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Grounding system models for electric current impulse
Electric Power Systems Research 177 (2019) 105981
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Grounding system models for electric current impulse M.F.B.R. Gonçalves
a,c,⁎
b
a
d
T b
, E.G. da Costa , A.F. Andrade , V.S. Brito , G.R.S. Lira , G.V.R. Xavier
a
Post-Graduate Program in Electrical Engineering — PPgEE, COPELE, UFCG, Brazil Electrical Engineering Department, Federal University of Campina Grande (UFCG), Brazil Federal Institute of Pernambuco (IFPE), Brazil d Federal Institute of Paraíba (IFPB), Brazil a
b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Grounding system Current impulse Transient effects Electric model
In this paper, two electrical models that simulate grounding system responses to current impulses with inductive or capacitive characteristics are presented. The models were elaborated from the analysis of voltage–current curves obtained from field tests. The characteristic curve of the relation between measured voltage and applied current (V × I) was used to identify the electric circuit model elements. In order to evaluate the proposed models, two grounding system configurations applied in electrical system and an additional configuration presented in the literature were used as case study. For each configuration, two models were evaluated: the proposed model and a literature model. The results of the proposed and literature model were evaluated and compared using calculated error statistics over time. The proposed model application resulted in values of total effective error lower than 5% in all analyzed cases, with equivalent error index values regarding the literature model and, in some cases, even smaller. The proposed model has more advantages in comparison to the literature model, since it has fewer and only linear elements. Due to the presentation of a simple and reliable configuration, the proposed circuits can be coupled, with greater ease and flexibility, to transient analysis programs and in insulation coordination studies.
1. Introduction Grounding systems have as main objective to make the soil a path of low impedance, securing people and equipment integrity, as well as to ensure the electrical system’s continuous operation [1,2]. Therefore, they must enable the potential equalization when electric currents are injected by the neutral of transformers, short circuits, switches and lightning discharges in the electrical system [3,4]. The electrical phenomena due to short-circuit, or phase unbalance have different characteristics from the switching or lightning discharge phenomena. The first ones occur essentially at industrial frequency (50 Hz or 60 Hz) and the latter are high-frequency phenomena (0.5 MHz to 10 MHz) with current amplitudes that may exceed 100 kA in the case of lightning discharges [3]. However, grounding systems are designed to attend only the requests at low frequency. In this case, the design and the analysis of a grounding system are done from a nonconservative simplification since the grounding impedance parameter is approximated to the grounding resistance parameter [4]. The analysis of the phenomena in low frequency is consolidated. On the other hand, researches are still handled in order to understand the phenomenon at high frequencies, as well its impact on electrical
⁎
systems and the influence on grounding systems designs. Some works, as presented in [6–8], analyze the phenomena at high frequencies through experimental evaluations, while other works, as shown in [9–12], use modeling from computational simulations. Among the studies involving experimental evaluation, it can be highlighted some results extracted from tests in ground rods and horizontal electrodes [13], grounding grids [14], wind turbine grounding systems [15], and counterpoise wires [16]. However, all the mentioned studies are subjected to financial limitations, which impose the use of low amplitude current impulse generator, limited physical space etc. Other works try to overcome the physical space limitation through the construction of reduced models [17,18]. Nonetheless, the use of reduced models does not ensure reproduction of real grounding system conditions, presenting uncertainties related mainly to the soil electrical characteristics, the effective length [19], the propagation and the transit time of electromagnetic waves in soil. In addition, researches that considered the ionization effects and current transient frequency spectrum were conducted in a controlled laboratory environment or did not evaluate complex geometries of a grounding system [20,21]. Researches that apply computational simulations to investigate the grounding system performance toward current impulses are
Corresponding author. E-mail address: [email protected] (M.F.B.R. Gonçalves).
https://doi.org/10.1016/j.epsr.2019.105981 Received 27 February 2019; Received in revised form 20 June 2019; Accepted 1 August 2019 Available online 27 August 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
Electric Power Systems Research 177 (2019) 105981
M.F.B.R. Gonçalves, et al.
2.2. Methodology
represented by models where transient effects such as ionization, inductive or capacitive behaviors are evaluated [5,22–24]. The ionization effect occurs only for high-intensity current impulses that cause high electric fields and, consequently, soil ionization. The effect of soil ionization is conservative, that is, it reduces the values of transient impedance [17,21,22]. However, the inductive behaviors, caused by the high frequencies involved in the impulses, can increase the values of transient impedance, presenting different performances for soils [5,6]. Grounding system behavior modeling by electric circuit allows its coupling to electromagnetic transient analysis programs, which can be used in insulation coordination studies, such as presented in [25]. Thus, this work proposes a grounding system model, based on an electric circuit, capable of representing the inductive or capacitive behaviors; the frequency components influence and the current impulse intensity. The designed model was based on the voltage and current waveforms obtained from an electric circuit model described in the literature [17], as well as from laboratory and field experiments. The main contributions of this paper can be summarized by the proposal of two new circuits composed only by linear elements (resistors, capacitors and inductors), differently from the circuits found in the literature that use non-linear elements, reducing the model complexity. In addition, the circuits are not only presented, but is also demonstrated how to calculate the necessary parameters for it use. Moreover, the models and simulations were attested by measurements in a real size dimension grounding system, differently from several literature papers. Therefore, the presented models are fit to be applied to transient analysis programs and in insulation coordination studies, aiding in the electrical systems design. The rest of the paper is organized as follows: Section 2 describes the experimental field tests; Section 3 presents the results obtained in the experimental tests; Section 4 details the methodology for defining the electrical circuits that model the grounding systems. The results are presented and discussed in Section. 5. Finally, in the section 6 are presented the conclusions extracted from this work.
i (t ) = I (e−at − e−bt )
(1)
2. Experimental tests
v (t ) = V (e−ct − e−dt ).
