JP7133442B2 - Lightning current waveform estimation method and lightning current waveform estimation device - Google Patents

Description

The present invention relates to a lightning current waveform estimation method and a lightning current waveform estimation device based on measured values of a magnetic field or electric field radiated by a lightning strike.

Conventionally, lightning strikes have caused damage to electric power facilities, and even now that lightning damage countermeasures for transmission and distribution lines have progressed, lightning strikes still account for the largest proportion of the causes of accidents. In addition, as lightning damage countermeasures have progressed, the cost performance of further countermeasures has declined compared to the past, and it is required to predict the effect obtained by adding countermeasures with high accuracy.

The frequency of lightning strikes and their current waveforms greatly affect the occurrence of power facility accidents due to lightning strikes. Therefore, if detailed information about these is obtained, it will contribute to the prediction of the effect of lightning damage countermeasures. Of these, the frequency of lightning strikes is observed by the lightning localization system (LLS). The LLS is disclosed in Patent Document 1, for example, and measures electromagnetic waves generated by a lightning strike using a plurality of sensors, and analyzes the measured electromagnetic waves to calculate the time and position of the lightning strike.

JP 2003-294824 A

However, such LLS cannot provide detailed information on the current waveform of a lightning strike. Other attempts have been made to estimate the peak value and charge amount of the lightning current based on the electromagnetic waves produced by the lightning strike, but there has been no method for estimating the lightning current waveform itself with high accuracy.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a highly accurate lightning current waveform estimation method and a lightning current waveform estimation device based on measured values of the radiated magnetic field or radiated electric field due to lightning strikes. .

The invention of claim 1 of the present invention is a method for estimating a lightning current waveform from discrete data of measured values of the magnetic field waveform of the radiated magnetic field or the electric field waveform of the radiated electric field due to a lightning strike, wherein the lightning current waveform is calculated by Maxwell's equations. In the formula for calculating the value at a distant observation point of the magnetic or electric field waveform generated from , obtaining a basic formula for obtaining a lightning current waveform including an integral term in the height direction, and in the basic formula, proceeding with integration sequentially in the height direction from the leading data of the discrete data of the measured magnetic field waveform or electric field waveform. , to obtain a lightning current waveform. The calculation formula itself based on Maxwell's equations is a known one and corresponds to a general geometric model that assumes a lightning strike on a flat ground. It can also be rephrased as a formula for calculating the value of the electric field waveform at a distant observation point. However, the equation for the value of the magnetic field waveform and the equation for the value of the electric field waveform are different equations, and the basic equations obtained from each are also different. The direction of integration is determined by the direction in which the lightning current wave propagates. In other words, if it is assumed that the current wave propagates upward from the ground surface to the thundercloud, the direction of integration is also upward from the ground surface, Assuming that the current wave propagates downward from the thundercloud to the ground surface, the direction of integration is also downward from the height of the thundercloud. The basic equation differs depending on whether the direction of integration, ie, the direction of propagation of the lightning current wave is upward or downward.

The invention of claim 2 of the present invention is characterized in that, in the basic equation, the discrete data is integrated over the entire height range of the thundercloud from the ground surface in the height direction. That is, when the current wave propagates upward, the integration is performed from the ground surface to the height of the thundercloud, and when the current wave propagates downward, the integration is performed from the height of the thundercloud to the ground surface.

According to a third aspect of the present invention, in the basic equation, the discrete data is integrated in the height direction over a partial range of the height of the thundercloud from the ground surface.

ただし、Iは電流、Xは磁界または電界、tは時間、K1、K2およびK3は所定の係数を表す。式（１）は、積分の回数を１回とした場合の上記基本式を変形して得られるものである。基本式は、放射磁界の式の場合と放射電界の式の場合、また落雷の電流波の伝搬方向が上向きの場合と下向きの場合とでそれぞれ式が異なるが、何れの式からも式（１）が得られる。ただし、K1、K2およびK3の値は、それぞれの場合で異なる。 According to a fourth aspect of the present invention, the method for estimating a lightning current waveform according to the third aspect includes a circuit based on equation (1) obtained from the basic equation when integrating only once in the height direction. Characterized by

where I is current, X is magnetic or electric field, t is time, and K1, K2 and K3 are given coefficients. Equation (1) is obtained by modifying the above basic equation when the number of times of integration is one. The basic equation differs depending on whether the radiated magnetic field or the radiated electric field is used, and whether the lightning current wave propagates upward or downward. ) is obtained. However, the values of K1, K2 and K3 are different in each case.

