CN105807136A - Harmonic emission level estimation method based on weighted support vector machine - Google Patents

Abstract

The invention relates to a harmonic emission level estimation method based on a weighted support vector machine.According to the method, the influence of background harmonics is considered, the Euclid distance serves as a measurement index, the Euclid distance of harmonic samples is utilized for serving as a weighted index to correct error requirements and penalty parameters of the support vector machine so as to form a weighted support vector machine regression model used for estimating system harmonic impedance, and therefore a harmonic emission level is solved, and the influence of the background harmonics can be effectively inhibited.Compared with the prior art, according to the harmonic emission level estimation method based on the weighted support vector machine, the system harmonic impedance is estimated according to the weighted support vector machine regression model, the quadratic programming problem of linear constraint is solved equivalently, the solution is unique, global and optimal, high prediction accuracy and robustness are achieved, and accurate regression can be conducted for power grid operation mode changes, namely, system harmonic impedance changes.

Description

A kind of harmonic emission level estimation method based on Weighted Support Vector

Technical field

The present invention relates to a kind of system harmonics emission level estimation method, especially relate to a kind of harmonic emission level estimation method based on Weighted Support Vector.

Background technology

Current electrical network, while developing rapidly, also brings many urgent problems.Wherein, non-linear on a large scale and impact load, after accessing electrical network, create serious electric harmonic pollution problem.Estimate that the harmonic pollution responsibility division of PCC point (points of common connection) is played vital effect by the harmonic emission level of user side and system side exactly.And the difficult point assessing harmonic emission level is in that the how estimating system harmonic impedance accurately when systematic parameter and power system operating mode are continually changing.

Generally, " intervention formula " and " non-intervention formula " is the system harmonic impedance method of estimation that two classes are main." intervention formula " method utilizes estimates harmonic impedance to electrical network harmonic/m-Acetyl chlorophosphonazo electric current or cut-offfing of certain branch road, and the intervention in this external world is likely to affect the normal operating condition of power system, it is impossible to widely use." non-intervention formula " method is then around detectable PCC point harmonic data and studies, excavate from given data and extract harmonic impedance information, specifically include that (1) fluctuates mensuration, when consideration background harmonics fluctuation is less, system harmonic impedance can be similar to and be replaced by the ratio of PCC point harmonic voltage and current wave momentum, simple and practical, therefore it is widely used.But the method requires that measuring parameter has higher accuracy and background harmonics kept stable；(2) Return Law, regression equation is derived according to power system equivalent circuit, and the intercept item in regression equation is regarded as constant, thus solving of harmonic impedance is converted into solving of regression coefficient, but the method also require that background harmonics kept stable with satisfied recurrence it is assumed that otherwise regression equation will lose original robustness.

At " harmonic emission level assessment method based on independent random vector covariance characteristics " (author: Hui Jin, Yang Honggeng, Lin Shunfu, Ma Yuchao. Automation of Electric Systems, 2009, in 07:27-31.), consider that in actual electric network, PCC point harmonic current is affected less by background harmonics, model is set up with the thought that independent random vector covariance is zero, derive the estimation formulas of harmonic impedance, weaken the interference of background harmonics fluctuation to a certain extent, but it requires that the fluctuation of harmonic current is dominated by user side, the fluctuation of harmonic voltage is dominated by both party jointly, when system fluctuation does not meet above-mentioned requirements, the method result of calculation is worth discussion further.

At " harmonic emission level based on impedance normalization trend discrimination is estimated " (author: Hui Jin, Yang Honggeng, full of leaves green grass or young crops. Proceedings of the CSEE, 2011,31 (10): 73-79.) in, propose employing impedance normalization trend discrimination and filter out the undulate quantity sample dominated by user side, and carry out with this that fluctuation is mensuration calculates system harmonic impedance.But, the range of application of the method is limited only to the industry of single character and meets, and the change of fundamental current and its harmonic current has stronger dependency.Therefore, reliability and the effectiveness of the method are restricted, and add the complexity of mensuration application of fluctuating simultaneously.

