A digital integrator based on Newton-Coates

Abstract

The present invention relates to a digital integrator based on Newton-Coates, and belongs to the technical field of signal processing in electrical measurement. The digital integrator of the present invention adopts an A / D converter and a digital integration unit, wherein the digital integration unit adopts a Newton-Coates algorithm to obtain a transfer function, and the transfer function does not require a non-integer delay factor and a composite structure, and the calculation process is simple and the calculation amount is small, and it is easy to implement; at the same time, the digital integrator has a simple structure, low technical difficulty in implementation, and reduced requirements on hardware.

Description

Technical Field

[0001] The invention relates to a digital integrator based on Newton-Coates, belonging to the technical field of signal processing in electrical measurement. Background Art

[0002] With the continuous increase in the capacity of the power system and the gradual improvement of the grid operation level, traditional transformers have exposed more and more shortcomings such as large size, heavy weight, easy to produce ferromagnetic resonance, small dynamic range, etc. Electronic transformers have the advantages of good insulation performance, strong anti-interference ability, no magnetic saturation and ferromagnetic resonance, and large dynamic range. They have adapted to the development of smart grids and have been widely used in power systems.

[0003] At present, the most commonly used electronic current transformer is the electronic current transformer based on the Rogowski coil, while the most commonly used electronic voltage transformer is the direct-measurement capacitance current type electronic voltage transformer based on the coaxial capacitor. The output signals of the above two electronic transformers are the differentials of the measured signals. The output voltage of the Rogowski coil is the differential of the primary current passing through it, and the output current of the coaxial capacitor is the differential of the primary voltage at both ends. When the output signal is in a differential relationship with the measured primary current / voltage, the size of the output signal will change with the fluctuation of the measured primary current / voltage frequency. Since the frequency of the power grid is not constant, but fluctuates within a small range, the output of the Rogowski coil or the coaxial capacitor will be affected by the frequency change. Therefore, it is necessary to add an integral link to eliminate the influence of frequency changes.

[0004] There are two commonly used integration methods: analog integrators and digital integrators. Analog integrators are generally composed of components such as resistors, capacitors, and operational amplifiers. Since these non-ideal components are dispersed, and factors such as temperature drift and time drift will cause integration errors, affecting the long-term stability of analog integrators. In order to improve this situation, although research on analog integrators is still ongoing, it is basically impossible to overcome the inherent zero drift and temperature drift of analog devices; on the other hand, the feedback and compensation design of analog integrators is not flexible enough, and this may introduce new errors. Therefore, the accuracy of analog integrators is not high, and the long-term operation stability is also poor.

[0005] Digital integration can avoid the problems of zero drift and temperature drift existing in analog integration, and has the advantages of stability, reliability and high repeatability. Commonly used are rectangular integration, trapezoidal integration and Simpson integration, but these digital integrators have large amplitude errors at high frequencies and are easily affected by factors such as the DC component in the signal.

[0006] In order to eliminate the influence of the above-mentioned adverse factors, a Chinese patent application document with application publication number CN104503294A proposes a trapezoidal-rectangular weighted digital integrator based on the DC feedback principle, which is mainly an improvement on the transfer function of the digital integrator. The transfer function of the trapezoidal-rectangular weighted digital integrator is shown in formula (1). Although the accuracy has been improved to a certain extent, it also makes the transfer function design complicated, introduces a non-integer delay factor, and requires the digital integrator to double the sampling frequency. In order to eliminate the influence of the DC component on the integral, a Butterworth low-pass filter is added to extract the DC component, and the PID algorithm is used as the DC component feedback unit. The integrator has high requirements on the performance of the hardware platform and has a large amount of calculation, and cannot meet the requirements of real-time performance and low hardware cost.

[0007]

[0008] In view of the above problems, a Chinese patent application document with application publication number CN104868900A proposes a high-precision digital integrator based on the Romberg algorithm, which provides a circuit structure as follows: Figure 1 As shown in Figure 2, the digital integrator decomposes the transfer function into two parts, as shown in formula (2). The sampling frequency in the main channel remains unchanged, and the output result of the error compensation channel with the sampling frequency halved is processed according to the Romberg algorithm as error compensation. The calculation speed is increased by the synchronous operation of two microprocessors, overcoming the problems of slow calculation speed and cumbersome design of complex transfer functions in single-channel systems. However, the problems of the integrator are also obvious. The transfer function contains non-integer delay factors. At the same time, the two microprocessors double the hardware cost. The parallel synchronous signal processing technology is difficult, has high requirements on CPU performance, and is susceptible to interference, which has a certain impact on system stability.

