WO2012152055A1

WO2012152055A1 - Accurate waveform measuring method for lightning strike-induced malfunctions of electrical transmission line

Info

Publication number: WO2012152055A1
Application number: PCT/CN2012/000519
Authority: WO
Inventors: 刘民; 陈家宏; 姚金霞; 云玉新; 钱冠军; 谷山强
Original assignee: 山东电力研究院
Priority date: 2011-05-10
Filing date: 2012-04-16
Publication date: 2012-11-15
Also published as: CN102288932A; CN102288932B

Abstract

An accurate waveform measuring method for lightning strike-induced malfunctions of an electrical transmission line, comprising: using a self-integrating, flexible, nonmagnetic cored Rogowski coil (9) to sample and measure the electric current on an electricity transmission line, and designing an correction system for correcting measured values. Different from the traditional correction method of increasing inductance and some current correction methods of using hardware circuitry, the present method utilizes a certain software algorithm to enable the transfer function of the correction system. When acquiring the transfer function of the correction system, first a pulse current generator is used to simulate a square wave output; the Rogowski coil (9) and a shunt resistance are sampled and measured; the input and output of the correction system are acquired on the basis of the correction system backward-restoring the measuring system; the least square method is used to calculate the impulse response of the correction system; a Hankel matrix is used to calculate the order of the transfer function; finally, the least square method is used to identify and solve the coefficient of the transfer function.

Description

Accurate measurement method for lightning strike fault waveform of transmission line

Technical field

The invention relates to a method for measuring a current waveform of a transmission line, in particular to an accurate measurement method for a lightning strike fault waveform of a transmission line, which is mainly used for correcting a low frequency distortion problem when a self-integrating Rogowski coil measures a lightning strike fault current of a transmission line.

Background technique

High-voltage transmission systems are extremely vulnerable to lightning strikes due to their wide distribution and large geometrical dimensions. The data show that 80% of transmission line faults are lightning strike faults, and the lightning-damage fault parameters caused by lightning are measured and analyzed to analyze the characteristics of the transmission system. An important topic in the field.

As a non-contact current transformer, Rogowski coil is widely used in the measurement of high-current pulses. The Rogowski coil is uniformly wound by a thin wire on a non-ferromagnetic skeleton. The vertical conductor of the current-carrying conductor passes through the core. The magnetic induction induces a voltage proportional to the rate of change of current at the output of the coil, and the output voltage is integrated by the integrator.

In practical applications, there are two types of self-integrating circuits and external integrating circuits according to different measurement objects. Self-integrating Rogowski coils are suitable for measuring low-frequency pulse currents. External integral Rogowski coils are suitable for measuring high-frequency pulse currents. In the lightning fault detection of transmission lines, the self-integrating flexible coreless Rogowski coil is used to sample and measure the current on the transmission line, but the self-integrating Rogowski coil is difficult to meet the self-integration condition when measuring the low-frequency component of the lightning failure. There will be low-frequency distortion problems. How to correct low-frequency distortion becomes a key issue for accurate measurement of lightning strike faults on transmission lines. The traditional method of correcting the waveform distortion of the self-integrating Rogowski coil is achieved by increasing the number of turns of the coil to increase the self-inductance of the coil. However, this method will reduce the sensitivity of the coil and increase the capacitance and transmission time of the coil port. The resulting output current rise time increases and other measurement errors. Summary of the invention

The technical problem to be solved by the invention is mainly the low frequency distortion problem of the self-integrating Rogowski coil in the lightning strike fault measurement of the transmission line, and an accurate measurement method of the lightning strike fault waveform of the transmission line is provided, which corrects the measured value of the distortion to achieve The purpose of accurate measurement of lightning strike waveforms.

