CN105974196B - A kind of high-precision power grid harmonic measure system and method - Google Patents
A kind of high-precision power grid harmonic measure system and method Download PDFInfo
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- CN105974196B CN105974196B CN201610416541.1A CN201610416541A CN105974196B CN 105974196 B CN105974196 B CN 105974196B CN 201610416541 A CN201610416541 A CN 201610416541A CN 105974196 B CN105974196 B CN 105974196B
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a kind of high-precision power grid harmonic measure system and methods, system includes computer, Signals Transfer Board and one or several harmonic measure nodes, wherein computer turns Serial Port Line by Serial Port Line or USB and is connected with Signals Transfer Board, the mains by harmonics monitoring of software installed in computer can read serial ports and transmit the data come up in real time, and analyze, handle, real-time display of then itemizing draws curve and preservation；Its method is：Computer is connected with Signals Transfer Board Step 1: turning Serial Port Line with Serial Port Line or USB；Step 2: being configured to harmonic measure node relevant parameter；Step 3: being sampled and being preserved in memory to voltage signal；Step 4: being read out from the specific memory described in step 3；Step 5: this step does not execute；Step 6: these data are preserved；Step 7: repeating step 3 to step 6.Advantageous effect：With preferable theory significance and practical value.
Description
Technical field
The present invention relates to a kind of harmonic measure system and method, more particularly to a kind of high-precision power grid harmonic measure system and
Method.
Background technology
Currently, harmonic wave can all be generated in the production of electric energy, transmission, conversion and the links that use.In electric system
Harmonic wave main source has generator, electrical power trans mission/distribution system, electronic power rectification equipment, electric arc furnaces, frequency conversion equipment, glow discharge spot lamp
Deng.Harmonic in Power System content increases rapidly, causes voltage waveform distortion, increases loss and the electrical equipment of transmission line of electricity
Loss, reduce power quality, damage electrical equipment.Harmonic wave and m-Acetyl chlorophosphonazo (the i.e. signal with non-integral multiple fundamental frequency
Component) added losses and fever of a variety of harm or influence, such as electric rotating machine etc. are caused on electric system, shorten and uses the longevity
Life；Resonance overvoltage causes failure and the loss of electrical equipment and equipment；Electrical energy measurement mistake；Interference is generated to communication system,
Telecommunications quality is set to decline；It automatically controls, the incorrect operation etc. of protective device.Therefore, real-time, accurate to grasp harmonic wave in power grid
Have great importance to power system security, economical operation with the real conditions (frequency and amplitude information) of m-Acetyl chlorophosphonazo component.
Currently, the method in terms of the theoretical research of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo and practical application has analog filtering
Device detection method is based on instantaneous reactive power detection method, based on neural network detection method, quickly diaphragm filter
(FFT), Prony waveform fittings, wavelet transformation (WT) and support vector machines (SVM) algorithm etc. are a variety of.Bandpass filtering is early stage mould
The basic principle of quasi- formula harmonic measuring device.Instantaneous reactive power theory can be used for the instantaneous detection of harmonic wave, it can also be used to idle
The harmonic wave controls fields such as compensation.Neural network detection method is with calculation amount is small, precision is high, real-time is good and anti-interference is good
Feature, still, neural network are used for the practical also many problems of engineering, such as：There is no the neural network configuration method of specification, needs
A large amount of training sample is wanted, how to determine that the sample number of needs does not have a method for normalizing, the precision of neural network has sample big
Dependence, etc..In fundametal compoment frequency fluctuation, fft algorithm is difficult to avoid that the frequency caused by non-synchronous sampling is let out
Leakage and fence effect and caused by measurement error.Prony waveform fitting methods are very sensitive to noise, calculated in practical application
It is not ideal enough to measure larger and effect.When wavelet transformation is applied to harmonic wave and m-Acetyl chlorophosphonazo measurement, due to the humorous of upper frequency
The measurement frequency band of wave and/or m-Acetyl chlorophosphonazo component is wider to cause frequency resolution to decline, it is difficult to two signals similar in crossover frequency
Component.Harmonic wave and/or inter-harmonic wave measuring method calculation amount based on support vector machines are larger and measurement accuracy is not high, are actually answering
Used time effect is not ideal enough.
In addition the theory and algorithm that existing Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo measure are only used for Gaussian noise background
Under harmonic measure problem.There is very more non-gaussian impact noises actually in electric system, such as by motor start and stop, electricity
The switching of net electric power, transformer start and stop and many signals and noise artificially generated, often all have such a non-gaussian
Shock feature, i.e., they more continually occur than Gaussian noise significantly data mutation；In the time domain, they show for reflection
Go out a large amount of notable spiking characteristics；It is reflected in probability density, they have more thick and heavy than Gaussian Profile " trail existing
As ".At this moment feasible harmonic wave and m-Acetyl chlorophosphonazo measure theory and algorithm are no longer valid under Gaussian noise.
A large amount of research work shows：This Non-Gaussian colored noise with shock feature can with α Stable distritations come
Characterization.Shao and Nikias is it is manifestly intended that α Stable distritations are suitable for the foundation of impact noise modeling：1. α Stable distritations are
Unique family of distributions for meeting broad sense central-limit theorem, it is not only reasonable in theory, but also compared with Gaussian Profile also
With the meaning more typically changed；2. α Stable distritations are the pole of the generation mechanism and propagation conditions that can keep natural noise process
Limit distribution；3. α Stable distritations are generalized Gaussian distributions, therefore the general characteristic with Gaussian Profile, i.e. stability and enclosed；
4. α Stable distritations can match with many real data of nature.
Invention content
The purpose of the present invention is to solve existing Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo to be asked present in measurement process
A kind of high-precision power grid harmonic measure system and method inscribed and provided.