(2)
2.1. Grounding system characterization
Tables 2 and 3 show the parameters obtained from the adjustment of curves from (1) and (2) for the grounding system configurations G1 and G2, respectively. The adjusted curves (voltage 1, current 1, voltage 2 and current 2) for the 20 kV and 25 kV charging voltages, referring to the grounding system configurations G1 and G2, respectively, can be seen in Figs. 5 and 6.
A current impulse generator was used to inject the impulses into the grounding systems. The impulse generator capacitors were charged with voltages of 20 kV and 25 kV. For each voltage level, three consecutive impulses were applied, with a 15-minute interval between each application, and the average of the signals was used to get current and voltage impulses. The schematic diagram of the experimental arrangement is shown in Fig. 2. The signal acquisition of the current impulses injected into the grounding system was carried out by a Pearson coil, with a sensitivity of 0.01 V/A ± 1%. The Pearson coil is connected to a digital oscilloscope. The voltage waveform in the grounding system was acquired through the digital oscilloscope (Tektronix TDS 2014) using high-voltage probes (Tektronix P6015A). Both voltage and current probes were close to the injection point. The generator grounding system was 100 m from the grounding system under test while it was at 100 m from the remote grounding, forming a 90-degree angle between the three. 3. Results of measurements 3.1. Field data processing The voltage and current signals acquired in field were imported into the MATLAB® software, and noise suppression techniques were applied. The measured curves (voltage 1, current 1, voltage 2 and current 2) for the 20 kV and 25 kV charging voltages, referring to the grounding system configurations G1 and G2, respectively, can be seen in Figs. 3 and 4. The signals were modeled using curve fitting through the exponential double model, and their parameters were used in commercial PSIM® software [26], such as:
Grounding systems were implanted in soils with different characteristics and configurations, named G1 and G2. The configuration G1 represents a typical grounding system of substations, while the configuration G2 represents a typical grounding system of overhead transmission line towers. Soil resistivity measurements in the proximities of the grounding system locations were performed using the Wenner method and were characterized based on two-layer stratification. The resistivity and depth values of the layers are shown in Table 1. The first grounding system configuration, G1, corresponds to a grounding system of 12 copper-clad steel rods with a diameter of 20 mm and a length of 2.40 m, interconnected by bare copper cables with a cross-sectional area of 35 mm² and buried at a depth of 0.30 m in soil. The second, G2, corresponds to a grounding system of 12 copperclad steel rods with a diameter of 20 mm and a length of 2.40 m, interconnected by bare copper cables with a cross-sectional area of 50 mm² and buried at a depth of 0.30 m in soil. Fig. 1 shows the grounding system configurations used in the tests.
3.2. Field data evaluation Fig. 7 shows the voltage versus current curves (V × I) for the G1 grounding system configuration. In Fig. 7, the blue arrows show the beginning and end directions of the V × I curves, and it can be observed that the maximum current value occurs before than the maximum voltage value, indicating that G1 grounding system configuration has capacitive behavior. For the G2 grounding system configuration, the maximum voltage value occurs before the maximum current value, as presented in Fig. 8, indicating that G2 grounding system configuration has inductive behavior.
Table 1 Grounding system soil characterization.
4. Proposed models
Soil Stratification Grounding system Configuration G1 G2
Layer h1A1 h2A1 h1A2 h2A2
Depth (m) 0–0.28 > 0.28 0–2.83 > 2.83
The proposed electrical models for grounding system representation were developed based on the presented experimental responses and reference models of grounding systems and surge arresters [8,17,27]. In order to represent the inductive and capacitive behaviors, two electrical circuits were proposed, as shown in Fig. 9.
Resistivity (Ω m) 33.47 49.61 39.62 196.57
2
Electric Power Systems Research 177 (2019) 105981
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Fig. 1. Representation of the grounding system configuration: (a) G1 upper view; (b) G2 side view; (c) G2 upper view.
4.1. Resistance R1 calculation
R1 =
For the capacitive circuit shown in Fig. 9a, it is considered that at the initial time of a surge (t = 0), the capacitor C is discharged. Thus, the RC branch initially behaves as a short circuit, since vR2(t = 0) = 0 and the initial grounding system dynamics is defined by the resistor R1. Thus:
R1 =
dv (0). di
V (d − c ) . I (b − a)
(4)
For the inductive circuit, it is considered that at the initial time (t = 0) of a surge, there is no current across the inductor L. The R2L branch can be regarded as instantaneously opened, remaining only the element R1. Thus, the resistance R1 of the inductive circuit is estimated similarly to the capacitive case, using (3) and (4).
