CN103020467A - Method for identifying transmission line parameters - Google Patents

Abstract

The invention discloses a method for identifying transmission line parameters. The method comprises the following steps: firstly, establishing a linear equation set for describing a transmission line model according to an equivalent model of a transmission line; dividing multiple sets of sampling data of a PMU (Phasor Measuring Unit) within a period of time into multiple data windows in fixed length; specific to the sampling data of each data window, utilizing a least square method to identify the parameters according to the established linear equation set, thereby obtaining an identifying result under each data window; arraying the identifying results under all the data windows in an ascending sort according to the magnitude sequence of the identifying results, thereby obtaining a row of sequencing statistics; and taking a median of the obtained sequencing statistics as a final parameter identifying result. According to the method, the identified parameters are closer to real parameters of the line and are more credible, and the error resistance is ultrahigh.

Description

A kind of method of transmission line parameter identification

Technical field

The present invention relates to technical field of power systems, relate in particular to a kind of method of transmission line parameter identification.

Background technology

At present, electric power system model and parameter are the foundations of the every calculating of power department and definite method of operation, therefore the accuracy of model and parameter is related to the safe and stable operation of electrical network, improves accuracy and the reliability of parameters of electric power system, and the safe and stable operation of electrical network is significant.

Transmission line of electricity is the carrier that electric system is carried; the whether accurate net result that directly has influence on relay protection setting calculating and select power system operation mode of its parameter; if the transmission line parameter that uses in the real work is inaccurate; may bring very large impact to electric system, even produce great electric power accident.Therefore along with the development of China's electric system, accuracy requirement for transmission line parameter is also more and more higher, but transmission line parameter is more complicated and be subjected to the impact of a lot of uncertain factors (weather, environment and geographical etc.) and change often, so that can't only rely on the theoretical exact value of obtaining these parameters of calculating, be subject to simultaneously the restriction of multiple condition.In addition, generally adopt the method for have a power failure test, manual measurement during the actual measurement transmission line parameter, also can not be reflected in the line parameter circuit value under the different operating modes.

And in actual applications, owing to being subject to the restriction of measurement mechanism accuracy and real-time, be difficult to obtain line double-end synchronization electric parameters, and online transmission line parameter is estimated only to rely on the state estimation of SCADA system, calculated amount is huge and accuracy is not high.

Summary of the invention

The method that the purpose of this invention is to provide a kind of transmission line parameter identification, the method make parameter that identification obtains more near the actual parameter of circuit, and be more credible, and have very strong robustness.

The objective of the invention is to be achieved through the following technical solutions, a kind of method of transmission line parameter identification comprises:

According to the Equivalent Model of transmission line of electricity, set up the system of linear equations of describing model of power transmission system;

The many group sampled data of phasor measurement unit PMU within a period of time is divided into a plurality of data windows that regular length is arranged;

For the sampled data of each data window, utilize least square method to carry out parameter identification according to the system of linear equations of setting up, obtain the identification result under each data window;

Identification result under each data window is pressed the size order ascending order of identification result and arranged, obtain a row sequencing statistical amount;

With the median of resulting sequencing statistical amount as final parameter identification result.

The system of linear equations of described description model of power transmission system is specially:

$\left[\begin{array}{c}{I}_{\mathrm{mR}}\\ I_{\mathrm{mI}}\\ I_{\mathrm{nR}}\\ I_{\mathrm{nI}}\\ P_m\\ Q_m\\ P_n\\ Q_n\end{array}\right]=\left[\begin{array}{ccc}{U}_m{\cos \mathrm{\θ}}_{\mathrm{un}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& -U_m{\sin \mathrm{\θ}}_{\mathrm{um}}\\ U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}\\ U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& {-U}_n{\sin \mathrm{\θ}}_{\mathrm{un}}\\ U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}\\ U_m^2-U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& 0\\ -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})-U_m^2& -U_m^2\\ U_n^2-U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& 0\\ -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})-U_n^2& -U_n^2\end{array}\right]\left[\begin{array}{c}g\\ b\\ y_c\end{array}\right]$

Wherein, I _MR, I _NR, I _MI, I _NIThe real part and the imaginary part that represent respectively circuit two ends electric current phasor; U _m, U _n, θ _Um, θ _UnThe amplitude and the phase angle that represent respectively circuit both end voltage phasor; P _m, P _n, Q _m, Q _nThe active power and the reactive power that represent respectively the circuit two ends; G, b represent real part and the imaginary part of 1/Z, and Z is the equivalent impedance of transmission line of electricity; y _cThe imaginary part of expression Y, Y is the equivalent susceptance of circuit.

