CN103412242A - Method for locating harmonic source based on independent rapid component analysis and mutual information - Google Patents

Abstract

The invention discloses a method for locating a harmonic source based on independent rapid component analysis and mutual information. Rapid components and slow components of measured harmonic voltages are separated; mean value removal and whitening are conducted on the rapid components of the harmonic voltages, an estimated harmonic admittance matrix is obtained through independent rapid component analysis, a harmonic current of the harmonic source is reconstructed, and finally the position of the harmonic source is located according to the mutual information between the estimated harmonic current and the measured harmonic voltages. According to the method, the number of parameters needing to be measured is small, calculation is simple, and the harmonic source is located accurately and reliably.

Description

A kind of localization method of harmonic source based on Fast Independent Component Analysis and mutual information

Technical field

The present invention relates to a kind of localization method of harmonic source based on Fast Independent Component Analysis and mutual information.

Background technology

Along with economical and scientific and technological development, in electric system, non-linear equipment and load roll up, as being widely used of D.C. high voltage transmission and flexible AC transmission equipment and electric arc furnaces, varying-speed motor, make harmonic sources in power system roll up, cause harmonic pollution.Harmonic pollution causes reducing equipment life, the line loss of the system that increases electric power, reduce its operational reliability, even causes the collapse of electric system.For guaranteeing the safe and stable operation of electric system, therefore, electric system need take the harmonic wave braking measure to administer harmonic wave, tackles simultaneously the harmonic pollution owner and carries out economic punishment, to reduce the generation of harmonic pollution.And administer with the prerequisite of punishment, be that harmonic source is positioned.

In the localization method of existing harmonic source, all need be at electric power networks parameter and topology information, the admittance matrix under especially different harmonic frequencies, under known prerequisite, adopt harmonic voltage, electric current etc. to measure data, carry out serial complicated calculations, estimate harmonic source.Due to the power system network complexity, be difficult to obtain electric system topological structure and network parameter (admittance matrix under different harmonic frequencies is difficult to obtain accurately especially) accurately, thereby accuracy and the precision of harmonic source location have much room for improvement.

Summary of the invention

The purpose of this invention is to provide a kind of localization method of harmonic source based on Fast Independent Component Analysis and mutual information, the parameter that the method requirement is surveyed is few, calculating is simple, the location of harmonic source is more accurate, reliable.

The present invention realizes that the technical scheme that its goal of the invention adopts is, a kind of localization method of harmonic source based on Fast Independent Component Analysis and mutual information, the steps include:

The harmonic voltage V of A, all buses of measurement _n(t), obtain the harmonic voltage matrix V (t) of bus, V (t)=[V ₁(t), V ₂(t) ..., V _n(t) ..., V _N(t)] ^TWherein n is the sequence number of bus, and t is the time, and T is transpose of a matrix;

B, use gliding smoothing wave filter are to harmonic voltage V _n(t) carry out filtering, obtain harmonic voltage V _n(t) V of component of voltage at a slow speed in _n,s(t), by harmonic voltage V _n(t) with it, subtract each other, obtain harmonic voltage V _n(t) the quick voltage component V in _n,f(t);

C, by quick voltage component V _n,f(t) the quick voltage Component Matrices V formed _f(t), V _f(t)=[V _{1, f}(t), V _{2, f}(t) ..., V _n,f(t) ..., V _N,f(t)] ^TGo average albefaction, obtain having the quick voltage component albefaction matrix V of zero-mean and unit covariance _f' (t), V _f' (t)=[V _1,' _f(t), V ₂' _{, f}(t) ..., V _n' _{, f}(t) ..., V _N' _{, f}(t)] ^T

D, to quick voltage component albefaction matrix V _f' (t) the application FastICA algorithm obtains separation matrix W, i.e. the admittance matrix W that the admittance of all buses forms; Then admittance matrix W and harmonic voltage matrix V (t) are multiplied each other, obtain the harmonic current matrix I (t) corresponding with harmonic voltage matrix V (t), I (t)=[I ₁(t), I ₂(t) ..., I _n(t) ..., I _N(t)] ^T, extract in the harmonic current matrix and be greater than zero harmonic current I _n(t), obtain non-zero harmonic current matrix I ' (t)=[I ₁' (t), I ₂' (t) ..., I _h' (t) ... I ' _H(t)] ^T, wherein h is greater than zero harmonic current I _n(t) sequence number, H is greater than zero harmonic current I _n(t) number;

E, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix of harmonic voltage matrix V (t)

Find out the maximum mutual information value of each row h in the mutual information matrix

These maximum mutual information values Corresponding harmonic voltage V _{N '}(t) the bus n ' at place, be harmonic source place bus.