High-precision power grid harmonic measure system provided by the invention includes computer, Signals Transfer Board and one or several humorous
Wave measurement node, wherein computer turn Serial Port Line by Serial Port Line or USB and are connected with Signals Transfer Board, and the power grid installed in computer is humorous
Wave monitoring of software can read serial ports and transmit the data come up in real time, and analyzes, handles, and real-time display of then itemizing draws song
Line and preservation；Zigbee coordinators, signal converting chip and DB9 interfaces are installed, wherein Zigbee coordinates on Signals Transfer Board
Device is the master controller of entire Zigbee network, for in network Zigbee routing or terminal distribution address, coordination data
Transmission path, and each harmonic measure node is transmitted into the data summarization to come up, computer is sent to by serial ports again.
Computer is that with DB9 interfaces or USB interface and can run the desktop computer of mains by harmonics monitoring of software, notes
Sheet or industrial personal computer.
Harmonic measure node includes that voltage transformer, current transformer, current-to-voltage convertor, clipping module, AD are adopted
Egf block, SD card module, microprocessor module, button, display screen and Zigbee routings or terminal, wherein the one of voltage transformer
Secondary side gets access to grid, and secondary side output voltage enters AD sampling modules, the maximum value of secondary side output voltage after clipping module
Less than the range of AD sampling modules；The primary side of current transformer gets access to grid, and secondary side output current is converted by Current Voltage
After device is converted to voltage signal, enter AD sampling modules using clipping module, the maximum value of transformed voltage signal is less than
The range of AD sampling modules；Current-to-voltage convertor is used to the current signal that current transformer exports being converted to AD sampling modules
Measurable voltage signal, clipping module are made of bi-directional voltage stabilizing pipe, and clamping voltag is less than the range but height of AD sampling modules
In the output voltage of voltage transformer and the output voltage of current-to-voltage convertor；AD sampling modules include AD sampling A/D chips and its
Peripheral circuit, AD sampling A/D chips are connected with microprocessor module, provide clock by microprocessor module, and will count by simultaneously mouth line
According to passing to microprocessor module；Microprocessor module is made of microprocessor and its peripheral circuit, and wherein microprocessor is
STM32F4 family chips, peripheral circuit constitute its system；SD card module is made of SD card slot and capacitance resistance, with microprocessor
Module is connected by spi bus, and the system for storing measurement data and harmonic measure node is arranged；By being keyed to microprocessor
On the I/O port of device module, the setting for harmonic measure node and scene inquiry measurement result；Display screen is LCD liquid crystal displays
Screen is connected with microprocessor module, is used for display system state and measurement result；Zigbee is route or terminal is the roads Zigbee
By device module or Zigbee terminal modules, be connected by universal serial bus with microprocessor module, realize harmonic measure node with
The data transfer of Zigbee coordinators and mains by harmonics monitoring of software.
Signal converting chip is MAX232 family chips or the chip of same function, and input terminal connects Zigbee coordinators,
Serial data for receiving Transistor-Transistor Logic level, output termination DB9 interfaces, for exporting the serial of the identifiable RS232 level of computer
Data.
High-precision power grid harmonic measuring method provided by the invention, method are as described below：
Computer is connected with Signals Transfer Board Step 1: turning Serial Port Line with Serial Port Line or USB, connects the electricity of Signals Transfer Board
Mains by harmonics monitoring of software is opened in source；Harmonic measure node is accessed in power grid to be measured, it, can be every if any multiple points to be measured
It is separately connected a harmonic measure node on a tested point, the power supply of each harmonic measure node is connected, at this time on Signals Transfer Board
Zigbee coordinators can be each harmonic measure node on Zigbee routing and terminal distribution address, to form Zigbee nets
Network；
Step 2: after the power supply of harmonic measure node is connected, the microprocessor module on harmonic measure node is started to work,
It first initializes each module, then reads the node configuration information in SD card module, and related to harmonic measure node
Parameter is configured；
Step 3: voltage transformer and current transformer on harmonic measure node are started to work, and by the voltage of power grid,
Electric current is converted into the collectable voltage signal of AD sampling modules, the microprocessor driven AD sampling modules pair in microprocessor module
These voltage signals are sampled and are preserved in memory；
Step 4: microprocessor in microprocessor module by network voltage, the corresponding digital signal of electric current from step 3
It is read out in the specific memory, the harmonic measuring method based on fractional order cumulant is used in combination to calculate separately out power grid electricity
Pressure, the fundamental wave of electric current and 1-63 harmonic wave；
Step 5: microprocessor in microprocessor module according to the node configuration information in SD card module by corresponding number
It is shown according to sending to display screen, if the node configuration information in SD card module, which is requirement, closes display screen, this step is not
It executes；
Step 6: microprocessor in microprocessor module is by the network voltage surveyed, the fundamental wave of electric current and 1-63 times
Harmonic data packing is stored sequentially in by time of measuring in SD card module, and is passed through plus node serial number and cyclic redundancy check
Zigbee network is sent in computer, is parsed these data by the data processing on backstage on mains by harmonics monitoring of software
And be shown on corresponding window, while these data can also be preserved；
Step 7: repeating step 3 to step 6, so cycle obtains network voltage and electric current at each harmonic measure node
Fundamental wave and each harmonic wave.
