CN105571617A - High precision digital integrator based on Gauss algorithm - Google Patents

High precision digital integrator based on Gauss algorithm Download PDF

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CN105571617A
CN105571617A CN201610002352.XA CN201610002352A CN105571617A CN 105571617 A CN105571617 A CN 105571617A CN 201610002352 A CN201610002352 A CN 201610002352A CN 105571617 A CN105571617 A CN 105571617A
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digital
analog
microprocessor
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high precision
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CN105571617B (en
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李振华
胡蔚中
赵爽
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Tongda electromagnetic energy Co.,Ltd.
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China Three Gorges University CTGU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D1/00—Measuring arrangements giving results other than momentary value of variable, of general application
    • G01D1/04—Measuring arrangements giving results other than momentary value of variable, of general application giving integrated values
    • G01D1/06—Measuring arrangements giving results other than momentary value of variable, of general application giving integrated values by intermittent summation
    • G01D1/08—Measuring arrangements giving results other than momentary value of variable, of general application giving integrated values by intermittent summation over fixed periods of time

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  • General Physics & Mathematics (AREA)
  • Analogue/Digital Conversion (AREA)
  • Emergency Protection Circuit Devices (AREA)

Abstract

The invention provides a high precision digital integrator based on a Gauss algorithm. The high precision digital integrator based on a Gauss algorithm comprises a high pass filter, an analog-to-digital converter, a microprocessor, a high precision clock and a digital-to-analog converter, wherein the high pass filter is used for eliminating a direct current interference signal and preventing integral saturation; the analog-to-digital converter performs sampling according to a command of the microprocessor, and converts an analog signal into a digital signal; the microprocessor generates a sampling time according to the sampling point number, and sends a trigger command to the analog-to-digital converter according to the time information transmitted from the high precision clock; whenever the required sampling points are sampled enough, the microprocessor calculates one time, and sends the calculated result to the digital-to-analog converter, and at the same time controls resetting of the high precision clock; and the digital-to-analog converter is used for converting the digital signal into the analog signal and outputting the result. The theoretical analysis and the simulation experiment can prove that the precision of the designed digital integrator is higher than the precision of a trapezoid or Simpson digital integrator with the same sampling point number, and is high in the anti-frequency fluctuation and harmonic wave interference capability after comparison.