At " the harmonic impedance method of estimation based on support vector machine " (author: Kang Jie; Xie Shaofeng; Liu Xiaoju; Wei Xiaojuan. protecting electrical power system and control; 2010; 22:131-134+205.) in; using PCC point harmonic data as input; utilize support vector regression regression estimates harmonic impedance; due to the Xie Shi global optimum of quadratic programming and unique; the method has good estimated accuracy and a generalization, but it does not consider the impact on impedance estimation result of the difference of harmonic measure data that background harmonics fluctuation causes, and estimated result is likely to deviation actual value.

At " the system side harmonic impedance based on broad sense Cauchy distribution is estimated " (author: Yang Shaobing, Wu orders profit. Proceedings of the CSEE, 2014, in 07:1159-1166.), the real part and the imaginary part that propose undulate quantity ratio obey broad sense Cauchy distribution on statistical nature, thus utilizing PearsonVII formula that the probability density of real part or imaginary part is carried out non-linear curve fitting pick out respective mode position, it is the estimated value of resistance and reactance.But the real part that the condition that the method is set up is system side and user-side harmonic source undulate quantity all obeys the normal distribution that average is 0, and the estimation difference caused by the harmonic source distribution character of both sides need to verify have certain limitation further.

Therefore, it is necessary to propose the more sane harmonic emission level estimation method reliably of one.

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and provide a kind of and consider that background harmonics impact, precision of prediction be high, the harmonic emission level estimation method based on Weighted Support Vector of strong robustness.

The purpose of the present invention can be achieved through the following technical solutions:

A kind of harmonic emission level estimation method based on Weighted Support Vector, it is characterised in that comprise the following steps:

S01, measures certain subharmonic voltage and current data on points of common connection, is divided into n sub-data segment according to certain sub-time period；

S02, for each sub-time period, every a pair harmonic voltage in corresponding subdata section is become with harmonic wave set of currents a bivector, using the set of all bivectors as training sample, using the input as Weighted Support Vector of the described training sample, using the output as Weighted Support Vector of the system harmonic impedance of this sub-time period, using the harmonic voltage of the adjacent sub-time period of this sub-time period and harmonic current as forecast sample；

S03, calculates the Euclidean distance of each training sample and corresponding forecast sample, determines the importance of training sample according to Euclidean distance, thus obtaining the weight coefficient s of error requirements ε and punishment parameter C in Weighted Support Vector regression model_i, reduce the impact on impedance estimation of foreign peoples's harmonic data with this, and then effectively suppress the impact of background harmonics fluctuation；

S04, according to the relation of training sample and system harmonic impedance and the weight coefficient s that tries to achieve_i, set up Weighted Support Vector regression model, training sample carried out repetition training, namely each sub-time period is trained, obtain the system harmonic impedance of adjacent sub-time period, wherein said Weighted Support Vector regression model particularly as follows:

$\underset{{\mathrm{\α}}^{(*)}\∈R^{2n}}{\min }=\frac{1}{2}\underset{i,j=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)K(x_i,x_j)+\mathrm{\ϵ}\underset{i=1}{\overset{n}{\Σ}}{t}_i({{\mathrm{\α}}_i}^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{n}{\Σ}}{y}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)---\left(1\right)$

The constraints of formula (1) is:

Wherein, α_iAnd α_i ^*The Lagrange multiplier being introduced into, and meet equation α_i×α_i ^*=0, α_i>=0, α_i ^*>=0, i represents the numbering of subdata section, is numbered from small to large according to Euclidean distance, i=1 ..., n, α_jAnd α_j ^*For Lagrange multiplier, x_iAnd x_jFor harmonic voltage, y_iFor harmonic current, K (x_i,x_j) it is the kernel function introduced, ε is error requirements, t_iBeing the weight coefficient of ε, C is punishment parameter, s_iIt it is the weight coefficient of C；

S05, estimates the harmonic emission level of this adjacent sub-time period according to the system harmonic impedance of adjacent sub-time period.

