SIMULATION OF GROUNDING SYSTEM IN SOIL WITH FREQUENCY-DEPENDENT SPECIFIC CONDUCTIVITY

Size: px

Start display at page:

Download "SIMULATION OF GROUNDING SYSTEM IN SOIL WITH FREQUENCY-DEPENDENT SPECIFIC CONDUCTIVITY"

Coral Beasley
5 years ago
Views:

1 DOI: /JEST.2438 УДК С.Л. Шишигин, А.В. Черепанов, Д.С. Шишигин Вологодский государственный университет, г. Вологда, Россия МОДЕЛИРОВАНИЕ ЗАЗЕМЛИТЕЛЯ В ГРУНТЕ С ЧАСТОТНО-ЗАВИСИМОЙ УДЕЛЬНОЙ ПРОВОДИМОСТЬЮ, -. -,,,. - -, -.,, - -,. Кв ва:,,,,,,. Са ва:..,..,... - // -. Е DOI: /JEST S.L. Shishigin, A.V. Cherepanov, D.S. Shishigin Vologda State University, Vologda, Russia SIMULATION OF GROUNDING SYSTEM IN SOIL WITH FREQUENCY-DEPENDENT SPECIFIC CONDUCTIVITY Specific conductivity of soil depends on frequency that must be taken into account in calculations of impulse processes in grounding systems under lightning current. The Fourier method currently does not require modification of the standard model of the grounding system, but the scope of its applications is limited by linear problems, and difficulties with the causality principle may arise. We have developed a timediscrete model of a grounding system in soil with arbitrary frequency-dependent complex specific conductivity, suitable for calculations of impulse transient processes using standard methods in time domain. It is shown on numerical examples that overvoltage impulses in grounding systems, which are located in high-resistance soil with frequency-dependent parameters, are significantly smoothed and attenuated under the influence of current impulses with short front and short duration. Keywords: soil specific conductivity, frequency-dependence, grounding system, discrete model, impulse processes, discrete circuits method, Vlach method. Citation: S.L. Shishigin, A.V. Cherepanov, D.S. Shishigin, Simulation of grounding system in soil with frequencydependent specific conductivity, St. Petersburg polytechnic university journal of engineering science and technology, 24(3)(218) 91 11, DOI: /JEST

2 Научно-технические ведомости CПбПУ. Естественные и инженерные науки. Том 24, 3, 218 В - () () - (),. - -, (1928.) K.S. Cole, R.H. Cole (1941.). - [1 3] - 1 -, 1, - ( 5 3). 3 1 % [2 5] [6, 7] -., -, (25 1 ) ( ), : (, ),,. - о -, - - [2 7]. : , - - -,. К, - [8 11]. -. И [9], - [9, 1], - [11],., - о, - - о. бо о. о, о о о оооо - [12]. ( )., -. -, -, 92

3 ,. -,. -, -, -. -., - ( = R + j I ).. J E j E, E. ( j) jr j ' = + I /. И - - [1 3] ( ). Чо мо оооо Cole Cole ( j) ( j), c (1) 1 (1 )( j ) c - ; ω, τ,, c ( c = 1 ). (1) - [12]. -,. - -,,,,. [8] [11] - [2]. [11] -., f ( f) 1 ; r ( f) 1, f (2), / 1 ; ( - ). Э, - о. [2], ( f) Kf ; 3 tan( ) 1 r ( f) Kf ; 2 6,73 K h( ) 1 ; h( ) 1,26 ; (3), /. Э, -. 93

4 Научно-технические ведомости CПбПУ. Естественные и инженерные науки. Том 24, 3, (а) - (), 1 (1), 1 (2),,5 (3),2 (4) / Fig. 1. Frequency-dependence of module of specific conductivity (а) and soil specific permittivity according to the Alipio Visacro model () when: 1 = 1 ms/m; 2 = 1 ms/m; 3 =,5 ms/m; 4 =,2 ms/m а) ). 2. (а) () Fig. 2. Grounding system field (a) and circuit () models (3) -, (. 1, а), - - (. 1, ). мо м Ц- - (. 2), ( - ) ( ) -, [13]. (. 2, а), - - G, C, M - 94

5 (). (. 2, а), (. 2, ). G C,, G C y. - G C. Э - -, ,,. G C о м оо о мо об - - о,,, EMTP. N - h. И (. 2, ) - Э, (. 3). -. [14],,, - (.. 3) -. Э, f =,25T 1, T 1 -,. z(jω) -. (jω) (t) [15],. - z(jω) (. 3, а) [13]. Э - y(jω) (. 3, ). а) ). 3. (а) () k Fig. 3. Discrete circuit of inductance (а) and capacitance () at time step k 95