According to the invention of claim 1 of the present invention, by obtaining a basic equation by transforming the equation based on Maxwell's equations assuming discrete data, the basic equation can be used to obtain the magnetic field waveform or The lightning current waveform can be estimated with high accuracy from the discrete data of the measured electric field waveform of the radiated electric field.

According to the invention of claim 2 of the present invention, the lightning strike current waveform can be estimated with higher accuracy by integrating the height range of the discharge path through which the current wave actually propagates.

According to the invention of claim 3 of the present invention, since the number of repetitions of calculation is reduced by limiting the range of integration to only a part, it is possible to prevent calculation results from diverging due to accumulation of calculation errors. , and the calculation result, that is, the estimation result of the lightning current waveform, can be obtained with sufficient accuracy.

According to the invention of claim 4 of the present invention, the lightning current waveform is output simply by inputting the measured magnetic field waveform or electric field waveform to this device, so that the lightning current waveform can be easily estimated. can.

FIG. 2 is an explanatory diagram showing a geometric model of a lightning strike, which is a premise of the lightning current waveform estimation method of the present invention; It is a conceptual diagram of a lightning discharge model, (a) shows a case where a current wave propagates upward from the ground surface, and (b) shows a case where a current wave propagates downward from a thundercloud. 4 is a graph showing a simulated lightning current waveform used for evaluating a lightning current waveform estimation method; 4 is a graph showing estimation results of lightning current waveforms using simulated lightning current waveforms, where (a) is a TL model, (b) is an MTLE model, and (c) is a MTLD model. 7 is a graph showing estimation results of lightning current waveforms using actually measured lightning current waveforms. 4 is a graph showing estimation results of a lightning strike current waveform using an actually measured magnetic field waveform, where (a) is the TL model, (b) is the MTLE model, and (c) is the MTLD model. 1 is a block diagram showing a circuit included in a lightning current waveform estimating device of the present invention; FIG.

Specific contents of the lightning current waveform estimating method and the lightning current waveform estimating device of the present invention will be described below. The method of the present invention estimates the current waveform of a lightning strike based on the magnetic field waveform or the electric field waveform of the lightning strike. It is based on the magnetic field waveform, and shows the case where the propagation direction of the current wave is upward.

FIG. 1 shows a geometric model of a lightning strike, which is the premise of the lightning current waveform estimation method. Here, it is assumed that a flat land with no difference in height is assumed, and a lightning discharge path DP (Discharge Path) through which a lightning current wave propagates extends vertically from the ground surface to a thunder cloud TC (Thunder Cloud) in the sky. Let O be the lower end of the lightning discharge path DP (thunder strike position on the ground surface), point O be the origin, the upward direction be the positive z direction, and h be the height of the thundercloud TC. In addition, let point P be a distant observation point sufficiently distant from point O, D (D>>h) be the distance between OP, point P and a point at height z on lightning discharge path DP (height of dz Let R be the distance between At this time, let θ be the angle (the angle formed above the line segment) formed by the line segment connecting the point P and the point of height z on the lightning discharge path DP and the lightning discharge path in the vertical direction. Further, an electric image EI (Electric Image) is assumed at the position of the vertically downward height -z of the point O. FIG. The distance between the point P and the point at height -z (electrical image EI) is also R. Let I(z,t) be the current propagating through the lightning discharge path DP, v be the propagation speed of the current, and H(R,t) be the magnetic field waveform of the radiated magnetic field due to the lightning strike observed at the point P. where t is time.

