wherein, the cubic spline interpolation calculation formula is as follows:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a).

The following working process of the direct-current distribution network switch characteristic testing system in the embodiment of the invention is specifically as follows:

(1) before the test begins, the TMR sensor is installed in a corresponding branch of the direct-current distribution network switch, and the main loop of the direct-current distribution network switch is not required to be moved due to the open-close design.

(2) The upper computer is provided with a communication protocol of an electronic current transformer and a tripping protocol of a direct current switch control protection module (see figure 1).

(3) The primary circuit (see fig. 1) is charged and the current in each circuit is monitored for normality.

(4) The upper computer sends a tripping command, the test host sends the tripping command to the direct current switch control and protection module according to a tripping protocol of a control or protection device of the direct current power distribution network, and the time t of the trip command at the time of going out is recorded₀。

(5) And recording the current changes of the electronic current transformer and the three TMR sensors.

(6) And analyzing and calculating the wave recording data, and recording the mutation time of each current. Obtaining 10ms data window to obtain initial value I of step of each branch current through filtering algorithm₀After the sudden change current is stabilized, the step final value I is obtained₁. With I₁-I₀The 90% value time of the time is used as the switch action completion time. In order to accurately obtain 90% step time, aiming at the quantization error of discrete sampling values of the optical fiber digital signal, generalized polynomial fitting is adopted to calculate the step of digital sampling outputInitial value I₀And step end value I₁And eliminating the noise error in the initial value and the influence of the overshoot fluctuation in the initial step period on the final step value, and providing an accurate basis for the step amplitude calculation and the subsequent 90% amplitude calculation. The generalized polynomial fit fits the data to a polynomial function represented by the following equation:

in the formula (f)_iOutput sequence, x, fitted to the best polynomial_iIs an input sequence, a_jIs a polynomial coefficient and m is a polynomial order.

Obtaining an accurate initial value I of step after curve fitting₀And step end value I₁And 90% value of step I₉₀After (initial value of step I)₀And step end value I₁)*0.9。

The sampling rate of the TMR sensor is 1MHz, the time dispersion error is 1us, interpolation calculation is not needed, and 90% step time t90 can be directly obtained. The sampling rate of the electronic current transformer is an uncertain value of a direct-current distribution network switch system, so that cubic spline interpolation calculation is carried out on the sampling value of the electronic current transformer in order to obtain accurate 90% step time.

Wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a). Obtaining the accurate step 90% time t after cubic spline interpolation calculation₉₀。

(7) And taking the time t0 of sending the switch tripping command as a time reference, and taking the time t90 of each branch current step 90% as a switch completion opening and closing process time stamp. Therefore, the overall action time sequence of the DC distribution network switch is obtained.

(8) Embodiment 2 for comparing the action timing sequence of each branch of the dc switch with the relevant standard and verifying the correctness of the action of the dc switch

The embodiment of the invention provides a method for testing the switching characteristics of a direct-current distribution network, which comprises the following steps:

sending a tripping command to a direct current switch control protection module in a direct current distribution network switch by using a test host based on a preset distribution network control protection tripping protocol, and recording the exit time t of the tripping command₀；

The method comprises the steps that a first local acquisition unit, a second local acquisition unit and a third local acquisition unit are used for acquiring the current of corresponding branches in a direct-current distribution network switch and sending the current to a test host;

calculating the step time of each branch circuit based on the received current of each branch circuit by using the test host;

calculating the step time of the electronic current transformer by using the test host based on the received current data sent by the electronic current transformer in the direct current distribution network switch;

and obtaining the action logic, the action time and the action time sequence of the direct current distribution network switch by using the test host based on the step time of each branch and the electronic current transformer.

In a specific implementation manner of the embodiment of the present invention, the step time calculation process of each branch includes:

at the moment of going out₀Recording the sudden change time of each branch current as a reference;

calculating the initial value I of the step of each branch current by using a data window through a filtering algorithm₀；

Polynomial fitting is carried out on each branch current, and a step final value I of each branch current is calculated₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time 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 moment of going out₀Recording the sudden 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 algorithm₀；

Carrying out cubic spline interpolation calculation on current data sent by the electronic current transformer to calculate the step final value I of each branch current₁；

Based on the initial value of step I₀And step end value I₁And calculating the step time of each branch.

Wherein, the cubic spline interpolation calculation formula is as follows:

wherein x is_iAnd x_i+1Are all the original sample points, y_iIs the original sampling point x_iCorresponding sampled value, y_i+1Is the original sampling point x_i+1Corresponding sampled values, x being interpolation points, y being interpolation quantities, y "_iIs y_iThe second derivative of (a); y'_i+1Is y_i+1The second derivative of (a).

The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.