CN105974196A - High-precision power grid harmonic wave measurement system and high-precision power grid harmonic wave measurement method - Google Patents

Abstract

The invention discloses a high-precision power grid harmonic wave measurement system and a high-precision power grid harmonic wave measurement method. The high-precision power grid harmonic wave measurement system comprises a computer, a signal adaptor board and one or a plurality of harmonic wave measurement nodes, wherein the computer is connected with the signal adaptor board through a serial-port wire or a USB-to-serial wire. Power grid harmonic monitoring software which is installed in the computer can perform real-time reading of data which are transmitted from a serial port, analysis and processing, real-time item-to-item displaying, curve drawing and storage. The high-precision power grid harmonic wave measurement method comprises the steps of a first step, connecting the computer with a signal adapter board by means of the serial-port wire or the USB-to-serial wire; a second step, configuring related parameter of the harmonic wave measurement node; a third step, sampling the voltage signal and storing the voltage signal in a memory; a fourth step, reading the voltage signal from the memory specified in the third step; a fifth step, preventing execution of this step; a sixth step, storing the data; and a seventh step, repeating the steps from the third step to the sixth step. The high-precision power grid harmonic wave measurement system and the high-precision power grid harmonic wave measurement method have advantages of relatively high theoretical meaning and high practical value.

Description

A kind of high accuracy electrical network harmonic measure system and method

Technical field

The present invention relates to a kind of harmonic measure system and method, particularly to one high accuracy electrical network harmonic measure system and Method.

Background technology

Currently, in the production, the links that transmits, change and use of electric energy, harmonic wave can all be produced.In power system Harmonic wave main source has electromotor, electrical power trans mission/distribution system, electronic power rectification equipment, electric arc furnace, frequency conversion equipment, glow discharge spot lamp Deng.Harmonic in Power System content increases rapidly, causes voltage waveform distortion, adds loss and the electrical equipment of transmission line of electricity Loss, reduce the quality of power supply, damage electrical equipment.Harmonic wave and m-Acetyl chlorophosphonazo (i.e. have the signal of non-integral multiple fundamental frequency Component) power system is caused added losses and the heating of multiple harm or impact, such as electric rotating machine etc., shorten and use the longevity Life；Resonance overvoltage, causes electrical equipment and the fault of equipment and loss；Electric energy metrical mistake；Communication system is produced interference, Make telecommunications Quality Down；Automatically control, the incorrect operation etc. of protection device.Therefore, in real time, grasp harmonic wave in electrical network accurately With the real conditions (frequency and amplitude information) of m-Acetyl chlorophosphonazo component, power system security, economical operation are had great importance.

Analog filtering is had currently, with respect to the theoretical research of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo and the method for actual application aspect Device detection method, based on instantaneous reactive power detection method, based on neutral net detection method, quickly diaphragm filter (FFT), Prony waveform fitting, wavelet transformation (WT) and support vector machine (SVM) algorithm etc. are multiple.Bandpass filtering is early stage mould The ultimate principle of plan 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 control fields such as compensation.Neutral net detection method has that amount of calculation is little, precision is high, real-time is good and anti-interference is good Feature, but, neutral net also has a lot of problem for engineering is actual, such as: do not have the neural network configuration method of specification, needs Wanting substantial amounts of training sample, how to determine that the sample number of needs does not has method for normalizing, sample is had big by the precision of neutral net Dependency, etc..In the case of fundametal compoment frequency fluctuation, fft algorithm is difficult to avoid that the frequency caused because of non-synchronous sampling is let out Leakage and fence effect and the measurement error that causes.Prony waveform fitting method is very sensitive to noise, calculates when reality is applied Measure compared with big and effect is not ideal enough.When wavelet transformation is applied to harmonic wave and m-Acetyl chlorophosphonazo measurement, due to having the humorous of upper frequency The measurement frequency band of ripple and/or m-Acetyl chlorophosphonazo component is wider causes frequency resolution to decline, it is difficult to two signals that crossover frequency is close Component.Harmonic wave based on support vector machine and/or inter-harmonic wave measuring method amount of calculation are relatively big and certainty of measurement is the highest, should in reality Used time effect is not ideal enough.

Theory and algorithm that the most existing Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo are measured all are only used for Gaussian noise background Under harmonic measure problem.Power system actually exists very many non-gaussian impact noises, such as by motor start and stop, electricity The switching of net electric power, transformator start and stop and many artificial signals produced and noise, the most all have such a non-gaussian Shock feature, i.e. there is significantly data sudden change the most continually than Gaussian noise in them；Being reflected in time domain, they manifest Go out substantial amounts of notable spiking characteristics；Being reflected in probability density, they have more thick and heavy " the trailing existing than Gauss distribution As ".At this moment feasible under Gaussian noise harmonic wave and m-Acetyl chlorophosphonazo measure theory and algorithm had lost efficacy.

Substantial amounts of research work shows: this Non-Gaussian colored noise with shock feature can come with α Stable distritation Characterize.Shao and Nikias is it is manifestly intended that α Stable distritation is applicable to the foundation of impact noise modeling: 1. α Stable distritation is Uniquely meeting the family of distributions of broad sense central limit theorem, it is rational the most in theory, and compared with Gauss distribution also There is the meaning more typically changed；2. α Stable distritation is the pole of generation mechanism and the propagation conditions that can keep natural noise process Limit distribution；3. α Stable distritation is generalized Gaussian distribution, therefore has the general characteristic of Gauss distribution, i.e. stability and enclosed； 4. α Stable distritation can match with many real data of nature.

Summary of the invention

The invention aims to solve existing Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo ask present in measurement process A kind of high accuracy electrical network harmonic measure system and method inscribed and provide.

The high accuracy electrical network harmonic measure system that the present invention provides includes computer, Signals Transfer Board and one or several humorous Wave measurement node, wherein computer turns Serial Port Line by Serial Port Line or USB and is connected with Signals Transfer Board, and the electrical network installed in computer is humorous Ripple monitoring of software can read serial ports in real time and transmit the data come up, and analyzes, processes, then subitem display in real time, drafting song Line and preservation；Being provided with Zigbee coordinator, signal converting chip and DB9 interface on Signals Transfer Board, wherein Zigbee coordinates Device is the master controller of whole Zigbee network, for routeing or terminal distribution address, coordination data to the Zigbee in network Transmission path, and the data summarization that the transmission of each harmonic measure node comes up is sent to computer by serial ports again.

Computer is with DB9 interface or USB interface and can to run the desktop computer of mains by harmonics monitoring of software, notes Basis or industrial computer.

Harmonic measure node includes voltage transformer, current transformer, current-to-voltage convertor, clipping module, AD adopt Original mold block, SD card module, microprocessor module, button, display screen and Zigbee route or terminal, wherein the one of voltage transformer Secondary side joint electrical network, secondary side output voltage enters AD sampling module, the maximum of secondary side output voltage after clipping module Range less than AD sampling module；The primary side of current transformer gets access to grid, and secondary side output electric current is changed through current/voltage After device is converted to voltage signal, then entering AD sampling module through clipping module, the maximum of the voltage signal after conversion is less than The range of AD sampling module；Current-to-voltage convertor is for being converted to AD sampling module by the current signal that current transformer exports Measurable voltage signal, clipping module is made up of bi-directional voltage stabilizing pipe, and its clamp voltage is less than the range of AD sampling module but high Output voltage and the output voltage of current-to-voltage convertor in voltage transformer；AD sampling module include AD sampling A/D chip and Peripheral circuit, AD sampling A/D chip is connected with microprocessor module, microprocessor module provide clock, and by parallel port line by number According to passing to microprocessor module；Microprocessor module is made up of microprocessor and peripheral circuit thereof, and wherein microprocessor is STM32F4 family chip, peripheral circuit constitutes its system；SD card module is made up of SD draw-in groove and capacitance resistance, with microprocessor Module is connected by spi bus, arranges for storing the system of measurement data and harmonic measure node；Button is connected to micro-process On the I/O port of device module, for setting and the on-the-spot inquiry measurement result of harmonic measure node；Display screen is LCD liquid crystal display Screen is connected with microprocessor module, for display system state and measurement result；Zigbee route or terminal are Zigbee road By device module or Zigbee terminal module, be connected by universal serial bus with microprocessor module, it is achieved harmonic measure node with The data transmission of Zigbee coordinator and mains by harmonics monitoring of software.