ただし、cは光速である。この式は、垂直アンテナを流れる電流から発生する磁界波形の遠方の観測点における値の計算式とも言い換えられる。 Based on these assumptions, the following formula based on Maxwell's equations is used as a calculation formula for the value at the distant observation point P of the magnetic field waveform H(R,t) generated from the lightning current I(z,t). (2) is known.

where c is the speed of light. This formula can also be rephrased as a formula for calculating the value of the magnetic field waveform generated from the current flowing through the vertical antenna at a distant observation point.

A lightning strike model used for evaluating the lightning current waveform estimation method of the present invention will also be mentioned. As a known lightning strike model, there is a transmission line model, the conceptual diagram of which is shown in FIG. Fig. 2(a) shows a case in which a lightning current wave propagates upward from the ground surface to a thundercloud TC at a velocity v, and Fig. 2(b) shows a case in which a lightning current wave propagates downward from the thundercloud TC to the ground surface at a velocity v This is the case when propagating with v. Here, it is assumed that the direction is upward as shown in FIG. 2(a). This transmission line model can be divided into a TL model (Transmission Line model), an MTLE model (Modified TL model with exponential current decay), and an MTLD model (Modified TL model with current distortion) depending on whether or not current attenuation and distortion are considered. being classified. The transmission line model used here is a model that assumes a return lightning stroke, and the TL model that is the basis of these models is a model in which current propagates through a lightning discharge path without attenuation or distortion. The MTLE model is a TL model that considers the exponential attenuation of the current on the lightning discharge path. Furthermore, the MTLD model is a model that considers distortion in addition to linear attenuation. These three models express the current wave attenuation characteristics on the lightning discharge path with different functions.

Equation (2) is a formula for obtaining the magnetic field waveform from the current of lightning strike, so it is the basis for obtaining the lightning current waveform (discrete data at the same time interval) from the discrete data of the measured magnetic field waveform by transforming it. get the formula

ただし、離散データに基づくので、dtは所定の数値（秒数）である。また、Rはzの関数R(z)である。さらに、sinθ=D/Rである。 For that purpose, first, in the integral term (second integral term) for obtaining the radiation component of the magnetic field on the right side of Equation (2), the time partial differential term of the current is replaced by two continuous discrete current waveforms Replace with the formula of the difference obtained from the difference of the data. As a result, the formula (2) is transformed into the following formula (3).

However, since it is based on discrete data, dt is a predetermined numerical value (number of seconds). Also, R is a function R(z) of z. Furthermore, sin θ=D/R.

Subsequently, the equation (3) is transformed into the following equation (4).

Here, of the two integral terms on the right side of equation (4), the earliest portion of the discrete data of the current waveform (corresponding to the current waveform data at the lower end of the lightning discharge path), that is, the first integral term By separating the portion corresponding to the integration from 0 to dz of from the integral term, the equation (4) is transformed into the following equation (5).

Then, the equation (5) is transformed into the following equation (6).

This formula (6) is the basic formula for determining the lightning current waveform. The lightning current waveform I(0,t－R _dz /c) can be obtained from the magnetic field waveform H(R,t) by Equation (6). You have to search in order. In practice, waveforms are obtained sequentially from the top data of the discrete data of the magnetic field waveform. Equation (6) has current terms on both the left and right sides, but the values used in the current terms on the right side are all determined prior to the current calculation step. That is, the current waveform data used when proceeding with the sequential integration in the height z direction uses current waveform data earlier in time as it goes up. In this way, the discrete data of the measured magnetic field waveform are sequentially integrated in the height direction over the entire range from the surface of the ground to the height of the thundercloud to obtain the lightning current waveform.

In this way, according to the equation (6), a feedback type calculation is performed in which the calculated current values are sequentially used in subsequent calculation steps. Hereinafter, such a calculation method will be referred to as an FB method (Feed Back method), and in particular, a calculation method according to Equation (6) will be referred to as an SFB method (Standard FB method).

The details of the results of estimating the lightning current waveform by this SFB method will be described later. When the current waveform was calculated, it was confirmed that the calculation result diverged. This is because the current value obtained earlier in the calculation process is used in subsequent calculations, so calculation errors accumulate and gradually increase.