6 Научно-технические ведомости CПбПУ. Естественные и инженерные науки. Том 24, 3, 218 о м мо м оо-мм мм y(jω). [13], Y(s),, -, y(t) = L 1 [Y(s)/s 2 ]. y(t) - - u(t) = t. - k- ykh ( h) ykh ( ) Yk, k ( N 1). h (. 3, ) GY ; J ; k (4) J Y u ( Y Y ) u ; k ( N1), k1 k1 km km1 m m1 G ; J k, - k-., - y(jω) (. 3, ). - (jω), - Cole Cole (1), (2), (3). (2): j ( f) j ( f) 4 f 1 j 1, f, j j j (5), (2). (5) (1),, Cole Cole r c =,5, η = 1, τ = 4/,, (1). - τ RC., - (5) «-», (2). К - (5) Y( j) G jc2 k j, (6) - -, -., - l, R 2l G kg; C kg; kg. ln l / R Э - (6) (. 4), : 1) - G; 2) (. 3, ) C; 3) (. 3, ) - (6),. -, -., (. 4), -, - о. (.. 3, ) (6): y( j) 2 k j. g g 96

7 Y( j) G jc2k j Y(jω) k Fig. 4. Discrete circuit of the grounding system element with frequency-dependent conductance Y(jω) at time step k ys () 2 k s, -,, 1 2 t yt () L ys ()/ s 4 kg. k ykh ( h) ykh ( ) Yk k k k h h g 4 g ( 1 ). (4), (. 3, ). - k (2) - : Y k,46,46 3,27( k 1) k,54 kg 1,461 ( ). h, (. 3, 4) (- ) у (jω), (. 2, ) - о., -, -. о боо мо м (. 5) -. - ( = = const) - (jω). -. = const (jω) - - (.. 5)., ( - 97

8 Научно-технические ведомости CПбПУ. Естественные и инженерные науки. Том 24, 3, 218, ), -, ( - ) - 3 % (. 5, а). ( ), ( ) -., -,, -. (), -, - - (, - ), - (. 5, ). -.,, - -., - (.. 5), ( 5 %), : 1,2/5 (а) 1/5 (), : 1 = ; 2 (jω) ; 3 (jω). : 22 ; 5 ; ; μr = 2, 2 ; 1 ; =,2 /, r = 1 Fig. 5. Potential at the center of the grounding grid when input current impulse of 1 A amplitude with linear front of: 1,2/5 μs (а) and 1/5 μs (), calculated: 1 when = ; 2 when (jω) using the Vlach method; 3 when (jω) using the Fourier method; grounding grid parameters: 22 m, grid step 5 m, steel rods, μr = 2, diameter 2 mm, immersion depth 1 m; soil parameters: =,2 ms/m, r = 1

9 б о о 1. -, (, ), -., -, ( ), , ,., -, -. Э -,, -. 6., -, - -, СПИСОК ЛИТЕРАТУРЫ 1. Visacro S., Alipio R., Vale M.H.M., Pereira C. The response of grounding electrodes to lightning currents: The effect of frequency dependent soil resistivity and permittivity // IEEE Trans. Electromagnetic Compatibility Vol. 53. No. 2. P Alipio R., Visacro S. Modeling the frequency dependence of electrical parameters of soil // IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 5. P Visacro S., Alipio R., Pereira C., Guimaraes M., Schroeder M.A.O. Lightning response of grounding grids: Simulated and experimental results // IEEE Trans. Electromagnetic Compatibility Vol. 57. No. 1. P Alipio R., Visacro S. Impulse efficiency of grounding electrodes: Effect of frequency-dependent soil parameters // IEEE Trans. Power Delivery Vol. 29. No. 2. P Akbari M., Sheshyekani K., Alemi M.R. The effect of frequency dependence of soil electrical parameters on the lightning performance of grounding systems // IEEE Trans. Electromagnetic Compatibility Vol. 55. No. 4. P Silveira F.H., Visacro S., Alipio R., De Conti A. Lightning-Induced Voltages Over Lossy Ground: The Effect of Frequency Dependence of Electrical Parameters of Soil // IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 5. P Akbari M., Sheshyekani K., Pirayesh A., Rachidi F., Paolone M., Borghetti A., Nucci C.A. Evaluation of lightning electromagnetic fields and their induced voltages on overhead lines considering the frequency de- 99

