CN104483577A - Electric power line parameter accuracy measurement method - Google Patents

Abstract

The invention belongs to the technical field of electrical power system parameter identification, and relates to a measurement method of electric power line parameter accuracy influenced by data errors. According to the method, influence of parameters of an equivalent circuit of a power transmission line on PMU (phase measurement unit) data sensitivity is determined, sensitivity of line parameters to PMU data errors is judged, a parameter accuracy calculation method is given, the quantitative influence degree of each data to power line parameters is judged according to the quantitative relation between data error increment and parameter deviation, and the measured PMU data quality and the parameter identification accuracy are improved. The design principle is reliable, scientificity of the judgment technology is high, the accuracy is high, quantification is accurate, the application range is wide, and the measurement efficiency is high.

Description

A kind of assay method of Electrical Power Line Parameter accuracy

Technical field:

The invention belongs to parameters of electric power system identification technique field, relate to the assay method that a kind of data error affects Electrical Power Line Parameter accuracy, particularly a kind of method measuring power circuit identified parameters and depart from exact value under PMU (synchronous phasor measurement unit) data produce error condition.

Background technology:

The accuracy of uniform transmission circuit Equivalent Circuit Parameter and electric power system tide analysis, state estimation, localization of fault, relay protection is adjusted, transient state is directly related with application functions such as dynamic stability calculating, along with the development of WAMS in electric system and the widespread use of PMU, the effective way of actual value of getting parms from actual measurement PMU data identification model parameters of electric power system, actual measurement PMU data can provide voltage phasor, effective value/the amplitude of electric current phasor and phase angle, there is higher precision, under the voltage phasor and electric current phasor known case of uniform transmission line two ends a certain moment PMU data, the parameter of transmission line π type equivalent circuit can be picked out.

The accuracy of transmission line identified parameters is subject to the impact of the PMU quality of data, and PMU quality of data instability has the reason of many aspects: one is occur in electric system that the fault such as sub-synchronous oscillation, low-frequency oscillation causes surveyed data can not reflect the normal operational condition of system; Two is that error appears in the links such as measurement mutual inductor, digital sample, Fourier transform, digital filtering in DATA REASONING and processing links, makes the data for parameter identification be different from real data.PMU data error causes the linear electrical parameter of institute's identification to depart from exact value, and state estimation, tidal current analysis, line loss calculation etc. are not matched with actual operating state, to analysis, the control generation adverse influence of electric system.If make the deviation of line parameter circuit value control within certain numerical value scope, will the PMU quality of data for parameter identification be claimed, thus quantitative relationship between Water demand PMU data error and institute's identified parameters deviation.

Summary of the invention:

The object of the invention is to the shortcoming overcoming prior art existence, seek the assay method that a kind of data error affects the accuracy of power transmission lines parameter, for voltage and current phasor effective value measurement error, phase angle measurement error in PMU data, provide rational data error index, the impact of data error on Electrical Power Line Parameter accuracy is shown, to obtain quantitative measurement result with sensitivity table.

To achieve these goals, the present invention first determines its impact on PMU data sensitive degree according to the parameter of power transmission lines equivalent circuit, then to judge that line parameter circuit value provides the computing method of parameter accuracy to the susceptibility of PMU data error, specifically comprise the following steps:

(1) select power transmission lines to be the π type Type Equivalent Circuit Model of uniform transmission line, determine admittance to be identified and impedance parameter, wherein admittance to be in parallelly made up of with holding susceptance, impedance by resistance and reactance in series;

(2) survey based on PMU voltage phasor, electric current phasor by the input end in uniform transmission line a certain moment and output terminal, according to Kirchhoff's current law (KCL), voltage law, calculate the admittance and impedance parameter exact value of determining this moment corresponding respectively;

(3) in the process determining admittance and impedance parameter exact value, first voltage and current phasor is expressed as the array configuration of real part and imaginary part, wherein real part is that voltage, current effective value and phase angle cosine are long-pending, and imaginary part is that voltage, current effective value and phase angle are sinusoidal long-pending; Carry out conversion and the abbreviation of admittance and impedance parameter again, be divided into real part and imaginary part, susceptance corresponds respectively to real part and the imaginary part of admittance with holding, resistance and reactance correspond respectively to real part and the imaginary part of impedance;

(4) susceptance, accommodation, resistance and reactance four line parameter circuit values are made to be the function of input terminal voltage effective value, input terminal voltage phase angle, input end current effective value, input end current phase angle, output end voltage effective value, output end voltage phase angle, output end current effective value and output end current phase angle eight variablees, ask partial derivative to obtain absolute sensitivity to eight variablees respectively described four line parameter circuit values, and then be converted into relative sensitivity;

(5) PMU data error is made to be presented as effective value error and phase angle error, effective value or phase angle error incremental representation, increment and the relative sensitivity product corresponding to parameter are the variable quantity that effective value or phase angle error cause parameter drift-out exact value, thus determine that data error affects the quantitative relationship of power transmission lines parameter accuracy.