Signal converting chip is MAX232 family chip or the chip of equal function, and input connects Zigbee coordinator, For receiving the serial data of Transistor-Transistor Logic level, output termination DB9 interface, for exporting the serial of computer discernible RS232 level Data.

The high accuracy electrical network harmonic measuring method that the present invention provides, its method is as described below:

Step one, turn Serial Port Line with Serial Port Line or USB computer is connected with Signals Transfer Board, connect the electricity of Signals Transfer Board Source, opens mains by harmonics monitoring of software；Harmonic measure node is accessed in electrical network to be measured, if any multiple points to be measured, can be often Connect a harmonic measure node on individual tested point respectively, connect the power supply of each harmonic measure node, now on Signals Transfer Board Zigbee coordinator can be on each harmonic measure node Zigbee route and terminal distribution address, to form Zigbee net Network；

Step 2, harmonic measure node power on after, the microprocessor module on harmonic measure node is started working, Each module is first initialized by it, then reads the node configuration information on SD card module, and is correlated with harmonic measure node Parameter configures；

Voltage transformer summation current transformer on step 3, harmonic measure node is started working, and by the voltage of electrical network, Electric current is converted into the collectable voltage signal of AD sampling module, the microprocessor driven AD sampling module pair in microprocessor module These voltage signals carry out sampling and being saved in internal memory；

Microprocessor in step 4, microprocessor module by digital signal corresponding to line voltage, electric current from step 3 Described specific internal memory reads out, and calculates electrical network electricity respectively with harmonic measuring method based on fractional order cumulant Pressure, the first-harmonic of electric current and the harmonic wave of 1-63 time；

Microprocessor in step 5, microprocessor module according to the node configuration information on SD card module by corresponding number Showing according to delivering to display screen, if the node configuration information on SD card module is requirement closes display screen, then this step is not Perform；

Microprocessor in step 6, microprocessor module is by the line voltage surveyed, the first-harmonic of electric current and 1-63 time Harmonic data packing is stored on SD card module by measuring time sequencing, and passes through plus node serial number and CRC check code Zigbee network is sent in computer, and mains by harmonics monitoring of software is processed by these data parsings out by the data on backstage And show on corresponding window, also these data can be preserved simultaneously；

Step 7, repetition step 3 are to step 6, and so circulation obtains line voltage and electric current at each harmonic measure node First-harmonic and the harmonic wave of each time.

Harmonic measuring method based on fractional order cumulant described in step 4, its concrete grammar is as follows:

The first step, fractional order square and fractional order cumulant function and the determination of standard:

(1) fractional order square and the determination of fractional order cumulant function:

If the characteristic function that Φ (u) is stochastic variable X, have

$m^{kp}={\mathrm{\Φ}}^{\left(kp\right)}\left(u\right)e^{-j\frac{\mathrm{\π}kp}{2}}{|}_{u=0}$

${C_{RL}}^{kp}=e^{-j\frac{\mathrm{\π}kp}{2}}\frac{{d_{RL}}^{kp}}{{\mathrm{dt}}^{kp}}ln\mathrm{\Φ}\left(u\right){|}_{u=0}$

In formula:For left Riemann-Liouville Fractional Derivative, 0 ＜ p≤1, k is arbitrary integer, claims m^kpWith RLC^kpIt is respectively fractional order square and fractional order cumulant, the fractional order cumulant of stochastic variable X^RLC^kpAlso can be designated as^RLcum^kp (·)；

(2) determination of fractional order cumulant standard:

Determine that fractional order cumulant standard is as follows:

Standard 1: set a₁,a₂,…,a_kFor constant, X (k)=[x₁,x₂,…,x_k] be stochastic variable, then

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\[a_1{x}_1^{p_1},a_2{x}_2^{p_2},...,a_k{x}_k^{p_k}\]\\ =a_1{a}_2...{a_k}^{RL}{\mathrm{cum}}^{kp}\[x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\]\end{array}$

In formula: kp=p₁+p₂+…+p_k

Standard 2: fractional order cumulant is symmetrical to its independent variable, in other words their value and the order nothing of independent variable Close, i.e.

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\[x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\]\\ {=}^{RL}{\mathrm{cum}}^{kp}\[x_{i_1}^{p_{i_1}},x_{i_2}^{p_{i_2}},...,x_{i_k}^{p_{i_k}}\]\end{array}$

Wherein, i₁,i₂,…,i_kIt is 1,2 ..., any one arrangement of k；

Standard 3: if k stochastic variable { x_iA subset and other parts independent, then

${}^{RL}{\mathrm{cum}}^{kp}\[x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\]\≡0$

Standard 4: if stochastic variable collection [x₁,x₂,…,x_k] and [y₁,y₂,…,y_k] be independent, then have

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\[{\left(x_1+y_1\right)}^{p_1},{\left(x_2+y_2\right)}^{p_2},...,{\left(x_k+y_k\right)}^{p_k}\]\\ {=}^{RL}{\mathrm{cum}}^{kp}\[x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\]{+}^{RL}{\mathrm{cum}}^{kp}\[y_1^{p_1},y_2^{p_2},...,y_k^{p_k}\]\end{array}$

Standard 5: for 2p rank fractional order cumulant^RLC^kp(τ), when τ=0, there is maximum, i.e.

|^RLC^kp(τ)|≤^RLC^kp(0)

Second step, fractional order square and the conversion formula of fractional order cumulant:

$m^{kp}\left(I\right)=\underset{l}{\Σ}\underset{k=1}{\overset{q}{\Π}}{C_{RL}}^{kp}\left(I_{l_k}\right)$

${C_{RL}}^{kp}\left(I\right)=\underset{l}{\Σ}{(-1)}^{(l-1)}(l-1)!\underset{k=1}{\overset{q}{\Π}}{m}^{kp}\left(I_{lk}\right)$

In formula: I_lBeing the set of the new element that the element in I generates through dividing combination, q represents I_lDivide contained by Number,Represent I_lIn kth divide,Q should be taken as 1,2 successively ..., k, k are the number of stochastic variable,Represent To all I_lFunction summation determined by corresponding set；

3rd step, fractional order cumulant are to α noise and the rejection ability of Gaussian noise and suppressing method:

α Stable distritation is a kind of generalized Gaussian distribution, and the characteristic function of standard α Stable distritation is:

Φ (u)=exp{-γ | u |^α}

In formula: parameter γ ＞ 0 is referred to as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is referred to as characteristic index, when characteristic index α=2, α Stable distritation deteriorates to Gauss distribution；

About fractional order cumulant to α noise and the rejection ability of Gaussian noise and suppressing method, there is a following theorem:

Theorem 1: the characteristic function of bidding quasi-α Stable distritation is as shown in above formula, and making m is that the minimum more than or equal to p is the most whole Number, then as p ＞ 0 and α ＞ 0, the p rank fractional order cumulant of standard α Stable distritation is:

(1) when α-p is not integer:

