JP2020079724A - Lightning current waveform estimation method and lightning current waveform estimation device - Google Patents

Abstract

To provide a highly accurate lightning current waveform estimation method and a lightning current waveform estimation device, based on measured values of a radiated magnetic field or a radiated electric field from a lightning strike.SOLUTION: The method of 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, includes the steps of: replacing a time partial differential term of a current with an expression of a difference in a calculation formula of a value at a distant observation point of the magnetic field waveform or the electric field waveform generated from a current of the lightning strike by the Maxwell's equation; separating a discrete data term that is the earliest in time from an integral term of the current to obtain a basic formula for calculating a lightning current waveform including the integral term in a height direction; and sequentially integrating in the height direction from beginning data of the discrete data of the measured magnetic field waveform or electric field waveform in the basic formula to obtain the lightning current waveform.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a lightning current waveform estimation method and a lightning current waveform estimation device based on a measured value of a radiation magnetic field or a radiation electric field due to a lightning strike.

  Conventionally, there has been an accident that damages electric power equipment due to lightning strikes, and even now that measures against lightning damage to transmission and distribution lines have advanced, lightning strikes still account for the largest proportion of accident causes. Further, due to the progress of such measures against lightning damage, the cost performance of further measures is lower than in the past, and it is required to highly accurately predict the effect obtained by adding the measures.

  The frequency of lightning strokes and their current waveforms greatly affect the occurrence of power equipment accidents due to lightning strikes. Therefore, if detailed information on these is obtained, it will contribute to the prediction of the effect of lightning damage countermeasures. Of these, the frequency of lightning strokes is observed by the lightning strike location system (LLS). The LLS is disclosed in, for example, Japanese Patent Laid-Open Publication No. 2004-242242, and electromagnetic waves generated by a lightning strike are measured by a plurality of sensors and analyzed to calculate the time and position of the lightning strike.

JP, 2003-294824, A

  However, such an LLS cannot obtain detailed information regarding the current waveform of a lightning strike. In addition, other attempts have been made to estimate the peak value of the lightning current and the charge amount based on the electromagnetic waves caused by lightning, but there has been no method for estimating the current waveform of lightning with high accuracy.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide a highly accurate lightning current waveform estimation method and a lightning current waveform estimation device based on a measured value of a radiation magnetic field or a radiation electric field due to a lightning strike. ..

  The invention of claim 1 of the present invention is a method of estimating a lightning current waveform from discrete data of measured values of a magnetic field waveform of a radiation magnetic field or a field waveform of a radiation electric field due to a lightning strike, the current of the lightning strike according to Maxwell's equation. In the calculation formula of the value at the distant observation point of the magnetic field waveform or the electric field waveform generated from, replace the time partial differential term of the current with the expression of the difference and separate the earliest discrete data term in time from the integral term of the current. , A basic formula for obtaining a lightning current waveform including an integral term in the height direction is obtained, and in the basic formula, the integration is sequentially performed in the height direction from the head data of the discrete data of the measured magnetic field waveform or electric field waveform. , It is characterized in that the lightning current waveform is obtained. Note that the calculation formula itself based on Maxwell's equation is a known one and corresponds to a general geometric model assuming a lightning strike on a flat surface, and "a magnetic field waveform generated from a current flowing through a vertical antenna or It is also referred to as a “calculation formula of a value at a distant observation point of an electric field waveform”. However, the equation for the value of the magnetic field waveform and the equation for the value of the electric field waveform are different, and the basic equations obtained from them are also different. Also, the direction of integration is determined by the direction in which the current wave of the lightning strike propagates, that is, assuming that the current wave propagates upward from the ground surface to the thundercloud, the direction of integration will also be upward from the ground surface, Assuming that the current wave propagates downward from the thundercloud to the surface of the earth, the direction of integration will also be downward from the height of the thundercloud. The basic formula is different depending on whether the direction of integration, that is, the direction of propagation of the current wave of a lightning strike is upward or downward.

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

  A third aspect of the present invention is characterized in that, in the basic formula, the discrete data is integrated in a partial range of a height of a thundercloud from a ground surface in a height direction.

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。 The invention according to claim 4 of the present invention comprises a circuit based on the equation (1) obtained from the basic equation in the case of integrating only once in the height direction in the method for estimating a lightning current waveform according to claim 3. Characterize.