The present invention is in implementation process, when there is error in certain voltage phasor or electric current phasor, there is the increment caused because of error in its effective value and phase angle, effective value increment and phase angle increment cause parameter drift-out amount sum respectively then for phasor errors causes the variable quantity of parameter drift-out exact value simultaneously; If when error appears in multiple voltage phasor, electric current phasor, each phasor increment causes parameter drift-out amount sum to be then the variable quantity that multiple phasor errors causes parameter drift-out exact value respectively.

The present invention compared with prior art, by the quantitative relation between data error increment and parameter drift-out amount, judges the quantitative effect degree of each data to Electrical Power Line Parameter, improves and surveys the PMU quality of data and the accuracy rate improving parameter identification; Its design concept is reliable, and judge that craft science is strong, accuracy is high, and quantitatively accurately, applied range, measuring and calculating efficiency is high.

Accompanying drawing illustrates:

Fig. 1 is uniform transmission line two ends each phasor positive dirction principle schematic that the embodiment of the present invention relates to.

Fig. 2 is the uniform transmission line π type equivalent circuit principle schematic that the embodiment of the present invention relates to.

Fig. 3 is the π type equivalent circuit principle schematic that parameter real part that the embodiment of the present invention relates to separates with imaginary part.

Embodiment:

Below by embodiment, also the invention will be further described by reference to the accompanying drawings.

Embodiment:

The concrete case that the present embodiment judges as an actual measurement, during enforcement, first to uniform transmission line parameter identification, Fig. 1 enters terminal voltage phasor for marking uniform transmission circuit electric current phasor with output end voltage phasor electric current phasor the schematic diagram of positive dirction; In electric system, uniform transmission line often uses the π type equivalent circuit shown in Fig. 2, and wherein Y is admittance, Z is impedance, and uniform transmission line model following formula represents:

$\left\{\begin{array}{c}{\stackrel{\·}{I}}_1+{\stackrel{\·}{I}}_2=\frac{Y}{2}({\stackrel{\·}{U}}_1+{\stackrel{\·}{U}}_2)\\ ({\stackrel{\·}{I}}_1-\frac{Y}{2}{\stackrel{\·}{U}}_1)Z=({\stackrel{\·}{U}}_1-{\stackrel{\·}{U}}_2)\end{array}\right.$

To the binary once linear equation of above-mentioned complex variable, by a certain moment point directly obtain the exact solution of parameter

$\left\{\begin{array}{c}Y=\frac{2({\stackrel{\·}{I}}_1+{\stackrel{\·}{I}}_2)}{{\stackrel{\·}{U}}_2+{\stackrel{\·}{U}}_1}\\ Z=\frac{({\stackrel{\·}{U}}_1-{\stackrel{\·}{U}}_2)({\stackrel{\·}{U}}_2+{\stackrel{\·}{U}}_1)}{{\stackrel{\·}{I}}_1{\stackrel{\·}{U}}_2-{\stackrel{\·}{I}}_2{\stackrel{\·}{U}}_1}\end{array}\right.$

Because actual measurement PMU data directly provide transmission line both end voltage phasor and electric current phasor, above parameter expression also referred to as the parameter identification value by PMU data gained.

Voltage phasor, electric current phasor effective value U, I and phase angle table θ of the present embodiment show, in phasor approach, the real part of phasor is that effective value and phase angle cosine are long-pending, and imaginary part is that effective value and phase angle are sinusoidal long-pending, and corresponding expression formula is

$\left\{\begin{array}{c}{\stackrel{\·}{U}}_1=U_1\cos {\mathrm{\θ}}_{u1}+j{U}_1\sin {\mathrm{\θ}}_{u1}\\ {\stackrel{\·}{I}}_1=I_1\cos {\mathrm{\θ}}_{i1}+j{I}_1\sin {\mathrm{\θ}}_{i1}\\ {\stackrel{\·}{U}}_2=U_2\cos {\mathrm{\θ}}_{u2}+j{U}_2\sin {\mathrm{\θ}}_{u2}\\ {\stackrel{\·}{I}}_2=I_2\cos {\mathrm{\θ}}_{i2}+j{I}_1\sin {\mathrm{\θ}}_{i2}\end{array}\right.$