Described step S03 is particularly as follows: define the subdata section sample weighting coefficient s of the shortest sample of Euclidean distance_i=1, t_i=0.01, the subdata section sample weighting coefficient s that Euclidean distance is the longest_i=0.01, t_i=1, the weight coefficient of all the other subdata section samples is calculated by linear interpolation:

$\left\{\begin{array}{c}{s}_i=\frac{l-i}{l-1}\\ t_i=\frac{li-1}{l-1}\end{array}\right.---\left(2\right)$

Wherein, l is the Euclidean distance of this subdata section sample, and i represents the numbering of subdata section, and Euclidean distance is more short, and sample importance is more big, the weight coefficient s of punishment parameter C_iMore big, the weight coefficient t of error requirements ε_iMore little.

Described system harmonic impedance is determined by following regression estimates function:

$y=\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x)+\stackrel{\‾}{b}---\left(3\right)$

WhereinFor Lagrange multiplier α_i ^*Estimation,For constant.

WhereinChoosing value is according to formula (4) or formula (5):

$\stackrel{\‾}{b}=y_j-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_j-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+{\mathrm{\ϵt}}_j---\left(4\right)$

$\stackrel{\‾}{b}=y_k-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_k^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_k)+{\mathrm{\ϵt}}_k---\left(5\right)$

WhereinRespectivelyReal part and imaginary.

Described harmonic emission level includes system harmonics emission level and user's harmonic emission level, following formula determine:

U_c-PCC=Z_sI_PCC(6)

U_s-PCC=Z_sI_s=U_PCC-U_c-PCC(7)

In formula, U_c-PCCFor custom system harmonic emission level, U_s-PCCFor system harmonics emission level, U_PCCFor certain subharmonic voltage of points of common connection, I_PCCFor certain subharmonic current of points of common connection, I_sFor system harmonics electric current, Z_sFor system harmonic impedance.

Compared with prior art, the invention have the advantages that

(1) impact of background harmonics is considered, not in the same time the harmonic voltage of points of common connection and harmonic current to estimating that the importance of harmonic impedance is different, using Euclidean distance as measurement index, therefore the index size direct reaction obtained harmonic wave sample is by background harmonics effect.

(2) utilize the Euclidean distance of harmonic wave sample as the error requirements of Weighted Guidelines correction support vector machine and punishment parameter, the Weighted Support Vector regression model for estimating system harmonic impedance is formed with this, thus solving harmonic emission level, therefore can effectively suppress the impact of background harmonics.

(3) according to Weighted Support Vector regression model estimating system harmonic impedance, be equivalent to solve the quadratic programming problem of linear restriction, its solution is unique, overall and optimum, there is higher precision of prediction and robustness, therefore power system operating mode is changed, namely can do accurate recurrence during system harmonic impedance change.

Accompanying drawing explanation

Fig. 1 is system side and user side schematic equivalent circuit；

Fig. 2 is the present embodiment algorithm flow schematic diagram；

Fig. 3 (a), Fig. 3 (b) are the voltage magnitude of the present embodiment points of common connection 3 subharmonic, current amplitude schematic diagram respectively；

Fig. 4 (a), Fig. 4 (b) are the impedance magnitude of the present embodiment system 3 subharmonic, impedance angle estimated result schematic diagram respectively.

Fig. 5 is the algorithm flow chart of the present embodiment Weighted Support Vector estimating system harmonic impedance.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is carried out premised on technical solution of the present invention, gives detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Embodiment

A kind of harmonic emission level estimation method based on Weighted Support Vector, it is characterised in that comprise the following steps:

S01, measures certain subharmonic voltage and current data on points of common connection, is divided into n sub-data segment according to certain sub-time period；

S02, for each sub-time period, every a pair harmonic voltage in corresponding subdata section is become with harmonic wave set of currents a bivector, using the set of all bivectors as training sample, using the input as Weighted Support Vector of the described training sample, using the output as Weighted Support Vector of the system harmonic impedance of this sub-time period, using the harmonic voltage of the adjacent sub-time period of this sub-time period and harmonic current as forecast sample；