(3) 4.2. Resistance R2 calculation
In the case of using the double exponential model presented at (1) and (2) for modeling the impulsive waveshapes, Eq. (3) can be rewritten as:
For the capacitive circuit, the resistance R2 is estimated at the point of the V × I curve where the derivative di is equal to the initial slope. dv The initial slope is given by: 3
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Fig. 2. Schematic diagram of the experimental arrangement. Table 2 Calculated Impulse parameters applying the double exponential model for G1 grounding system configuration. Generator charging voltage (kV)
20 25
Calculated parameters for the current impulse
Calculated parameters for the voltage impulse
I (A)
a (s−1)
b (s−1)
V (V)
c (s−1)
d (s−1)
3872 4437
29720 29630
174900 175200
10202 11210
28580 28360
118400 118200
Table 3 Calculated impulse parameters applying the double exponential model for G2 grounding system configuration. Generator charging voltage (kV)
Fig. 3. Measured voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G1. 20 25
Calculated parameters for the current impulse I (A)
a (s−1)
2949 4220
19190 21280
b (s−1) 86500 77350
Calculated parameters for the voltage impulse V (V)
c (s−1)
d (s−1)
23580 29850
18230 18610
332400 318600
Fig. 4. Measured voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G2.
dv = R1 di
Fig. 5. Adjusted voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G1.
(5)
Besides, for the circuit of Fig. 9a, the voltage across the current source can be expressed as:
v = R1 i + vR2.
dv R2 dt
(6)
= 0. Therefore, at this point the current in the capacitor is zero and:
v (t2) = (R1 + R2 ) i (t2).
Differentiating (6) with respect to time and using (5), it follows that, at time t2, when the slope of the V × I curve is equal to the initial slope,
Thus, the resistance R2 of the capacitive circuit is calculated: 4
(7)
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circuit of Fig. 9b:
i=
v + i2. R1
(9)
By differentiating (9) and, again, using (5), it follows that, at a time t2, di when the slope of the V × I curve is equal to the initial slope, dt2 = 0. Therefore, the voltage v is fully applied on the resistor R2 and, at this instant t2:
1 1⎞ i (t2) = v (t2) ∙ ⎛ + . R2 ⎠ ⎝ R1 ⎜
⎟
(10)
Hence, the resistance R2 of the inductive circuit can be calculated as:
i (t ) 1⎤ R2 = 1/ ⎡ 2 − . ⎢ R1 ⎥ ⎣ v (t2) ⎦ Fig. 6. Adjusted voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G2.
(11)
4.3. Calculation of the capacitance C The capacitance C can be calculated from the time of peak current, di indicated by t1. This is, when t = t1, dt = 0 ., Thus, by differentiating (6) with respect to time, one obtains:
dvR2 dv (t1) = (t1). dt dt
(12)
Besides, the relationship between the total voltage v and the voltage vR2 in the R2C branch is given by: (13)
vR2 = v − R1 i.
Thus, by replacing (12) and (13) in expression (14) for the current in the branch R2C:
i=
v2 dv + C 2, R2 dt
(14)
the expression (15) for the capacitance C can be obtained:
R v (t1) ⎤ dv C = ⎡ ⎛1 + 1 ⎞ i (t1) − / (t1). ⎢⎝ R2 ⎠ R2 ⎥ ⎣ ⎦ dt
Fig. 7. V × I curves for the 20 kV and 25 kV charging voltages for the G1 grounding system configuration.
⎜
⎟
(15)
4.4. Inductance L calculation The inductance L can be calculated considering different time instants. During a lightning discharge, the overvoltage peak value is usually considered as a critical parameter. Thereby the proposed model considers the voltage peak time t1 for the inductance calculation. When dv t = t1, dt = 0 . By differentiating (9) with respect to time, it follows that:
di2 di (t1) = (t1). dt dt
(16)
Besides, the total current i and the current iR2 in the branch RL are related by:
iR2 = i −
v . R1
(17)
Thus, by replacing (16) and (17) in (18) for the voltage in branch RL: Fig. 8. V × I curves for the 20 kV and 25 kV charging voltages for the G2 grounding system configuration.
R2 =
v (t2) − R1. i (t2)
v = R2 iR2 + L
di2 , dt
(18)
the inductance L can be calculated as: (8)
R di L = ⎡ ⎛1 + 2 ⎞ v (t1) − R2 i (t1)⎤/ (t1). ⎢⎝ ⎥ dt R1 ⎠ ⎣ ⎦ ⎜
For the inductive circuit, (5) also holds true. Then, by analyzing the 5
⎟
(19)
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Fig. 9. Proposed circuit for electric models (a) capacitive and (b) inductive.
Fig. 10. Experimental test circuit and scale model used in [17].
5. Reference model
6. Model evaluation
In [17], the authors proposed a model based on electric circuits capable of representing the transient effects of a grounding system subjected to current impulses. They conducted experimental tests on a scale model grounding system, as shown in Fig. 10. The authors proposed the circuit presented in Fig. 11 in order to represent the grounding system impulse response, as well the methods to calculate the circuit parameters through data obtained from tests. The development of the equations and the definition of the parameters of the proposed circuit are further detailed in [17].