The harmonic measuring method based on fractional order cumulant described in step 4, the specific method is as follows：
The determination of the first step, fractional order square and fractional order accumulation flow function and standard：
(1) determination of fractional order square and fractional order accumulation flow function：
If Φ (u) is the characteristic function of stochastic variable X, have
In formula：For left Riemann-Liouville Fractional Derivatives, 0 ＜ p≤1, k is arbitrary integer, claims mkp
WithRLCkpRespectively the fractional order square of stochastic variable X and fractional order cumulant, fractional order cumulantRLCkpAlso it can be denoted asRLcumkp
(·)；
(2) determination of fractional order cumulant standard：
Determine that fractional order cumulant standard is as follows：
Standard 1：If a1,a2,…,akFor constant, X (k)=[x1,x2,…,xk] be stochastic variable, then
In formula：Kp=p1+p2+…+pk
Standard 2：Fractional order cumulant is symmetrical, the sequence nothing of their magnitude and independent variable in other words to its independent variable
It closes, i.e.,
Wherein, i1,i2,…,ikIt is 1,2 ..., any one arrangement of k；
Standard 3：If k stochastic variable { xiA subset and other parts it is independent, then
Standard 4：If stochastic variable collection [x1,x2,…,xk] and [y1,y2,…,yk] be independent, then have
Standard 5：For 2p rank fractional order cumulantsRLCkp(τ) has maximum value as τ=0, i.e., |RLCkp(τ)|≤RLCkp
(0)
The conversion formula of second step, fractional order square and fractional order cumulant：
In formula：IlIt is the set for the new element that the element in I is generated by dividing combination, q indicates IlIn contained division
Number,Indicate IlIn kth divide,Q should be taken as 1,2 successively ..., k, and k is of stochastic variable
Number,It indicates to all IlFunction determined by corresponding set is summed；
Third step, fractional order cumulant are to the rejection ability and suppressing method of α noises and Gaussian noise：
α Stable distritations are a kind of generalized Gaussian distributions, and the characteristic function of standard α Stable distritations is：
Φ (u)=exp-γ | u |α}
In formula：Parameter γ ＞ 0 are known as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is known as characteristic index, as characteristic index α=2,
It is Gaussian Profile that α Stable distritations, which are degenerated,；
About fractional order cumulant to the rejection ability and suppressing method of α noises and Gaussian noise, there is following theorem：
Theorem 1：The characteristic function of quasi- α Stable distritations is marked with as shown in above formula, it is just whole more than or equal to the minimum of p to enable m
Number, then as p ＞ 0 and α ＞ 0, the p rank fractional order cumulants of standard α Stable distritations are：
(1) when α-p are not integer：
(2) when 1≤p- α≤m are integer；
RLCp=0
For the p rank fractional order cumulants of standard α Stable distritation signals, when taking p ＜ α and when α-p are not integer, p
Rank fractional order cumulant exists and is zero, since Gaussian Profile is a special case in standard α Stable distritations as α=2, because
This, fractional order cumulant still sets up gaussian signal, this be fractional order cumulant to the rejection condition of α and Gaussian noise and
Suppressing method, since the fractional order cumulant of α noises and Gaussian noise is zero, i.e., as p ＜ α and when α-p are not integer, meaning
It and both noises is completely inhibited, therefore, fractional order cumulant has extremely strong rejection ability to α noises and Gaussian noise；
4th step, the mains by harmonics based on fractional order cumulant measure method of estimation：
(1) method of estimation of fractional order square and fractional order cumulant：
It, can be straight according to the definition of fractional order square and fractional order cumulant when known to the characteristic function of random process x (k)
It connects and calculates fractional order square and fractional order cumulant, when characteristic function is unknown, using one group of Observable sample of X (k) to its point
Number rank square and fractional order cumulant are estimated, using the conversion formula of fractional order square and fractional order cumulant, can be divided
The estimation of number rank cumulant, carries out score with the estimation of the 2p rank fractional order squares of random sequence x (k) and fractional order cumulant here
The method of estimation of rank square and fractional order cumulant；
(2) estimation of fractional order square:
IfIt can be obtained according to the definition of fractional order square for one group of Observable sample of stationary random process x (t)
Its 2p rank fractional order square is estimated as
Here N is number of samples；
(3) estimation of fractional order cumulant:
According to 2p rank cumulantsConversion formula has
Due toIt is to utilizeWithPass throughConversion formula
It obtains, thereforeIt is also unbiased consistent Estimation；Various different fractional-orders can be obtained using similar method
Fractional order square and fractional order cumulant estimation；
(4) the harmonic frequency method of estimation of network voltage, electric current：
If the signal of Voltage Harmonic：
A in formulaiAnd ωi∈ (- π, π) is respectively the multiple amplitude and frequency of i-th of harmonic signal；It is independent random variable
And it obeys and is uniformly distributed in the section [- π, π]；63 be the overtone order for needing to measure；nα(k) it is standard α symmetric-stable distributions
(sas), and known to characteristic index α；ng(k) it is zero-mean colored Gaussian noise, its spectrum density is unknown；Assuming that ng(k) and nα
(k) independently of each other；
To Voltage Harmonic signal x (k), 2p (α≤2 2p ＜) rank fractional order cumulant is taken, by fractional order cumulant
Canonical function 1,3,4 and theorem 1, have
In (2) formula, if τ=0, (2) formula is rewritten into k × k and ties up cumulant matrices by 1 ..., k-1 (k ＞ 63)：
Then x1(k) and x2(k) 2pthRank cumulant can be written to following formula again：
Here FiIt is by complex exponentialThe n dimensional vector n matrixes of the k of composition × 1,
I=1,2 ..., 63, wherein ω1,ω2,…ωiThe frequency of estimation is sought to, H is associate matrix, and T is transposed matrix.ai
For the amplitude of mains by harmonics signal；
Write (4) formula as matrix form：
F=[F in formula1,F2,…,Fq] it is that a k × 63 ties up matrix,It is one
Real diagonal matrix, because mains by harmonics includes 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noiseOrder be exactly 63, to matrixSingular value decomposition SVD is carried out, and singular value is arranged in descending order, is obtained
(6) formula：
In view of matrixOrder be 63, thereforeOnly 63 non-zero singular values, that is to say, that：σ1≥σ2
≥…≥σ63＞ σ63+1=...=σk=0