The technical solution adopted by the present invention to solve the technical problem thereof is:

An accurate measurement method for a lightning strike fault waveform of a transmission line, the steps of which are:

Step S-1, using a flexible non-magnetic core Rogowski coil self-integration circuit to sample and measure the current on the transmission line to determine the traveling wave current in the line in the line;

Step S-2: acquiring an input and output of the calibration system;

The Rogowski coil is loaded into the output circuit of the pulse current generator, and the parameters of the inrush current generator are adjusted to output a square wave pulse of 2 ms, and the voltage of the sampling resistor of the Rogowski self-integration loop and the shunt of the inrush current generator are simultaneously applied. The values are sampled and measured, and N sets of sample values are respectively obtained. The sampled value on the shunt is the input value of the measurement system, and the sampled value on the sampling resistor is the output value of the measurement system; the sampled data is converted into a standard current input and output measurement value. _Mq ( , y ₀ (k) , so it can be assumed that the input and output of the correction system are = , y(k) = u ₀ (k);

Step S-3: calculating an impulse response of the calibration system according to the input and output;

Set the calibration system to a linear, time-invariant system, then the system inputs "(0, weight function 0, theoretical output can be expressed as:

z(t) =

J k(t - )u{ )d

Adding all the noise effects to a single noise source, set to), then correct the actual output of the system to be; 0 = ^) + 1^) _; where, is the theoretical output of the system, V is the noise, Actual output;

Discrete sampling with the sampling period T yields = Tk(kT-iT)u(iT), let g(kT)^Tk(kT), and assumes that the system is stable and its settling time is limited, ie t>pT after that

y(kT)= g(kT-iT)u(iT)+v(kT)

i=kp where T is the sampling period, ^ΑΓ-ίΓ is the weight function after discretization, ι Τ) is the system input after discretization, Α:Γ-/Γ) is the impulse response of the system, ζ(^Γ For the discretized system theory output, ν(:Γ) is the discretized noise, :Γ) is the actual output of the discretized system, and ρ is the selected number of impulse response points;

Substituting the sample values obtained in step S-2 into the above equation, and eliminating the sampling period to obtain a system of equations consisting of Ν-ρ+1 equations, written in vector form is:

u(p) u(p-l) (0)

u(p+l) u(p) u(l)

JV u(N) u(Nl)

The above formula is Y=UG+V, and the error between the theoretical output value and the actual output value is V=Y-UG;

Where u(i) is the system input sample value, g(i) is the system's impulse response, v(i) is the noise, y(i) is the actual output sample value of the system, and p is the selected impulse response point, N For the number of data collected on the system input and output, the sampling period is eliminated; The impulse response sequence G is obtained by the least squares method: the set error index is

p+m

J= v =V ^T V = (Y- UGf (Y - UG) = YY ^T - G ^T U ^T Y -Y ^T UG + G ^T U ^U U ^T UG i=m

Deviate J from G and let the result be zero, and find a set of G to make the error index J the smallest,

-2J Y+2LflG^0

Thus the least squares estimate of the impulse response G = (ifir ¹ ) υ ^τ γ;

Step S-4: determining the order n of the transfer function by using the Hankel matrix method;

Step S-5, using the least square method to obtain the coefficients Ai={ai, a ₂ , . . . , a„} ^T and B={b _b b ₂ , . . . , b _n } ^{T of the} transfer function from the impulse response of the system.

In the step S-1, the method for determining the traveling wave current is: ignoring the port capacitance, using the formula

At t (A+ ) "A) ^", ignoring the voltage drop across the resistor, the above equation is simplified to ^ ₂ = ^, by measuring the voltage across the sampling resistor, the traveling wave current in the line can be obtained; The inductance and resistance of the coil itself are respectively the sampling resistance, the current to be measured is the current in the coil circuit, M is the mutual inductance between the coil and the power transmission line, and n is the number of turns of the coil.

In the step S-4, when determining the order n of the transfer function, the pulse transfer function of the correction system is set as:

Using the impulse response sequence G={g(l), g(2), '", g(p)} ^T determined in step S-3

Hankel matrix,

g(k) g(k+l) g(k+/-l),

g(k+l) g(k+2) g(k+/)

H{l,k) = g(k+/-l) g(k+/) g(k+2/-2). Where 1 is the order of the Hankel matrix; k is the sequence number of the first impulse response selected in the Hankel matrix, selected between 1 and p-1+2; where 1 is the order of the Hankel matrix, k is The sequence number of the first impulse response selected in the Hankel matrix, p is the number of points of the impulse response, and g (i) is the system impulse response;

According to the relationship between the impulse response function and the transfer function, at l ^ n, rank[H(l, k) ]=n, for l ^n+l, theoretically the value of the matrix determinant should be zero, in practical applications. , due to the noise error, the value of the matrix determinant will not be actually zero, but will be significantly reduced; first calculate the average of each order Hankel matrix determinant, then