10 Научно-технические ведомости CПбПУ. Естественные и инженерные науки. Том 24, 3, 218 pendence of soil electrical parameters // IEEE Trans. Electromagnetic Compatibility Vol. 55. No. 5. P Cavka D., Mora N., Rachidi F. A comparison of frequency-dependent soil models: application to the analysis of grounding systems // IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 2. P Luo S., Chen Z. Iterative methods for extracting causal time-domain parameters // IEEE Trans. Microwave Theory and Techniques. 25. Vol. 53. No.3. P Becerra J., Vega F., Rachidi F. Extrapolation of a truncated spectrum with Hilbert transform for obtaining causal impulse responses // IEEE Trans. Electromagnetic Compatibility Vol. 59. No. 2. P , Чо А.В.,.. -- // И К. Э..:, // Э C В И., К...: Alipio R., Visacro S. Time-domain analysis of frequency-dependent electrical parameters of soil // IEEE Trans. Electromagnetic Compatibility Vol. 59. No. 3. P СВЕДЕНИЯ ОБ АВТОРАХ ИИИ оо а авщ а В ав ва ctod28@yandex.ru ЧАВ А Воо аа В ав ва alex1234_91@mail.ru ИИИ м аа а ава В ав ва shishigind@yandex.ru Даа и аьи в аци: REFERENCES [1] Visacro S., Alipio R., Vale M.H.M., Pereira C. The response of grounding electrodes to lightning currents: The effect of frequency dependent soil resistivity and permittivity. IEEE Trans. Electromagnetic Compatibility Vol. 53. No. 2. P [2] Alipio R., Visacro S. Modeling the frequency dependence of electrical parameters of soil. IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 5. P [3] Visacro S., Alipio R., Pereira C., Guimaraes M., Schroeder M.A.O. Lightning response of grounding grids: Simulated and experimental results. IEEE Trans. Electromagnetic Compatibility Vol. 57. No. 1. P [4] Alipio R., Visacro S. Impulse efficiency of grounding electrodes: Effect of frequency-dependent soil parameters. IEEE Trans. Power Delivery Vol. 29. No. 2. P [5] Akbari M., Sheshyekani K., Alemi M.R. The effect of frequency dependence of soil electrical parameters on the lightning performance of grounding systems. IEEE Trans. Electromagnetic Compatibility Vol. 55. No. 4. P [6] Silveira F.H., Visacro S., Alipio R., De Conti A. Lightning-Induced Voltages Over Lossy Ground: The Effect of Frequency Dependence of Electrical Parameters of Soil. IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 5. P [7] Akbari M., Sheshyekani K., Pirayesh A., Rachidi F., Paolone M., Borghetti A., Nucci C.A. Evaluation of lightning electromagnetic fields and their induced voltages on overhead lines considering the frequency dependence of soil electrical parameters. IEEE Trans. Electromagnetic Compatibility Vol. 55. No. 5. P [8] Cavka D., Mora N., Rachidi F. A comparison of frequency-dependent soil models: application to the 1

11 analysis of grounding systems. IEEE Trans. Electromagnetic Compatibility Vol. 56. No. 2. P [9] Luo S., Chen Z. Iterative methods for extracting causal time-domain parameters. IEEE Trans. Microwave Theory and Techniques. 25. Vol. 53. No.3. P [1] Becerra J., Vega F., Rachidi F. Extrapolation of a truncated spectrum with Hilbert transform for obtaining causal impulse responses. IEEE Trans. Electromagnetic Compatibility Vol. 59. No. 2. P [11] Shishigin S.L., Cherepanov A.V., Shishigin D.S. Raschet zazemliteley v grunte s chastotno-zavisimymi parametrami [Grounding systems calculation in soil with frequency-dependent parameters]. Izvestiya Tulskogo gosudarstvennogo universiteta. Tekhnicheskiye nauki S (rus.) [12] Matveyev B.K. Elektrorazvedka [Electrical exploration]. M.: Nedra, s. (rus.) [13] Shishigin S.L. Matematicheskiye modeli I metody rascheta zazemlyayushchikh ustroystv [Mathematical models and calculation methods of grounding devices]. Elektrichestvo S (rus.) [14] Vlakh I., Singkhal K. Mashinnyye metody analiza i proyektirovaniya elektronnykh skhem [Machine methods of analysis and electronic curcuits design]. M.: Radio i svyaz s. (rus.) [15] Alipio R., Visacro S. Time-domain analysis of frequency-dependent electrical parameters of soil. IEEE Trans. Electromagnetic Compatibility Vol. 59. No. 3. P THE AUTHORS SHISHIGIN Sergei L. Vologda state university ctod28@yandex.ru CHEREPANOV Aleksei V. Vologda state university alex1234_91@mail.ru SHISHIGIN Dmitrii S. Vologda state university shishigind@yandex.ru Received: ,

Lightning Transients on Branched Distribution Lines Considering Frequency-Dependent Ground Parameters

Lightning Transients on Branched Distribution Lines Considering Frequency-Dependent Ground Parameters 214 International Conference on Lihtnin Protection (ICLP), Shanhai, China Lihtnin Transients on Branched Distribution Lines Considerin Frequency-Dependent Ground Parameters Alberto De Conti LRC Lihtnin