${C_{RL}}^p=\left\{\begin{array}{cc}0,& \mathrm{\&alpha;}-p>0\\ -\mathrm{\&gamma;}\mathrm{\&Gamma;}(\mathrm{\&alpha;}+1)e^{-j\frac{\mathrm{\&pi;}k\mathrm{\&alpha;}}{2}},& \mathrm{\&alpha;}=p\\ \mathrm{\&infin;},& \mathrm{\&alpha;}-p<0\end{array}\right.$

(2) when 1≤p-α≤m is integer；

^RLC^p=0

For the p rank fractional order cumulant of standard α Stable distritation signal, when taking p ＜ α, or when 1≤p-α≤m is integer Time, its p rank fractional order cumulant exists and is zero, owing to Gauss distribution is a spy when α=2 in standard α Stable distritation Example, therefore, gaussian signal is still set up by fractional order cumulant, and this is fractional order cumulant to α and the suppression of Gaussian noise Condition and suppressing method, owing to the fractional order cumulant of α noise and Gaussian noise is zero, i.e. as p ＜ α, it is meant that to this two Planting completely inhibiting of noise, therefore, fractional order cumulant has extremely strong rejection ability to α noise and Gaussian noise；

4th step, mains by harmonics based on fractional order cumulant measurement method of estimation:

(1) fractional order square and the method for estimation of fractional order cumulant:

When the characteristic function of stochastic process x (k) is known, it is possible to the definition according to fractional order square and fractional order cumulant is straight Connect calculating fractional order square and fractional order cumulant, when characteristic function is unknown, utilize one group of Observable sample of X (k) to its point Number rank square and fractional order cumulant are estimated, utilize fractional order square and the conversion formula of fractional order cumulant, it is possible to divided The estimation of number rank cumulant, carries out mark with the 2p rank fractional order square of random sequence x (k) and the estimation of fractional order cumulant here Rank square and the method for estimation of fractional order cumulant；

(2) estimation of fractional order square:

IfFor one group of Observable sample of stationary random process x (t), according to the definition of fractional order square, can obtain Being estimated as of its 2p rank fractional order square

${\hat{m}}_x^p\&lsqb;x\left(k\right)\&rsqb;=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}{x}^p\left(k\right)$

${\hat{m}}_{2x}^{2p}\left(m\right)=\frac{1}{N-\left|m\right|}\underset{k=1}{\overset{N-\left|m\right|}{\&Sigma;}}{x}^p\left(k\right)x^p(k+m),m=0,\&PlusMinus;1,\&PlusMinus;2,...$

Here N is number of samples；

(3) estimation of fractional order cumulant:

According to 2p rank cumulantConversion formula, has

$\begin{array}{c}\hat{C}_{2x}^{2p}{}_{RL}\left(m\right)={\hat{m}}_{2x}^{2p}\left(m\right)-{\hat{m}}_x^p\left(x\left(k\right)\right){\hat{m}}_x^p\left(x\left(k+m\right)\right)\\ =\frac{1}{N-\left|m\right|}\underset{i=1}{\overset{N-\left|m\right|}{\&Sigma;}}{x}^p\left(i\right)x^p\left(i+m\right)-{\&lsqb;\frac{1}{N}\underset{i=1}{\overset{N}{\&Sigma;}}{x}^p\left(i\right)\&rsqb;}^2,m=0,\&PlusMinus;1,\&PlusMinus;2,...\end{array}$

Due toIt is to utilizeWithPass throughConversion formula obtains, because of ThisAlso it is unbiased consistent Estimation；Use similar method i.e. can get various different fractional-order fractional order square and The estimation of fractional order cumulant；

(4) the harmonic frequency method of estimation of line voltage, electric current:

If the signal of Voltage Harmonic:

A in formula_iAnd ω_i∈ (-π, π) is respectively multiple amplitude and the frequency of i-th harmonic signal；It it is independent random variable And it is uniformly distributed [-π, π] interval obedience；63 is the overtone order needing to measure；n_αK () is standard α symmetric-stable distribution , and characteristic index α is known (sas)；n_gK () is zero-mean colored Gaussian noise, its spectrum density is unknown；Assume n_g(k) and n_α K () is separate；

To Voltage Harmonic signal x (k), take 2p (2p ＜ α≤2) rank fractional order cumulant, by fractional order cumulant Canonical function 1,3,4 and theorem 1, have

In (2) formula, if τ=0,1 ..., k-1 (k ＞ 63), (2) formula be rewritten into k × k tie up cumulant matrices:

Then x₁(k) and x₂The 2p of (k)^thRank cumulant can be written to again following formula:

$C_{xx}^{2p}{}_{RL}=\underset{i=1}{\overset{q}{\&Sigma;}}{a}_i^2{F}_i{F}_i^H---\left(4\right)$

Here F_iIt is by complex exponentialK × 1 n dimensional vector n the matrix of composition,i =1,2 ..., 63, wherein ω₁,ω₂,......ω_iSeeking to the frequency estimated, H is associate matrix, and T is transposed matrix. a_iAmplitude for mains by harmonics signal；

(4) formula is write as matrix form:

$C_{xx}^{2p}{}_{RL}={\mathrm{FPF}}^H---\left(5\right)$

F=[F in formula₁,F₂,…,F_q] it is that matrix is tieed up in k × 63,It it is a reality Diagonal matrix, because mains by harmonics comprises 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noise's Order is exactly 63, to matrixCarry out singular value decomposition SVD, and singular value arranged in descending order, obtain (6) formula:

$C_{xx}^{2p}{}_{RL}=U\&Sigma;V^H---\left(6\right)$

In view of matrixOrder be 63, thereforeOnly 63 non-zero singular value, say, that: σ₁≥σ₂ ≥…≥σ₆₃＞ σ₆₃₊₁=...=σ_k=0

Assume: 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,…,v_q]

V₂=[v_q+1,v_q+2,…,v_k] (8)

In like manner, singular vectors matrix U is decomposed into matrix in block form U=[U₁,U₂], here

U₁=[u₁,u₂,…,u_q]

U₂=[u_q+1,u_q+2,…,u_k] (9)

So (6) formula just can be written to:

$C_{xx}^{2p}{}_{RL}=\&lsqb;U_1,U_2\&rsqb;\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{V}_1^H\\ V_2^H\end{array}\right]---\left(10\right)$

Through above-mentioned catabolic process, can obtain:

$C_{xx}^{2p}{}_{RL}=U_1{\&Sigma;}_1{V}_1^H---\left(11\right)$

$C_{xx}^{2p}{}_{RL}{V}_2=0---\left(12\right)$

(6) formula is substituted in (13) formula:

FPF^HV₂=0 (13)

Because F is associate matrix, and P is a non-zero diagonal matrix, so:

F^HV₂=0 (14)

This means that matrix F and matrix V₂It is orthogonal；

AssumeSo based on MUSIC algorithm harmonic frequency can be by (15) formula meter Obtain:

$P_{MUSIC}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{\left|\right|F^H{V}_2\left|\right|}=0---\left(15\right)$

With ω as transverse axis, make P_MUSIC(ω) frequencies omega of=0_iThe frequency of 63 harmonic signals of mains by harmonics signal；

(5) mains by harmonics based on fractional order cumulant measures specifically comprising the following steps that of method of estimation

Step 1: calculate line voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant, obtains its main feature Value σ₁,σ₂,…,σ₆₃With sub-eigenvalue σ²；

Step 2: rightCarry out (SVD) singular value decomposition, utilize formula (16) to calculate MUSIC and compose P_MUSIC(ω_i)；

Step 3: find out P_MUSIC(ω_i) 63 peak values, their frequencies omega to be asked_1,,ω₂,ω_3,......ω₆₃'s Estimated value, is the frequency of each harmonic；

Step 4: the frequencies omega that will try to achieve_1,,ω₂,ω_3,......ω₆₃In substitution formula (4) formula, just can obtain by calculating To line voltage, amplitude that electric current each harmonic is corresponding.