[0009]

[0010] Therefore, the current digital integrator has a complex structure, requires a large amount of algorithm calculation, has high hardware requirements, is not easy to implement, and is easily interfered with. Summary of the invention

[0011] The purpose of the present invention is to provide a digital integrator based on Newton-Coates to solve the problems of complex structure, difficult implementation and high hardware requirements of current digital integrators.

[0012] In order to solve the above technical problems, the present invention provides a digital integrator based on Newton-Coates, which includes:

[0013] A / D converter, used for continuously sampling the differential signal output by the electronic transformer and converting the analog signal into a digital signal;

[0014] The digital integration unit is used to calculate the sampling results according to the differential equation corresponding to the set transfer function, and the transfer function is obtained by using the Newton-Coates algorithm.

[0015] The digital integrator of the present invention adopts an A / D converter and a digital integration unit, wherein the digital integration unit adopts a Newton-Coates algorithm to obtain a transfer function, and the transfer function does not require a non-integer delay factor and a composite structure, and the calculation process is simple and the calculation amount is small, and it is easy to implement; at the same time, the digital integrator has a simple structure, low technical difficulty in implementation, and reduced requirements for hardware.

[0016] Furthermore, the transfer function adopted by the digital integrator is:

[0017]

[0018] Where z is the transformed expression of the time series signal in the complex frequency domain, and T is the sampling period.

[0019] Furthermore, the difference equation determined by the transfer function is:

[0020] y(n)=y(n-1)-y(n-2) / 24+T / 24*[9*x(n)+19*x(n-1)–5*x(n-2)+x(n-3)].

[0021] Furthermore, the digital integrator also includes an operational amplifier for amplifying the differential signal output by the electronic transformer and sending the amplified signal to the A / D converter.

[0022] Furthermore, the A / D converter is a 16-bit sampling chip ADS8688.

[0023] Furthermore, the digital integration unit is implemented using the MSP430FR6972 chip.

[0024] Furthermore, the set value is the number of sampling points per cycle of the A / D converter. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a structural diagram of a two-microprocessor parallel signal processing circuit used in an existing digital integrator;

[0026] Figure 2 It is the basic principle block diagram of the digital integrator of the present invention;

[0027] Figure 3 is a processing flow chart of the digital integrator of the present invention;

[0028] Figure 4 is the frequency response curve of the digital integrator of the present invention;

[0029] Figure 5 It is a circuit structure block diagram of the digital integrator of the present invention;

[0030] Figure 6 4 is a waveform diagram of sampling data in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings.

[0032] Aiming at the problems existing in the existing integrators, the present invention uses the Newton-Coates algorithm to propose a digital integrator based on Newton-Coates. The digital integrator adopts a transfer function determined by the m-th order Newton-Coates algorithm. The transfer function has no non-integer delay factor and no complex structure. The calculation process is simple and the amount of calculation is small, so it is easy to implement.

[0033] Before introducing the digital integrator of the present invention in detail, a brief introduction to the Newton-Coates correlation algorithm is first given. A simple continuous integration formula is shown in formula (3).

[0034]

[0035] in,

[0036]

[0037] Formula (4) can be obtained from the m-order Newton interpolation polynomial to obtain formula (5):

[0038]

[0039] in,

[0040]

[0041] t k+i =t k +iT,

[0042] i=0,1…m-1,q=0,1…m,T is the sampling period.

[0043] make but:

[0044]

[0045] Substituting formula (6) into formula (4), we get:

[0046]

[0047] Furthermore, the z-transform of equation (3) is equation (8), and the z-transform of equation (7) is equation (9):

[0048]

[0049]

[0050] Furthermore, from equation (8) and equation (9), we can get:

[0051]

[0052]

[0053]

[0054] Δ i D(z)=(-1) i (1-z -1 ) i , i=0,1,...,m (10c)

[0055] Among them, 1≤p≤m, z=e jω , T is the sampling period.