Description

A kind of high accuracy number integrator based on Gauss algorithm
Technical field
The present invention relates to power system measuring field, be specifically related to a kind of high accuracy number integrator based on Gauss algorithm, effectively can resist the harmonious wave interference of frequency jitter.
Background technology
Along with electric system is constantly to UHV (ultra-high voltage), Large Copacity future development, when being in electric system under the faults such as short circuit, can by the short-circuit current much larger than rated current in electronic current mutual inductor, protective current transformer, should ensure certain accuracy, guarantee protective relaying device correct operation, this specifies electronic current mutual inductor used for relay protection " combination misalignment " with regard to requiring that the combination misalignment of electronic current mutual inductor meets in GB/T20840.8: the effective value of the instantaneous value of secondary current and the difference of primary current instantaneous value under steady state (SS), comprise the higher hamonic wave occurred in primary current and secondary current, this generalization by the representation of groups reflects the mutual inductor such as ratio and angular difference important performance data.Meanwhile, as the key link of signal processing, the accuracy of integrator is related to the accuracy of whole system.Integrator is widely used in power system measuring and control field, air core coil electronic current mutual inductor or straight survey capacitance current type electronic type voltage transformer, the output of its secondary side is the differential of primary current or voltage, recover signal directly proportional with primary current/voltage, just must there is corresponding integral element, and the calculating of combination misalignment carries out data processing after needing to carry out integration to the output of its secondary side again, therefore the design of high precision integral element is the key guaranteeing electronic mutual inductor combination misalignment accuracy in computation.
Pertinent literature is pointed out, and digital integrator is only applicable to the measurement in short-term under power frequency component.Although this is because the simulation accuracy of arithmetic of digital integral is in the ideal case higher, but due to reasons such as frequency jitter (imperfect power frequency 50Hz) harmonious wave interference in real system, the integral algorithms such as complexification rectangle, trapezoidal, Simpson are difficult to ensure precision, more than generation during two kinds of interference, combination misalignment sharply increases, the main cause that this is complexification rectangle, trapezoidal, Simpson formula is difficult to employing in reality detects.In addition on the one hand, the size of sample frequency is also the major reason affecting above arithmetic accuracy, increases sample frequency and often increases hardware use cost, increase operand and time delay simultaneously, reduce sample frequency and then cannot meet relevant accuracy requirement.In fact, in mathematical principle, trapezoid formula and Simpson formula are the most basic integral approach formula.But their precision is poor.When calculating with Unequal distance node, the conventional quadrature formulas of Gauss type calculates, and it is under interstitial content same case, and order of accuarcy is higher, good stability.Therefore, the high-precision characteristic of Gauss formula makes it be enough to opposing frequency jitter and humorous wave interference, also without the need to requiring too high sample frequency.Herein based on Gauss algorithm 2 formula, design a kind of high accuracy number integrator, have higher precision than existing digital integrator when identical sampled point number, be more suitable for the engineering site needs of complex environment simultaneously.
Summary of the invention
For current digital integrator Problems existing, the invention provides a kind of high accuracy number integrator based on Gauss algorithm.The interference that sample mode brings to resist frequency jitter and higher hamonic wave has been redesigned according to Gauss algorithm, theoretical analysis and emulation experiment show, design periodic sampling 80 point, when signal frequency fluctuates at 49.5 ~ 50.5Hz, designed digital integrator combination misalignment is only 8 × 10 -7left and right; even if superpose 2 ~ 13 subharmonic on Fundamental-frequency Current; combination misalignment also can control within 0.13%; relatively trapezoidal and Simpson's digital integrator performance wants excellent many; the use of protection electronic current mutual inductor has sizable advantage; also suitably can change sampling number according to the accuracy requirement of measurement electronic current mutual inductor, be applicable to measurement electronic current mutual inductor simultaneously.
The technical solution adopted in the present invention is:
A kind of high accuracy number integrator based on Gauss algorithm, comprise Hi-pass filter, analog to digital converter, microprocessor, high precision clock, digital to analog converter, high precision clock sends clock signal to microprocessor, microprocessor sends trigger command to analog to digital converter according to marking the moment, control analog to digital converter to sample, Hi-pass filter is for extracting and eliminating the DC influence in differential signal, transfer to after digital signal through analog to digital converter afterwards, send into microprocessor, after N number of sampled point in the one-period set by obtaining calculates, Microprocessor S3C44B0X high precision clock resets, enter next cycle carry out continuation sampling or stop, and the signal exported after calculating feeding digital to analog converter is converted to simulating signal, Output rusults.
Use high precision clock to carry out generation time signal, time signal is sent in microprocessor.Microprocessor regenerates sampling instant according to sampling number N set in the cycle, in sampling instant, trigger command is sent to analog to digital converter, can control high precision clock and reset after obtain enough sampled points within a cycle.
The novel transport function designed in the microprocessor is: this transport function is according to 2 formula design in Gauss algorithm, and structural rate Simpson transport function is simple, but under same sampling number last Output rusults precision again higher than trapezoidal and Simpson formula.
Analog to digital converter, according to the trigger command sampling in microprocessor, belong to unequal interval sampling, but sampling interval T calculates according to the time 0.02s of one-period and the fixed value of the ratio of sampling number N in the calculation.
This integrator can, according to measuring or the requirement of protection mutual inductor, arrange different unit period sampling number N to satisfy the demand, but its precision be again far above the trapezoidal of same sampling number or Simpson's digital integrator.
When this integrator exists 2 ~ 13 subharmonic interference, designed digital integrator combination misalignment is the highest is no more than 0.13%, is enough to meet on-the-spot complicated engineering-environment needs.
This integrator is when system signal frequency ± 0.5Hz fluctuates among a small circle, and designed digital integrator combination misalignment is only 8 × 10 -7left and right, negligible.
The present invention relates to a kind of high accuracy number integrator based on Gauss algorithm, technique effect is as follows:
1), for the ability that the current digital integrator shortage humorous wave interference of opposing and frequency jitter are disturbed, precision affects the problems such as larger by sample frequency, the present invention proposes a kind of high accuracy number integrator based on Gauss algorithm, primary voltage signal is obtained by sampling unequal interval node, high precision integration restoring function can be realized under relatively less unit period sampling number, simultaneously effectively can resist frequency jitter and humorous wave interference, more excellent than existing trapezoidal, Simpson's digital integrator performance is many.
2), because designed transport function is similar to rectangle transport function, so Simpson's transport function calculating amount will be lacked many relatively, but within a cycle under same sampling number, its combination misalignment is again much smaller than Simpson and trapezoidal transport function, and transport function structure more simply more easily designs relative to Simpson formula.
3), in engineering; when measured signal is standard sine signal and sample frequency is higher; select trapezoidal or Simpson's algorithm can realize good integration restoring function; but when signal frequency among a small circle in fluctuation or signal there is harmonic component time; as shown in Figure 3 and Figure 4; designed digital integrator performance wants superior many, and this point is most important for protection electronic current mutual inductor, especially at the scene circumstance complication and interference larger time.
4), for measurement electronic current mutual inductor, if meet 0.2S or 0.05 grade requirement, just must use Simpson's algorithm or adopt higher sample frequency, increase operand or use the hardware such as high performance analog to digital converter, and the digital integrator using Gauss algorithm to design can accomplish low sample frequency high precision completely, reduce costs minimizing calculated amount.
Accompanying drawing explanation
Fig. 1 is theory diagram of the present invention.
Fig. 2 is software flow pattern of the present invention.
Fig. 3 is the trapezoidal combination misalignment logarithmic graph with Gauss algorithm when there is harmonic wave.
The combination misalignment figure of trapezoidal algorithm and Gauss algorithm when Fig. 4 is frequency jitter.
Fig. 5 is the simulation experiment result:
Fig. 5 (a) is existence 3,5,7 subharmonic time designed integrator simulation result and desired result contrast.
Fig. 5 (b) is existence 3,5,7 subharmonic time Simpson's integrator and designed digital integrator absolute error contrast.
Fig. 5 (c) is existence 3,5,7 subharmonic time trapezoidal integration device and designed digital integrator absolute error contrast.
Fig. 5 (d) is existence 3,5,7 subharmonic time designed digital integrator absolute error curve.
Embodiment
As shown in Figure 1, a kind of high accuracy number integrator based on Gauss algorithm, comprises Hi-pass filter 1, analog to digital converter 2, microprocessor 3 and high precision clock 4, digital to analog converter 5 five parts.Hi-pass filter 1 is for extracting and eliminating the DC influence in differential signal, high precision clock 4 sends time signal to microprocessor 3, microprocessor 3 sends trigger command to analog to digital converter 2 according to marking the moment, control analog to digital converter 2 to sample, afterwards after analog to digital converter 2 transfers digital signal to, send into microprocessor 3, when meet one-period N point calculate after microprocessor 3 control high precision clock 4 and reset, enter next cycle carry out continuation sampling or stop, and be converted to simulating signal by calculating the signal feeding digital to analog converter 5 exported, Output rusults.
Described Gauss algorithm is basic according to as follows:
∫ a b f ( x ) d x ≈ b - a 2 ∫ - 1 1 f ( b - a 2 + b + a 2 t ) d t
∫ - 1 1 f ( x ) d x = f ( - 1 3 ) + f ( 1 3 )
Wherein [a, b] is integrating range, and the algebraic accuracy of this formula is higher than trapezoidal and Simpson formula.
The described high accuracy number integrator based on Gauss algorithm needs the software flow taked as shown in Figure 2:
(1), initialization sampling channel, setting one-period in sampling number N, again draw the one-period internal trigger moment according to sampling number, sample mode be set as by triggering sampling.
Trigger instants generating mode is:
1. generate vectorial a=0:0.02/N:(0.02-0.02/N)
2. generate vectorial b=0.02/N:0.02/N:0.02
3. generate vectorial t=± 3 -0.5(b-a)
4. by each element in vectorial t by size permutation and combination become new vectorial t, be trigger instants.
(2), clock reset, start timing, clock signal is sent into microprocessor.
(3), microprocessor 3 is sampled at trigger instants trigger mode number converter 2, meet N number of point then to calculate once by transport function, in calculating, sampling interval T is fixed value 0.02/N, send into digital to analog converter 2 afterwards and be converted to analog signal output, preserve and show result, high precision clock resets, resampling.
(4), discontented N number of point then continues sampling.
Described microprocessor 3 adopts model to be TMS320F206, need according to sampling number in one-period, generate trigger instants, send trigger command according to trigger instants, calculating sampling is counted to control clock and is reset, and the novel transport function designed by Gauss algorithm 2 formula is as follows:
H ( z ) = T 2 1 1 - z - 1
Described high precision clock 4 uses model for SD2001E, for microprocessor 3 provides precise time information, resets at fixed time according to microprocessor instructs simultaneously.
Described digital to analog converter 2 and analog to digital converter 5 adopt 16 high-speed AD 7621, are mainly used in the mutual conversion between simulating signal and digital signal, receive trigger command and then work and once obtain a sampled point.
Described Hi-pass filter 1 uses analog device Hi-pass filter, and the DC influence signal in the differential signal that filtering primary side transmits, improves digital integrator effect.
Described digital integrator has the ability of better opposing frequency jitter and humorous wave interference, the combination misalignment formula according to evaluating protection electronic current mutual inductor performance in GB/T20840.8:
ϵ c = 100 I p t s k T Σ n = 1 ( k r d i s ( n ) - i p ( t n ) ) 2
As shown in Figure 3 and Figure 4, gather 80 points in one-period, when frequency jitter is at 49.5 ~ 50.5Hz, Gauss algorithm combination misalignment remains on 8 × 10 to the result drawn -7near, even if overtone order is increased to 13 times, combination misalignment also can control about 0.13%, and its performance is better than trapezoidal transport function.The emulation experiment completed such as Fig. 5 demonstrates this result, have 3 at the same time, 5,7 subharmonic time, one-period is sampled 80 points, and designed digital integrator absolute error is less than trapezoidal with Simpson's digital integrator integrator, and the order of magnitude is also 10 -6near, be less than 10 of trapezoidal digital integrator -3with 10 of Simpson's digital integrator -5.
A kind of high accuracy number integrator based on Gauss algorithm of the present invention, use for reference the high precision characteristic of Gauss integration algorithm, not by the impact of frequency jitter, also stronger resistivity is had for humorous wave interference, during one-period 80 sampled point work, the combination misalignment of stable state lower integral link can be controlled in 8 × 10 -7within, designed transport function comparatively Simpson formula is simple, but precision is again higher than this formula, is applicable to measuring and protection air core coil electronic current mutual inductor simultaneously.Existing digital integrator adds a high precision clock can realize, there is stronger practicality.