式（７）は、式（６）における積分の範囲の上限を、hからn・dzに替えたものであり、n回積分することを表している（ただし、h>n・dzである）。式（８）は、ＭＦＢ法における雷撃モデルの一般式である。伝送線路型モデルを想定しており、G(z)は減衰項であって、ＴＬモデルにおいてはG(z)=1、ＭＴＬＥモデルにおいてはG(z)=exp(－z/λ)（λは電流の指数関数的な減衰を表すパラメータ）、ＭＴＬＤモデルにおいてはG(z)=1－z/H_p（H_pは電流の線形的な減衰を表すパラメータ）となる。また、P(z,t)は変歪項であって、減衰項であるG(z)からは切り離せるものとしており、ＭＴＬＤモデルにおいてのみ規定されている。式（９）は、積分をn回でやめた計算値（式（７））を、積分を全ての範囲（0からhまで）で行った場合に得られる値に近づけるための振幅補正式である。積分をn回でやめるということは、積分を全ての範囲で行った場合に比べて、雷放電路を短く想定することになる。その分、電流の振幅が大きな値で算出されるので、それを補正するものである。 Therefore, as a calculation method different from the SFB method, in the above basic formula (Equation (6)), the integration in the height z direction is not performed over the entire range from the ground surface to the height h of the thundercloud, but from the ground surface to A possible method is to perform within a portion of the height h of the thundercloud, that is, to stop up to n (n is an integer equal to or greater than 1) upwards from the ground surface. This calculation method is called an MFB method (Modified FB method). The following equations (7) to (9) express this in equations.

Equation (7) is obtained by replacing the upper limit of the range of integration in Equation (6) from h to n dz, and represents n times of integration (where h>n dz). . Formula (8) is a general formula for a lightning strike model in the MFB method. A transmission line model is assumed, and G(z) is an attenuation term, G(z)=1 in the TL model and G(z)=exp(-z/λ)(λ is a parameter representing exponential decay of current), and in the MTLD model G(z)=1-z/H _p (H _p is a parameter representing linear decay of current). Also, P(z,t) is a distortion term, which is separable from G(z), which is an attenuation term, and is specified only in the MTLD model. Equation (9) is an amplitude correction equation for bringing the calculated value (equation (7)) after n times of integration closer to the value obtained when integration is performed over the entire range (from 0 to h). . Stopping the integration after n times assumes a shorter lightning discharge path than when the integration is performed over the entire range. Since the amplitude of the current is calculated as a large value by that amount, it is corrected.

これはすなわち、高さ方向の積分を１回だけにしたものである。この場合、積分項はなくなり、式はより単純な形になる。式（１０）を補正する式は、式（９）と同じである（ただし、右辺の分子は積分ではなくなる）。 Furthermore, the following formula (10) is obtained by setting n=1 in formula (7).

This means that the integration in the height direction is performed only once. In this case there is no integral term and the equation is in a simpler form. The equation for correcting equation (10) is the same as equation (9) (except that the numerator on the right side is no longer an integral).

Next, the lightning current waveform estimation method (SFB method and MFB method) of the present invention will be evaluated using simulated lightning current waveforms. The evaluation method is to calculate the magnetic field waveform from the simulated lightning current waveform by Equation (2), and estimate and calculate the lightning current waveform from the magnetic field waveform by the estimation method of the present invention. The simulated lightning current waveform is shown in Fig. 3. It is a triangular wave with a crest value of 100 kA, a crest length of 10 μs, and a current value of 0 at 150 μs from the maximum crest point, and is discrete data at intervals of 0.1 μs. This current waveform is referred to as tI below.

FIG. 4 shows the result of calculation using the simulated lightning current waveform shown in FIG. 3 by the above SFB method (equation (6)) and MFB method (n=1, equation (10)). A TL model, an MTLE model, and an MTLD model were used as the lightning model. In addition, the parameter values used for the calculation are the height of the lightning discharge path h = 1000 m, the distance between the lightning strike position and the observation point D = 10000 m, and the propagation velocity of the lightning current wave v = 100 m/μs, which are common to all models. .