After calculating the ratio of the mean value, => L, when it is observed that the start is significantly reduced, and A is significantly increased, it can be determined. The value of 1 at this time is the order n of the transfer function of the correction system; or another type is used. For a more direct determination method, the value of A is calculated, and the value corresponding to the first maximum value of A is equal to the order n of the correction system transfer function. Where p is the selected number of impulse response points, ίί, , ₊₁ is the average of the Hankel matrix determinant, and D is the ratio of the mean of the Hankel matrix determinant.

In the step S-5, the method for obtaining the coefficient of the transfer function is:

The transfer function of the system is:

The pulse transfer function, g(k) is the number of times and from 0

To n, from n+1 to p can be combined

When p>2n, consider the error, set the error to ^, according to z_ "the same number of coefficients are equal, get two sets of equations, written in vector form is

The above two can be abbreviated as

Use the least squares estimate to find the coefficient A, = {ai,a ₂ ,..., a _n }':

Error ε: G, A- G ₂ , the set error index is ε ^τ ε = A ₁ ^T G ₁ ^T G ₁ A -AG^G/G.Ai+G^, J is differentiated from A, and the result is obtained Zero, get a set of coefficient columns..., a _n } ^{T to} make J the smallest, find the coefficient A^CG/G 'G, ^ ; The coefficient to be obtained AF{ _ai , a ₂ ,..., a _n } ^{T is} substituted into B=A ₂ G ₃ to obtain a coefficient B={b _1} b ₂ , ..., b„} ^T .

The present invention designs a calibration system that inputs the measured values of the self-integrating Rogowski coil into the calibration system. A high-precision measurement that approximates the original input current can be obtained at its output. Such a correction system is essentially an inverse system of the original measurement system, the input value of which is the output value of the measurement system, and the output value is approximately equal to the input value of the measurement system, so that the measurement part and the correction part together form an ideal Proportional link, restore the lightning strike waveform with zero distortion as much as possible.

In view of the fact that the current hardware integration circuit compensates for the voltage neglected in the self-integration model, the correction scheme is too complicated. A correction system using software algorithm is proposed: According to the correction system, the original measurement system is reversed. Restore this feature by measuring the self-integration

The input and output values of the Rogowski coil indirectly obtain the input and output of the correction system; knowing the input and output of a system, the system simulation method is used to realize the approximate simulation of a system transfer function.

The transfer function of the correction system is mainly composed of the following steps: the square wave pulse is simulated by the pulse current generator, and the output of the sampling resistor in the shunt and the self-integrating Rogowski coil measurement system is sampled and measured, thereby obtaining the correction system indirectly. Input and output; use the input and output to calculate the impulse response of the correction system by least squares method; use the least squares identification to transform the impulse response into the transfer function of the system, wherein the order of the transfer function is obtained by the Hankel matrix method.

The invention has the beneficial effects of avoiding the problem of easy saturation, low sensitivity and high current rise time caused by increasing the number of turns of the coil or adding the iron core to increase the inductance, thereby reducing the low frequency distortion caused by the low frequency distortion. Some methods of correcting by using a hardware integration circuit have the advantages that the measurement circuit is simple and easy to implement.

DRAWINGS

Figure 1 is a schematic block diagram of the design of the entire measurement method.

Figure 2 is an equivalent circuit diagram of a Rogowski coil.

Figure 3 is a circuit schematic diagram of a simulation experiment using a pulse current generator. In the figure, 1 is the sampling resistor, 2 is the equivalent port capacitance of the Rogowski coil 3 is the equivalent resistance of the Rogowski coil, 4 is the self-inductance of the Rogowski coil, 5 is the mutual inductance of the ideal Rogowski coil, and 6 is the discharge ball gap. 7 is the total equivalent inductance of the discharge loop, 8 is the total equivalent capacitance of the discharge loop, 9 is the Rogowski coil, 10 is the sampling resistor, 11 is the shunt, 12 is the charging power supply, 13 is the step-up transformer, 14 is the silicon Heap, 15 protection resistors, 16 is the main capacitor.

detailed description

The invention will be further described below in conjunction with the drawings and embodiments.