Described the many group sampled data of phasor measurement unit PMU within a period of time is divided into a plurality of data windows that regular length is arranged, specifically comprises:

Phasor measurement unit PMU is divided into K data window in the N of following period of time group sampled data, contains m group sampled data in each data window, m 1, suppose N=K*m, K is integer and K〉1;

Or, in the N of following period of time group sampled data, continuously be divided into N-m data window every one group of data for phasor measurement unit PMU, and contain m group sampled data, m in each data window 1.

Described size order ascending order arrangement of the identification result under each data window being pressed identification result obtains a row sequencing statistical amount, specifically comprises:

If the group of the K under each data window identification result is x _i(i=1,2 ..., K), then arrange to such an extent that the sequencing statistical amount is x by ascending order ₍₁₎≤ x ₍₂₎≤ ... ≤ x _(j)≤ ... x _(K)(j=1,2 ..., K).

Described final parameter identification result is:

As seen from the above technical solution provided by the invention, at first according to the Equivalent Model of transmission line of electricity, set up the system of linear equations of describing model of power transmission system; The many group sampled data of phasor measurement unit PMU within a period of time is divided into a plurality of data windows that regular length is arranged; For the sampled data of each data window, utilize least square method to carry out parameter identification according to the system of linear equations of setting up, obtain the identification result under each data window; Identification result under each data window is pressed the size order ascending order of identification result and arranged, obtain a row sequencing statistical amount; With the median of resulting sequencing statistical amount as final parameter identification result.The method makes parameter that identification obtains more near the actual parameter of circuit, and is more credible, and has very strong robustness.

Description of drawings

In order to be illustrated more clearly in the technical scheme of the embodiment of the invention, the accompanying drawing of required use was done to introduce simply during the below will describe embodiment, apparently, accompanying drawing in the following describes only is some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite of not paying creative work, can also obtain other accompanying drawings according to these accompanying drawings.

Fig. 1 is the method flow schematic diagram of the described transmission line parameter identification of the embodiment of the invention;

Fig. 2 is the Π type Equivalent Model schematic diagram of middle transmission line of electricity that the embodiment of the invention gives an actual example;

Fig. 3 is that the embodiment of the invention 1 is based on the sequencing statistical amount schematic diagram of the line parameter circuit value identification result of PSCAD emulated data;

Fig. 4 is the sequencing statistical amount schematic diagram of line parameter circuit value identification result when 1 bad data occurring in the PSCAD emulated data in the embodiment of the invention 1;

Fig. 5 is that the embodiment of the invention 2 is based on the sequencing statistical amount schematic diagram of the line parameter circuit value identification result of PMU measured data.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the invention, the technical scheme in the embodiment of the invention is clearly and completely described, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on embodiments of the invention, those of ordinary skills belong to protection scope of the present invention not making the every other embodiment that obtains under the creative work prerequisite.

The embodiment of the invention has proposed a kind of transmission line parameter discrimination method based on phasor measurement unit PMU data and medion estimator, utilizes the PMU data, and the parameter of identification transmission line of electricity makes parameter that identification obtains more near the actual parameter of circuit, and is more credible; Simultaneously owing to the sampling period of PMU is short, within a period of time, can obtain a large amount of sampled datas, the embodiment of the invention is divided into a plurality of data windows with a large amount of sampled datas, respectively based on the sampled data identified parameters of each data window, thereby obtains a large amount of parameter identification results; The embodiment of the invention is further also extracted final line parameter circuit value identification result based on the medion estimator principle with very strong robustness in a large amount of identification results.Below in conjunction with accompanying drawing the embodiment of the invention is described in further detail, is illustrated in figure 1 as the method flow schematic diagram of the described transmission line parameter identification of the embodiment of the invention, described method comprises:

Step 11: according to the Equivalent Model of transmission line of electricity, set up the system of linear equations of describing model of power transmission system.