Here, I is current, X is magnetic field or electric field, t is time, and K1, K2, and K3 are predetermined coefficients. Expression (1) is obtained by modifying the above basic expression when the number of times of integration is one. The basic formulas are different for the case of the radiated magnetic field and the formula of the radiated electric field, and for the case where the current direction of the lightning strike is upward and downward, respectively. ) Is obtained. However, the values of K1, K2 and K3 are different in each case.

  According to the first aspect of the present invention, a basic formula is obtained from a calculation formula based on Maxwell's equation by transforming the formula on the premise of discrete data. By this basic formula, a magnetic field waveform of a radiation magnetic field due to a lightning strike 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 second aspect of the present invention, the lightning current waveform can be estimated with higher accuracy by performing integration over the range of the height of the discharge path where the current wave actually propagates.

  According to the invention of claim 3 of the present invention, the number of iterations of the calculation is reduced by making only a part of the integration range, so that it is possible to prevent the calculation results from diverging due to the accumulation of calculation errors. Therefore, the calculation result, that is, the estimation result of the lightning current waveform is obtained with sufficient accuracy.

  According to the invention of claim 4 of the present invention, since the lightning current waveform is output only by inputting the measured magnetic field waveform or electric field waveform to this device, it is possible to easily estimate the lightning current waveform. it can.

It is explanatory drawing which shows the geometric model of the lightning strike used as the premise of the lightning current waveform estimation method of this invention. It is a conceptual diagram of a lightning discharge model, (a) shows the case where a current wave propagates upwards from the ground surface, (b) shows the case where a current wave propagates downwards from a thundercloud. It is a graph which shows the simulated lightning current waveform used for evaluation of the lightning current waveform estimation method. It is a graph which shows the estimation result of a lightning current waveform using a simulated lightning current waveform, (a) is a TL model, (b) is an MTLE model, (c) is a case where an MTLD model is used. It is a graph which shows the estimation result of the lightning current waveform using the measured lightning current waveform. It is a graph which shows the estimation result of the lightning current waveform using a measured magnetic field waveform, (a) is a TL model, (b) is an MTLE model, (c) is a case where an MTLD model is used. It is a block diagram showing the circuit with which the lightning current waveform estimation apparatus of this invention is equipped.

  The specific details of the method of estimating the current waveform of lightning current and the apparatus for estimating the current waveform of lightning current of the present invention will be described below. The method of the present invention is to estimate a lightning current waveform based on a magnetic field waveform or an electric field waveform due to a lightning strike, and there is a case where the current wave propagation direction is upward or downward in the lightning strike, but here, first, 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 a premise of the method of estimating the current waveform of a lightning strike. Here, it is assumed that there is no level difference in level ground, and a lightning discharge path DP (Discharge Path) through which a current wave of a lightning strike propagates extends vertically from the ground surface to a thunder cloud TC above. It is assumed that the lower end of the lightning discharge path DP (lightning strike position on the ground surface) is a point O, the point O is the origin, the upward direction is the positive z direction, and the height of the thundercloud TC is h. Further, an observation point far away from the point O is defined as a point P, a distance between OPs is D (D>>h), and a point of a height z on the lightning discharge path DP (a height of dz). R is the distance to the area having. At this time, the angle formed by the line segment connecting the point P and the point of height z on the lightning discharge path DP and the vertically oriented lightning discharge path (the angle formed above the line segment) is θ. Further, an electric image EI (Electric Image) is hypothesized at a position at a height −z in the vertically downward direction of the point O. The distance between the point P and the point of height -z (electrical image EI) is also R. The current propagating through the lightning discharge path DP is I(z,t), the current propagation velocity is v, and the magnetic field waveform of the radiation magnetic field due to the lightning strike observed at the point P is H(R,t). However, 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 such a premise, as a formula for calculating the value of the magnetic field waveform H(R,t) generated from the lightning current I(z,t) at the distant observation point P, the following formula based on Maxwell's equation is used. (2) is known.

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

  In addition, the lightning stroke model used for the evaluation of the method for estimating the lightning current waveform of the present invention will also be mentioned. As a known lightning stroke model, there is a transmission line type model, and its conceptual diagram is shown in FIG. 2(a) shows the case where the current wave of a lightning strike propagates upward from the ground surface to the thundercloud TC at a speed v, and FIG. 2(b) shows the current wave of a lightning strike downwards from the thundercloud TC to the ground surface. This is the case when propagating in v. Here, it is assumed that the case of FIG. This transmission line type model is classified 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 taken into consideration. being classified. The transmission line type model used here is a model assuming return stroke, and the TL model which is the source of them is a model in which a current propagates through a lightning discharge path without attenuation or distortion. Further, the MTLE model is a model in which the attenuation according to the exponential function of the current on the lightning discharge path is considered in the TL model. Furthermore, the MTLD model is a model that considers distortion in addition to linear damping. These three models represent the attenuation characteristics of the current wave on the lightning discharge path by different functions.