As shown in FIG. 1, the method for measuring the current waveform of a transmission line according to the present invention has five main components:

Step S-1, using a flexible non-magnetic core Rogowski coil self-integration circuit to sample and measure the current on the transmission line, as shown in FIG. 3, respectively, the inductance and resistance of the coil itself, A is a sampling resistance, and is set as the current to be measured. , for the current in the coil loop, regardless of the effect of the port capacitance

M§ =^

At ) at ) " ^ ", ignore the voltage drop across the resistor, the above equation is simplified to ^ ^"Z' ₂ = ' ₂ , by measuring the voltage across the sampling resistor, you can find the traveling wave current in the line; Where n is the number of turns of the coil;

The experimental measurement and analysis of the traveling wave current of the transmission line is carried out. The self-integrating Rogowski coil has a good high-frequency response to the simulated lightning current standard wave, but the problem of low-frequency distortion is widespread.

Step S-2: Acquire the input and output of the correction system.

When using software algorithms to simulate the transfer function of a system, there is no real hardware circuit, and the input and output of the calibration system cannot be directly measured. However, according to the correction system, the original measurement system is inversely restored. The characteristics of the calibration system can be approximated by measuring the input and output of the measurement system consisting of the original self-integrating Rogowski coils.

In order to ensure that the correction system has an average correction effect on various types of lightning strike waveforms, a square wave input is used to obtain the input and output of the correction system. As shown in Fig. 2, the Rogowski coil is first loaded into the output circuit of the pulse current generator, and the parameters of the inrush current generator are adjusted to output a square wave pulse of 2 ms. At the same time, the sampling resistance and the inrush current of the Rogowski self-integration loop occur. The voltage value on the shunt of the device is sampled and measured, and N sets of sampled values are respectively obtained. The sampled value on the shunt is the input value of the measuring system, and the sampled value on the sampling resistor is the output value of the measuring system. Convert sampled data to standard current input and output measurements. ( , y ₀ (k) , so it can be assumed that the input and output of the correction system are _w (A = y. (A:), y(k) = u ₀ (k) o Step S- 3: Calculate according to input and output Correct the impulse response of the system.

Assuming the correction system is a linear, time-invariant system, the system inputs "(0, weight function W0, theoretical output ζ(ί) can be expressed as:

z(t)= kit-X)u( )dX

J

Equivalently add all noise effects to a single noise source, set to ^ (0, then the actual output of the calibration system is xo+); use the sampling period τ for discrete sampling to obtain z(t7 (^ r i'r), let g (kT) = Tk(kT), and assume that the system is stable and its settling time is finite, ie after t>pT ^)«0, then: z{kT)= X _g (kT-iTXiT)

i=kp y(kT)= χ _g {kT-iT)u(iT)+v(kT) Where T is the sampling period, z^T) is the discretized system input, A tr- _Z T) is the discretized weight function, g(^r-ir) is the system's impulse response, and ζ(ΑΓ) is the discrete The theoretical output of the system, _y (kT) is the actual output of the discretized system, the noise is white noise, P is the number of selected impulse response points; in order to obtain P impulse response values G={g(0), g(2 ), -, g(p)} ^T , the N sets of data obtained in step S-2 can be substituted into the above equation to obtain a system of N-p+1 equations, which is written as a vector form:

The impulse response sequence G is obtained by the least squares method: the set error index is

Differentiating J from G and letting the result be zero, we can find a set of G-order error indicators J is the smallest,

-2LfY+2l/W=0

Thus, the least squares estimate of the impulse response G = (U ^T lT) lJ ^T Y is obtained. (The impulse response sequence G is an intermediate variable, which is an unknown quantity in step s-3, and is obtained by matrix calculation, expressed as G=(UTU-1)UTY _{; it} has been calculated in step s-4, and can be expressed Is the general representation of the matrix G={g(l),g(2), ,g(p)}T)

Step S-4: Determine the order n of the transfer function using the Hankel matrix method.

Assume that the pulse transfer function of the calibration system is:

Constructing a Hankel matrix using the impulse response sequence G={g(l), g(2), '", g(p)} ^T determined in step S-3,

Where 1 is the order of the Hankel matrix, k is the sequence number of the first impulse response selected in the Hankel matrix, which determines which impulse response values constitute the Hankel matrix, which can range from 1 to p-1 +2 Choose between.