Beneficial effects of the present invention:

1, the fractional order cumulant that the present invention proposes solves higher order cumulants compared to Higher Order Cumulants, fractional order cumulant The signal processing of any (0 ＜ α≤2) Stable distritation process including Gaussian process that amount could not solve.

2, the present invention propose fractional order cumulant be a linear operator, and fractional order statistic be one non-linear Operator.

3, the fractional order cumulant that the present invention proposes is the expansion to Higher Order Cumulants and development.It is by Higher Order Cumulants Definition has positive integer territory to expand to whole arithmetic number territory, can suppress α noise well.Improve the robustness of signal.

4, present invention firstly provides higher harmonics mains by harmonics measurement based on fractional order cumulant and there is preferable theory Meaning and practical value.

Accompanying drawing explanation

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 workflow diagram of the present invention.

1, computer 2, Signals Transfer Board 3, harmonic measure node 4, voltage transformer

5, current transformer 6, current-to-voltage convertor 7, clipping module 8, AD sampling module

9, SD card module 10, microprocessor module 11, button 12, display screen

13, Zigbee route or terminal 14, electrical network.

Detailed description of the invention

Refer to shown in Fig. 1, Fig. 2 and Fig. 3:

The high accuracy electrical network harmonic measure system that the present invention provides includes computer 1, Signals Transfer Board 2 and one or several Harmonic measure node 3, wherein computer 1 turns Serial Port Line by Serial Port Line or USB and is connected with Signals Transfer Board 2, installs in computer 1 Mains by harmonics monitoring of software can read serial ports in real time and transmit the data come up, and analyzes, processes, then subitem display in real time, Draw curve and preservation；Zigbee coordinator, signal converting chip and DB9 interface are installed, wherein on Signals Transfer Board 2 Zigbee coordinator is the master controller of whole Zigbee network, for routeing to the Zigbee in network or terminal distribution ground Location, coordination data transmission path, and the data summarization that the transmission of each harmonic measure node 3 comes up is sent to electricity by serial ports again Brain.

Computer 1 is with DB9 interface or USB interface and can to run the desktop computer of mains by harmonics monitoring of software, pen Remember this or industrial computer.

Harmonic measure node 3 include voltage transformer 4, current transformer 5, current-to-voltage convertor 6, clipping module 7, AD sampling module 8, SD card module 9, microprocessor module 10, button 11, display screen 12 and Zigbee route or terminal 13, wherein The primary side of voltage transformer 4 gets access to grid 14, and secondary side output voltage enters AD sampling module 8, secondary after clipping module 7 The maximum of side output voltage is less than the range of AD sampling module 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, then enter AD sampling module 8 through clipping module 7, conversion After the maximum of voltage signal less than the range of AD sampling module 8；Current-to-voltage convertor 6 is for by defeated for current transformer 5 The current signal gone out is converted to the measurable voltage signal of AD sampling module 8, and clipping module 7 is made up of bi-directional voltage stabilizing pipe, its pincers Position voltage is less than the range of AD sampling module 8 but is higher than output voltage and the output of current-to-voltage convertor 6 of voltage transformer 4 Voltage；AD sampling module 8 includes that AD sampling A/D chip and peripheral circuit thereof, AD sampling A/D chip are connected with microprocessor module 10, by Microprocessor module 10 provides clock, and passes data to microprocessor module 10 by parallel port line；Microprocessor module 10 Being made up of microprocessor and peripheral circuit thereof, wherein microprocessor is STM32F4 family chip, and peripheral circuit constitutes its system； SD card module 9 is made up of SD draw-in groove and capacitance resistance, is connected by spi bus with microprocessor module 10, is used for storing measurement The system of data and harmonic measure node is arranged；Button 11 is connected on the I/O port of microprocessor module 10, surveys for harmonic wave The setting of amount node 3 and on-the-spot inquiry measurement result；Display screen 12 is that LCD liquid crystal display screen is connected with microprocessor module 10 Connect, for display system state and measurement result；Zigbee route or terminal 13 be Zigbee router-module or Zigbee end End module, is connected by universal serial bus with microprocessor module 10, it is achieved harmonic measure node 3 and Zigbee coordinator and electrical network The data transmission of Detecting Power Harmonics software.

Signal converting chip is MAX232 family chip or the chip of equal function, and input connects Zigbee coordinator, For receiving the serial data of Transistor-Transistor Logic level, output termination DB9 interface, for exporting the serial of computer discernible RS232 level Data.

The high accuracy electrical network harmonic measuring method that the present invention provides, its method is as described below:

Step one, turn Serial Port Line with Serial Port Line or USB computer 1 is connected with Signals Transfer Board 2, connect Signals Transfer Board 2 Power supply, open mains by harmonics monitoring of software；Harmonic measure node 3 is accessed in electrical network 14 to be measured, if any multiple points to be measured, A harmonic measure node 3 can be connected on each tested point respectively, connect the power supply of each harmonic measure node 3, now signal Zigbee coordinator on keyset 2 can be the Zigbee route on each harmonic measure node 3 and terminal distribution address, with group Become Zigbee network；

Step 2, harmonic measure node 3 power on after, the microprocessor module 10 on harmonic measure node 3 starts Work, each module is first initialized by it, then reads the node configuration information on SD card module 9, and saves harmonic measure Point 3 relevant parameters configure；

Voltage transformer 4 summation current transformer 5 on step 3, harmonic measure node 3 is started working, and by electrical network 14 Voltage, electric current are converted into the collectable voltage signal of AD sampling module 8, and microprocessor driven AD in microprocessor module 10 is adopted These voltage signals are sampled and are saved in internal memory by original mold block 8；

Microprocessor in step 4, microprocessor module 10 by digital signal corresponding to electrical network 14 voltage, electric current from step Specific internal memory described in rapid three reads out, and calculates electricity respectively with harmonic measuring method based on fractional order cumulant Net 14 voltage, the first-harmonic of electric current and the harmonic wave of 1-63 time；

Microprocessor in step 5, microprocessor module 10 according to the node configuration information on SD card module 9 by correspondence Data deliver to display screen 12 and show, if the node configuration information on SD card module 9 is requirement closes display screen, then This step does not performs；

Electrical network 14 voltage, the first-harmonic of electric current and the 1-63 that microprocessor in step 6, microprocessor module 10 will be surveyed Secondary harmonic data packing is stored on SD card module 9 by measuring time sequencing, and passes through plus node serial number and CRC check code Zigbee network is sent in computer 1, and mains by harmonics monitoring of software processes these data parsings by the data on backstage Come and show on corresponding window, also these data can be preserved simultaneously；

Step 7, repetition step 3 are to step 6, and so circulation obtains electrical network 14 voltage and electricity at each harmonic measure node 3 The first-harmonic of stream and the harmonic wave of each time.