  Since the formula (2) is a formula for obtaining the magnetic field waveform from the current of the lightning strike, it is modified to obtain the basic waveform for obtaining the lightning current waveform (discrete data at the same time interval) from the discrete data of the measured magnetic field waveform. Get the expression.

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, the time partial differential term of the current in the integral term (second integral term) for obtaining the radiation component of the magnetic field on the right side of the equation (2) is set to two discrete discrete current waveforms. Replace with the formula of difference calculated from the difference of data. As a result, the equation (2) is transformed into the following equation (3).

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

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

Here, of the two integration terms on the right side of the equation (4), the temporally earliest part 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 integration term By separating the part corresponding to the integration from 0 to dz of the above from the integral term, the expression (4) is transformed into the following expression (5).

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

This equation (6) is the basic equation for obtaining the lightning current waveform. From equation (6), the current waveform I(0,t−R _dz /c) of the lightning strike is obtained from the magnetic field waveform H(R,t), but in the calculation, from the earliest part of the current waveform data in time. It is necessary to seek in order. Actually, the waveform is sequentially obtained from the leading data of the discrete data of the magnetic field waveform. In the equation (6), current terms exist on both the left side and the right side, but the values used for the current terms on the right side are all required before the calculation step at that time. That is, as the current waveform data used when progressively advancing the integration in the height z direction, the current waveform data that is temporally earlier is used as it goes upward. Thus, the discrete data of the measured magnetic field waveform is used to sequentially perform integration over the entire range from the ground surface to the height of the thundercloud in the height direction to obtain the lightning current waveform.

  As described above, according to the equation (6), it is possible to perform the feedback type calculation in which the obtained current value is sequentially used in the subsequent calculation steps. Hereinafter, such a calculation method is referred to as an FB method (Feed Back method), and particularly, a calculation method according to Expression (6) is referred to as an SFB method (Standard FB method).

  The details of the estimation result of the lightning current waveform by this SFB method will be described later, but under various conditions (height h of thundercloud, distance D from the strike position to the observation point, etc.) When the current waveform was calculated, it was confirmed that the calculation results diverged. This is because the current value previously obtained in the calculation process is used for the subsequent calculation, and therefore the calculation errors are accumulated 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 equation (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. A possible method is to do it within a part of the height h of the thundercloud, that is, to stop upward from the surface up to n (n is an integer of 1 or more) times. This calculation method is called the MFB method (Modified FB method). This is represented by the following equations (7) to (9).

Expression (7) is the upper limit of the range of integration in Expression (6) changed from h to n·dz, and represents integration n times (where h>n·dz). . Expression (8) is a general expression of the lightning stroke model in the MFB method. Assuming a transmission line model, G(z) is an attenuation term, G(z)=1 in the TL model and G(z)=exp(−z/λ) (λ in the MTLE model. Is a parameter representing an exponential decay of current), and G(z)=1−z/H _p (H _p is a parameter representing linear decay of current) in the MTLD model. Further, P(z,t) is a distortion term that can be separated from G(z), which is the attenuation term, and is defined only in the MTLD model. The formula (9) is an amplitude correction formula for making the calculated value (formula (7)) obtained by stopping the integration n times, close to the value obtained when the integration is performed in the entire range (0 to h). .. Stopping the integration in n times means that the lightning discharge path is assumed to be shorter than the case where the integration is performed in the entire range. The amplitude of the current is calculated to have a large value correspondingly, and this 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 expression (10) is the expression (7) with n=1.

That is, the integration in the height direction is performed only once. In this case, there is no integral term and the formula has a simpler form. The formula for correcting the formula (10) is the same as the formula (9) (however, the numerator on the right side is not an integral).

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

  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)). The TL model, MTLE model, and MTLD model were used as the lightning stroke model. The parameter values used in the calculation were the height of the lightning discharge path h = 1000 m, the distance D between the lightning position and the observation point D = 10000 m, the propagation velocity of the lightning current wave v = 100 m / μs, which was common to all models. ..