The model evaluation was done using: the two grounding system configurations analyzed, G1 and G2; the grounding system configuration of [17]; the proposed models (inductive and capacitive) and the model presented in [17]. The grounding system configuration of [17] consists of a simple grounding rod reproduced in reduced model. The proposed circuit of Fig. 9 and the circuit presented in [17] were simulated in the PSIM® software. As circuit inputs, the current impulse according to (1) and the calculated parameters for the 20 kV and 25 kV generator charging voltages were considered. The simulations have as output the voltage waveforms over time. In order to evaluate the reliability of the proposed model, the simulated voltage waveform was
Fig. 11. Schematic representation of the proposed circuit of [17]. 6
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compared with the measured voltages through the performance metrics R² and RMSE (root-mean-square error). The coefficient of determination, also called R2, is an adjustment measure of the generalized linear statistical model and it varies between 0 and 1 [28]. The closer to 1 is the R2, the better is the fit between the reference and estimated variables. The RMSE evaluates the fit between an estimator and the observed values [28]. The lower the RMSE value, the better is the fit between the estimated and observed values. The models evaluation resulted in three different cases. Case 1 and Case 2 consisted of modeling the impulsive response of the grounding system configurations G1 and G2 (Fig. 1), respectively. The capacitive and inductive proposed models, presented in Figs. 9a and b, were applied for the Cases 1 and 2, respectively. In order to evaluate the proposed models accuracy, the model presented in [17], shown in Fig. 11, was used as reference for both cases. Finally, the Case 3 consisted of modeling the impulsive response of the grounding system configuration of [17], presented in Fig. 10, using the inductive proposed model and the model presented in [17].
Table 5 Values of the circuit elements calculated using the methodology of [17]. RL (Ω)
RN0(Ω)
RN (mΩ)
LN (μH)
A
α
1.595
24.726
24.726
100
−94.986
0.280
6.1. Case 1: grounding system G1 The proposed capacitive model was chosen after the characterization of the grounding system configuration G1 through its V × I curve shown in Fig. 7. Then, (4), (11) and (15) were applied to determine the values of the elements R1, R2 and C from a computational routine that has as input the voltage and current waveforms shown in Fig. 7. Table 4 shows the values of the calculated circuit elements. The methodology used by [17] was implemented in a computational routine to determine the values of the circuit elements presented in [17], which has as input the voltage and current waveforms shown in Fig. 7. Table 5 shows the values of the calculated circuit elements. In Fig. 12, the voltage waveforms obtained from the simulations are shown in the time domain. In Figs. 13 and 14, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed capacitive circuit and the circuit presented in [17] are shown in Table 6. When comparing the results from Figs. 12, 13 and 14, we verified that the proposed capacitive model was more efficient in representing the response of the grounding system configuration G1. Its application resulted in smaller errors and peak voltage values closer to the measured value. Both models presented better results for the impulse with 25 kV charging voltage. A possible explanation for the higher errors presented by the model developed in [17] can be associated to the model conception, since it was developed focused in grounding systems with inductive response.
Fig. 12. Simulated voltage by applying the methods for the grounding system configuration G1.
Fig. 13. Coefficient of determination R² over time for the simulations of the grounding system configuration G1.
6.2. Case 2: grounding system G2 The choice of the proposed inductive model was similar to Case 1 using the V × I curve shown in Fig. 8. Then, (4), (11) and (19) were applied to determine the values of the elements R1, R2 and L from a computational routine that has as input the voltage and current waveforms shown in Fig. 8. Tables 7 and 8 show the values of the calculated circuit elements by the proposed model and the model presented in [17], respectively. In Fig. 15, the voltage waveforms obtained from the simulations are
shown in the time domain. In Figs. 16 and 17, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed inductive circuit and the circuit presented in [17] are shown in Table 9. When comparing the results from Figs. 15, 16 and 17, it has been shown that both models presented relatively small errors. The literature model [17] error is smaller when the total impulse time is considered. However, the proposed model presents minor errors during the rise time and for the peak voltage. The best performance of the model presented in [17] for case 2 when compared to Case 1 was expected due to the inductive essence of the model.
Table 4 Values of the circuit elements calculated for grounding system configuration G1. R1 (Ω)
R2 (Ω)
C (μF)
1.595
0.824
11.058
7
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Fig. 15. Simulated voltage by applying the methods for the grounding system configuration G2.
Fig. 14. RMSE calculated for the simulated response of the grounding system configuration G1. Table 6 Error metrics calculated for the case 1.
Capacitive circuit Circuit presented in Ref. [17]
Generator charging voltage (kV)
R²
Maximum RMSE (%)
Peak voltage error (%)
20 25 20 25
0.94 0.95 0.67 0.91
5.6 4.3 11.8 8.6
3.5 1.5 11.6 3.7
Table 7 Values of the circuit elements calculated for grounding system configuration G2. R1 (Ω)
R2 (Ω)
L (μH)
37.58
13.41
153.0
Fig. 16. Coefficient of determination R² over time for the simulations of the grounding system configuration G2.