In this step, the system of linear equations of described description model of power transmission system is:

$\left[\begin{array}{c}{I}_{\mathrm{mR}}\\ I_{\mathrm{mI}}\\ I_{\mathrm{nR}}\\ I_{\mathrm{nI}}\\ P_m\\ Q_m\\ P_n\\ Q_n\end{array}\right]=\left[\begin{array}{ccc}{U}_m{\cos \mathrm{\θ}}_{\mathrm{un}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& -U_m{\sin \mathrm{\θ}}_{\mathrm{um}}\\ U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}\\ U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& {-U}_n{\sin \mathrm{\θ}}_{\mathrm{un}}\\ U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}\\ U_m^2-U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& 0\\ -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})-U_m^2& -U_m^2\\ U_n^2-U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& 0\\ -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})-U_n^2& -U_n^2\end{array}\right]\left[\begin{array}{c}g\\ b\\ y_c\end{array}\right]$

Wherein, I _MR, I _NR, I _MI, I _NIThe real part and the imaginary part that represent respectively circuit two ends electric current phasor; U _m, U _n, θ _Um, θ _UnThe amplitude and the phase angle that represent respectively circuit both end voltage phasor; P _m, P _n, Q _m, Q _nThe active power and the reactive power that represent respectively the circuit two ends; G, b represent real part and the imaginary part of 1/Z, and Z is the equivalent impedance of transmission line of electricity; y _cThe imaginary part of expression Y, Y is the equivalent susceptance of circuit.

Further, the matrix form of this system of linear equations is: Ax=β.

For instance, the below comes the system of linear equations derivation of above-mentioned model of power transmission system is described with instantiation, be Π type Equivalent Model according to transmission line of electricity in the present embodiment, be illustrated in figure 2 as the Π type Equivalent Model schematic diagram of middle transmission line of electricity that the embodiment of the invention gives an actual example, among Fig. 2:

With Be respectively the electric current and voltage vector at circuit two ends; Z is the equivalent impedance of circuit; Y is the equivalent susceptance of circuit.

Voltage, the current equation of transmission line of electricity first and last end are as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{I}}_m=\frac{Y}{2}{\stackrel{\·}{U}}_m+({\stackrel{\·}{U}}_m-{\stackrel{\·}{U}}_n)/Z\\ {\stackrel{\·}{I}}_n=\frac{Y}{2}{\stackrel{\·}{U}}_n+({\stackrel{\·}{U}}_n-{\stackrel{\·}{U}}_m)/Z\end{array}\right.---\left(1\right)$

Equivalent for lumped parameter: Z=R+jX is the circuit equivalent impedance; Y=jB is equivalent line susceptance, and B=2 π fC, f are power frequency 50Hz, and C is the whole ground capacitance of circuit.

Equivalent for distribution parameter:

$\left\{\begin{array}{c}Z=Z_c\sinh \mathrm{\γL}\\ Y=\frac{2(\cosh \mathrm{\γ}-1)}{Z_c\sinh \mathrm{\γL}}\end{array}\right.$

Wherein, Z _cBe wave impedance, γ is propagation coefficient, and L is line length.

The circuit of PMU is installed for both-end, and PMU can measure voltage, the current vector and meritorious, idle at two ends.Electric current, the power equation of first and last end are launched by its real part and imaginary part respectively, get the system of linear equations of following model of power transmission system:

$\left[\begin{array}{c}{I}_{\mathrm{mR}}\\ I_{\mathrm{mI}}\\ I_{\mathrm{nR}}\\ I_{\mathrm{nI}}\\ P_m\\ Q_m\\ P_n\\ Q_n\end{array}\right]=\left[\begin{array}{ccc}{U}_m{\cos \mathrm{\θ}}_{\mathrm{un}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& -U_m{\sin \mathrm{\θ}}_{\mathrm{um}}\\ U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}\\ U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& {-U}_n{\sin \mathrm{\θ}}_{\mathrm{un}}\\ U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}\\ U_m^2-U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& 0\\ -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})-U_m^2& -U_m^2\\ U_n^2-U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& 0\\ -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})-U_n^2& -U_n^2\end{array}\right]\left[\begin{array}{c}g\\ b\\ y_c\end{array}\right]---\left(2\right)$

Further formula (2) can be written as matrix form is:

Ax=β （3）

Wherein, I _MR, I _NR, I _MI, I _NIThe real part and the imaginary part that represent respectively circuit two ends electric current phasor; U _m, U _n, θ _Um, θ _UnThe amplitude and the phase angle that represent respectively circuit both end voltage phasor; P _m, P _n, Q _m, Q _nThe active power and the reactive power that represent respectively the circuit two ends; G, b represent real part and the imaginary part of 1/Z, and Z is the equivalent impedance of transmission line of electricity; y _cThe imaginary part of expression Y, Y is the equivalent susceptance of circuit.