  FIGS. 4A to 4C show calculation results when the TL model, the MTLE model, and the MTLD model are used, and the graphs are calculated using the simulated lightning current waveforms tI and tI. The current waveform Icht1 obtained by the SFB method using the magnetic field waveforms cHt and cHt and the current waveform Icht2 obtained by the MFB method using the cHt are shown. The cHt of each graph shows the attenuation and the like according to the characteristics of the model used. The current waveforms (Icht1, Icht2) estimated from these cHt agree with 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 current waveform tI. However, when 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 were calculated as a combination of various values other than the above, the calculation results sometimes diverged. (In all cases where Icht1 did not diverge, Icht1 was exactly the same as tI).

  On the other hand, the current waveform Icht2 estimated and calculated by the MFB method has a slight difference from the simulated lightning current waveform tI, but is indistinguishable from the graph of FIG. Then, as in the case of the SFB method, when h, D, and v are calculated as a combination of various values, the most stable estimation result can be obtained when the number of integrations in the height direction is n=1. did it. Moreover, even if n is larger than 1, the reproducibility of the current waveform is not necessarily improved.

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

  First, FIG. 5 shows the results calculated by the SFB method (Equation (6)) and the MFB method (n=1, Equation (10)) using the magnetic field waveform cH calculated from mI by Equation (2). Show. The TL model was used as the lightning stroke model. The parameter values used for the calculation (height h of lightning discharge path, distance D between lightning strike position and observation point) were determined to be those in which cH had the shape closest to the measured magnetic field waveform mH.

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

  More specifically, including the examples other than those shown in the graph of FIG. 5, the current waveform Ich1 by the SFB method could completely reproduce mI in all cases where the calculation result did not diverge. Further, in all cases, the current waveform Ich2 obtained by the MFB method was able to reproduce mI in a nearly perfect form without diverging the calculation results. From this result, the SFB method has the highest accuracy except when the calculation result diverges, and the MFB method does not diverge the calculation result, and the result is surely obtained, and has the accuracy close to that of the SFB method. It was confirmed that

  Further, FIG. 6 shows the result calculated by the above MFB method (n=1, formula (10)) using the actually measured magnetic field waveform mH. The TL model, MTLE model, and MTLD model were used as the lightning stroke model. In addition, the parameter values (height h of the lightning discharge path, distance D between the lightning strike position and the observation point) used for the calculation are the same as in the case of FIG. did.

  FIGS. 6A to 6C show calculation results when using the TL model, the MTLE model, and the MTLD model, respectively, and each graph is obtained by the MFB method using the measured lightning current waveforms mI and cH. The current waveform Imh2 obtained by the MFB method from the current waveform Ich2 and mH is shown. Of these, the current waveform Ich2 estimated from cH matches mI on the graph in any model. The result confirmed using the simulated lightning current waveform was confirmed even when the measured waveform was used.

  On the other hand, in the current waveform Imh2 estimated from the actually measured magnetic field waveform mH, an error occurs in the current portion where the fluctuation before and after the pulse is relatively small, and particularly the error after the pulse is large. It is considered that this is because the gain of the low frequency component was reduced due to the frequency characteristic of the system that measured mH. However, this error is practically no problem, and it can be said that the lightning current waveform can be reproduced with sufficiently high accuracy from the measured magnetic field waveform.

  As described above, according to the SFB method of the method for estimating the lightning current waveform of the present invention, the basic equation (Equation (6)) is obtained by transforming the equation based on Maxwell's equation (Equation (1)) into an equation that assumes discrete data. By obtaining this, it is possible to estimate the lightning current waveform from the discrete data of the measured values of the magnetic field waveform of the radiated magnetic field due to the lightning strike. At this time, since the integration is performed for the range of the height of the discharge path in which the current wave actually propagates, the estimation result with the highest accuracy can be obtained if there is no divergence.

  Further, in the SFB method, there is a case where the calculation results are diverged due to accumulation of calculation errors by integrating over the entire range from the ground surface to the actual height of the thundercloud. However, the MFB method of the lightning current waveform estimation method of the present invention According to, it is possible to prevent the divergence of the calculation result by integrating in a part of the height of the thundercloud from the surface of the earth, that is, stopping the integration in the middle of the height direction (n times). 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 a form that does not have an integral term (repetitive calculation), so it is easier to calculate, and even in that case, divergence of the calculation result is prevented and sufficient accuracy is obtained. The result of is obtained.