Figures 4(a) to (c) show the calculation results when using the TL model, MTLE model, and MTLD model, respectively. A current waveform Icht1 obtained by the SFB method using the magnetic field waveforms cHt, and a current waveform Icht2 obtained by the MFB method using cHt are shown. For cHt in each graph, attenuation etc. according to the characteristics of the model used appear. Current waveforms (Icht1, Icht2) estimated from these cHts match tI on the graph in any model.

More specifically, the current waveform Icht1 estimated and calculated by the SFB method completely matched the simulated lightning strike current waveform tI. However, when we calculated the height h of the lightning discharge path, the distance D between the lightning strike position and the observation point, and the propagation velocity v of the lightning current wave, there were cases where the calculation results diverged. (For all non-divergence cases, Icht1 was perfectly consistent with tI).

On the other hand, the current waveform Icht2 estimated and calculated by the MFB method was slightly different from the simulated lightning strike current waveform tI, but could not be identified on the graph of FIG. As in the case of the SFB method, when h, D, and v were calculated using various combinations of values, the most stable estimation results were obtained when the number of times of integration in the height direction was n = 1. did it. Also, even if n is larger than 1, the reproducibility of the current waveform does not necessarily increase.

Next, the lightning current waveform estimation method (SFB method and MFB method) of the present invention will be evaluated using actually measured lightning current waveforms. The evaluation method is to calculate the magnetic field waveform from the actually measured lightning current waveform by formula (2), estimate and calculate the lightning current waveform from the magnetic field waveform by the estimation method of the present invention, and from the actually measured magnetic field waveform, A lightning strike current waveform is estimated and calculated by the estimation method of the invention. In the following, this actually measured lightning current waveform is referred to as mI.

First, using the magnetic field waveform cH calculated from mI by Equation (2), the results calculated by the above SFB method (Equation (6)) and MFB method (n = 1, Equation (10)) are shown in FIG. show. A TL model was used as the lightning strike model. The parameter values used in the calculation (height h of the lightning discharge path, distance D between the lightning strike position and the observation point) were determined to be the values that cH had the closest shape to the measured magnetic field waveform mH.

The graph of FIG. 5 shows the current waveform Ich1 obtained by the SFB method from the actually measured lightning strike current waveforms mI and cH, and the current waveform Ich2 obtained by the MFB method from cH. Current waveforms (Ich1, Ich2) estimated from cH match mI on the graph.

More specifically, the current waveform Ich1 by the SFB method, including examples other than those shown in the graph of FIG. 5, could perfectly reproduce mI in all cases where the calculation results did not diverge. In addition, the current waveform Ich2 by the MFB method was able to reproduce mI in a nearly perfect form without divergence of the calculation results in all cases. From this result, the SFB method has the highest accuracy except when the calculation result diverges, and the MFB method can reliably obtain the calculation result without divergence, and has almost the same accuracy as the SFB method. It was confirmed that

Further, FIG. 6 shows the result of calculation by the above MFB method (n=1, formula (10)) using the actually measured magnetic field waveform mH. A TL model, an MTLE model, and an MTLD model were used as the lightning model. In addition, the parameter values used in the calculation (height h of the lightning discharge path, distance D between the lightning strike position and the observation point) were determined to be the values that determined that cH had the shape closest to mH, as in the case of Fig. 5. did.

Figures 6(a) to (c) show the calculation results when using the TL model, MTLE model, and MTLD model, respectively. The current waveform Imh2 obtained by the MFB method is shown from the current waveform Ich2 and mH obtained. Among them, the current waveform Ich2 estimated from cH matches mI on the graph in any model. The results confirmed by using the simulated lightning current waveform were also confirmed by using the measured waveform.

On the other hand, the current waveform Imh2 estimated from the measured magnetic field waveform mH has an error in the current portion where the fluctuation is relatively small before and after the pulse, and the error is particularly large after the pulse. This is thought to be due to the fact that the gain of the low-frequency component was reduced due to the frequency characteristics of the system in which mH was measured. However, this error is not a problem in practice, and it can be said that the lightning current waveform was reproduced with sufficiently high accuracy from the actually measured magnetic field waveform.