Step 12: phasor measurement unit PMU is divided into a plurality of data windows that regular length is arranged in many groups sampled data of following period of time.

In this step, set up by above-mentioned steps 11 after the system of linear equations of description model of power transmission system, again phasor measurement unit PMU is divided into a plurality of data windows that regular length is arranged in many groups sampled data of following period of time, specifically:

Phasor measurement unit PMU is divided into K data window in the N of following period of time group sampled data, contains m group sampled data in each data window, m 1, suppose N=K*m, K is integer and K〉1;

Or, in the N of following period of time group sampled data, continuously be divided into N-m data window every one group of data for phasor measurement unit PMU, and contain m group sampled data, m in each data window 1.

Step 13: for the sampled data of each data window, utilize least square method to carry out parameter identification according to the system of linear equations of setting up, obtain the identification result under each data window.

In this step, according to the model equation of the transmission line of electricity that obtains, the recycling least square method is carried out parameter identification with the sampled data of K data window respectively, obtains K group parameter identification result.

For instance, above-mentioned formula (3) is linear redundant equation group, finds the solution with traditional least square method, owing to being subjected to the impact of measurement noise large with the PMU data identification parameter in the single moment, the data in available a plurality of moment improve the redundance of equation, slacken the impact of measurement noise.

Can get thus, the least square identification result of above-mentioned transmission line parameter is

$\hat{x}={\left(A^T\mathrm{PA}\right)}^{-1}{A}^T\mathrm{P\β}---\left(4\right)$

Wherein, P is each constantly weight matrix of data, thinks that at this each moment weight equates.

Step 14: the size order of the identification result under each data window being pressed identification result is arranged by ascending order, obtains a row sequencing statistical amount.

In this step, this K group identification result is carried out ascending order (or descending) by its size arrange, obtain a sequencing statistical amount of showing size order.

For example, if the group of the K under each data window identification result x _i(i=1,2 ..., K), then arrange to get sequencing statistical amount x by ascending order ₍₁₎≤ x ₍₂₎≤ ... ≤ x _(j)≤ ... x _(K)(j=1,2 ..., K).

Step 15: with the median of resulting sequencing statistical amount as final parameter identification result.

In this step, as final parameter identification result, final parameter identification result is with the median of this row sequencing statistical amount:

From above-mentioned formula (5) as can be known, if K is odd number, median is exactly the symcenter of sequencing statistical amount; If K is even number, then median is the mean value of two sequencing statistical amounts in the middle of being positioned at.

In the specific implementation, a large amount of identification results is approximate Normal Distribution, generally uses the mean value of identification result as final parameter identification result; And median has only utilized the sequencing information of identification result, the size of one or two sequencing statistical amount in the middle of its size only depends on, little with the magnitude relationship of other sequencing statistical amounts, and the median that bad identification result only has influence on identification result around symcenter very among a small circle in variation, so median has very strong robustness.In theory, even there is the bad data of half nearly in the PMU data, median still can be obtained preferably identification result, is the strongest method of estimation of robustness.Medion estimator just is this from the maximum different of Estimation of Mean, and this also is that medion estimator has very strong robustness and reason that Estimation of Mean does not have.

The below comes the method for above-mentioned transmission line parameter identification is proved with concrete example:

Embodiment one

The present embodiment 1 is built the transmission line of electricity that a list returns 500KV in PSCAD, line parameter circuit value is set to resistance R=1.916 Ω, reactance X=35.180 Ω, all ground capacitance C=2.193uF.Electric current and voltage with the circuit two ends is vectorial, meritorious and idle as PMU measurement amount, and sampling interval is 10ms, and sampling 6s is totally 600 groups data identification line parameter circuit value.Each data window contains 10 groups of sampled datas, totally 60 data windows.