Compared with prior art, effective benefit of the present invention is:

The present invention utilizes the mutual independence between harmonic source, by harmonic voltage being carried out to the harmonic admittance matrix that Fast Independent Component Analysis obtains estimating, the harmonic current of reconstruct harmonic source, and then the position of orienting harmonic source according to the harmonic current of estimating and the mutual information between harmonic voltage.The location of harmonic source more accurately, reliably.Its requirement is surveyed the harmonic voltage of every bus, without measuring meritorious or reactive power, and the network topology structure that also need not obtain and parameter, the parameter that requirement is surveyed is few, calculating is simple.Simultaneously, be difficult to because it need not obtain the network topology structure and the parameter that accurately obtain, the location of its harmonic source also more accurately, reliably.

In above-mentioned D step, to quick voltage component albefaction matrix V _f' (t) the application FastICA algorithm specific practice that obtains admittance matrix W is: selects a random initial matrix W, press following iterative formula iterative computation:

$W^{+}=E\left[V_f^{\′}\left(t\right)g\left(W^T{V}_f^{\′}\left(t\right)\right)\right]-E\left[V_f^{\′}\left(t\right)\frac{\mathrm{dg}\left(W^T{V}_f^{\′}\left(t\right)\right)}{{\mathrm{dW}}^T{V}_f^{\′}\left(t\right)}\right]W$

W=W ⁺/||W ⁺||

In formula, W ⁺The iterative value of W, || W ⁺|| be W ⁺2 norms; E[] be the average computing; g(W ^TV _f' (t)) be W ^TV _f' (t) hyperbolic tangent function,

For g (W ^TV _f' (t)) to W ^TV _f' (t) partial derivative.

Apply this quick isolated component method in the separation of blind source, can carry out admittance matrix reconstruct accurately in the condition of parameters of electric power system the unknown, and iterations is few, calculated amount is few, but Fast Convergent is to stationary value.

In above-mentioned E step, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix of harmonic voltage matrix V (t) $M(I\′\left(t\right),V\left(t\right))\left\{m_{V_n\left(t\right),I_h^{\′}\left(t\right)}\right\}$ Formula be:

M(I′(t),V(t))=H(I′(t))-H(I′(t)|V(t))

In formula, and H (I ' (t)) be all non-zero harmonic current I _h' (t) probability density function p (I _h' (t)) the matrix of differential entropy, $H(I\′\left(t\right))=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}p\left(I_h^{\′}\left(t\right)\right)\log p\left(I_h^{\′}\left(t\right)\right);$

H (I ' (t) | V (t)) be all non-zero harmonic current I _h' (t) with all measurement harmonic voltage V _nThe matrix of the differential entropy (t), $H(I\′\left(t\right)|V\left(t\right))=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}p\left(V_n\left(t\right)\right)p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right))\log p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right)),$ P (V wherein _n(t)) be harmonic voltage V _n(t) probability density function, p (I _h' (t) | V _n(t)) be harmonic voltage V _n(t) non-zero harmonic current I under condition _h' (t) probability density function.

Like this, the application mutual information can overcome in related coefficient the limitation that requires linear dependence, and considers the probability density function of harmonic current, has improved the accuracy of harmonic source location.

The present invention is described in further detail below in conjunction with embodiment.

Embodiment

Embodiment

A kind of embodiment of the present invention is that a kind of localization method of harmonic source based on Fast Independent Component Analysis and mutual information, the steps include:

The harmonic voltage V of A, all buses of measurement _n(t), obtain the harmonic voltage matrix V (t) of bus, V (t)=[V ₁(t) _,V ₂(t) ..., V _n(t) ..., V _N(t)] ^T, wherein n is the sequence number of bus, and t is the time, and T is transpose of a matrix;

B, use gliding smoothing wave filter are to harmonic voltage V _n(t) carry out filtering, obtain harmonic voltage V _n(t) V of component of voltage at a slow speed in _n,s(t), by harmonic voltage V _n(t) with it, subtract each other, obtain harmonic voltage V _n(t) the quick voltage component V in _n,f(t);

C, by quick voltage component V _n,f(t) the quick voltage Component Matrices V formed _f(t), V _f(t)=[V _{1, f}(t), V _{2, f}(t) ..., V _n,f(t) ..., V _N,f(t)] ^TGo average albefaction, obtain having the quick voltage component albefaction matrix V of zero-mean and unit covariance _f' (t), V _f' (t)=[V _1,' _f(t), V ₂' _{, f}(t) ..., V _n' _{, f}(t) ..., V _N' _{, f}(t)] ^T