As described above, according to the SFB method of the lightning current waveform estimation method of the present invention, the calculation formula (formula (1)) based on Maxwell's equations is transformed into the basic formula (formula (6)) assuming discrete data. With this basic formula, the lightning current waveform can be estimated from the discrete data of the measured magnetic field waveform of the magnetic field emitted by the lightning strike. At this time, since the integration is performed for the height range of the discharge path through which the current wave actually propagates, the estimation result with the highest accuracy can be obtained if the current wave does not diverge.

In addition, in the SFB method, integration over the entire range from the ground surface to the actual height of the thundercloud may cause calculation errors to accumulate and cause the calculation results to diverge. , it is possible to prevent the divergence of the calculation results by integrating in a part of the height of the thundercloud from the ground surface, that is, by stopping the integration halfway (n times) in the height direction. , the calculation result, that is, the estimation result of the lightning current waveform, is obtained with sufficient accuracy. In particular, by setting n=1, the basic formula has no integral term (repeated calculation), so it can be calculated more easily. result is obtained.

Next, a method (group of equations) for estimating the lightning current waveform based on the magnetic field waveform caused by a lightning strike, assuming that the current wave propagates downward from the thundercloud (the case shown in FIG. 2(b)). indicates The desired current waveform is a waveform corresponding to the lightning current at the lowest end of the lightning discharge path. In the following, each formula corresponds to the formula when it is assumed that the current wave propagates upward. That is, equation (11) corresponds to equation (6) (SFB method), equations (12) to (14) correspond to equations (7) to (9) (MFB method), and equation (15) is (10) (when n=1 in the MFB method). And the unexplained letters are the same as in the corresponding formulas above.

The basic idea for the downward propagating current wave is the same as for the upward propagating current wave described above. However, the function G(z) that defines the attenuation of the current on the lightning discharge path must be set so that the current at the bottom end of the lightning discharge path does not become zero.

The method for estimating the lightning current waveform in the case where the current wave propagates downward, which is based on the magnetic field waveform caused by the lightning strike, has the same effect as the method for estimating the current wave in the case where the current wave propagates upward. It is.

Next, a method (group of equations) for estimating a lightning current waveform, which is based on the electric field waveform due to lightning and is assumed to propagate upward from the ground surface, will be described. Since the relational expression between the lightning current and the associated electric field is similar to that of the magnetic field, the same concept as that based on the above magnetic field waveform can be applied to the estimation of the lightning current waveform.

First, in the geometric model of a lightning strike shown in Fig. 1, at point P, instead of the magnetic field waveform H(R,t) of the radiated magnetic field due to the lightning strike, the electric field waveform E(R,t) of the radiated electric field due to the lightning strike is observed. shall be Based on these premises, the following equation based on Maxwell's equations is used as a calculation formula for the value at the distant observation point P of the electric field waveform E(R,t) generated from the lightning current I(z,t). (16) is known.

Then, based on the same idea as the above equation (2) was transformed into equation (6) via equations (3) to (5), equation (16) is transformed into the following equation (17) .

This formula (17) is based on the electric field waveform due to lightning, and is the basic formula (SFB method) for determining the lightning current waveform when it is assumed that the current wave propagates upward from the ground surface.

In addition, in the above basic formula (formula (17)), the formula (MFB method) when the integration in the height z direction is stopped up to n (n is an integer of 1 or more) upward from the ground surface is as follows. Equation (18).

なお、ＭＦＢ法（式（１８）および式（１９））における補正式は、上記の式（８）および式（９）と同じである。 Furthermore, the following formula (19) is obtained by setting n=1 in formula (18).

The correction formulas in the MFB method (formulas (18) and (19)) are the same as the above formulas (8) and (9).

Next, a method (group of equations) for estimating the lightning current waveform based on the electric field waveform due to lightning, assuming that the current wave propagates downward from the thundercloud, will be described. The desired current waveform is a waveform corresponding to the lightning current at the lowest end of the lightning discharge path. In the following, each formula corresponds to the formula when it is assumed that the current wave propagates upward. That is, equation (20) corresponds to equation (17) (SFB method), equation (21) corresponds to equation (18) (MFB method), and equation (22) corresponds to equation (19) (MFB modulus n=1). And the unexplained letters are the same as in the corresponding formulas above.