Be illustrated in figure 3 as the embodiment of the invention 1 based on the sequencing statistical amount schematic diagram of the line parameter circuit value identification result of PSCAD emulated data, as shown in table 1 below based on the identification result of each parameter of medion estimator and Estimation of Mean respectively:

Table 1

Can find out from the result of two kinds of estimations of above-mentioned table 1: when emulated data does not have error in measurement, the parameter result of medion estimator and Estimation of Mean almost is just the same, and the estimated accuracy of reactance X and capacitor C is very high, the estimated accuracy of resistance R is bigger than normal a little, but also in the permissible error scope.Therefore, this has shown that the line parameter circuit value discrimination method based on the median principle is effective.

Under the actual conditions, metric data is the noise that contains approximate Normal Distribution.In order to verify the validity of medion estimator when metric data contains Gaussian noise, measuring the poor Gaussian noise of stack certain standard in electric current phasor and the power data.In concrete the application, PMU is 0.002 to the standard deviation of the error in measurement of current amplitude, is 0.0017rad to the standard deviation of the error in measurement of phase angle; Standard deviation to the error in measurement of power is 0.005.The identification result of medion estimator and Estimation of Mean is as shown in table 2 below when containing Gaussian noise:

Table 2

Can find out from the identification result of upper table 2, when metric data contained less Gaussian noise, medion estimator also was effectively, and the precision of identification result will be better than Estimation of Mean.

Further, be the robustness of checking medion estimator, the random bad data that produces in metric data, owing to random perturbation, the 305th metric data of PMU departed from true value, produced bad data, departs from true value about 20% in this supposition.

Be illustrated in figure 4 as the sequencing statistical amount schematic diagram of line parameter circuit value identification result when 1 bad data occurring in the PSCAD emulated data in the embodiment of the invention 1, the identification result of medion estimator and Estimation of Mean is as shown in table 3 below during based on bad data:

Table 3

From the sequencing statistical discharge curve of above-mentioned table 3 identification result as can be known, the existence of 1 bad data makes the identification result serious distortion of least square, thereby also so that the error of Estimation of Mean becomes large, has reached 43% such as the error of resistance; But the result of medion estimator is still keeping very high precision, not affected by any of bad data.As can be known, medion estimator has very strong robustness.Strengthen the number of bad data, Estimation of Mean is no longer valid, and the identification precision of medion estimator is still very high.The ratio of bad data reaches close to 50% the time in theory, and medion estimator also may be effective.

Embodiment two

The present embodiment utilizes the PMU measured data of certain electrical network 500KV transmission line of electricity to carry out parameter identification.This 500KV circuit is double loop, and the length on this loop line road is 115.8km, and wire type is LGJ-4*400, and without aerial earth wire, the parameter theory value is: resistance R=2.316 Ω, reactance X=32.424 Ω, all ground capacitance C=1.505uF.The PMU steady state data of existing two time periods, the error in measurement of PMU is relatively very little, and sampling interval is 10ms.The data of every period are 6s, totally 600 groups data identification line parameter circuit value; Each data window contains 10 groups of sampled datas, totally 60 data windows.

Be illustrated in figure 5 as the embodiment of the invention 2 based on the sequencing statistical amount schematic diagram of the line parameter circuit value identification result of PMU measured data, as shown in table 4 below based on the identification result of each parameter of medion estimator and Estimation of Mean respectively:

Table 4

Can find out based on the identification result of PMU measured data from upper table 4, the identification result of three parameters all has certain discrepancy with theoretical value, but identifier is the actual parameter of coincidence circuit more, because identifier has taken into full account the effect of the various factorss such as the space layout of circuit, residing geographical environment and operating condition, identification result is more credible; This has shown that also the parameter based on each element of PMU measured data identification electrical network is to be of practical significance very much and necessary.In addition, the identification result of medion estimator and Estimation of Mean is almost identical, shows that medion estimator is effective.

In sum, the method for transmission line parameter identification of the present invention makes parameter that identification obtains more near the actual parameter of circuit, and is more credible, has simultaneously very strong robustness.