According to the relationship between the impulse response function and the transfer function, when there is l^n, rank[H(l,k)]=n, for l^n+l, the value of the matrix determinant should be zero in practical application. Because of the noise error, the value of the matrix determinant is not actually zero, but it is significantly reduced. First calculate the various orders of the Hankel moment, and then calculate the ratio of the average value to increase, you can determine

The value is the order n of the correction system transfer function; or another more direct decision method, the calculated value, the first maximum value corresponding to 1 value is equal to the order n of the correction system transfer function.

Step S-5, using the least squares method to obtain the coefficients of the transfer function from the impulse response of the system

··', a„} ^T -3⁄4 B={b], b ₂ , ···, b _n } ^T .

Because the transfer function of the system is:

The relationship between the pulse transfer function and the transfer function is

Will

0 expand, and follow _ζ -" from 0 to _η , from _η+1 to _ρ

Consolidate,

When p>2n, considering the error, according to the z-"the same number of coefficients are equal, we can get two groups, written in vector form is

1 0

«1 1 0 0 Si

1 0

^a n-\ ... IJ g _n J

1 0 0 0

. 】 1 0 0

; ; 1 0

The above two formulas can be abbreviated as G ^G^ e , B=A ₂ G ₃ , and then the least squares estimation is used to obtain the coefficient Ai={ai,a ₂ ,..., a„} ^T : error ε = dA- G ₂ , the set error index is J = ε ^τ ε = A ₁ ^T G ₁ ^T G ₁ A _{1 -} A ₁ ^T G ₁ ^{T -} G ₂ ^T G ₁ A ₁ + G ₂ ^T G ₂ , J differentiates ₁ and makes the result zero. It can be found to find a set of coefficient columns: {a:, a ₂ ,..., let J be the smallest.

Substituting the obtained coefficient···, aJ ^T into B=A ₂ G ₃ yields a coefficient B={b _b b ₂ , 〜, bJ ^T .

Claims

Claim

A method for accurately measuring a lightning strike fault waveform of a transmission line, characterized in that: the step is: Step S-1, using a flexible non-magnetic core Rogowski coil self-integration circuit to sample and measure the current on the transmission line, and determine the line Traveling wave current in the line;

Step S-2: obtaining the input and output of the correction system;

The Rogowski coil is loaded into the output circuit of the pulse current generator, and the parameters of the inrush current generator are adjusted to output a square wave pulse, and the voltage value of the sampling resistor of the Rogowski self-integration loop and the shunt of the inrush current generator is simultaneously performed. Sampling measurement, respectively obtain N sets of sample values, the sample value on the shunt is the input value of the measurement system, the sample value on the sampling resistor is the output value of the measurement system; convert the sampled data into a standard current input and output measurement value y _Q (k), it can be assumed that the input and output of the correction system are _W (A = y ₀ (k), y (k) = u ₀ (k);

Step S-3: calculating the impulse response of the calibration system according to the input and output;

Set the calibration system to a linear, time-invariant system, then the system inputs "(0, weight function 0, system theory output z (0 can be expressed as:

Appropriately add all noise effects to a single noise source, set to), then correct the actual output of the system as; ί) = ζ( )+τ (0 _; discrete sampling with sample period Τ yields Γ ( :Γ) = ^ 73⁄4: (Α:Γ- 7 (ζΤ), order

/=100

g(kT) = Tk(kT) , and assuming that the system is stable, its settling time is limited, that is, after t>pT, tX has:

y(kT) = χ _g (kT-iTMiT)+v(kT)

i=k-p Where τ is the sampling period, which is the discretized system input, which is the weight function after discretization, g( rr-zT) is the impulse response of the system, ζ^:Γ) is the theoretical output of the discretized system, _y (kT) For the discretized system actual output, the noise ^) is white noise, and Ρ is the selected number of impulse response points; the Ν group sample values obtained in step S-2 are substituted into the above equation to obtain the equations composed of Ν-p+1 equations. , after the sampling period is removed, written in vector form is - u(P) u(pl) (0)

u(p+l) u(p) (l)