Table 8 Values of the circuit elements calculated using the methodology of [17] and V × I curve presented in Fig. 8 as input. RL (Ω)
RN0(Ω)
RN (mΩ)
LN (μH)
A
α
37.49
8.631
8.631
100.0
0.0329
1.0842
6.3. Case 3: reference grounding system As circuit inputs, the current impulses measured in the experimental tests for two different charge levels of generator called (a) and (b), as described in [17], were considered. The determination of the values of the proposed inductive circuit elements and of the circuit presented in [17] was done analogously to Case 2 and are presented in Tables 10 and 11, respectively. In Fig. 18, the voltage waveforms obtained from the simulations are shown in the time domain. In Figs. 19 and 20, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed inductive circuit and the circuit presented in [17] are shown in Table 12. When comparing the results from Figs. 18, 19 and 20, it has been shown that both models presented relatively small errors and
Fig. 17. RMSE calculated for the simulated response of the grounding system configuration G2.
8
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Table 9 Error metrics calculated for the Case 2.
Inductive circuit Circuit presented in Ref. [17]
Generator charging voltage (kV)
R²
Maximum RMSE (%)
Peak voltage error (%)
20 25 20 25
0.999 0.996 1.000 0.999
1.2 1.9 1.2 1.4
0.4 0.9 0.6 1.9
Table 10 Values of the circuit elements calculated for grounding system configuration of [17] using the proposed inductive circuit. R1 (Ω)
R2 (Ω)
L (μH)
385.6
455.1
697.3
Fig. 19. Coefficient of determination R² over time of the grounding system configuration of [17].
Table 11 Values of the circuit elements calculated using the methodology of [17]. RL (Ω) 385
RN0(Ω) 39.2
RN (mΩ) 39.2
LN (μH) 100
α
A 6.08 × 10
−8
2.06
Fig. 20. RMSE of the grounding system configuration of [17]. Table 12 Error metrics calculated for the Case 3. Fig. 18. Simulated voltage by applying the methods for the grounding system configuration of [17]. Inductive circuit
coefficient R² values greater than or equal to 0.97. In addition, for the higher voltages tested, the proposed model generally presented smaller errors when compared to the reference model. This fact may indicate a conservative characteristic of the proposed model, representing an attractive feature for the application in transient analysis programs.
Circuit presented in Ref. [17]
Experimental tests of Ref. [17]
R²
Maximum RMSE (%)
Peak voltage error (%)
(a) (b) (a) (b)
0.98 0.97 0.99 0.97
5.3 4.7 2.2 8.3
6.0 4.9 1.8 5.1
of the grounding systems applied in its evaluation with values of total RMSE lower than 5%, of peak voltage error lower than 6% and of R² higher than 0.94 in all analyzed cases. Despite its simplicity, the proposed model presented total errors with equivalent values regarding the literature model and, in some cases, even smaller. The proposed model has advantages such as greater ease of parameter calculation and circuit implementation, which presents only linear elements, differently from the circuits found in the literature that use non-linear elements, reducing the model complexity. In addition, smaller errors were observed for higher test voltages, which may indicate a conservative characteristic of the model when applied to studies of transient analysis and insulation coordination. Finally, the model proposed in this work is capable of representing the inductive or capacitive behaviors of grounding systems. In their
7. Conclusions In this work, two electrical models of grounding systems capable of representing capacitive and inductive responses were proposed as well expressions for estimating its parameters from curves V-I obtained from measurements with current impulse generator. For the elaboration and evaluation of the models, experimental tests were carried out in two different grounding systems of real size dimensions that simulate real configurations applied in the electric system. The results of the proposed model were compared, through calculated statistics over time (R2 and RMSE), with the results of the experimental tests and also with results obtained from the literature. The proposed models were able to represent the impulsive response 9
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evaluation, we considered effects of the frequency components and different current impulse intensities. However, the method has a practical limitation, since it depends of the obtaining of preliminary waveform information (current and voltage) about the prevailing grounding system behavior (inductive or capacitive). Due to the presentation of a simple and reliable configuration, the proposed circuits can be coupled, with greater ease and flexibility, to electromagnetic transient analysis programs and in insulation coordination studies.