Next, based on the magnetic field waveform due to lightning strike, the method of estimating the lightning strike current waveform (formula group) when the current wave is assumed to propagate downward from the thundercloud (the case shown in FIG. 2B) Indicates. The required current waveform is a waveform corresponding to the lightning strike current at the bottom end of the lightning discharge path. In the following, each equation corresponds to the equation when it is assumed that the above current wave propagates upward. That is, formula (11) corresponds to formula (6) (SFB method), formulas (12) to (14) correspond to formulas (7) to (9) (MFB method), and formula (15) is It corresponds to the equation (10) (when n=1 in the MFB method). And the unexplained characters are the same as in the corresponding formula above.

  The basic idea when the current wave propagates downward is the same as the case where the current wave propagates upward. However, the function G(z) that regulates the attenuation of the current on the lightning discharge path must be set so that the current at the lowest end of the lightning discharge path does not become zero.

  Then, the method of estimating the lightning current waveform when the current wave propagates downward, which is based on the magnetic field waveform due to the lightning strike, has the same effect as the estimation method when the current wave propagates upward. It is a thing.

  Next, based on the electric field waveform due to lightning strike, the method (formula group) of estimating the current waveform of lightning strike when the current wave is assumed to propagate upward from the ground surface is shown. Since the relational expression between the lightning current and the electric field associated therewith is similar to that of the magnetic field, the same idea as that based on the above-mentioned magnetic field waveform can be applied to the estimation of the lightning current waveform.

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

Then, according to the same idea that the above equation (2) is transformed into the equation (6) via the equations (3) to (5), the equation (16) is transformed into the following equation (17). ..

  This equation (17) is based on the electric field waveform due to a lightning strike, and is a basic equation (SFB method) for obtaining a lightning strike current waveform when it is assumed that a 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 upward n times (n is an integer of 1 or more) from the ground surface is as follows: It is the formula (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 equation (19) is the equation (18) with n=1.

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

Next, based on the electric field waveform due to a lightning strike, the method of estimating the current waveform of a lightning strike (formula group) when the current wave is assumed to propagate downward from the thundercloud is shown. The required current waveform is a waveform corresponding to the lightning strike current at the bottom end of the lightning discharge path. In the following, each equation corresponds to the equation when it is assumed that the above current wave propagates upward. That is, the equation (20) corresponds to the equation (17) (SFB method), the equation (21) corresponds to the equation (18) (MFB method), and the equation (22) corresponds to the equation (19) (MFB method). Mod n = 1). And the unexplained characters are the same as in the corresponding formula above.

  Thus, the method of estimating the lightning current waveform when it is based on the electric field waveform due to lightning and when the current wave propagates upward and downward is the same as the estimation method when it is based on the above-mentioned magnetic field waveform. The effect of is obtained.

  Further, hereinafter, a lightning strike current waveform estimating device used for actually performing estimation based on the lightning strike current waveform estimating method of the present invention will be described. 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 propagation direction of the current wave of the lightning strike is upward or downward, but here, Description will be made assuming 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 equation (10) when n=1 in the MFB method, the measured lightning current is assumed to be the lightning current on the surface of the ground, which is the lower end of the lightning discharge path, and thus can be set to R _{dz ≈D} . Further, 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).

Further, in Expression (23), when the coefficient is replaced and simplified, it is transformed into the following Expression (24). However, dz=v·dt.

The expression (24) has the same form as the above expression (1), but the magnetic field or electric field X(t) in the expression (1) is a magnetic field H(t). Then, the values of K1, K2, and K3 in this case are as in the following Expression (25). However, R=R _{dz ≈D} .

  A block diagram of this equation (24) is shown in FIG. The circuit configured based on this block diagram inputs the measured magnetic field waveform signal due to lightning strike and reproduces and outputs the lightning strike current waveform signal. Therefore, the lightning current waveform can be easily estimated because the lightning current waveform is output only by inputting the measured magnetic field waveform to the device provided with this circuit.

  Here, an example of estimation will be shown. The TL model was used as the lightning stroke model. If the distance D between the lightning 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 value of each coefficient in equation (24) is K1≒199246259,K2 ≈0.0006283, K3≈5.003×10^-9. Furthermore, assuming that the height of the lightning discharge path is h=1000 m, the amplitude correction value by equation (9) is about 0.015 times, and by multiplying I(t) of equation (24) by 0.015, the lightning current waveform can be estimated. The 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 set according to each parameter of the observation equipment or the like, or the values may be variable.