S03, calculates each subdata section training sample and the distance of corresponding forecast sample, determines the importance of training sample according to Euclidean distance, thus obtaining the weight coefficient s of error requirements ε and punishment parameter C in Weighted Support Vector regression model_i, reduce the impact on impedance estimation of foreign peoples's harmonic data with this, and then effectively suppress the impact of background harmonics fluctuation；

S04, according to the relation of training sample and system harmonic impedance and the weight coefficient s that tries to achieve_i, set up Weighted Support Vector regression model, training sample carried out repetition training, obtain the system harmonic impedance of adjacent sub-time period, wherein said Weighted Support Vector regression model particularly as follows:

$\underset{{\mathrm{\α}}^{(*)}\∈R^{2n}}{\min }=\frac{1}{2}\underset{i,j=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)K(x_i,x_j)+\mathrm{\ϵ}\underset{i=1}{\overset{n}{\Σ}}{t}_i({{\mathrm{\α}}_i}^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{n}{\Σ}}{y}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)---\left(1\right)$

The constraints of formula (1) is:

Wherein, α_iAnd α_i ^*The Lagrange multiplier being introduced into, and meet equation α_i×α_i ^*=0, α_i>=0, α_i ^*>=0, i represents the numbering of subdata section, is numbered from small to large according to Euclidean distance, i=1 ..., n, α_jAnd α_j ^*For Lagrange multiplier, x_iAnd x_jFor harmonic voltage, y_iFor harmonic current, K (x_i,x_j) it is the kernel function introduced, ε is error requirements, t_iBeing the weight coefficient of ε, C is punishment parameter, s_iIt it is the weight coefficient of C；

S05, estimates harmonic emission level according to system harmonic impedance.

Described step S03 is particularly as follows: arrange the weight coefficient s of the shortest subdata section sample of Euclidean distance_i=1, t_i=0.01, the subdata section sample weighting coefficient s that Euclidean distance is the longest_i=0.01, t_i=1, the weight coefficient of all the other samples is calculated by linear interpolation:

$\left\{\begin{array}{c}{s}_i=\frac{l-i}{l-1}\\ t_i=\frac{li-1}{l-1}\end{array}\right.---\left(2\right)$

Wherein, l is Euclidean distance, and i represents the numbering of subdata section, and Euclidean distance is more short, and sample importance is more big, the weight coefficient s of punishment parameter C_iMore big, the weight coefficient t of error requirements ε_iMore little.

Described system harmonic impedance is determined by following regression estimates function:

$y=\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x)+\stackrel{\‾}{b}---\left(3\right)$

WhereinFor Lagrange multiplier α_i ^*Estimation,For constant,Choosing value is according to formula (4) or formula (5):

$\stackrel{\‾}{b}=y_j-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_j-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+{\mathrm{\ϵt}}_j---\left(4\right)$

$\stackrel{\‾}{b}=y_k-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_k^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_k)+{\mathrm{\ϵt}}_k---\left(5\right)$

WhereinRespectivelyReal part and imaginary.

Described harmonic emission level includes system harmonics emission level and user's harmonic emission level, following formula determine:

U_c-PCC=Z_sI_PCC(6)

U_s-PCC=Z_sI_s=U_PCC-U_c-PCC(7)

In formula, U_c-PCCFor custom system harmonic emission level, U_s-PCCFor system harmonics emission level, U_PCCFor certain subharmonic voltage of points of common connection, I_PCCFor certain subharmonic current of points of common connection, I_sFor system harmonics electric current, Z_sFor system harmonic impedance.

The present invention difference according to points of common connection place harmonic measure data, utilize Euclidean distance as the error requirements of Weighted Guidelines correction support vector machine, the weighting parameters of punishment parameter is determined by linear interpolation, the Weighted Support Vector regression model for estimating system harmonic impedance is formed, thus solving harmonic emission level with this.

Below technical scheme is described in detail from principle angle:

1, system side and user side equivalent circuit

The equivalent-circuit model of harmonic analysis in power system is as shown in Figure 1.In figure: I_sAnd Z_sRepresent equal currents source and the harmonic impedance of system side subharmonic respectively；I_cAnd Z_cRepresent equal currents source and the harmonic impedance of user side subharmonic respectively；U_PCCAnd I_PCCFor measuring the data obtained, represent PCC (commonly connected) certain subharmonic voltage put and electric current respectively.