tall-mast for human safety, Electr. Power Syst. Res. 153 (2017) 119–127. [8] M. Loboda, Z. Pochanck, A numerical identification of dynamic model parameters of surge soil conduction based on experimental data, International Conference on Lightning Protection, Berlin, 1992. [9] L. Grcev, Lightning surge efficiency of grounding grids, IEEE Trans. Power Delivery 26 (3) (2011) 1692–1699. [10] P. Sarajcev, S. Vujevic, D. Lovric, Interfacing harmonic electromagnetic models of grounding systems with the EMTP-ATP software package, Renewable Energy 68 (2014) 163–170. [11] M. Gonçalves, E. Costa, J. Silva, F. Araujo, C. Oliveira Filho, Electric model of current impulse generator applied to ground grids, 20th International Symposium on High Voltage Engineering (ISH), Buenos Aires, 2017. [12] R.M.A. Velásquez, J.V.M. Lara, Failures in overhead lines grounding system and a new improve in the IEEE and national standards, Eng. Fail. Anal. 100 (2019) 103–118. [13] R. Alipio, S. Visacro, Impulse efficiency of grounding electrodes: effect of frequency dependent soil parameters, IEEE Trans. Power Delivery 29 (2) (2014) 716–723. [14] S. Visacro, R. Alipio, C. Pereira, M. Guimarães, M.A.O. Schroeder, Lightning response of grounding grids: simulated and experimental results, IEEE Trans. Electromagn. Compat 57 (1) (2015) 121–127. [15] N.A. Kafshgari, N. Ramezani, H. Nouri, Effects of high frequency modeling & grounding system parameters on transient recovery voltage across vacuum circuit breakers for capacitor switching in wind power plants, Electri. Power Energy Syst. 104 (2018) 159–168. [16] C. Caetano, J. Paulino, W. Boaventura, A. Lima, I. Lopes, E. Cardoso, A conductor arrangement that overcomes the effective length issue in transmission line grounding: full-scale measurements, ICLP (2018). [17] R.A.C. Altafim, L. Gonçalves, R.A.P. Altafim, R.C. Creppeb, A. Piantini, One-port nonlinear electric circuit for simulating grounding systems under impulse current, Electr. Power Syst. Res. 130 (2016) 259–265. [18] A. Geri, G.M. Veca, E. Garbagnati, G. Sartorio, Non-linear behaviour of ground electrodes under lightning surge currents: computer modelling and comparison with experimental results, IEEE Trans. Magn. 28 (2) (1992) 1442–1445. [19] N. Harid, H. Griffiths, S. Mousa, D. Clark, S. Robson, A. Haddad, On the analysis of impulse test results on grounding systems, IEEE Trans. Ind. Appl. 51 (6) (2015) 5324–2334. [20] R. Alípio, S. Visacro, Frequency dependence of soil parameters: effect on the lightning response of grounding electrodes, IEEE Trans. Electromagn. Compat. 55 (1) (2013) 132–139. [21] M. Mokhtari, Z. Abdul-Malek, Z. Salam, An improved circuit-based model of a grounding electrode by considering the current rate of rise and soil ionization factors, IEEE Trans. Power Delivery 30 (1) (2015) 211–219. [22] A.C. Liew, M. Darveniza, Dynamic model of impulse characteristics of concentrated earths, Proc. Inst. Electr. Eng. 121 (2) (1974) 123–135. [23] S. Sekioka, M.I. Lorentzou, M.P. Philippakou, J.M. Prousalidis, Current-dependent grounding resistance model based on energy balance of soil ionization, IEEE Trans. Power Delivery 21 (1) (2006) 194–201. [24] G. Ala, P.L. Buccheri, P. Romano, F. Viola, Finite difference time domain simulation of earth electrodes soil ionisation under lightning surge condition, IET Sci. Meas. Technol. 2 (2008) 134–145. [25] R.M.A. Velásquez, J.V.M. Lara, Model for failure analysis for overhead lines with distributed parameters associated to atmospheric discharges, Eng. Fail. Anal. 100 (2019) 406–427. [26] POWERSIM, PSIM® User’s Guide, v. 10.0. Available at: Powersim Inc., 2016, https://powersimtech.com/drive/uploads/2016/06/PSIM-User-Manual.pdf. [27] S. Tominaga, K. Azumi, Y. Shibuya, M. Imataki, Y. Fujiwara, S. Nishida, Protective performance of metal oxide surge arrester based on the dynamic V-I characteristics, IEEE Trans. Power Apparatus Syst. (6) (1979) 1860–1871 PAS-98. [28] A.L. GARCIA, Probability, Statistics, and Random Processes for Electrical Engineering, 3rd ed., Pearson Education, 2008.
Funding This research received no external funding. Conflicts of interest The authors declare no conflict of interest. CRediT authorship contribution statement M.F.B.R. Gonçalves: Methodology. E.G. da Costa: Methodology, Writing - review & editing, Conceptualization. A.F. Andrade: Methodology. V.S. Brito: . G.R.S. Lira: Supervision. G.V.R. Xavier: Writing - review & editing. Acknowledgments The authors want to acknowledge the Postgraduate Program in Electrical Engineering (PPgEE) of the Federal University of Campina Grande (UFCG), the Coordination for the Improvement of Higher Level Education Personnel (CAPES), the National Council for Technological and Scientific Development (CNPq) and the Light Energia S.A. References [1] G. Kindermann, J.M. Campagnolo, Electrical Grounding (in Portuguese), 3rd ed., Sagra-DC Luzzatto, Porto Alegre, Brazil, 1995. [2] S. Visacro, Grounding and Earthing: Basic Concepts, Measurements and Instrumentation, Grounding Strategies (in Portuguese), 2nd ed., ArtLiber Edit., São Paulo, Brazil, 2002. [3] Protection against lightning — Part 1: general principles, Int. Stand. IEC (2010) 62305–62311. [4] R. Rüdenberg, Grounding principles and practice I — fundamental considerations on ground currents, Electr. Eng. 64 (1) (1945) 1–13. [5] S. Visacro, G. Rosado, Response of grounding electrodes to impulsive currents: an experimental evaluation, IEEE Trans. Electromagn. Compat. 51 (1) (2009) 161–164. [6] N. Harid, H. Griffiths, S. Mousa, D. Clark, S. Robson, A. Haddad, On the analysis of impulse test results on grounding systems, IEEE Trans. Ind. Appl. 51 (6) (2015) 5324–5334. [7] J.J. Pantoja, F. Roman, F. Amortegui, C. Rivera, Lightning grounding system of a
10
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Grounding system models for electric current impulse M.F.B.R. Gonçalves
a,c,⁎
b
a
d
T b
, E.G. da Costa , A.F. Andrade , V.S. Brito , G.R.S. Lira , G.V.R. Xavier
a
Post-Graduate Program in Electrical Engineering — PPgEE, COPELE, UFCG, Brazil Electrical Engineering Department, Federal University of Campina Grande (UFCG), Brazil Federal Institute of Pernambuco (IFPE), Brazil d Federal Institute of Paraíba (IFPB), Brazil a
b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Grounding system Current impulse Transient effects Electric model