The above; only for the better embodiment of the present invention, but protection scope of the present invention is not limited to this, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (5)

1. the method for a transmission line parameter identification is characterized in that, comprising:

According to the Equivalent Model of transmission line of electricity, set up the system of linear equations of describing model of power transmission system;

The many group sampled data of phasor measurement unit PMU within a period of time is divided into a plurality of data windows that regular length is arranged;

For the sampled data of each data window, utilize least square method to carry out parameter identification according to the system of linear equations of setting up, obtain the identification result under each data window;

Identification result under each data window is pressed the size order ascending order of identification result and arranged, obtain a row sequencing statistical amount;

With the median of resulting sequencing statistical amount as final parameter identification result.

2. the method for described transmission line parameter identification according to claim 1 is characterized in that, the system of linear equations of described description model of power transmission system is specially:

$\left[\begin{array}{c}{I}_{\mathrm{mR}}\\ I_{\mathrm{mI}}\\ I_{\mathrm{nR}}\\ I_{\mathrm{nI}}\\ P_m\\ Q_m\\ P_n\\ Q_n\end{array}\right]=\left[\begin{array}{ccc}{U}_m{\cos \mathrm{\θ}}_{\mathrm{un}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& -U_m{\sin \mathrm{\θ}}_{\mathrm{um}}\\ U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}-U_n{\cos \mathrm{\θ}}_{\mathrm{un}}& U_m{\cos \mathrm{\θ}}_{\mathrm{um}}\\ U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_m{\sin \mathrm{\θ}}_{\mathrm{um}}-U_n{\sin \mathrm{\θ}}_{\mathrm{un}}& {-U}_n{\sin \mathrm{\θ}}_{\mathrm{un}}\\ U_n{\sin \mathrm{\θ}}_{\mathrm{un}}-U_m{\sin \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}-U_m{\cos \mathrm{\θ}}_{\mathrm{um}}& U_n{\cos \mathrm{\θ}}_{\mathrm{un}}\\ U_m^2-U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& 0\\ -U_m{U}_n\sin ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})& U_m{U}_n\cos ({\mathrm{\θ}}_{\mathrm{um}}-{\mathrm{\θ}}_{\mathrm{un}})-U_m^2& -U_m^2\\ U_n^2-U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& 0\\ -U_n{U}_m\sin ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})& U_n{U}_m\cos ({\mathrm{\θ}}_{\mathrm{un}}-{\mathrm{\θ}}_{\mathrm{um}})-U_n^2& -U_n^2\end{array}\right]\left[\begin{array}{c}g\\ b\\ y_c\end{array}\right]$

Wherein, I _MR, I _NR, I _MI, I _NIThe real part and the imaginary part that represent respectively circuit two ends electric current phasor; U _m, U _n, θ _Um, θ _UnThe amplitude and the phase angle that represent respectively circuit both end voltage phasor; P _m, P _n, Q _m, Q _nThe active power and the reactive power that represent respectively the circuit two ends; G, b represent real part and the imaginary part of 1/Z, and Z is the equivalent impedance of transmission line of electricity; y _cThe imaginary part of expression Y, Y is the equivalent susceptance of circuit.

3. the method for described transmission line parameter identification according to claim 1 is characterized in that, described the many group sampled data of phasor measurement unit PMU within a period of time is divided into a plurality of data windows that regular length is arranged, and specifically comprises:

Phasor measurement unit PMU is divided into K data window in the N of following period of time group sampled data, contains m group sampled data in each data window, m 1, suppose N=K*m, K is integer and K〉1;

Or, in the N of following period of time group sampled data, continuously be divided into N-m data window every one group of data for phasor measurement unit PMU, and contain m group sampled data, m in each data window 1.

4. the method for described transmission line parameter identification according to claim 3 is characterized in that, the described size order ascending order that identification result under each data window is pressed identification result is arranged, and obtains a row sequencing statistical amount, specifically comprises:

If the group of the K under each data window identification result is x _i(i=1,2 ..., K), then arrange to such an extent that the sequencing statistical amount is x by ascending order ₍₁₎≤ x ₍₂₎≤ ... ≤ x _(j)≤ ... x _(K)(j=1,2 ..., K).

5. the method for described transmission line parameter identification according to claim 4 is characterized in that, described final parameter identification result is:

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