In this way, the method of estimating the lightning current waveform based on the electric field waveform of a lightning strike when the current wave propagates upward and downward is the same as the estimation method based on the magnetic field waveform described above. It is intended to exhibit the action and effect of.

Further, a lightning current waveform estimating device used for actually performing estimation based on the lightning current waveform estimating method of the present invention will be described below. This estimation device can be applied in any case, regardless of whether the estimation method is based on a magnetic field waveform or an electric field waveform, and whether the current wave propagation direction of a lightning strike is upward or downward. Description will be made on the assumption that the estimation method is based on the magnetic field waveform and the propagation direction of the current wave is upward.

さらに、式（２３）において、係数を置き換えて簡略化すると、以下の式（２４）に変形される。ただし、dz=v・dtである。

式（２４）は、上記の式（１）と同じ形であるが、式（１）における磁界または電界X(t)を、磁界H(t)としたものである。そして、この場合のK1、K2およびK3の値は、以下の式（２５）のとおりとなる。ただし、R=R_dz≒Dである。

In formula (10) when n=1 in the MFB method, the lightning current to be measured is assumed to be the lightning current on the ground surface, which is the lower end of the lightning discharge path, so R _{dz ≈D} . Also, since it is not necessary to consider the time delay until the electromagnetic wave reaches the antenna, the equation (10) is transformed into the following equation (23).

Furthermore, if the coefficients are replaced in the equation (23) for simplification, the equation (23) is transformed into the following equation (24). However, dz=v·dt.

Equation (24) has the same form as Equation (1) above, but replaces the magnetic field or electric field X(t) in Equation (1) with the magnetic field H(t). The values of K1, K2, and K3 in this case are given by the following equation (25). However, R=R _{dz ≈D} .

A block diagram of this equation (24) is shown in FIG. A circuit configured based on this block diagram receives a magnetic field waveform signal due to a measured lightning strike, and reproduces and outputs a lightning current waveform signal. Therefore, simply by inputting a measured magnetic field waveform into a device having this circuit, a lightning current waveform is output, so that the lightning current waveform can be easily estimated.

Here is an example of estimation. A TL model was used as the lightning strike model. When the distance between the lightning strike position and the observation point is D = 10000m, the propagation velocity of the lightning current wave is v = 150m/μs, and the sampling interval is dt = 0.1μs, the values of each coefficient in Equation (24) are K1 ≒ 199246259, K2 ≈0.0006283, K3≈5.003×10^-9. Furthermore, assuming that the height of the lightning discharge path is h = 1000m, the amplitude correction value obtained by Equation (9) is approximately 0.015 times. value is obtained. Each of these numerical values is an example, but in an actual circuit, the values of K1, K2 and K3 may be determined according to each parameter of observation equipment and the like, or the values may be variable.

As described above, this estimation device can be applied in any case, regardless of whether the estimation method is based on the magnetic field waveform or the electric field waveform, and whether the current wave propagation direction of a lightning strike is upward or downward. Yes, and in either case the form of equation (24) is the same. However, when based on the electric field waveform, the magnetic field H is replaced with the electric field E. Also, in each case the values of K1, K2 and K3 are different.

If the estimation method is based on the magnetic field waveform and the current wave propagation direction is downward, the values of K1, K2 and K3 are given by the above equation (25). However, it is R= _Rh .

When the estimation method is based on the electric field waveform and the propagation direction of the current wave is upward, the values of K1, K2 and K3 are given by the following equation (26). However, R=R _{dz ≈D} .

If the estimation method is based on the electric field waveform and the current wave propagation direction is downward, the values of K1, K2 and K3 are given by equation (26) above. However, it is R= _Rh .

The circuit based on the above block diagram may be hardware configured by combining circuit elements, or may be software that operates on a personal computer, PLC, or the like.

A more detailed description will now be given of the case where the circuit is software running on a personal computer. In this case, the computer serves as the lightning current waveform estimation device, and the computer executes the lightning current waveform estimation program.

A computer consists of an input device such as a keyboard and a mouse, an output device such as a display, a CPU that executes program instructions in order, and a storage device that stores programs, data necessary for executing programs, calculation results, etc. It is a standard component.