In this paper, two electrical models that simulate grounding system responses to current impulses with inductive or capacitive characteristics are presented. The models were elaborated from the analysis of voltage–current curves obtained from field tests. The characteristic curve of the relation between measured voltage and applied current (V × I) was used to identify the electric circuit model elements. In order to evaluate the proposed models, two grounding system configurations applied in electrical system and an additional configuration presented in the literature were used as case study. For each configuration, two models were evaluated: the proposed model and a literature model. The results of the proposed and literature model were evaluated and compared using calculated error statistics over time. The proposed model application resulted in values of total effective error lower than 5% in all analyzed cases, with equivalent error index values regarding the literature model and, in some cases, even smaller. The proposed model has more advantages in comparison to the literature model, since it has fewer and only linear elements. Due to the presentation of a simple and reliable configuration, the proposed circuits can be coupled, with greater ease and flexibility, to transient analysis programs and in insulation coordination studies.
1. Introduction Grounding systems have as main objective to make the soil a path of low impedance, securing people and equipment integrity, as well as to ensure the electrical system’s continuous operation [1,2]. Therefore, they must enable the potential equalization when electric currents are injected by the neutral of transformers, short circuits, switches and lightning discharges in the electrical system [3,4]. The electrical phenomena due to short-circuit, or phase unbalance have different characteristics from the switching or lightning discharge phenomena. The first ones occur essentially at industrial frequency (50 Hz or 60 Hz) and the latter are high-frequency phenomena (0.5 MHz to 10 MHz) with current amplitudes that may exceed 100 kA in the case of lightning discharges [3]. However, grounding systems are designed to attend only the requests at low frequency. In this case, the design and the analysis of a grounding system are done from a nonconservative simplification since the grounding impedance parameter is approximated to the grounding resistance parameter [4]. The analysis of the phenomena in low frequency is consolidated. On the other hand, researches are still handled in order to understand the phenomenon at high frequencies, as well its impact on electrical
⁎
systems and the influence on grounding systems designs. Some works, as presented in [6–8], analyze the phenomena at high frequencies through experimental evaluations, while other works, as shown in [9–12], use modeling from computational simulations. Among the studies involving experimental evaluation, it can be highlighted some results extracted from tests in ground rods and horizontal electrodes [13], grounding grids [14], wind turbine grounding systems [15], and counterpoise wires [16]. However, all the mentioned studies are subjected to financial limitations, which impose the use of low amplitude current impulse generator, limited physical space etc. Other works try to overcome the physical space limitation through the construction of reduced models [17,18]. Nonetheless, the use of reduced models does not ensure reproduction of real grounding system conditions, presenting uncertainties related mainly to the soil electrical characteristics, the effective length [19], the propagation and the transit time of electromagnetic waves in soil. In addition, researches that considered the ionization effects and current transient frequency spectrum were conducted in a controlled laboratory environment or did not evaluate complex geometries of a grounding system [20,21]. Researches that apply computational simulations to investigate the grounding system performance toward current impulses are
Corresponding author. E-mail address: [email protected] (M.F.B.R. Gonçalves).
https://doi.org/10.1016/j.epsr.2019.105981 Received 27 February 2019; Received in revised form 20 June 2019; Accepted 1 August 2019 Available online 27 August 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
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2.2. Methodology
represented by models where transient effects such as ionization, inductive or capacitive behaviors are evaluated [5,22–24]. The ionization effect occurs only for high-intensity current impulses that cause high electric fields and, consequently, soil ionization. The effect of soil ionization is conservative, that is, it reduces the values of transient impedance [17,21,22]. However, the inductive behaviors, caused by the high frequencies involved in the impulses, can increase the values of transient impedance, presenting different performances for soils [5,6]. Grounding system behavior modeling by electric circuit allows its coupling to electromagnetic transient analysis programs, which can be used in insulation coordination studies, such as presented in [25]. Thus, this work proposes a grounding system model, based on an electric circuit, capable of representing the inductive or capacitive behaviors; the frequency components influence and the current impulse intensity. The designed model was based on the voltage and current waveforms obtained from an electric circuit model described in the literature [17], as well as from laboratory and field experiments. The main contributions of this paper can be summarized by the proposal of two new circuits composed only by linear elements (resistors, capacitors and inductors), differently from the circuits found in the literature that use non-linear elements, reducing the model complexity. In addition, the circuits are not only presented, but is also demonstrated how to calculate the necessary parameters for it use. Moreover, the models and simulations were attested by measurements in a real size dimension grounding system, differently from several literature papers. Therefore, the presented models are fit to be applied to transient analysis programs and in insulation coordination studies, aiding in the electrical systems design. The rest of the paper is organized as follows: Section 2 describes the experimental field tests; Section 3 presents the results obtained in the experimental tests; Section 4 details the methodology for defining the electrical circuits that model the grounding systems. The results are presented and discussed in Section. 5. Finally, in the section 6 are presented the conclusions extracted from this work.
i (t ) = I (e−at − e−bt )
(1)
2. Experimental tests
v (t ) = V (e−ct − e−dt ).