Harmonic measuring method based on fractional order cumulant described in step 4, its concrete grammar is as follows:

The first step, fractional order square and fractional order cumulant function and the determination of standard:

(1) fractional order square and the determination of fractional order cumulant function:

If the characteristic function that Φ (u) is stochastic variable X, have

$m^{kp}={\mathrm{\&Phi;}}^{\left(kp\right)}\left(u\right)e^{-j\frac{\mathrm{\&pi;}kp}{2}}{|}_{u=0}$

${C_{RL}}^{kp}=e^{-j\frac{\mathrm{\&pi;}kp}{2}}\frac{{d_{RL}}^{kp}}{{\mathrm{dt}}^{kp}}ln\mathrm{\&Phi;}\left(u\right){|}_{u=0}$

In formula:For left Riemann-Liouville Fractional Derivative, 0 ＜ p≤1, k is arbitrary integer, claims m^kp With^RLC^kpIt is respectively fractional order square and fractional order cumulant, the fractional order cumulant of stochastic variable X^RLC^kpAlso can be designated as^RLcum^kp (·)；

(2) determination of fractional order cumulant standard:

Determine that fractional order cumulant standard is as follows:

Standard 1: set a₁,a₂,…,a_kFor constant, X (k)=[x₁,x₂,…,x_k] be stochastic variable, then

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\&lsqb;a_1{x}_1^{p_1},a_2{x}_2^{p_2},...,a_k{x}_k^{p_k}\&rsqb;\\ =a_1{a}_2...{a_k}^{RL}{\mathrm{cum}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;\end{array}$

In formula: kp=p₁+p₂+…+p_k

Standard 2: fractional order cumulant is symmetrical to its independent variable, in other words their value and the order nothing of independent variable Close, i.e.

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;\\ {=}^{RL}{\mathrm{cum}}^{kp}\&lsqb;x_{i_1}^{p_{i_1}},x_{i_2}^{p_{i_2}},...,x_{i_k}^{p_{i_k}}\&rsqb;\end{array}$

Wherein, i₁,i₂,…,i_kIt is 1,2 ..., an arrangement of k；

Standard 3: if k stochastic variable { x_iA subset and other parts independent, then

${}^{RL}{\mathrm{cum}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;\&equiv;0$

Standard 4: if stochastic variable collection [x₁,x₂,…,x_k] and [y₁,y₂,…,y_k] be independent, then have

$\begin{array}{c}{}^{RL}{\mathrm{cum}}^{kp}\&lsqb;{\left(x_1+y_1\right)}^{p_1},{\left(x_2+y_2\right)}^{p_2},...,{\left(x_k+y_k\right)}^{p_k}\&rsqb;\\ {=}^{RL}{\mathrm{cum}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;{+}^{RL}{\mathrm{cum}}^{kp}\&lsqb;y_1^{p_1},y_2^{p_2},...,y_k^{p_k}\&rsqb;\end{array}$

Standard 5: for 2p rank fractional order cumulant^RLC^kp(τ), when τ=0, there is maximum, i.e.

|^RLC^kp(τ)|≤^RLC^kp(0)

Second step, fractional order square and the conversion formula of fractional order cumulant:

$m^{kp}\left(I\right)=\underset{l}{\&Sigma;}\underset{k=1}{\overset{q}{\&Pi;}}{C_{RL}}^{kp}\left(I_{l_k}\right)$

${C_{RL}}^{kp}\left(I\right)=\underset{l}{\&Sigma;}{(-1)}^{(l-1)}(l-1)!\underset{k=1}{\overset{q}{\&Pi;}}{m}^{kp}\left(I_{lk}\right)$

In formula: I_lBeing the set of the new element that the element in I generates through dividing combination, q represents I_lDivide contained by Number,Represent I_lIn kth divide,Q should be taken as 1,2 successively ..., k, k are the number of stochastic variable,Table Show all I_lFunction summation determined by corresponding set；

3rd step, fractional order cumulant are to α noise and the rejection ability of Gaussian noise and suppressing method:

α Stable distritation is a kind of generalized Gaussian distribution, and the characteristic function of standard α Stable distritation is:

Φ (u)=exp{-γ | u |^α}

In formula: parameter γ ＞ 0 is referred to as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is referred to as characteristic index, when characteristic index α=2, α Stable distritation deteriorates to Gauss distribution；

About fractional order cumulant to α noise and the rejection ability of Gaussian noise and suppressing method, there is a following theorem:

Theorem 1: the characteristic function of bidding quasi-α Stable distritation is as shown in above formula, and making m is that the minimum more than or equal to p is the most whole Number, then as p ＞ 0 and α ＞ 0, the p rank fractional order cumulant of standard α Stable distritation is:

(1) when α-p is not integer:

${C_{RL}}^p=\left\{\begin{array}{cc}0,& \mathrm{\&alpha;}-p>0\\ -\mathrm{\&gamma;}\mathrm{\&Gamma;}(\mathrm{\&alpha;}+1)e^{-j\frac{\mathrm{\&pi;}k\mathrm{\&alpha;}}{2}},& \mathrm{\&alpha;}=p\\ \mathrm{\&infin;},& \mathrm{\&alpha;}-p<0\end{array}\right.$

(2) when 1≤p-α≤m is integer；

^RLC^p=0

For the p rank fractional order cumulant of standard α Stable distritation signal, when taking p ＜ α, or when 1≤p-α≤m is integer Time, its p rank fractional order cumulant exists and is zero, owing to Gauss distribution is a spy when α=2 in standard α Stable distritation Example, therefore, gaussian signal is still set up by fractional order cumulant, and this is fractional order cumulant to α and the suppression of Gaussian noise Condition and suppressing method, owing to the fractional order cumulant of α noise and Gaussian noise is zero, i.e. as p ＜ α, it is meant that to this two Planting completely inhibiting of noise, therefore, fractional order cumulant has extremely strong rejection ability to α noise and Gaussian noise；

4th step, mains by harmonics based on fractional order cumulant measurement method of estimation:

(1) fractional order square and the method for estimation of fractional order cumulant:

When the characteristic function of process x (k) immediately is known, it is possible to the definition according to fractional order square and fractional order cumulant is straight Connect calculating fractional order square and fractional order cumulant, when characteristic function is unknown, utilize one group of Observable sample of X (k) to its point Number rank square and fractional order cumulant are estimated, utilize fractional order square and the conversion formula of fractional order cumulant, it is possible to divided The estimation of number rank cumulant, carries out mark with the 2p rank fractional order square of random sequence x (k) and the estimation of fractional order cumulant here Rank square and the method for estimation of fractional order cumulant；

(2) estimation of fractional order square:

IfFor one group of Observable sample of stationary random process x (t), according to the definition of fractional order square, can obtain Being estimated as of its 2p rank fractional order square

${\hat{m}}_x^p\&lsqb;x\left(k\right)\&rsqb;=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}{x}^p\left(k\right)$

${\hat{m}}_{2x}^{2p}\left(m\right)=\frac{1}{N-\left|m\right|}\underset{k=1}{\overset{N-\left|m\right|}{\&Sigma;}}{x}^p\left(k\right)x^p(k+m),m=0,\&PlusMinus;1,\&PlusMinus;2,...$

Here N is number of samples；

(3) estimation of fractional order cumulant:

According to 2p rank cumulantConversion formula, has

$\begin{array}{c}\hat{C}_{2x}^{2p}{}_{RL}\left(m\right)={\hat{m}}_{2x}^{2p}\left(m\right)-{\hat{m}}_x^p\left(x\left(k\right)\right){\hat{m}}_x^p\left(x\left(k+m\right)\right)\\ =\frac{1}{N-\left|m\right|}\underset{i=1}{\overset{N-\left|m\right|}{\&Sigma;}}{x}^p\left(i\right)x^p\left(i+m\right)-{\&lsqb;\frac{1}{N}\underset{i=1}{\overset{N}{\&Sigma;}}{x}^p\left(i\right)\&rsqb;}^2,m=0,\&PlusMinus;1,\&PlusMinus;2,...\end{array}$

Due toIt is to utilizeWithPass throughConversion formula Obtain, thereforeAlso it is unbiased consistent Estimation；Similar method is used i.e. to can get various different fractional-order Fractional order square and the estimation of fractional order cumulant；

(4) the harmonic frequency method of estimation of electrical network 14 voltage, electric current:

If the signal of electrical network 14 voltage harmonic:

A in formula_iAnd ω_i∈ (-π, π) is respectively multiple amplitude and the frequency of i-th harmonic signal；It it is independent random variable And it is uniformly distributed [-π, π] interval obedience；63 is the overtone order needing to measure；n_αK () is standard α symmetric-stable distribution , and characteristic index α is known (sas)；n_gK () is zero-mean colored Gaussian noise, its spectrum density is unknown；Assume n_g(k) and n_α K () is separate；

To electrical network 14 voltage harmonic signal x (k), take 2p (2p ＜ α≤2) rank fractional order cumulant, by fractional order cumulant Canonical function 1,3,4 and theorem 1, have

In (2) formula, if τ=0,1 ..., k-1 (k ＞ 63), (2) formula be rewritten into k × k tie up cumulant matrices:

Then x₁(k) and x₂The 2p of (k)^thRank cumulant can be written to again following formula:

$C_{xx}^{2p}{}_{RL}=\underset{i=1}{\overset{q}{\&Sigma;}}{a}_i^2{F}_i{F}_i^H---\left(4\right)$

Here F_iIt is by complex exponentialK × 1 n dimensional vector n the matrix of composition, I=1,2 ..., 63, wherein ω₁,ω₂,......ω_iSeeking to the frequency estimated, H is associate matrix, and T is transposition square Battle array.a_iAmplitude for mains by harmonics signal；

(4) formula is write as matrix form:

$C_{xx}^{2p}{}_{RL}={\mathrm{FPF}}^H---\left(5\right)$

F=[F in formula₁,F₂,…,F_q] it is that matrix is tieed up in k × 63,It it is one Real diagonal matrix, because mains by harmonics comprises 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noiseOrder be exactly 63, to matrixCarry out singular value decomposition SVD, and singular value is arranged in descending order, obtain (6) formula:

$C_{xx}^{2p}{}_{RL}=U\&Sigma;V^H---\left(6\right)$

In view of matrixOrder be 63, thereforeOnly 63 non-zero singular value, say, that: σ₁≥ σ₂≥…≥σ₆₃＞ σ₆₃₊₁=...=σ_k=0

Assume: 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,…,v_q]

V₂=[v_q+1,v_q+2,…,v_k] (8)

In like manner, singular vectors matrix U is decomposed into matrix in block form U=[U₁,U₂], here

U₁=[u₁,u₂,…,u_q]

U₂=[u_q+1,u_q+2,…,u_k] (9)

So (6) formula just can be written to:

$C_{xx}^{2p}{}_{RL}=\&lsqb;U_1,U_2\&rsqb;\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{V}_1^H\\ V_2^H\end{array}\right]---\left(10\right)$

Through above-mentioned catabolic process, can obtain:

$C_{xx}^{2p}{}_{RL}=U_1{\&Sigma;}_1{V}_1^H---\left(11\right)$

$C_{xx}^{2p}{}_{RL}{V}_2=0---\left(12\right)$

(6) formula is substituted in (13) formula:

FPF^HV₂=0 (13)

Because F is associate matrix, and P is a non-zero diagonal matrix, so:

F^HV₂=0 (14)

This means that matrix F and matrix V₂It is orthogonal；

AssumeSo based on MUSIC algorithm harmonic frequency can be by (15) formula It is calculated:

$P_{MUSIC}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{\left|\right|F^H{V}_2\left|\right|}=0---\left(15\right)$

With ω as transverse axis, make P_MUSIC(ω) frequencies omega of=0_iThe frequency of 63 harmonic signals of mains by harmonics signal；

(5) the specifically comprising the following steps that of electrical network 14 harmonic measure method of estimation based on fractional order cumulant

Step 1: calculate electrical network 14 voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant, obtains Qi Zhute Value indicative σ₁,σ₂,…,σ₆₃With sub-eigenvalue σ²；

Step 2: rightCarry out (SVD) singular value decomposition, utilize formula (16) to calculate MUSIC and compose P_MUSIC(ω_i)；

Step 3: find out P_MUSIC(ω_i) 63 peak values, their frequencies omega to be asked_1,,ω₂,ω_3,......ω₆₃'s Estimated value, is the frequency of each harmonic；

Step 4: the frequencies omega that will try to achieve_1,,ω₂,ω_3,......ω₆₃In substitution formula (4) formula, just can obtain by calculating To electrical network 14 voltage, amplitude that electric current each harmonic is corresponding.

Claims (6)

1. a high accuracy electrical network harmonic measure system, it is characterised in that: include computer, Signals Transfer Board and one or several Harmonic measure node, wherein computer turns Serial Port Line by Serial Port Line or USB and is connected with Signals Transfer Board, the electrical network installed in computer Detecting Power Harmonics software can read serial ports in real time and transmit the data come up, and analyze, process, then subitem display in real time, drafting Curve and preservation；Zigbee coordinator, signal converting chip and DB9 interface, wherein Zigbee association are installed on Signals Transfer Board Tune device is the master controller of whole Zigbee network, for routeing to the Zigbee in network or terminal distribution address, coordination number According to transmission path, and the data summarization that the transmission of each harmonic measure node comes up is sent to computer by serial ports again.

A kind of high accuracy electrical network harmonic measure system the most according to claim 1, it is characterised in that: described computer is band There are DB9 interface or USB interface and the desktop computer of mains by harmonics monitoring of software, notebook or industrial computer can be run.

A kind of high accuracy electrical network harmonic measure system the most according to claim 1, it is characterised in that: described harmonic measure Node include voltage transformer, current transformer, current-to-voltage convertor, clipping module, AD sampling module, SD card module, Microprocessor module, button, display screen and Zigbee route or terminal, wherein the primary side of voltage transformer gets access to grid, secondary Side output voltage enters AD sampling module after clipping module, and the maximum of secondary side output voltage is less than AD sampling module Range；The primary side of current transformer gets access to grid, and secondary side output electric current is converted to voltage signal through current-to-voltage convertor After, then entering AD sampling module through clipping module, the maximum of the voltage signal after conversion is less than the range of AD sampling module； The current signal that current-to-voltage convertor is used for current transformer exports is converted to the measurable voltage signal of AD sampling module, Clipping module is made up of bi-directional voltage stabilizing pipe, and its clamp voltage is less than the range of AD sampling module but is higher than the output of voltage transformer The output voltage of voltage and current electric pressure converter；AD sampling module includes AD sampling A/D chip and peripheral circuit thereof, and AD samples core Sheet is connected with microprocessor module, microprocessor module provide clock, and pass data to microprocessor by parallel port line Module；Microprocessor module is made up of microprocessor and peripheral circuit thereof, and wherein microprocessor is STM32F4 family chip, outward Enclose circuit and constitute its system；SD card module is made up of SD draw-in groove and capacitance resistance, with microprocessor module by spi bus even Connect, arrange for storing the system of measurement data and harmonic measure node；Button is connected on the I/O port of microprocessor module, Setting and on-the-spot inquiry measurement result for harmonic measure node；Display screen is LCD liquid crystal display screen and microprocessor module It is connected, for display system state and measurement result；Zigbee route or terminal are Zigbee router-module or Zigbee Terminal module, is connected by universal serial bus with microprocessor module, it is achieved harmonic measure node and Zigbee coordinator and electrical network The data transmission of Detecting Power Harmonics software.

A kind of high accuracy electrical network harmonic measure system the most according to claim 1, it is characterised in that: described signal converting Chip is MAX232 family chip or the chip of equal function, and input connects Zigbee coordinator, for receiving Transistor-Transistor Logic level Serial data, output termination DB9 interface, for exporting the serial data of computer discernible RS232 level.