The following description assumes that the method for estimating the lightning current waveform is based on the magnetic field waveform of a lightning strike and that the current wave propagates upward. Only different. When the lightning current waveform estimation program is executed by a computer, the computer functions as various means (measured value input means, calculation means, result output means), and the measured value input means enters the measured value input step according to commands from the CPU. is executed, the calculation means executes the calculation step, and the result output means executes the result output step, thereby estimating the lightning current waveform.

When this program is executed, first the measured value input means functions and the measured value input step is executed. In the measured value input step, an input of a measured value of the magnetic field waveform of the radiation magnetic field caused by the lightning strike is accepted. At this time, the measured value is sampled at a predetermined interval dt, and the result is stored in a storage device. At the same time, input is also accepted for each parameter value (distance D between the lightning strike position and the observation point, propagation velocity v of the lightning current wave, etc., which are calculated by, for example, LLS) required for subsequent calculations. and save it to the storage device.

Next, the computing means functions to perform the computing steps. In the calculation step, equations (24) and (25) stored in the storage device, the measured value of the magnetic field waveform, and the values of other parameters (inputted in the measured value input step and according to the observation equipment etc. previously entered and stored in a storage device). Then, each value is substituted into the equation to calculate the current waveform.

Next, the result output means functions to execute the result output step. In the result output step, the current waveform calculated in the calculation step is output and stored in the storage device, and the current waveform is displayed in the form of a graph or the like on the output device as necessary. With that, the program ends.

This lightning current waveform estimation program may be automatically executed when lightning strikes, may be arbitrarily executed by the operator, or may be executed by another program or system. It may be executed based on the request of Further, this lightning current waveform estimation program may be executed as dedicated software, may be executed on general-purpose spreadsheet software, etc., or may be executed by another program or system. may be incorporated in

Furthermore, in the above calculation step, instead of the equations (24) and (25), the equations of the SFB method (equation (6), equation (11), equation (17), equation (20)), MFB method (Equation (7) to Equation (9), Equation (12) to Equation (14), Equation (18), Equation (21)) or the formula when n = 1 in the MFB method (Equation (10) , Equations (15), (19), and (22)), the lightning current waveform estimation method of the present invention may be executed by a personal computer or the like.

The present invention is not limited to the above embodiments, and can be modified as appropriate within the spirit of the invention. For example, the MFB method is not limited to the case of n=1, and integration may be performed multiple times. Even in that case, it is possible to suppress the divergence of the calculation results by reducing the number of repetitions of the calculation.

The lightning current waveform estimation method and lightning current waveform estimation device of the present invention can be applied to lightning damage to various facilities such as transmission lines, distribution lines, substations, wind power generation facilities, wireless towers, railways, and high structures such as buildings. It can be used for concrete examination of countermeasures.

Claims (4)

A method for estimating a lightning current waveform from discrete data of measured values of a magnetic field waveform of a radiated magnetic field or an electric field waveform of a radiated electric field due to a lightning strike, comprising:
In Maxwell's equations for calculating the value of the magnetic or electric field waveform generated by the lightning current at a distant observation point, the time partial derivative term of the current is replaced by the difference equation, and the integral term of the current Isolating the fast discrete data terms to obtain the basic formula for the lightning current waveform including the integral term for the height direction,
A method of estimating a lightning current waveform in the basic equation, wherein integration is performed sequentially in the height direction from the leading data of the discrete data of the measured magnetic field waveform or electric field waveform to determine the lightning current waveform. 2. The method of estimating a lightning current waveform according to claim 1, wherein in said basic equation, said discrete data is integrated in the height direction over the entire range of the height of the thundercloud from the surface of the ground. 2. The method for estimating a lightning current waveform according to claim 1, wherein in said basic equation, said discrete data is integrated in a height direction over a partial range of the height of the thundercloud from the ground surface. 4. A lightning current waveform estimation device according to claim 3, comprising a circuit based on formula (1) obtained from said basic formula in the case of integrating only once in the height direction.

where I is current, X is magnetic or electric field, t is time, and K1, K2 and K3 are given coefficients.

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