According to circuit theory, below equation can be derived:

U_PCC=I_PCCZ_s+I_sZ_s(1)

U_PCC=-I_PCCZ_c+I_cZ_c(2)

Formula (1), (2) can be obtained after arranging:

$U_{PCC}=\frac{Z_s\·Z_c}{(Z_s+Z_c)}\·I_s+\frac{Z_s\·Z_c}{(Z_s+Z_c)}\·I_c---\left(3\right)$

$I_{PCC}=\frac{Z_c}{(Z_s+Z_c)}\·I_c-\frac{Z_s}{(Z_s+Z_c)}\·I_s---\left(4\right)$

System harmonic impedance Z is can be seen that by formula (3), (4)_sWith U_PCC、I_PCCBetween be respectively provided with non-linear relation, and the regression estimates of nonlinear system is had good precision and generalization ability by support vector regression.Therefore it is presumed that training sample setWherein x_kFor the U that PCC point measurement obtains_PCCAnd I_PCCThe vector of composition, y_kIt is then system side harmonic impedance Z_s, n is sample number.Support vector regression by choosing suitable kernel function K (x, x '), training sample set is learnt and constructs regression estimates function by suitable error requirements ε and punishment parameter C, thus utilizing regression estimates function to try to achieve Z_s。

2, Weighted Support Vector regression model

Given training set T={ (x_i,y_i), i=1,2 ..., n) }, wherein input x_i∈R^N, export y_i∈ R, n are sample number, and selecting ε-insensitive function is | y-f (x) |=max{0, | y-f (x) |-ε }, wherein f (x) is the regression hyperplane of structure, introduces ξ_i, ξ^* _iControl error with C and generalization ability and error are compromised.Meanwhile, nonlinear problem is adopted functionInput data are mapped to a higher dimensional space in the hope of obtaining linear model, and defineFor kernel function, for replacing the inner product operation of vector, then the decision function of support vector regression structure is shown in formula (5):

$y=\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x)+\stackrel{\‾}{b}---\left(5\right)$

When adopting support vector machine structure regression estimates function, it is typically converted into structure and solves convex quadratic programming problem:

$\left.\begin{array}{c}\underset{{\mathrm{\α}}^{(*)}\∈R^{2n}}{\min }=\frac{1}{2}\underset{i,j=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)K(x_i,x_j)+\\ \mathrm{\ϵ}\underset{i=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{n}{\Σ}}{y}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)\\ \begin{array}{cc}s.t.& \underset{i=1}{\overset{n}{\Σ}}({\mathrm{\α}}_i-{{\mathrm{\α}}_i}^{*})=0,\end{array}\\ 0\≤{\mathrm{\α}}_i^{(*)}\≤C,i=1,\mathrm{...},n\end{array}\right\}---\left(6\right)$

In formula (6), introduce Lagrange multiplier α_iAnd α_i ^*, and meet equation α_i×α_i ^*=0, α_i>=0, α_i ^*>=0 (i=1 ..., n)；α_jAnd α_j ^*For Lagrange multiplier, x_iAnd x_jFor harmonic voltage, y_iFor harmonic current, K (x_i,x_j) it is the kernel function introduced.

And calculated as below try to achieve

$\stackrel{\‾}{b}=y_j-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+t_j,{\stackrel{\‾}{\mathrm{\α}}}_j>0---\left(7\right)$

$\stackrel{\‾}{b}=y_k-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_k)+\mathrm{\ϵ},{\stackrel{\‾}{\mathrm{\α}}}_k^{*}>0---\left(8\right)$

Wherein, support that vector isWithIt is asynchronously the sample point of zero, with two parts outside border on its point border.Borderline support vector is α_i∈ (0, C/n),Or α_i=0,And the support vector outside border is α_i=C/n,Or α_i=0,