D, to quick voltage component albefaction matrix V _f' (t) the application FastICA algorithm obtains separation matrix W, i.e. the admittance matrix W that the admittance of all buses forms; Then admittance matrix W and harmonic voltage matrix V (t) are multiplied each other, obtain the harmonic current matrix I (t) corresponding with harmonic voltage matrix V (t), I (t)=[I ₁(t), I ₂(t) ..., I _n(t) ..., I _N(t)] ^T, extract in the harmonic current matrix and be greater than zero harmonic current I _n(t), obtain non-zero harmonic current matrix I ' (t)=[I ₁' (t), I ₂' (t) ..., I _h' (t) ... I ' _H(t)] ^T, wherein h is greater than zero harmonic current I _n(t) sequence number, H is greater than zero harmonic current I _n(t) number;

Wherein, to quick voltage component albefaction matrix V _f' (t) the application FastICA algorithm specific practice that obtains admittance matrix W is: selects a random initial matrix W, press following iterative formula iterative computation:

$W^{+}=E\left[V_f^{\′}\left(t\right)g\left(W^T{V}_f^{\′}\left(t\right)\right)\right]-E\left[V_f^{\′}\left(t\right)\frac{\mathrm{dg}\left(W^T{V}_f^{\′}\left(t\right)\right)}{{\mathrm{dW}}^T{V}_f^{\′}\left(t\right)}\right]W$

W=W ⁺/||W ⁺||

In formula, W ⁺The iterative value of W, || W ⁺|| be W ⁺2 norms; E[] be the average computing; g(W ^TV _f' (t)) be W ^TV _f' (t) hyperbolic tangent function,

For g (W ^TV _f' (t)) to W ^TV _f' (t) partial derivative.

E, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix of harmonic voltage matrix V (t)

Find out the maximum mutual information value of each row h in the mutual information matrix

These maximum mutual information values Corresponding harmonic voltage V _{N '}(t) the bus n ' at place, be harmonic source place bus.

Wherein, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix of harmonic voltage matrix V (t) $M(I\′\left(t\right),V\left(t\right))\left\{m_{V_n\left(t\right),I_h^{\′}\left(t\right)}\right\}$ Formula be:

M(I′(t),V(t))=H(I′(t))-H(I′(t)|V(t))

In formula, and H (I ' (t)) be all non-zero harmonic current I _h' (t) probability density function p (I _h' (t)) the matrix of differential entropy, $H(I\′\left(t\right))=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}p\left(I_h^{\′}\left(t\right)\right)\log p\left(I_h^{\′}\left(t\right)\right);$

H (I ' (t) | V (t)) be all non-zero harmonic current I _h' (t) with all measurement harmonic voltage V _nThe matrix of the differential entropy (t), $H(I\′\left(t\right)|V\left(t\right))=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}p\left(V_n\left(t\right)\right)p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right))\log p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right)),$ P (V wherein _n(t)) be harmonic voltage V _n(t) probability density function, p (I _h' (t) | V _n(t)) be harmonic voltage V _n(t) non-zero harmonic current I under condition _h' (t) probability density function.

In order to verify reliability of the present invention and accuracy, above method has been carried out to following emulation experiment.

Emulation experiment:

Emulation experiment is to carry out simulation calculation in IEEE-14 node test system, and this system contains 3 harmonic sources, lays respectively at bus n '=3,6,13, and its harmonic current data is from New York ISO.

The simulation experiment result is as follows:

Table 1 for the non-zero harmonic current matrix I ' that obtains based on 5 subharmonic (t) and the mutual information matrix between harmonic voltage matrix V (t)

Maximum mutual information value corresponding to 1,2,3 row in this matrix numerical value of underscore (in the table with) is respectively

$m_{V_{n^{\text{'}}}\left(t\right),I_2^{\′\left(t\right)}}=m_{V_3\left(t\right),I_2^{\′}\left(t\right)}=1.24,$ $m_{V_{n^{\text{'}}}\left(t\right),I_3^{\′\left(t\right)}}=m_{V_{13}\left(t\right),I_3^{\′}\left(t\right)}=1.11.$ The harmonic voltage V that these three mutual information values are corresponding _{N '}(t) the bus n ' at place=3,6,13, be harmonic source place bus n '=3,6,13.Visible, the inventive method can accurately be oriented harmonic source.

Table 1

Table 2,3 is respectively the harmonic current I on the bus 3,6,13 that in emulation experiment, step D obtains _n(t) with its on related coefficient and the mean square deviation of actual harmonic current.

Table 2

Table 3

By table 2,3 visible, the harmonic current I that the inventive method step D draws _n(t) substantially identical with actual harmonic current.Illustrate that the inventive method is to estimating well harmonic current I _n(t), thus can well locate harmonic source.