5. a high accuracy electrical network harmonic measuring method, it is characterised in that: its method is as described below:

Step one, turn Serial Port Line with Serial Port Line or USB computer be connected with Signals Transfer Board, connect the power supply of Signals Transfer Board, Open mains by harmonics monitoring of software；Harmonic measure node is accessed in electrical network to be measured, if any multiple points to be measured, can treat each Connect a harmonic measure node on measuring point respectively, connect the power supply of each harmonic measure node, now on Signals Transfer Board Zigbee coordinator can be the Zigbee route on each harmonic measure node and terminal distribution address, to form Zigbee net Network；

Step 2, harmonic measure node power on after, the microprocessor module on harmonic measure node is started working, and it is first Each module is initialized, then reads the node configuration information on SD card module, and to harmonic measure node relevant parameter Configure；

Voltage transformer summation current transformer on step 3, harmonic measure node is started working, and by the voltage of electrical network, electric current Being converted into the collectable voltage signal of AD sampling module, the microprocessor driven AD sampling module in microprocessor module is to these Voltage signal carries out sampling and being saved in internal memory；

Microprocessor in step 4, microprocessor module by digital signal corresponding to line voltage, electric current from described in step 3 Specific internal memory in read out, and with harmonic measuring method based on fractional order cumulant calculate respectively line voltage, The first-harmonic of electric current and the harmonic wave of 1-63 time；

Corresponding data are sent by the microprocessor in step 5, microprocessor module according to the node configuration information on SD card module Showing to display screen, if the node configuration information on SD card module is requirement closes display screen, then this step does not performs；

Microprocessor in step 6, microprocessor module is by the line voltage surveyed, the first-harmonic of electric current and the harmonic wave of 1-63 time Data packing is stored on SD card module by measuring time sequencing, and passes through Zigbee net plus node serial number and CRC check code Network is sent in computer, mains by harmonics monitoring of software is processed by the data on backstage and these data parsings out and is shown On corresponding window, also these data can be preserved simultaneously；

Step 7, repetition step 3 are to step 6, and so circulation obtains line voltage and the base of electric current at each harmonic measure node Ripple and the harmonic wave of each time.

A kind of high accuracy electrical network harmonic measuring method the most according to claim 5, it is characterised in that: described in step 4 Harmonic measuring method based on fractional order cumulant, its concrete grammar is as follows:

The first step, fractional order square and fractional order cumulant function and the determination of standard:

(1) fractional order square and the determination of fractional order cumulant function:

If the characteristic function that Φ (u) is stochastic variable X, have

$m^{kp}={\mathrm{\&Phi;}}^{\left(kp\right)}\left(u\right)e^{-j\frac{\mathrm{\&pi;}kp}{2}}{|}_{u=0}$

${C_{RL}}^{kp}=e^{-j\frac{\mathrm{\&pi;}kp}{2}}\frac{{d_{RL}}^{kp}}{{\mathrm{dt}}^{kp}}ln\mathrm{\&Phi;}\left(u\right){|}_{u=0}$

In formula:For left Riemann-Liouville Fractional Derivative, 0 ＜ p≤1, k is arbitrary integer, claims m^kpWith^RLC^kp It is respectively fractional order square and fractional order cumulant, the fractional order cumulant of stochastic variable X^RLC^kpAlso can be designated as^RLcum^kp(·)；

(2) determination of fractional order cumulant standard:

Determine that fractional order cumulant standard is as follows:

Standard 1: set a₁,a₂,…,a_kFor constant, X (k)=[x₁,x₂,…,x_k] be stochastic variable, then

$\begin{array}{c}c_{RL}{\mathrm{um}}^{kp}\&lsqb;a_1{x}_1^{p_1},a_2{x}_2^{p_2},...,a_k{x}_k^{p_k}\&rsqb;\\ =a_1{a}_2...a_{k}c_{RL}{\mathrm{um}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;\end{array}$

In formula: kp=p₁+p₂+…+p_k

Standard 2: fractional order cumulant is symmetrical to its independent variable, their value is unrelated with the order of independent variable in other words, I.e.

$\begin{array}{c}c_{RL}{\mathrm{um}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;\\ =c_{RL}{\mathrm{um}}^{kp}\&lsqb;x_{i_1}^{p_{i_1}},x_{i_2}^{p_{i_2}},...,x_{i_k}^{p_{i_k}}\&rsqb;\end{array}$

Wherein, i₁,i₂,…,i_kIt is 1,2 ..., any one arrangement of k；

Standard 3: if k stochastic variable { x_iA subset and other parts independent, then

$c_{RL}{\mathrm{um}}^{kp}(x_1^{p_1},x_2^{p_2},...,x_k^{p_k})\&equiv;0$

Standard 4: if stochastic variable collection [x₁,x₂,…,x_k] and [y₁,y₂,…,y_k] be independent, then have

$\begin{array}{c}c_{RL}{\mathrm{um}}^{kp}\&lsqb;{\left(x_1+y_1\right)}^{p_1},{\left(x_2+y_2\right)}^{p_2},...,{\left(x_k+y_k\right)}^{p_k}\&rsqb;\\ =c_{RL}{\mathrm{um}}^{kp}\&lsqb;x_1^{p_1},x_2^{p_2},...,x_k^{p_k}\&rsqb;+c_{RL}{\mathrm{um}}^{kp}\&lsqb;y_1^{p_1},y_2^{p_2},...,y_k^{p_k}\&rsqb;\end{array}$

Standard 5: for 2p rank fractional order cumulant^RLC^kp(τ), when τ=0, there is maximum, i.e.

|^RLC^kp(τ)|≤^RLC^kp(0)

Second step, fractional order square and the conversion formula of fractional order cumulant:

$m^{kp}\left(I\right)=\underset{l}{\&Sigma;}\underset{k=1}{\overset{q}{\&Pi;}}{C_{RL}}^{kp}\left(I_{l_k}\right)$

${C_{RL}}^{kp}\left(I\right)=\underset{l}{\&Sigma;}{(-1)}^{(l-1)}(l-1)!\underset{k=1}{\overset{q}{\&Pi;}}{m}^{kp}\left(I_{lk}\right)$

In formula: I_lBeing the set of the new element that the element in I generates through dividing combination, q represents I_lDivide contained by is individual Number,Represent I_lIn kth divide,Q should be taken as 1,2 successively ..., k, k are the number of stochastic variable,Table Show all I_lFunction summation determined by corresponding set；

3rd step, fractional order cumulant are to α noise and the rejection ability of Gaussian noise and suppressing method:

α Stable distritation is a kind of generalized Gaussian distribution, and the characteristic function of standard α Stable distritation is:

Φ (u)=exp{-γ | u |^α}

In formula: parameter γ ＞ 0 is referred to as the coefficient of dispersion；Parameter alpha ∈ (0,2] it is referred to as characteristic index, when characteristic index α=2, α is steady Determine distribution and deteriorate to Gauss distribution；

About fractional order cumulant to α noise and the rejection ability of Gaussian noise and suppressing method, there is a following theorem:

Theorem 1: the characteristic function of bidding quasi-α Stable distritation is as shown in above formula, and making m is the minimum positive integer more than or equal to p, then As p ＞ 0 and α ＞ 0, the p rank fractional order cumulant of standard α Stable distritation is:

(1) when α-p is not integer:

${C_{RL}}^p=\left\{\begin{array}{cc}0,& \mathrm{\&alpha;}-p>0\\ -\mathrm{\&gamma;}\mathrm{\&Gamma;}(\mathrm{\&alpha;}+1)e^{-j\frac{\mathrm{\&pi;}k\mathrm{\&alpha;}}{2}},& \mathrm{\&alpha;}=p\\ \mathrm{\&infin;},& \mathrm{\&alpha;}-p<0\end{array}\right.$