The real part of parameter in the equivalent circuit of π shown in Fig. 2 is separated with imaginary part, Fig. 3 is the π equivalent circuit that parameter real part separates with imaginary part, in Fig. 3 susceptance G be admittance Y real part, hold B is the imaginary part of admittance Y, resistance R is impedance Z real part, reactance X is the imaginary part of impedance Z; The voltage phasor, the electric current phasor that separate real part and imaginary part are obtained for line translation of going forward side by side in admittance Y parameter identifier, abbreviation

$G+\mathrm{jB}=\frac{2[(I_1\cos {\mathrm{\θ}}_{i1}+I_2\cos {\mathrm{\θ}}_{i2})+j(I_1\sin {\mathrm{\θ}}_{i1}+I_2\sin {\mathrm{\θ}}_{i2})]}{(U_1\cos {\mathrm{\θ}}_{u1}+U_2\cos {\mathrm{\θ}}_{u2})+j(U_1\sin {\mathrm{\θ}}_{u1}+U_2\sin {\mathrm{\θ}}_{u2})}$

If

a＝U ₁cosθ _u1+U ₂cosθ _u2

b＝U ₁sinθ _u1+U ₂sinθ _u2

c＝I ₁cosθ _i1+I ₂cosθ _i2

d＝I ₁sinθ _i1+I ₂sinθ _i2

Then have

$G+\mathrm{jB}=\frac{2(c+\mathrm{jd})}{a+\mathrm{jb}}\text{=}\frac{2(\mathrm{ca}+\mathrm{db})}{a^2+b^2}+j\frac{2(\mathrm{da}-\mathrm{cb})}{a^2+b^2};$

In electric system, susceptance G is approximately 0, and its size is not generally considered, and holds B

$B=\frac{2(\mathrm{da}-\mathrm{cb})}{a^2+b^2},$

If x is unique variable, then when respectively amount is constant for other, variable x change will cause B to change, and available partial derivative represents the sensitivity that B changes for x

$\frac{\∂B}{\∂x}=\frac{2(a^2+b^2)(d\frac{\∂a}{\∂x}+a\frac{\∂d}{\∂x}-b\frac{\∂c}{\∂x}-c\frac{\∂b}{\∂x})-4(\mathrm{da}-\mathrm{cb})(a\frac{\∂a}{\∂x}+b\frac{\∂b}{\∂x})}{{(a^2+b^2)}^2}$

Then B is for input terminal voltage effective value U ₁the sensitivity of change is

$\frac{\∂B}{\∂U_1}=\frac{2(a^2+b^2)(d\cos {\mathrm{\θ}}_{u1}-c{\sin \mathrm{\θ}}_{u1})-4(\mathrm{da}-\mathrm{cb})(a\cos {\mathrm{\θ}}_{u1}+b{\sin \mathrm{\θ}}_{u1})}{{(a^2+b^2)}^2}$

If B and U ₁represent with relative variation, corresponding relative sensitivity is

$\frac{U_1}{B}\frac{\∂B}{\∂U_1}=\frac{U_1(d\cos {\mathrm{\θ}}_{u1}-c\sin {\mathrm{\θ}}_{u1})}{(\mathrm{da}-\mathrm{cb})}-\frac{2U_1(a\cos {\mathrm{\θ}}_{u1}+b\sin {\mathrm{\θ}}_{u1})}{(a^2+b^2)}$

B is for θ _u1the sensitivity of change is

$\frac{\∂B}{\∂{\mathrm{\θ}}_{u1}}=\frac{-2(a^2+b^2)(d{U}_1\sin {\mathrm{\θ}}_{u1}+c{U}_1\cos {\mathrm{\θ}}_{u1})+4(\mathrm{da}-\mathrm{cb})(a{U}_1\sin {\mathrm{\θ}}_{u1}-b{U}_1\cos {\mathrm{\θ}}_{u1})}{{(a^2+b^2)}^2}$

If B relative variation represents, θ _u1change actual change amount rad represents, corresponding relative sensitivity is

$\frac{1}{B}\frac{\∂B}{\∂{\mathrm{\θ}}_{u1}}=\frac{-U_1(d\sin {\mathrm{\θ}}_{u1}+c\cos {\mathrm{\θ}}_{u1})}{(\mathrm{da}-\mathrm{cb})}+\frac{2U_1(a\sin {\mathrm{\θ}}_{u1}-b\cos {\mathrm{\θ}}_{u1})}{(a^2+b^2)}$

B is to variable U ₂, θ _u2, I ₁, θ _i1, I ₂, θ _i2the computing method of relative sensitivity are with similar above.