Claims (5)

1. the high accuracy number integrator based on Gauss algorithm, comprise Hi-pass filter (1), analog to digital converter (2), microprocessor (3), high precision clock (4), digital to analog converter (5), it is characterized in that: high precision clock (4) sends clock signal to microprocessor (3), microprocessor (3) sends trigger command to analog to digital converter (2) according to marking the moment, control analog to digital converter (2) to sample, Hi-pass filter (1) is for extracting and eliminating the DC influence in differential signal, afterwards after analog to digital converter (2) transfers digital signal to, send into microprocessor (3), after N number of sampled point in the one-period set by obtaining calculates, microprocessor (3) controls high precision clock (4) clearing, enter next cycle carry out continuation sampling or stop, and the signal exported after calculating feeding digital to analog converter (5) is converted to simulating signal, Output rusults.
2. a kind of high accuracy number integrator based on Gauss algorithm according to claim 1, is characterized in that: use high precision clock (4) to carry out generation time signal, time signal is sent in microprocessor (3).
3. a kind of high accuracy number integrator based on Gauss algorithm according to claim 1, it is characterized in that, microprocessor (3) regenerates sampling instant according to sampling number N set in the cycle, in sampling instant, trigger command is sent to analog to digital converter (2), high precision clock (4) can be controlled reset after obtain enough sampled points within a cycle.
4. a kind of high accuracy number integrator based on Gauss algorithm according to claim 1, is characterized in that, in microprocessor (3), the novel transport function of design is:
5. according to claims 1 to 4 any one based on the high accuracy number integrator of Gauss algorithm, it is characterized in that, analog to digital converter (2) according in microprocessor (3) trigger command sampling, belong to unequal interval sampling.
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CN106092147A (en) * 2016-07-29 2016-11-09 中国原子能科学研究院 A kind of digital integrator for superconducting cyclotron magnetic-field measurement
CN107707259A (en) * 2017-11-01 2018-02-16 兰州大学 A kind of method of analog signal sampling and reconstruct
CN109030890A (en) * 2018-07-16 2018-12-18 三峡大学 A kind of digital integrator based on time-interleaved method
CN117076823A (en) * 2023-09-25 2023-11-17 国网四川省电力公司营销服务中心 Ripple component analysis method, system, equipment and medium based on Gaussian integration method

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106092147A (en) * 2016-07-29 2016-11-09 中国原子能科学研究院 A kind of digital integrator for superconducting cyclotron magnetic-field measurement
CN106092147B (en) * 2016-07-29 2018-04-20 中国原子能科学研究院 A kind of digital integrator for superconducting cyclotron magnetic-field measurement
CN107707259A (en) * 2017-11-01 2018-02-16 兰州大学 A kind of method of analog signal sampling and reconstruct
CN107707259B (en) * 2017-11-01 2020-11-03 兰州大学 Method for sampling and reconstructing analog signal
CN109030890A (en) * 2018-07-16 2018-12-18 三峡大学 A kind of digital integrator based on time-interleaved method
CN117076823A (en) * 2023-09-25 2023-11-17 国网四川省电力公司营销服务中心 Ripple component analysis method, system, equipment and medium based on Gaussian integration method

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