(2) when 1≤p-α≤m is integer；

^RLC^p=0

For the p rank fractional order cumulant of standard α Stable distritation signal, when taking p ＜ α, or when 1≤p-α≤m is integer, its p Rank fractional order cumulants exists and is zero, owing to Gauss distribution is a special case when α=2 in standard α Stable distritation, because of This, gaussian signal is still set up by fractional order cumulant, this be fractional order cumulant to the rejection condition of α and Gaussian noise and Suppressing method, owing to the fractional order cumulant of α noise and Gaussian noise is zero, i.e. as p ＜ α, it is meant that to both noises Completely inhibit, therefore, fractional order cumulant has extremely strong rejection ability to α noise and Gaussian noise；

4th step, mains by harmonics based on fractional order cumulant measurement method of estimation:

(1) fractional order square and the method for estimation of fractional order cumulant:

When the characteristic function of stochastic process x (k) is known, it is possible to directly count according to the definition of fractional order square and fractional order cumulant Calculate fractional order square and fractional order cumulant, when characteristic function is unknown, utilize one group of Observable sample of X (k) to its fractional order Square and fractional order cumulant are estimated, utilize fractional order square and the conversion formula of fractional order cumulant, it is possible to obtain fractional order The estimation of cumulant, carries out fractional order square with the 2p rank fractional order square of random sequence x (k) and the estimation of fractional order cumulant here Method of estimation with fractional order cumulant；

(2) estimation of fractional order square:

IfFor one group of Observable sample of stationary random process x (t), according to the definition of fractional order square, its 2p rank can be obtained Being estimated as of fractional order square

${\hat{m}}_x^p\&lsqb;x\left(k\right)\&rsqb;=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}{x}^p\left(k\right)$

${\hat{m}}_{2x}^{2p}\left(m\right)=\frac{1}{N-\left|m\right|}\underset{k=1}{\overset{N-\left|m\right|}{\mathrm{\&Sigma;}}}{x}^p\left(k\right)x^p(k+m),m=0,\&PlusMinus;1,\&PlusMinus;2,...$

Here N is number of samples；

(3) estimation of fractional order cumulant:

According to 2p rank cumulantConversion formula, has

$\begin{array}{c}\hat{C}_{2x}^{2p}{}_{RL}\left(m\right)={\hat{m}}_{2x}^{2p}\left(m\right)-{\hat{m}}_x^p\left(x\left(k\right)\right){\hat{m}}_x^p\left(x\left(k+m\right)\right)\\ =\frac{1}{N-\left|m\right|}\underset{i=1}{\overset{N-\left|m\right|}{\mathrm{\&Sigma;}}}{x}^p\left(i\right)x^p\left(i+m\right)-{\&lsqb;\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}^p\left(i\right)\&rsqb;}^2,m=0,\&PlusMinus;1,\&PlusMinus;2,...\end{array}$

Due toIt is to utilizeWithPass throughConversion formula obtains , thereforeAlso it is unbiased consistent Estimation；Similar method is used i.e. to can get dividing of various different fractional-order Number rank square and the estimation of fractional order cumulant；

(4) the harmonic frequency method of estimation of line voltage, electric current:

If the signal of Voltage Harmonic:

A in formula_iAnd ω_i∈ (-π, π) is respectively multiple amplitude and the frequency of i-th harmonic signal；Be independent random variable and It is uniformly distributed [-π, π] interval obedience；63 is the overtone order needing to measure；n_αK () is standard α symmetric-stable distribution , and characteristic index α is known (sas)；n_gK () is zero-mean colored Gaussian noise, its spectrum density is unknown；Assume n_g(k) and n_α K () is separate；

To Voltage Harmonic signal x (k), take 2p (2p ＜ α≤2) rank fractional order cumulant, by the standard of fractional order cumulant Function 1,3,4 and theorem 1, have

In (2) formula, if τ=0,1 ..., k-1 (k ＞ 63), (2) formula be rewritten into k × k tie up cumulant matrices:

Then x₁(k) and x₂The 2p of (k)^thRank cumulant can be written to again following formula:

$C_{xx}^{2p}{}_{RL}=\underset{i=1}{\overset{q}{\&Sigma;}}{a}_i^2{F}_i{F}_i^H---\left(4\right)$

Here F_iIt is by complex exponentialK × 1 n dimensional vector n the matrix of composition, I=1,2 ..., 63, wherein ω₁,ω₂,......ω_iSeeking to the frequency estimated, H is associate matrix, and T is transposition square Battle array, a_iAmplitude for mains by harmonics signal；

(4) formula is write as matrix form:

$C_{xx}^{2p}{}_{RL}={\mathrm{FPF}}^H---\left(5\right)$

F=[F in formula₁,F₂,…,F_q] it is that matrix is tieed up in k × 63,It is that a reality is right Angular moment battle array, because mains by harmonics comprises 63 harmonic signals, and it can easily be proven that matrix under the conditions of additive noise's Order is exactly 63, to matrixCarry out singular value decomposition SVD, and singular value arranged in descending order, obtain (6) formula:

$C_{xx}^{2p}{}_{RL}={\mathrm{U\&Sigma;V}}^H---\left(6\right)$

In view of matrixOrder be 63, thereforeOnly 63 non-zero singular value, say, that: σ₁≥σ₂≥…≥ σ₆₃＞ σ₆₃₊₁=...=σ_k=0

Assume: 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,…,v_q]

V₂=[v_q+1,v_q+2,…,v_k] (8)

In like manner, singular vectors matrix U is decomposed into matrix in block form U=[U₁,U₂], here

U₁=[u₁,u₂,…,u_q]

U₂=[u_q+1,u_q+2,…,u_k] (9)

So (6) formula just can be written to:

$C_{xx}^{2p}{}_{RL}=\&lsqb;U_1,U_2\&rsqb;\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{V}_1^H\\ V_2^H\end{array}\right]---\left(10\right)$

Through above-mentioned catabolic process, can obtain:

$C_{xx}^{2p}{}_{RL}=U_1{\mathrm{\&Sigma;}}_1{V}_1^H---\left(11\right)$

$C_{xx}^{2p}{}_{RL}{V}_2=0---\left(12\right)$

(6) formula is substituted in (13) formula:

FPF^HV₂=0 (13)

Because F is associate matrix, and P is a non-zero diagonal matrix, so:

F^HV₂=0 (14)

This means that matrix F and matrix V₂It is orthogonal；

AssumeSo based on MUSIC algorithm harmonic frequency can be calculated by (15) formula Obtain:

$P_{MUSIC}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{\left|\right|F^H{V}_2\left|\right|}=0---\left(15\right)$

With ω as transverse axis, make P_MUSIC(ω) frequencies omega of=0_iThe frequency of 63 harmonic signals of mains by harmonics signal；

(5) mains by harmonics based on fractional order cumulant measures specifically comprising the following steps that of method of estimation

Step 1: calculate line voltage, current harmonics signalThe Eigenvalues Decomposition of cumulant, obtains its dominant eigenvalue σ₁, σ₂,…,σ₆₃With sub-eigenvalue σ²；

Step 2: rightCarry out (SVD) singular value decomposition, utilize formula (16) to calculate MUSIC and compose P_MUSIC(ω_i)；

Step 3: find out P_MUSIC(ω_i) 63 peak values, their frequencies omega to be asked_1,,ω₂,ω_3,......ω₆₃Estimation Value, is the frequency of each harmonic；

Step 4: the frequencies omega that will try to achieve_1,,ω₂,ω_3,......ω₆₃In substitution formula (4) formula, can be obtained by electricity by calculating Net voltage, the amplitude that electric current each harmonic is corresponding.