Again the voltage phasor of separately real part and imaginary part, electric current phasor are obtained for line translation of going forward side by side in impedance Z parameter identification value, abbreviation

$R+\mathrm{jX}=\frac{({U_1}^2\cos 2{\mathrm{\θ}}_{u1}-{U_2}^2\cos 2{\mathrm{\θ}}_{u2})+({U_1}^2\sin 2{\mathrm{\θ}}_{u1}-{U_2}^2\sin 2{\mathrm{\θ}}_{u2})}{[I_1{U}_2\cos ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})-I_2{U}_1\cos ({\mathrm{\θ}}_{i2}+{\mathrm{\θ}}_{u1})]+j[I_1{U}_2\sin ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})-I_2{U}_1\sin ({\mathrm{\θ}}_{i2}+{\mathrm{\θ}}_{u1})]}$

If

e＝I ₁U ₂cos(θ _i1+θ _u2)-I ₂U ₁cos(θ _i2+θ _u1)

f＝I ₁U ₂sin(θ _i1+θ _u2)-I ₂U ₁sin(θ _i2+θ _u1)

g＝U ₁ ²cos2θ _u1-U ₂ ²cos2θ _u2

h＝U ₁ ²sin2θ _u1-U ₂ ²sin2θ _u2

Then have

$R+\mathrm{jX}=\frac{g+\mathrm{jh}}{e+\mathrm{jf}}=\frac{\mathrm{ge}+\mathrm{hf}}{e^2+f^2}+j\frac{\mathrm{he}-\mathrm{gf}}{e^2+f^2}$

Resistance R:

$R=\frac{\mathrm{ge}+\mathrm{hf}}{e^2+f^2}$

If x is unique variable

$\frac{\∂R}{\∂x}=\frac{(e^2+f^2)(e\frac{\∂g}{\∂x}+g\frac{\∂e}{\∂x}+h\frac{\∂f}{\∂x}+f\frac{\∂h}{\∂x})-2(\mathrm{ge}+\mathrm{hf})(e\frac{\∂e}{\∂x}+f\frac{\∂f}{\∂x})}{{(e^2+f^2)}^2}$

R is for I ₁the relative sensitivity of change is

$\begin{array}{c}\frac{I_1}{R}\frac{\∂R}{\∂I_1}=\frac{I_1{U}_2[g\cos ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})+h\sin ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})]}{\mathrm{ge}+\mathrm{hf}}\\ -\frac{2I_1{U}_2[e\cos ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})+f\sin ({\mathrm{\θ}}_{i1}+{\mathrm{\θ}}_{u2})]}{e^2+f^2}\end{array}$

R is for θ _i1the relative sensitivity of change is

$\begin{array}{c}\frac{1}{R}\frac{\∂R}{\∂{\mathrm{\θ}}_{i1}}=\frac{I_1{U}_2[-g\sin ({\mathrm{\θ}}_{u2}+{\mathrm{\θ}}_{i1})+h\cos ({\mathrm{\θ}}_{u2}+{\mathrm{\θ}}_{i1})]}{\mathrm{ge}+\mathrm{fh}}\\ -\frac{2U_2{I}_1[f\cos ({\mathrm{\θ}}_{u2}+{\mathrm{\θ}}_{i1})-e\sin ({\mathrm{\θ}}_{u2}+{\mathrm{\θ}}_{i1})]}{e^2+f^2}\end{array}$

R is to variable U ₁, θ _u1, U ₂, θ _u2, I ₂, θ _i2the computing method of relative sensitivity are with similar above.

Reactance X:

$X=\frac{\mathrm{he}-\mathrm{gf}}{e^2+f^2}$

Reactance X is to variable U ₁, θ _u1, U ₂, θ _u2, I ₁, θ _i1, I ₂, θ _i2the computing method of relative sensitivity and resistance R to variable U ₁, θ _u1, U ₂, θ _u2, I ₁, θ _i1, I ₂, θ _i2the computing method of relative sensitivity similar.