Assuming that：Σ1=diag [σ1,σ2,…,σ63] (7)
And singular vector matrix V is decomposed into matrix in block form V=[V1,V2], here
V1=[v1,v2,…,vq]
V2=[vq+1,vq+2,…,vk] (8)
Similarly, singular vectors matrix U is decomposed into matrix in block form U=[U1,U2], here
U1=[u1,u2,…,uq]
U2=[uq+1,uq+2,…,uk] (9)
(6) formula can be written in this way：
By above-mentioned decomposable process, can obtain：
(6) formula is substituted into (13) formula：
FPFHV2=0 (13)
Because F is associate matrix, and P is a non-zero diagonal matrix, so：
FHV2=0 (14)
This means that matrix F and matrix V2It is orthogonal；
Assuming thatHarmonic frequency in this way based on MUSIC algorithms can be by (15) formula
It is calculated：
Using ω as horizontal axis, make PMUSICThe frequencies omega of (ω)=0iThe frequency of 63 harmonic signals of mains by harmonics signal；
(5) mains by harmonics based on fractional order cumulant measures method of estimation and is as follows：
Step 1：Calculate network voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant, obtains Qi Zhute
Value indicative σ1,σ2,…,σ63With sub-eigenvalue σ2；
Step 2：It is right(SVD) singular value decomposition is carried out, calculating MUSIC using formula (15) composes PMUSIC(ωi)；
Step 3：Find out PMUSIC(ωi) 63 peak values, they are exactly frequencies omega to be asked1,ω2,ω3…ω63Estimation
Value, the as frequency of each harmonic；
Step 4：The frequencies omega that will be acquired1,ω2,ω3…ω63In substitution formula (4) formula, power grid can be obtained by by calculating
Voltage, the corresponding amplitude of electric current each harmonic.
Beneficial effects of the present invention：
1, fractional order cumulant proposed by the present invention solves higher order cumulants compared to Higher Order Cumulants, fractional order cumulant
Measure the signal processing for any (0 α≤2 ＜) the Stable distritation process including Gaussian process that could not be solved.
2, fractional order cumulant proposed by the present invention is a linear operator, and fractional order statistic is one non-linear
Operator.
3, fractional order cumulant proposed by the present invention is the expansion and development to Higher Order Cumulants.It is by Higher Order Cumulants
Definition has positive integer domain to expand to entire positive real number domain, can inhibit α noises well.Improve the robustness of signal.
4, being measured present invention firstly provides the higher harmonics mains by harmonics based on fractional order cumulant has preferable theory
Meaning and practical value.
Description of the drawings
Fig. 1 is system global structure schematic diagram of the present invention.
Fig. 2 is harmonic measure node structure schematic diagram of the present invention.
Fig. 3 is harmonic measure node procedure work flow diagram of the present invention.
1, computer 2, Signals Transfer Board 3, harmonic measure node 4, voltage transformer 5, current transformer 6, electric current electricity
Pressure converter 7, clipping module 8, AD sampling modules 9, SD card module 10, microprocessor module 11, button 12, display screen
13, Zigbee routings or terminal 14, power grid.
Specific implementation mode
It please refers to Fig.1, shown in Fig. 2 and Fig. 3：
High-precision power grid harmonic measure system provided by the invention includes computer 1, Signals Transfer Board 2 and one or several
Harmonic measure node 3, wherein computer 1 turn Serial Port Line by Serial Port Line or USB and are connected with Signals Transfer Board 2, are installed in computer 1
Mains by harmonics monitoring of software can read serial ports and transmit the data come up in real time, and analyzes, handles, real-time display of then itemizing,
Draw curve and preservation；Zigbee coordinators, signal converting chip and DB9 interfaces are installed on Signals Transfer Board 2, wherein
Zigbee coordinators are the master controllers of entire Zigbee network, for in network Zigbee routings or terminal distribution
Location, coordination data transmission path, and each harmonic measure node 3 is transmitted into the data summarization to come up, electricity is sent to by serial ports again
Brain.
Computer 1 is that with DB9 interfaces or USB interface and can run the desktop computer of mains by harmonics monitoring of software, pen
Remember this or industrial personal computer.
Harmonic measure node 3 include voltage transformer 4, current transformer 5, current-to-voltage convertor 6, clipping module 7,
AD sampling modules 8, SD card module 9, microprocessor module 10, button 11, display screen 12 and Zigbee routings or terminal 13, wherein
The primary side of voltage transformer 4 gets access to grid 14, and secondary side output voltage enters AD sampling modules 8 after clipping module 7, secondary
The maximum value of side output voltage is less than the range of AD sampling modules 8；The primary side of current transformer 5 gets access to grid 14, and secondary side is defeated
Go out electric current after current-to-voltage convertor 6 is converted to voltage signal, enters AD sampling modules 8, conversion using clipping module 7
The maximum value of voltage signal afterwards is less than the range of AD sampling modules 8；Current-to-voltage convertor 6 is used for current transformer 5 is defeated
The current signal gone out is converted to 8 measurable voltage signal of AD sampling modules, and clipping module 7 is made of bi-directional voltage stabilizing pipe, pincers
Position voltage is less than the output of the range of AD sampling modules 8 but output voltage and current-to-voltage convertor 6 higher than voltage transformer 4
Voltage；AD sampling modules 8 include AD sampling A/D chips and its peripheral circuit, and AD sampling A/D chips are connected with microprocessor module 10, by
Microprocessor module 10 provides clock, and passes data to microprocessor module 10 by simultaneously mouth line；Microprocessor module 10
It is made of microprocessor and its peripheral circuit, wherein microprocessor is STM32F4 family chips, and peripheral circuit constitutes its system；
SD card module 9 is made of SD card slot and capacitance resistance, is connect by spi bus with microprocessor module 10, is measured for storing
Data and the setting of the system of harmonic measure node；Button 11 is connected on the I/O port of microprocessor module 10, is surveyed for harmonic wave
Measure setting and the scene inquiry measurement result of node 3；Display screen 12 is that LCD liquid crystal display screen is connected with microprocessor module 10
It connects, is used for display system state and measurement result；Zigbee is route or terminal 13 is that Zigbee router-modules or Zigbee are whole
End module is connected with microprocessor module 10 by universal serial bus, realizes harmonic measure node 3 and Zigbee coordinators and power grid
The data transfer of Detecting Power Harmonicies software.