[0056] Let m = 3, p = 1, and increase the delay factor, then we get:

[0057]

[0058] Based on this, the present invention proposes a digital integrator based on Newton-Coates, whose structure is as follows: Figure 2 As shown, it includes an operational amplifier, an A / D converter and a digital integration unit, wherein the input end of the operational amplifier is used to receive the differential signal output by the electronic transformer, amplify the received differential signal, and send the amplified signal to the A / D converter; the A / D converter is used to continuously sample the amplified differential signal and convert the analog signal into a digital signal; the digital integration unit is used to calculate the sampling result according to the differential equation corresponding to the set transfer function, wherein the transfer function is shown in formula (11), and the differential equation derived from the transfer function is:

[0059] y(n)=y(n-1)-y(n-2) / 24+T / 24*[9*x(n)+19*x(n-1)–5*x(n-2)+x(n-3)] (12)

[0060] Visible and Figure 1Compared with the integrator in the invention, the integrator of the present invention eliminates the high-pass filter, the false touch compensation channel link, the proportional link and the accumulation link, and has a simpler structure, low technical difficulty in implementation, and reduced hardware requirements; at the same time, compared with the existing transfer function formula (1) and transfer function formula (2), the transfer function formula (11) of the present invention has no non-integer delay factor, no composite structure, a simple calculation process and a small amount of calculation, and is easier to implement.

[0061] The working process of the digital integrator based on Newton-Coates of the present invention is as follows: Figure 3 As shown, when initializing the A / D converter, the number of sampling points per cycle N of the signal is set according to the requirements, and the continuous sampling mode is adopted; the A / D converter starts sampling, and when the number of sampling points n ≥ N, that is, the number of sampling points required for the transfer function operation is met, the calculation result is obtained according to the transfer function differential equation (12), and then the calculation result is processed according to the engineering requirements. The above steps complete an operation process; during the operation process, because the A / D converter is set to the continuous sampling mode, new sampling points can be continuously obtained, thereby realizing continuous operation and processing of data. The integrator frequency response curve is shown in Figure 4 shown.

[0062] Specifically, the digital integration unit in the present invention can be implemented by using an MCU, such as Figure 5 As shown in the figure, for example, the MSP430FR6972 chip is used, the A / D converter is the 16-bit sampling chip ADS8688, and 80 points are sampled per cycle. The MCU sampling calculation runs for 10 minutes, and the sampled raw data and the data calculated by the digital integrator differential equation are as follows Figure 6 As shown, the input original signal contains Gaussian white noise, DC component, and harmonics. Figure 6 It can be seen from the output signal that the integrator of the present invention effectively filters out the harmonics and Gaussian white noise, and suppresses the accumulation of DC components.

Claims

1. A digital integrator based on Newton-Coates, characterized in that: The digital integrator includes: A / D converter, used for continuously sampling the differential signal output by the electronic transformer and converting the analog signal into a digital signal; A digital integration unit, used to calculate the sampling results according to a differential equation corresponding to a set transfer function, wherein the transfer function is obtained using a Newton-Coates algorithm; The transfer function used by the digital integrator is: Where z is the transformed expression of the time series signal in the complex frequency domain, and T is the sampling period.

2. The Newton-Coates-based digital integrator according to claim 1, characterized in that: The difference equation determined by the transfer function is: y(n) = y(n-1) -y(n-2) / 24 + T / 24*[9*x( n) + 19*x(n-1) – 5*x(n-2) + x(n-3)] .

3. The Newton-Coates-based digital integrator according to claim 1 or 2, characterized in that: The digital integrator also includes an operational amplifier for amplifying the differential signal output by the electronic mutual inductor and sending the amplified signal to the A / D converter.

4. The Newton-Coates-based digital integrator according to claim 1 or 2, characterized in that: The A / D converter is a 16-bit sampling chip ADS8688.

5. The Newton-Coates-based digital integrator according to claim 1 or 2, characterized in that: The digital integration unit is implemented using the MSP430FR6972 chip.

6. The Newton-Coates-based digital integrator according to claim 1 or 2, characterized in that: The set value is the number of sampling points per cycle of the A / D converter.

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