In above-mentioned quadratic programming problem, error requirements ε and punishment parameter C chooses the key being to affect Support vector regression result.The size of ε represents the regression model requirement to training sample error, and ε value is more little means that the requirement to model regression accuracy is more high, and the regression function precision solved is also more high.Punishment parameter C represents the punishment to the sample data beyond error requirements ε, C value is more little mean the sample punishment dynamics beyond error requirements more little, thus increasing training error.In support vector machine method, regression model need to determine error requirements ε and the value of punishment parameter C at the beginning, and remains unchanged in calculating later, namely for all of harmonic data, and its error requirements and what the punishment beyond error requirements was just as.But reality is when computing system harmonic impedance, consider the impact of background harmonics fluctuation, not in the same time the harmonic voltage of PCC point and harmonic current to estimating that the importance of harmonic impedance is different, the data importance more little by background harmonics influence of fluctuations is more big, harmonic wave sample for different importances should select different error requirements and punishment parameter to use restraint, thus reducing the impact on impedance estimation of the importance little harmonic data.

It is therefore proposed that adopt the weighted support vector regression computing system side harmonic impedance improved.Original error requirements ε and punishment parameter C changes into ε t accordingly_iAnd Cs_i, the convex quadratic programming problem of formula (6) is namely converted into:

$\left.\begin{array}{c}\underset{{\mathrm{\α}}^{(*)}\∈R^{2n}}{\min }=\frac{1}{2}\underset{i,j=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)K(x_i,x_j)+\\ \mathrm{\ϵ}\underset{i=1}{\overset{n}{\Σ}}{t}_i({{\mathrm{\α}}_i}^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{n}{\Σ}}{y}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)\\ \begin{array}{cc}s.t.& \underset{i=1}{\overset{n}{\Σ}}({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})=0,\end{array}\\ 0\≤{{\mathrm{\α}}_i}^{(*)}\≤{\mathrm{Cs}}_i,=1,\mathrm{...},n\end{array}\right\}---\left(9\right)$

3, weight coefficient

In Weighted Support Vector, first answer the importance of quantized samples, then determine the weighting parameters t of the error requirements ε and punishment parameter C of each sample using the importance of sample as Weighted Guidelines_iAnd s_i.In order to quantify the importance of each sample data, adopt Euclidean distance as quantizating index, calculate the distance of test sample and each training sample, and by distance size, training sample is resequenced.Euclidean distance is more short, and sample importance is more big, the weight parameter s of punishment parameter C_iMore big, the weight parameter t of error requirements ε_iMore little.Therefore, the weight parameter s of the shortest sample of distance is set herein_i=1, t_i=0.01；It is s apart from farthest sample weight parameter_i=0.01, t_i=1.Finally, utilize the sample parameter under two kinds of extreme cases, calculated the weight parameter of all the other samples by linear interpolation.

$\left.\begin{array}{c}{s}_i=\frac{l-b}{l-1}-\frac{1-b}{l-1}i\\ t_i=\frac{la-1}{l-1}+\frac{l-a}{l-1}i\end{array}\right\}---\left(10\right)$

Wherein, l is Euclidean distance；Parameter a=0, b=0.

4, system harmonic impedance is estimated

System harmonic impedance is determined by following regression estimates function:

$y=\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x)+\stackrel{\‾}{b}---\left(11\right)$

Wherein, the constant term in regression functionOptional fetch bit is in open interval (0, C)ComponentOrIf what choose isThen

$\stackrel{\‾}{b}=y_j-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+{\mathrm{\ϵt}}_j---\left(12\right)$

If what choose isThen

$\stackrel{\‾}{b}=y_k-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_k)+{\mathrm{\ϵt}}_k---\left(13\right)$

Utilize the harmonic voltage U that PCC point records_PCCWith harmonic current I_PCCThe vector of composition is as the input of Weighted Support Vector, i.e. training sample setIn x_k；y₁For system harmonic impedance Z_sInitial value, y_k(k=2,3 ...) return, for k-1 time, the Z obtained_sValue.Concrete steps are as shown in Figure 5:

A, certain subharmonic voltage obtained according to points of common connection measurement and current data, be divided into N number of subdata section according to certain sub-time period；