Signal converting chip is MAX232 family chips or the chip of same function, and input terminal connects Zigbee coordinators,
Serial data for receiving Transistor-Transistor Logic level, output termination DB9 interfaces, for exporting the serial of the identifiable RS232 level of computer
Data.
High-precision power grid harmonic measuring method provided by the invention, method are as described below：
Computer 1 is connected with Signals Transfer Board 2 Step 1: turning Serial Port Line with Serial Port Line or USB, connects Signals Transfer Board 2
Power supply, open mains by harmonics monitoring of software；Harmonic measure node 3 is accessed in power grid 14 to be measured, if any multiple points to be measured,
It can be separately connected a harmonic measure node 3 on each tested point, connect the power supply of each harmonic measure node 3, at this time signal
Zigbee coordinators on pinboard 2 can be Zigbee routings and terminal distribution address on each harmonic measure node 3, with group
At Zigbee network；
Step 2: after the power supply of harmonic measure node 3 is connected, the microprocessor module 10 on harmonic measure node 3 starts
Work, first initializes each module, then reads the node configuration information in SD card module 9, and to harmonic measure section
3 relevant parameters of point are configured；
Step 3: voltage transformer 4 on harmonic measure node 3 and current transformer 5 are started to work, and by power grid 14
Voltage, electric current are converted into 8 collectable voltage signal of AD sampling modules, and the microprocessor driven AD in microprocessor module 10 is adopted
Egf block 8 samples these voltage signals and is preserved in memory；
Step 4: microprocessor in microprocessor module 10 by 14 voltage of power grid, the corresponding digital signal of electric current from step
It is read out in specific memory described in rapid three, the harmonic measuring method based on fractional order cumulant is used in combination to calculate separately out electricity
14 voltage of net, the fundamental wave of electric current and 1-63 harmonic wave；
Step 5: the microprocessor in microprocessor module 10 will be corresponded to according to the node configuration information in SD card module 9
Data send to display screen 12 and shown, if the node configuration information in SD card module 9, which is requirement, closes display screen,
This step does not execute；
Step 6: microprocessor in microprocessor module 10 is by 14 voltage of power grid surveyed, the fundamental wave and 1-63 of electric current
Secondary harmonic data packing is stored sequentially in by time of measuring in SD card module 9, and is passed through plus node serial number and cyclic redundancy check
Zigbee network is sent in computer 1, is parsed these data by the data processing on backstage on mains by harmonics monitoring of software
Come and be shown on corresponding window, while these data can also be preserved；
Step 7: repeating step 3 to step 6, so cycle obtains 14 voltage of power grid and electricity at each harmonic measure node 3
The fundamental wave of stream and each harmonic wave.
The harmonic measuring method based on fractional order cumulant described in step 4, the specific method is as follows：
The determination of the first step, fractional order square and fractional order accumulation flow function and standard：
(1) determination of fractional order square and fractional order accumulation flow function：
If Φ (u) is the characteristic function of stochastic variable X, have
In formula：For left Riemann-Liouville Fractional Derivatives, 0 ＜ p≤1, k is arbitrary integer, claims mkp
WithRLCkpRespectively the fractional order square of stochastic variable X and fractional order cumulant, fractional order cumulantRLCkpAlso it can be denoted asRLcumkp
(·)；
(2) determination of fractional order cumulant standard：
Determine that fractional order cumulant standard is as follows：
Standard 1：If a1,a2,…,akFor constant, X (k)=[x1,x2,…,xk] be stochastic variable, then
In formula：Kp=p1+p2+…+pk
Standard 2：Fractional order cumulant is symmetrical, the sequence nothing of their magnitude and independent variable in other words to its independent variable
It closes, i.e.,
Wherein, i1,i2,…,ikIt is 1,2 ..., an arrangement of k；
Standard 3：If k stochastic variable { xiA subset and other parts it is independent, then
Standard 4：If stochastic variable collection [x1,x2,…,xk] and [y1,y2,…,yk] be independent, then have
Standard 5：For 2p rank fractional order cumulantsRLCkp(τ) has maximum value as τ=0, i.e., |RLCkp(τ)|≤RLCkp
(0)
The conversion formula of second step, fractional order square and fractional order cumulant：
In formula：IlIt is the set for the new element that the element in I is generated by dividing combination, q indicates IlIn contained division
Number,Indicate IlIn kth divide,Q should be taken as 1,2 successively ..., k, and k is the number of stochastic variable,It indicates to all IlFunction determined by corresponding set is summed；
Third step, fractional order cumulant are to the rejection ability and suppressing method of α noises and Gaussian noise：
α Stable distritations are a kind of generalized Gaussian distributions, and the characteristic function of standard α Stable distritations is：
Φ (u)=exp-γ | u |α}
In formula：Parameter γ ＞ 0 are known as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is known as characteristic index, as characteristic index α=2,
It is Gaussian Profile that α Stable distritations, which are degenerated,；
About fractional order cumulant to the rejection ability and suppressing method of α noises and Gaussian noise, there is following theorem：
Theorem 1：The characteristic function of quasi- α Stable distritations is marked with as shown in above formula, it is just whole more than or equal to the minimum of p to enable m