That is, there is Y4JG+V, the error between the theoretical output value and the actual output value is V=Y-UG _;

The impulse response sequence is obtained by least squares method G: The set error index is

Λλ-πι

j = ^ _v f = v ^T V = (Y- UG) ^T (Y - UG) = YY ^T - G ^T U ^T Y - Y ^T UG + G ^T U ^U U ^T UG im

-2L/Y+2l/U3=0 to obtain the least squares estimate of the impulse response G= (UV ¹ ) U ^T Y _;

Step S-5, using the least squares method to obtain the coefficients {ai, a ₂ , ..., a _n } ^T and B = {bb ₂ , ···, b _n } ^{T of the} transfer function from the impulse response of the system.

The method for accurately measuring a lightning strike fault waveform of a power transmission line according to claim 1, wherein in the step S-1, the method for determining the traveling wave current is to use the principle of electromagnetic coupling of the Rogowski coil. ώ ^{¾ ¾,} ^ ά when (+) ", the voltage drop across the resistor is ignored, the equation reduces to = ^ ^^", by measuring the voltage across the sampling resistor, it is possible to obtain a traveling wave current lines;

Among them, the inductance and resistance of the coil itself, Μ is the mutual inductance between the coil and the power transmission line, Α is the sampling resistance, the current to be measured is the current in the coil circuit, and n is the number of turns of the coil.

The method for accurately measuring a lightning strike fault waveform of a power transmission line according to claim 1, wherein in the step S-4, the method for determining the order n of the transfer function is to calculate the average trend of the determinant of each order matrix. Determine n, set the pulse transfer function of the correction system to:

Using the impulse response sequence G determined in step S-3: {g(l), g(2), '", g(p)} ^Y

Hankel matrix,

( g(k) g(k+l) ... g(k+/-l),

g(k+l) g(k+2) ... g(k+/)

H{l,k) =

,g(k+/-l) g(k+/)

Where 1 is the order of the Hankel matrix, and k is the number of the first impulse response value selected in the Hankel matrix, selected between 1 and P-1+2;

Let n be the system transfer function order, according to the relationship between the impulse response function and the transfer function, at l^n, r _a nk[H(l,k)]=n, for 1 η+1, theoretically matrix determinant The value should be zero. In practical applications, the value of the matrix determinant will not be actually zero due to the noise error, but it will be significantly reduced. First, the average value of each order Hankel matrix determinant is calculated, p is the impulse response. Points, then The average value of the Hankel matrix determinant is ^ = det[H(/, )] , and then the average is calculated.

The ratio A =#", when it is observed that the start is significantly reduced, and A is significantly increased, it can be determined. The value of 1 at this time is the order η of the transfer function of the correction system; or another way of more direct judgment, Calculating the value of A, the first maximum value corresponding to D, is equal to the order I of the correction system transfer function.

The method for accurately measuring a lightning strike fault waveform of a power transmission line according to claim 1, wherein in the step S-5, the method for obtaining a coefficient of the transfer function is to calculate a coefficient of the transfer function by using a least square method.

Let the system's transfer function be:

The relationship between the system impulse response and the transfer function is H(z- '^Σ^^)^ , unfolded, and according to the number of times from 0 to n, from η+1

Consolidate,

When p>2n, considering the error, let the error be ε, according to ζ-"the same number of coefficients are equal, get two sets of equations, written in vector form is

a, 1 0 0

; ; 1 0

««. „- 1 ... 1

The above two vector equations can be abbreviated as

Then use the least squares estimate to find the coefficient A to produce { _ai , 3⁄4, -, a„} ^T :

The error ε = GA- G ₂ , the set error index is J = ε ^τ ε = A ₁ ^T G ₁ ^T G ₁ A _{1 -} A ₁ ^T G ₁ ^{T -} G ₂ ^T G ₁ A ₁ + G ₂ ^T G ₂ , the J pairs are differentiated and the result is zero, and a set of coefficient columns A^ia^,... is obtained, and J is minimized, and the coefficient A _{1 =} (GM ^ ^l G ; the coefficient to be obtained { , 3⁄4, · · ^·,} τ substituting B = A ₂ G ₃ to obtain the coefficient _{B = {b "b 2,} ~, b"} T.