B, for each subdata section, the bivector formed using the harmonic voltage in this period and electric current is as training sample；The input of Weighted Support Vector is training sample, is output as system harmonic impedance, it was predicted that sample is harmonic voltage and the electric current of the points of common connection of adjacent time interval；

C, determine the importance of sample according to Euclidean distance, thus obtaining the weight coefficient of error requirements ε and punishment parameter C in Weighted Support Vector regression model, reduce the impact on impedance estimation of foreign peoples's harmonic data with this, and then effectively suppress the impact of background harmonics fluctuation；

D, set up the regression model of Weighted Support Vector according to the relation of training sample and system harmonic impedance and the sample importance weight coefficient tried to achieve, and with this model, sample is carried out repetition training, obtain the system harmonic impedance of adjacent time interval.

5, harmonic emission level is estimated

According to IEC IEC61000-3-6, certain harmonic emission level of PCC point point is defined as by user: the variable quantity of points of common connection place subharmonic voltage/electric current before and after subscriber access system, namely can be regarded as the influence amount to PCC point place subharmonic after subscriber access system.

Before and after subscriber access system, PCC point place subharmonic voltage is respectively as follows:

U_PCC-pre=I_sZ_s(14)

U_PCC-post=I_sZ_s+I_PCCZ_s(15)

Two formulas are subtracted each other and are namely obtained user's harmonic voltage transmission level:

U_c-PCC=Z_sI_PCC(16)

System harmonics voltage discharge level is:

U_s-PCC=Z_sI_s=U_PCC-U_c-PCC(17)

The present invention is applied in the 150kV bus of the industrial DC electric arc furnace of a 100MVA, and system short circuit capacity is 7500MVar.Measurement data is recorded with the sample frequency of 6400Hz by LEMTOPAS1000 series power analysis instrument.Fig. 3 (a), 3 (b) represent that PCC point records continuous 10 hours of one day 3 interior subharmonic voltages and current amplitude.

Assessment result:

It is respectively adopted four kinds of methods to surveying 3 subharmonic data by 60min segmentation computing system harmonic impedance, result of calculation is as follows: method 1 (binary regression method) utilizes method of least square regression estimates harmonic impedance, intercept in regression equation can change with background harmonics fluctuation, so that the Return Law loses original robustness, cause that the fluctuation of impedance estimation result is bigger；Method 2 (support vector machine method) utilizes Support vector regression to solve harmonic impedance, due to its Xie Shi global optimum and unique, there is good precision, but it does not consider that background harmonics fluctuation causes the problem of differences between samples, cause that the regression estimates of support vector machine deviates actual value in local；Method 3 (independent random vector method) utilizes the weak dependence of PCC point harmonic current and background harmonics to derive the estimation formulas of harmonic impedance, restrained effectively the impact of background harmonics fluctuation, and estimated result is comparatively steady；Method 4 (institute of the present invention extracting method) utilizes the thought to error requirements ε and punishment parameter C weighting to solve method 2 Problems existing, estimated result improves significantly, compared with method 3, estimated result is more smooth, the method can suppress the impact that background harmonics fluctuates better, having better precision and stability, concrete outcome is such as shown in Fig. 4 (a), 4 (b).

Calculating PCC point user side and system side harmonic voltage transmission level by the system harmonic impedance tried to achieve, emission level 95% probit obtained is as shown in table 1, demonstrates accuracy and the effectiveness of institute of the present invention extracting method further.

Table 1 user and system side harmonic voltage transmission level 95% probit

Claims (5)

1. the harmonic emission level estimation method based on Weighted Support Vector, it is characterised in that comprise the following steps:

S01, measures certain subharmonic voltage interior of certain time period on points of common connection and current data, is divided into n sub-data segment according to certain sub-time period；

S02, for each sub-time period, every a pair harmonic voltage in corresponding subdata section is become with harmonic wave set of currents a bivector, using the set of all bivectors as training sample, using the input as Weighted Support Vector of the described training sample, using the output as Weighted Support Vector of the system harmonic impedance of this sub-time period, using the harmonic voltage of the adjacent sub-time period of this sub-time period and harmonic current as forecast sample；