Number, then as p ＞ 0 and α ＞ 0, the p rank fractional order cumulants of standard α Stable distritations are：
(1) when α-p are not integer：
(2) when 1≤p- α≤m are integer；
RLCp=0
For the p rank fractional order cumulants of standard α Stable distritation signals, when taking p ＜ α and when α-p are not integer, p
Rank fractional order cumulant exists and is zero, since Gaussian Profile is a special case in standard α Stable distritations as α=2, because
This, fractional order cumulant still sets up gaussian signal, this be fractional order cumulant to the rejection condition of α and Gaussian noise and
Suppressing method, since the fractional order cumulant of α noises and Gaussian noise is zero, i.e., as p ＜ α and when α-p are not integer, meaning
It and both noises is completely inhibited, therefore, fractional order cumulant has extremely strong rejection ability to α noises and Gaussian noise；
4th step, the mains by harmonics based on fractional order cumulant measure method of estimation：
(1) method of estimation of fractional order square and fractional order cumulant：
It, can be straight according to the definition of fractional order square and fractional order cumulant when known to the characteristic function of process x (k) immediately
It connects and calculates fractional order square and fractional order cumulant, when characteristic function is unknown, using one group of Observable sample of X (k) to its point
Number rank square and fractional order cumulant are estimated, using the conversion formula of fractional order square and fractional order cumulant, can be divided
The estimation of number rank cumulant, carries out score with the estimation of the 2p rank fractional order squares of random sequence x (k) and fractional order cumulant here
The method of estimation of rank square and fractional order cumulant；
(2) estimation of fractional order square:
IfIt can be obtained according to the definition of fractional order square for one group of Observable sample of stationary random process x (t)
Its 2p rank fractional order square is estimated as
Here N is number of samples；
(3) estimation of fractional order cumulant:
According to 2p rank cumulantsConversion formula has
Due toIt is to utilizeWithPass throughConversion formula
It obtains, thereforeIt is also unbiased consistent Estimation；Various different fractional-orders can be obtained using similar method
Fractional order square and fractional order cumulant estimation；
(4) the harmonic frequency method of estimation of 14 voltage of power grid, electric current：
If the signal of 14 voltage harmonic of power grid：
A in formulaiAnd ωi∈ (- π, π) is respectively the multiple amplitude and frequency of i-th of harmonic signal；It is independent random variable
And it obeys and is uniformly distributed in the section [- π, π]；63 be the overtone order for needing to measure；nα(k) it is standard α symmetric-stable distributions
(sas), and known to characteristic index α；ng(k) it is zero-mean colored Gaussian noise, its spectrum density is unknown；Assuming that ng(k) and nα
(k) independently of each other；
To 14 voltage harmonic signal x (k) of power grid, 2p (α≤2 2p ＜) rank fractional order cumulant is taken, by fractional order cumulant
Canonical function 1,3,4 and theorem 1, have
In (2) formula, if τ=0, (2) formula is rewritten into k × k and ties up cumulant matrices by 1 ..., k-1 (k ＞ 63)：
Then x1(k) and x2(k) 2pthRank cumulant can be written to following formula again：
Here FiIt is by complex exponentialThe n dimensional vector n matrixes of the k of composition × 1,
I=1,2 ..., 63, wherein ω1,ω2,......ωiThe frequency of estimation is sought to, H is associate matrix, and T is transposition square
Battle array.aiFor the amplitude of mains by harmonics signal；
Write (4) formula as matrix form：
F=[F in formula1,F2,…,Fq] it is that a k × 63 ties up matrix,It is one
Real diagonal matrix, because mains by harmonics includes 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noiseOrder be exactly 63, to matrixSingular value decomposition SVD is carried out, and singular value is arranged in descending order, is obtained
(6) formula：
In view of matrixOrder be 63, thereforeOnly 63 non-zero singular values, that is to say, that：σ1≥σ2
≥…≥σ63＞ σ63+1=...=σk=0
Assuming that：
Σ1=diag [σ1,σ2,…,σ63] (7)
And singular vector matrix V is decomposed into matrix in block form V=[V1,V2], here
Similarly, singular vectors matrix U is decomposed into matrix in block form U=[U1,U2], here
(6) formula can be written in this way：
By above-mentioned decomposable process, can obtain：
(6) formula is substituted into (13) formula：
FPFHV2=0 (13)
Because F is associate matrix, and P is a non-zero diagonal matrix, so：
FHV2=0 (14)
This means that matrix F and matrix V2It is orthogonal；
Assuming thatHarmonic frequency in this way based on MUSIC algorithms can be by (15) formula
It is calculated：
Using ω as horizontal axis, make PMUSICThe frequencies omega of (ω)=0iThe frequency of 63 harmonic signals of mains by harmonics signal；
(5) the 14 harmonic measure method of estimation of power grid based on fractional order cumulant is as follows：
Step 1：Calculate power grid 14 voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant obtains its master
Characteristic value σ1,σ2,…,σ63With sub-eigenvalue σ2；
Step 2：It is right(SVD) singular value decomposition is carried out, calculating MUSIC using formula (15) composes PMUSIC(ωi)；
Step 3：Find out PMUSIC(ωi) 63 peak values, they are exactly frequencies omega to be asked1,ω2,ω3…ω63Estimation
Value, the as frequency of each harmonic；
Step 4：The frequencies omega that will be acquired1,ω2,ω3…ω63In substitution formula (4) formula, power grid can be obtained by by calculating
14 voltages, the corresponding amplitude of electric current each harmonic.