The present embodiment is got North China Power Telecommunication Network ten thousand (entirely) and is carried out parameter identification along the actual measurement PMU data in (justice) line a certain moment, and above-mentioned moment actual measurement PMU data are: perfectly sound side voltage phasor effective value U ₁for 301.5kV, phase angle theta _u1for 1.867rad, electric current phasor effective value I ₁for 1133A, phase angle theta _i1for 1.946rad; Side, Shunyi voltage phasor effective value U ₂for 297.3kV, phase angle theta _u2for 1.680rad, electric current phasor effective value I ₂for 1130A, phase angle theta _i2for-1.437rad; Pick out and corresponding to above-mentioned moment uniform transmission line parameter be: hold B=9.128 × 10 ^-4s; Resistance R=6.178 Ω; Reactance X=49.02 Ω; Again according to the relative sensitivity formula of deriving, calculate ten thousand fair line above-mentioned moment parameter B, R, X respectively to perfectly sound side voltage effective value U above ₁, voltage phase angle θ _u1, current effective value I ₁, current phase angle θ _i1sensitivity, result of calculation is in table 1; To side, Shunyi voltage effective value U ₂, voltage phase angle θ _u2, current effective value I ₂, current phase angle θ _i2sensitivity, result of calculation is in table 2;

Table 1: parameter is to the sensitivity of perfectly sound survey voltage, electric current

Table 2: parameter surveys the sensitivity of voltage, electric current to Shunyi

Can know that the effective value and phase angle error of finding out voltage, electric current are to the influence degree of parametric results accuracy according to the numerical value in table 1, table 2, hold B large by the impact of current phase angle, impact by other amount is all smaller, resistance R is all large by the impact of voltage effective value and phase angle, current phase angle, but it is less by the impact of current effective value, reactance X is large by the impact of voltage phase angle, and the impact by other amount is all smaller.

If the present embodiment given parameters allows the scope departing from exact value, can directly calculate the error that PMU data allow; If allow parameter B change ± 5%, work as U ₁during independent change, then its variation error absolute value should be less than 9.968%; Work as θ _i2during independent change, then its variation error absolute value is less than 0.01207rad; If U ₁error Absolute Value during independent change reaches 9.968%, and the change of parameter resistance R then reaches ± and 402.0%, can obtain thus surveying the quantitative relationship that PMU data error causes identified parameters deviation.

Claims (2)

1. the assay method of an Electrical Power Line Parameter accuracy, it is characterized in that first determining its impact on PMU data sensitive degree according to the parameter of power transmission lines equivalent circuit, then to judge that line parameter circuit value provides the computing method of parameter accuracy to the susceptibility of PMU data error, specifically comprise the following steps:

(1) select power transmission lines to be the π type Type Equivalent Circuit Model of uniform transmission line, determine admittance to be identified and impedance parameter, wherein admittance to be in parallelly made up of with holding susceptance, impedance by resistance and reactance in series;

(2) survey based on PMU voltage phasor, electric current phasor by the input end in uniform transmission line a certain moment and output terminal, according to Kirchhoff's current law (KCL), voltage law, calculate the admittance and impedance parameter exact value of determining this moment corresponding respectively;

(3) in the process determining admittance and impedance parameter exact value, first voltage and current phasor is expressed as the array configuration of real part and imaginary part, wherein real part is that voltage, current effective value and phase angle cosine are long-pending, and imaginary part is that voltage, current effective value and phase angle are sinusoidal long-pending; Carry out conversion and the abbreviation of admittance and impedance parameter again, be divided into real part and imaginary part, susceptance corresponds respectively to real part and the imaginary part of admittance with holding, resistance and reactance correspond respectively to real part and the imaginary part of impedance;

(4) susceptance, accommodation, resistance and reactance four line parameter circuit values are made to be the function of input terminal voltage effective value, input terminal voltage phase angle, input end current effective value, input end current phase angle, output end voltage effective value, output end voltage phase angle, output end current effective value and output end current phase angle eight variablees, ask partial derivative to obtain absolute sensitivity to eight variablees respectively described four line parameter circuit values, and then be converted into relative sensitivity;

(5) PMU data error is made to be presented as effective value error and phase angle error, effective value or phase angle error incremental representation, increment and the relative sensitivity product corresponding to parameter are the variable quantity that effective value or phase angle error cause parameter drift-out exact value, thus determine that data error affects the quantitative relationship of power transmission lines parameter accuracy.

2. the assay method of Electrical Power Line Parameter accuracy according to claim 1, when it is characterized in that error appears in a voltage phasor or electric current phasor, there is the increment caused because of error in its effective value and phase angle, effective value increment and phase angle increment cause parameter drift-out amount sum respectively then for phasor errors causes the variable quantity of parameter drift-out exact value simultaneously; If when error appears in multiple voltage phasor, electric current phasor, each phasor increment causes parameter drift-out amount sum to be then the variable quantity that multiple phasor errors causes parameter drift-out exact value respectively.