Claims (3)

1. the localization method of the harmonic source based on Fast Independent Component Analysis and mutual information, the steps include:

The harmonic voltage V of A, all buses of measurement _n(t), obtain the harmonic voltage matrix V (t) of bus, V (t)=[V ₁(t), V ₂(t) ..., V _n(t) ..., V _N(t)] ^T, wherein n is the sequence number of bus, and t is the time, and T is transpose of a matrix;

B, use gliding smoothing wave filter are to harmonic voltage V _n(t) carry out filtering, obtain harmonic voltage V _n(t) V of component of voltage at a slow speed in _{N, s}(t), by harmonic voltage V _n(t) with it, subtract each other, obtain harmonic voltage V _n(t) the quick voltage component V in _{N, f}(t);

C, by quick voltage component V _{N, f}(t) the quick voltage Component Matrices Vf (t) formed, V _f(t)=[V _{1, f}(t), V _{2, f}(t) ..., V _{N, f}(t) ..., V _{N, f}(t)] ^TGo average albefaction, obtain having the quick voltage component albefaction matrix V of zero-mean and unit covariance ' _f(t), V ' _f(t)=[V ' _{1, f}(t), V ' _{2, f}(t) ..., V ' _{N, f}(t) ..., V ' _{N, f}(t)] ^T

D, to quick voltage component albefaction matrix V ' _f(t) the application FastICA algorithm obtains separation matrix W, i.e. the admittance matrix W that the admittance of all buses forms; Then admittance matrix W and harmonic voltage matrix V (t) are multiplied each other, obtain the harmonic current matrix I (t) corresponding with harmonic voltage matrix V (t), I (t)=[I ₁(t), I ₂(t) ..., I _n(t) ..., I _N(t)] ^T, extract in the harmonic current matrix and be greater than zero harmonic current I _n(t), obtain non-zero harmonic current matrix I ' (t)=[I ' ₁ (t), I ' ₂ (t) ..., I ' _h (t) ..., I ' _H (t)] ^T ,Wherein h is greater than zero harmonic current I _n(t) sequence number, H is greater than zero harmonic current I _n(t) number;

E, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix M of harmonic voltage matrix V (t) (I ' (t),

Find out the maximum mutual information value of each row h in the mutual information matrix

These maximum mutual information values Corresponding harmonic voltage V _{N '}(t) the bus n ' at place, be harmonic source place bus.

2. the localization method of the harmonic source based on Fast Independent Component Analysis and mutual information according to claim 1 is characterized in that: in described D step, to quick voltage component albefaction matrix V ' _f(t) the application FastICA algorithm specific practice that obtains admittance matrix W is: selects a random initial matrix W, press following iterative formula iterative computation:

$W^{+}=E\left[V_f^{\′}\left(t\right)g\left(W^T{V}_f^{\′}\left(t\right)\right)\right]-E\left[V_f^{\′}\left(t\right)\frac{\mathrm{dg}\left(W^T{V}_f^{\′}\left(t\right)\right)}{d{W}^T{V}_f^{\′}\left(t\right)}\right]W$

W＝W ⁺/||W ⁺||

In formula, W ⁺The iterative value of W, || W ⁺|| be W ⁺2 norms; E[] be the average computing; g(W ^TV ' _f(t)) be W ^TV ' _f(t) hyperbolic tangent function,

For g (W ^TV ' _f(t)) to W ^TV ' _f(t) partial derivative.

3. the localization method of the harmonic source based on Fast Independent Component Analysis and mutual information according to claim 1, it is characterized in that: in described E step, calculate non-zero harmonic current matrix I ' (t) and the mutual information matrix M of harmonic voltage matrix V (t) (I ' (t)

Formula be:

M(I′(t)，V(t))＝H(I′(t))-H(I′(t)|V(t))

In formula, and H (I ' (t)) be all non-zero harmonic current I ' _hProbability density function p (t) (I ' _h(t)) matrix of differential entropy, $H\left(I^{\′}\left(t\right)\right)=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}p\left(I_h^{\′}\left(t\right)\right)\log p\left(I_h^{\′}\left(t\right)\right);$

H (I ' (t) | V (t)) be all non-zero harmonic current I ' _h(t) with all measurement harmonic voltage V _nThe matrix of the differential entropy (t), $H\left(I^{\′}\left(t\right)\right|V\left(t\right))=-\underset{h=1}{\overset{H}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}p\left(V_n\left(t\right)\right)p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right))\log p\left(I_h^{\′}\left(t\right)\right|V_n\left(t\right)),$ P (V wherein _n(t)) be harmonic voltage V _n(t) probability density function, p (I ' _h(t) | V _n(t) be harmonic voltage V _n(t) non-zero harmonic current I ' under condition _h(t) probability density function.