Claims (1)
1. a kind of high-precision power grid harmonic measuring method, it is characterised in that：Its method is as described below：
Computer is connected with Signals Transfer Board Step 1: turning Serial Port Line with Serial Port Line or USB, connects the power supply of Signals Transfer Board,
Open mains by harmonics monitoring of software；Harmonic measure node is accessed in power grid to be measured, if any multiple points to be measured, can be waited for each
It is separately connected a harmonic measure node on measuring point, the power supply of each harmonic measure node is connected, at this time on Signals Transfer Board
Zigbee coordinators can be Zigbee routings and terminal distribution address on each harmonic measure node, to form Zigbee nets
Network；
Step 2: after the power supply of harmonic measure node is connected, the microprocessor module on harmonic measure node is started to work, elder generation
Each module is initialized, then reads the node configuration information in SD card module, and to harmonic measure node relevant parameter
It is configured；
Step 3: voltage transformer and current transformer on harmonic measure node are started to work, and by the voltage of power grid, electric current
It is converted into the collectable voltage signal of AD sampling modules, the microprocessor driven AD sampling modules in microprocessor module are to these
Voltage signal is sampled and is preserved in memory；
Step 4: the microprocessor in microprocessor module by network voltage, the corresponding digital signal of electric current from described in step 3
Specific memory in read out, be used in combination the harmonic measuring method based on fractional order cumulant calculate separately out network voltage,
The fundamental wave of electric current and 1-63 harmonic wave；Harmonic measuring method based on fractional order cumulant is as follows：
The determination of the first step, fractional order square and fractional order accumulation flow function and standard：
(1) determination of fractional order square and fractional order accumulation flow function：
If Φ (u) is the characteristic function of stochastic variable X, have
In formula：For left Riemann-Liouville Fractional Derivatives, 0 ＜ p≤1, k is arbitrary integer, claims mkpWithRLCkp
Respectively the fractional order square of stochastic variable X and fractional order cumulant, fractional order cumulantRLCkpAlso it can be denoted asRLcumkp(·)；
(2) determination of fractional order cumulant standard：
Determine that fractional order cumulant standard is as follows：
Standard 1：If a1,a2,…,akFor constant, X (k)=[x1,x2,…,xk] be stochastic variable, then
In formula：Kp=p1+p2+…+pk
Standard 2：Fractional order cumulant is symmetrical to its independent variable, their magnitude is unrelated with the sequence of independent variable in other words,
I.e.
Wherein, i1,i2,…,ikIt is 1,2 ..., any one arrangement of k；
Standard 3：If k stochastic variable { xiA subset and other parts it is independent, then
Standard 4：If stochastic variable collection [x1,x2,…,xk] and [y1,y2,…,yk] be independent, then have
Standard 5：For 2p rank fractional order cumulantsRLCkp(τ) has maximum value, i.e., as τ=0
|RLCkp(τ)|≤RLCkp(0)
The conversion formula of second step, fractional order square and fractional order cumulant：
In formula：IlIt is the set for the new element that the element in I is generated by dividing combination, q indicates IlIn contained division
Number,Indicate IlIn kth divide,Q should be taken as 1,2 successively ..., k, and k is the number of stochastic variable,It indicates to all IlFunction determined by corresponding set is summed；
Third step, fractional order cumulant are to the rejection ability and suppressing method of α noises and Gaussian noise：
α Stable distritations are a kind of generalized Gaussian distributions, and the characteristic function of standard α Stable distritations is：
Φ (u)=exp-γ | u |α}
In formula：Parameter γ ＞ 0 are known as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is known as characteristic index, as characteristic index α=2, α is steady
It is Gaussian Profile that fixed distribution, which is degenerated,；
About fractional order cumulant to the rejection ability and suppressing method of α noises and Gaussian noise, there is following theorem：
Theorem 1：The characteristic function of quasi- α Stable distritations is marked with as shown in above formula, it is the minimum positive integer more than or equal to p to enable m, then
As p ＞ 0 and α ＞ 0, the p rank fractional order cumulants of standard α Stable distritations are：
(1) when α-p are not integer：
(2) when 1≤p- α≤m are integer；
RLCp=0
For the p rank fractional order cumulants of standard α Stable distritation signals, when taking p ＜ α and when α-p are not integer, p ranks point
Number rank cumulants exist and are zero, since Gaussian Profile is a special case in standard α Stable distritations as α=2, point
Number rank cumulant still sets up gaussian signal, this is rejection condition and inhibition of the fractional order cumulant to α and Gaussian noise
Method, since the fractional order cumulant of α noises and Gaussian noise is zero, i.e., as p ＜ α and when α-p are not integer, it is meant that right
Both noises completely inhibit, and therefore, fractional order cumulant has extremely strong rejection ability to α noises and Gaussian noise；
4th step, the mains by harmonics based on fractional order cumulant measure method of estimation：
(1) method of estimation of fractional order square and fractional order cumulant：
When known to the characteristic function of random process x (k), can directly it be counted according to the definition of fractional order square and fractional order cumulant
Fractional order square and fractional order cumulant are calculated, when characteristic function is unknown, using one group of Observable sample of X (k) to its fractional order
Square and fractional order cumulant are estimated, using the conversion formula of fractional order square and fractional order cumulant, can obtain fractional order
The estimation of cumulant carries out fractional order square with the estimation of the 2p rank fractional order squares of random sequence x (k) and fractional order cumulant here