  As described above, this estimation device can be applied to any case regardless of whether the estimation method is based on the magnetic field waveform or the electric field waveform, and whether the current direction of the lightning strike is upward or downward. And, in any case, the form of formula (24) is the same. However, when based on the electric field waveform, the electric field E is used instead of the magnetic field H. Also, in each case, the values of K1, K2 and K3 are different.

When the estimation method is based on the magnetic field waveform and the propagation direction of the current wave is downward, the values of K1, K2, and K3 are as in the above equation (25). However, R=R _h .

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 as in the following Expression (26). However, R=R _{dz ≈D} .

When the estimation method is based on the electric field waveform and the propagation direction of the current wave is downward, the values of K1, K2, and K3 are as in the above equation (26). However, R=R _h .

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

  Here, the case where the circuit is software that operates in a personal computer will be described in more detail. In this case, the computer serves as a lightning current waveform estimation device, and the lightning current waveform estimation program is executed in the computer.

  The computer includes an input device such as a keyboard and a mouse, an output device such as a display, a CPU that sequentially executes program instructions, and a storage device that stores the program, data necessary for executing the program, calculation results, and the like. It is a standard component.

  In the following, it is assumed that the method of estimating the current waveform of a lightning strike is based on the magnetic field waveform due to a lightning strike and the current wave propagates upward, but in other cases, the equations and parameters are Only different. When the computer executes the lightning current waveform estimation program, the computer functions as various means (measurement value input means, calculation means, result output means), and the measurement value input means causes the measurement value input means to perform the measurement value input step. Then, the calculation means executes the calculation step, and the result output means executes the result output step to estimate the lightning current waveform.

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

  Next, the calculation means is activated and the calculation step is executed. In the calculation step, the equation (24), the equation (25), the measured value of the magnetic field waveform and the value of each of the other parameters stored in the storage device (according to those input in the measured value input step and the observation equipment etc.) (Previously input and stored in the storage device) is read. Then, each value is substituted into the equation to calculate the current waveform.

  Next, the result output means is activated and the result output step is executed. 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 on the output device in the form of a graph or the like as necessary. This is the end of the program.

  This lightning current waveform estimation program may be automatically executed when a lightning strike occurs, may be arbitrarily executed by an operator, or may be another program or system. It may be performed based on the request of. The lightning current waveform estimation program may be executed as dedicated software, may be executed on general-purpose spreadsheet software, or may be a separate program or system. May be incorporated into the.

  Furthermore, in the above calculation step, the formulas (24) and (25) are replaced with formulas (formula (6), formula (11), formula (17), formula (20)) of the above SFB method, and MFB. Formula (formula (7)-formula (9), formula (12)-formula (14), formula (18), formula (21)) or the formula (formula (10) when n=1 in the MFB method) , (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-mentioned embodiment, but can be appropriately modified within the scope 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 result by reducing the number of repetitions of the calculation.

  The lightning current waveform estimation method and the lightning current waveform estimation apparatus of the present invention are used for various facilities such as power 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 measures.

Claims (4)

A method of estimating a lightning current waveform from discrete data of measured values of a magnetic field waveform of a radiated magnetic field or a radiated electric field waveform due to a lightning strike,
In the formula for calculating the value at the distant observation point of the magnetic field waveform or electric field waveform generated from the current of a lightning strike by Maxwell's equation, replace the time partial differential term of the current with the equation of the difference, By separating the early discrete data terms, we obtained the basic equation for obtaining the lightning current waveform including the integral term in the height direction,
A lightning strike current waveform estimation method characterized in that, in the basic equation, a lightning strike current waveform is obtained by sequentially performing integration in the height direction from the leading data of discrete data of the measured magnetic field waveform or electric field waveform.   2. The lightning current waveform estimation method according to claim 1, wherein, in the basic formula, the discrete data is integrated over the entire range of the height of the thundercloud from the ground surface in the height direction.   The lightning current waveform estimation method according to claim 1, wherein, in the basic equation, the discrete data is integrated in a partial range of height of a thundercloud from the ground surface in the height direction. The lightning current waveform estimation apparatus according to claim 3, further comprising a circuit based on the equation (1) obtained from the basic equation in the case of integrating only once in the height direction.

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

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