S03, calculate the training sample of each subdata section and the Euclidean distance of corresponding forecast sample, the importance of training sample is determined, thus obtaining the weight coefficient of the weight coefficient of error requirements ε and punishment parameter C in Weighted Support Vector regression model according to Euclidean distance；

S04, according to the relation of training sample and system harmonic impedance and the weight coefficient s that tries to achieve_i, set up Weighted Support Vector regression model, the training sample of each sub-time period be trained, obtain the system harmonic impedance of adjacent sub-time period, wherein Weighted Support Vector regression model particularly as follows:

$\underset{{\mathrm{\α}}^{(*)}\∈R^{2n}}{min}=\frac{1}{2}\underset{i,j=1}{\overset{n}{\Σ}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)K(x_i,x_j)+\mathrm{\ϵ}\underset{i=1}{\overset{n}{\Σ}}{t}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)-\underset{i=1}{\overset{n}{\Σ}}{y}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)---\left(1\right)$

The constraints of formula (1) is:

Wherein, i represents the numbering of subdata section, is numbered from small to large according to Euclidean distance, i=1 ..., n, α_iAnd α_i ^*The Lagrange multiplier being introduced into, and meet equation α_i×α_i ^*=0, α_i>=0, α_i ^*>=0, α_jAnd α_j ^*For Lagrange multiplier, x_i,And x_jFor harmonic voltage, y_i,For harmonic current, K (x_i,,x_j) it is the kernel function introduced, ε is error requirements, t_iFor the weight coefficient of ε, C is punishment parameter, s_iWeight coefficient for C；

S05, estimates the harmonic emission level of this adjacent sub-time period according to the system harmonic impedance of adjacent sub-time period.

2. a kind of harmonic emission level estimation method based on Weighted Support Vector according to claim 1, it is characterised in that described step S03 is particularly as follows: define the weight coefficient s of the shortest subdata section sample of Euclidean distance₀=1, t₀=0.01, the subdata section sample weighting coefficient s that Euclidean distance is the longest_n=0.01, t_n=1, the weight coefficient of all the other subdata section samples is calculated by linear interpolation:

$\left\{\begin{array}{c}{s}_i=\frac{l_i-i}{l_i-1}\\ t_i=\frac{l_{i}i-1}{l_i-1}\end{array}\right.---\left(2\right)$

Wherein, l_iFor the Euclidean distance of this subdata section sample, i represents the numbering of subdata section, i=2 ... n-1.

3. a kind of harmonic emission level estimation method based on Weighted Support Vector according to claim 1, it is characterised in that described system harmonic impedance is determined by following regression estimates function:

$y=\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_i^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+\stackrel{\‾}{b}---\left(3\right)$

WhereinFor Lagrange multiplier α_i ^*Estimation,For constant.

4. a kind of harmonic emission level estimation method based on Weighted Support Vector according to claim 3, it is characterised in that whereinChoosing value is according to formula (4) or formula (5):

$\stackrel{\‾}{b}=y_j-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_j-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_j)+{\mathrm{\ϵt}}_j---\left(4\right)$

$\stackrel{\‾}{b}=y_k-\underset{i=1}{\overset{n}{\Σ}}({\stackrel{\‾}{\mathrm{\α}}}_k^{*}-{\stackrel{\‾}{\mathrm{\α}}}_i)K(x_i,x_k)+{\mathrm{\ϵt}}_k---\left(5\right)$

WhereinRespectivelyReal part and imaginary.

5. a kind of harmonic emission level estimation method based on Weighted Support Vector according to claim 1, it is characterised in that in described step S05, harmonic emission level includes system harmonics emission level and user's harmonic emission level, following formula determine:

U_c-PCC=Z_sI_PCC(6)

U_s-PCC=U_PCC-U_c-PCC(7)

In formula, U_c-PCCFor user's harmonic emission level, U_s-PCCFor system harmonics emission level, U_PCCFor certain subharmonic voltage of points of common connection, I_PCCFor certain subharmonic current of points of common connection, Z_sFor system harmonic impedance.