With the method for estimation of fractional order cumulant；
(2) estimation of fractional order square:
IfIts 2p can be obtained according to the definition of fractional order square for one group of Observable sample of stationary random process x (t)
Rank fractional order square is estimated as
Here N is number of samples；
(3) estimation of fractional order cumulant:
According to 2p rank cumulantsConversion formula has
Due toIt is to utilizeWithPass throughConversion formula obtains
, thereforeIt is also unbiased consistent Estimation；It can be obtained point of various different fractional-orders using similar method
The estimation of number rank square and fractional order cumulant；
(4) the harmonic frequency method of estimation of network voltage, electric current：
If the signal of Voltage Harmonic：
A in formulaiAnd ωi∈ (- π, π) is respectively the multiple amplitude and frequency of i-th of harmonic signal；Be independent random variable and
It obeys and is uniformly distributed in the section [- π, π]；63 be the overtone order for needing to measure；nα(k) it is standard α symmetric-stable distributions
(sas), and known to characteristic index α；ng(k) it is zero-mean colored Gaussian noise, its spectrum density is unknown；Assuming that ng(k) and nα
(k) independently of each other；
To Voltage Harmonic signal x (k), 2p (α≤2 2p ＜) rank fractional order cumulant is taken, by the standard of fractional order cumulant
Function 1,3,4 and theorem 1, have
In (2) formula, if τ=0, (2) formula is rewritten into k × k and ties up cumulant matrices by 1 ..., k-1 (k ＞ 63)：
Then x1(k) and x2(k) 2pthRank cumulant can be written to following formula again：
Here FiIt is by complex exponentialThe n dimensional vector n matrixes of the k of composition × 1, Wherein ω1,ω2,......ωiThe frequency of estimation is sought to, H is associate matrix, and T is transposition
Matrix, aiFor the amplitude of mains by harmonics signal；
Write (4) formula as matrix form：
F=[F in formula1,F2,…,Fq] it is that a k × 63 ties up matrix,It is that a reality is right
Angular moment battle array, because mains by harmonics includes 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noise's
Order is exactly 63, to matrixSingular value decomposition SVD is carried out, and singular value is arranged in descending order, obtains formula (6)：
In view of matrixOrder be 63, thereforeOnly 63 non-zero singular values, that is to say, that：σ1≥σ2≥…
≥σ63＞ σ63+1=...=σk=0
Assuming that：
Σ1=diag [σ1,σ2,…,σ63] (7)
And singular vector matrix V is decomposed into matrix in block form V=[V1,V2], here
Similarly, singular vectors matrix U is decomposed into matrix in block form U=[U1,U2], here
(6) formula can be written in this way：
By above-mentioned decomposable process, can obtain：
(6) formula is substituted into formula (13)：
FPFHV2=0 (13)
Because F is associate matrix, and P is a non-zero diagonal matrix, so：
FHV2=0 (14)
This means that matrix F and matrix V2It is orthogonal；
Assuming thatHarmonic frequency in this way based on MUSIC algorithms can be calculated by (15) formula
It arrives：
Using ω as horizontal axis, make PMUSICThe frequencies omega of (ω)=0iThe frequency of 63 harmonic signals of mains by harmonics signal；
(5) mains by harmonics based on fractional order cumulant measures method of estimation and is as follows：
Step 1：Calculate network voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant obtains its dominant eigenvalue
σ1,σ2,…,σ63With sub-eigenvalue σ2；
Step 2：It is right(SVD) singular value decomposition is carried out, calculating MUSIC using formula (15) composes PMUSIC(ωi)；
Step 3：Find out PMUSIC(ωi) 63 peak values, they are exactly frequencies omega to be asked1,ω2,ω3…ω63Estimated value, i.e.,
For the frequency of each harmonic；
Step 4：The frequencies omega that will be acquired1,ω2,ω3…ω63In substitution formula (4), by calculate can be obtained by network voltage,
The corresponding amplitude of electric current each harmonic；
Step 5: the microprocessor in microprocessor module send corresponding data according to the node configuration information in SD card module
It is shown to display screen, if the node configuration information in SD card module, which is requirement, closes display screen, this step does not execute；
Step 6: microprocessor in microprocessor module is by the network voltage surveyed, the fundamental wave of electric current and 1-63 harmonic wave
Data packing is stored sequentially in by time of measuring in SD card module, and passes through Zigbee nets plus node serial number and cyclic redundancy check
Network is sent in computer, these data are parsed by the data processing on backstage on mains by harmonics monitoring of software and include
On corresponding window, while these data can also be preserved；
Step 7: repeating step 3 to step 6, so cycle obtains the base of network voltage and electric current at each harmonic measure node
Wave and each harmonic wave.
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| CN101566649A (en) * | 2009-05-27 | 2009-10-28 | 重庆大学 | Harmonic detection method in a power system |
| CN102721890A (en) * | 2012-07-02 | 2012-10-10 | 上海仪器仪表研究所 | Practical monitoring device for virtual terminal power grid |
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| CN105137184A (en) * | 2015-09-21 | 2015-12-09 | 广东电网有限责任公司东莞供电局 | 10kV bus harmonic monitoring method based on feeder line protection |
| CN105319389A (en) * | 2015-12-07 | 2016-02-10 | 吉林大学 | High-precision and wide-range ultrasonic wind speed measuring system and method |
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| CN1046982A (en) * | 1989-05-30 | 1990-11-14 | 山东省煤炭科学研究所 | Power system harmonizing wave measuring method and measuring instrument |
| CN101566649A (en) * | 2009-05-27 | 2009-10-28 | 重庆大学 | Harmonic detection method in a power system |
| CN102721890A (en) * | 2012-07-02 | 2012-10-10 | 上海仪器仪表研究所 | Practical monitoring device for virtual terminal power grid |
| CN104237635A (en) * | 2014-09-17 | 2014-12-24 | 国家电网公司 | Harmonic wave quantitative measurement method of power system |
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