(2)
2.1. Grounding system characterization
Tables 2 and 3 show the parameters obtained from the adjustment of curves from (1) and (2) for the grounding system configurations G1 and G2, respectively. The adjusted curves (voltage 1, current 1, voltage 2 and current 2) for the 20 kV and 25 kV charging voltages, referring to the grounding system configurations G1 and G2, respectively, can be seen in Figs. 5 and 6.
A current impulse generator was used to inject the impulses into the grounding systems. The impulse generator capacitors were charged with voltages of 20 kV and 25 kV. For each voltage level, three consecutive impulses were applied, with a 15-minute interval between each application, and the average of the signals was used to get current and voltage impulses. The schematic diagram of the experimental arrangement is shown in Fig. 2. The signal acquisition of the current impulses injected into the grounding system was carried out by a Pearson coil, with a sensitivity of 0.01 V/A ± 1%. The Pearson coil is connected to a digital oscilloscope. The voltage waveform in the grounding system was acquired through the digital oscilloscope (Tektronix TDS 2014) using high-voltage probes (Tektronix P6015A). Both voltage and current probes were close to the injection point. The generator grounding system was 100 m from the grounding system under test while it was at 100 m from the remote grounding, forming a 90-degree angle between the three. 3. Results of measurements 3.1. Field data processing The voltage and current signals acquired in field were imported into the MATLAB® software, and noise suppression techniques were applied. The measured curves (voltage 1, current 1, voltage 2 and current 2) for the 20 kV and 25 kV charging voltages, referring to the grounding system configurations G1 and G2, respectively, can be seen in Figs. 3 and 4. The signals were modeled using curve fitting through the exponential double model, and their parameters were used in commercial PSIM® software [26], such as:
Grounding systems were implanted in soils with different characteristics and configurations, named G1 and G2. The configuration G1 represents a typical grounding system of substations, while the configuration G2 represents a typical grounding system of overhead transmission line towers. Soil resistivity measurements in the proximities of the grounding system locations were performed using the Wenner method and were characterized based on two-layer stratification. The resistivity and depth values of the layers are shown in Table 1. The first grounding system configuration, G1, corresponds to a grounding system of 12 copper-clad steel rods with a diameter of 20 mm and a length of 2.40 m, interconnected by bare copper cables with a cross-sectional area of 35 mm² and buried at a depth of 0.30 m in soil. The second, G2, corresponds to a grounding system of 12 copperclad steel rods with a diameter of 20 mm and a length of 2.40 m, interconnected by bare copper cables with a cross-sectional area of 50 mm² and buried at a depth of 0.30 m in soil. Fig. 1 shows the grounding system configurations used in the tests.
3.2. Field data evaluation Fig. 7 shows the voltage versus current curves (V × I) for the G1 grounding system configuration. In Fig. 7, the blue arrows show the beginning and end directions of the V × I curves, and it can be observed that the maximum current value occurs before than the maximum voltage value, indicating that G1 grounding system configuration has capacitive behavior. For the G2 grounding system configuration, the maximum voltage value occurs before the maximum current value, as presented in Fig. 8, indicating that G2 grounding system configuration has inductive behavior.
Table 1 Grounding system soil characterization.
4. Proposed models
Soil Stratification Grounding system Configuration G1 G2
Layer h1A1 h2A1 h1A2 h2A2
Depth (m) 0–0.28 > 0.28 0–2.83 > 2.83
The proposed electrical models for grounding system representation were developed based on the presented experimental responses and reference models of grounding systems and surge arresters [8,17,27]. In order to represent the inductive and capacitive behaviors, two electrical circuits were proposed, as shown in Fig. 9.
Resistivity (Ω m) 33.47 49.61 39.62 196.57
2
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Fig. 1. Representation of the grounding system configuration: (a) G1 upper view; (b) G2 side view; (c) G2 upper view.
4.1. Resistance R1 calculation
R1 =
For the capacitive circuit shown in Fig. 9a, it is considered that at the initial time of a surge (t = 0), the capacitor C is discharged. Thus, the RC branch initially behaves as a short circuit, since vR2(t = 0) = 0 and the initial grounding system dynamics is defined by the resistor R1. Thus:
R1 =
dv (0). di
V (d − c ) . I (b − a)
(4)
For the inductive circuit, it is considered that at the initial time (t = 0) of a surge, there is no current across the inductor L. The R2L branch can be regarded as instantaneously opened, remaining only the element R1. Thus, the resistance R1 of the inductive circuit is estimated similarly to the capacitive case, using (3) and (4).
(3) 4.2. Resistance R2 calculation
In the case of using the double exponential model presented at (1) and (2) for modeling the impulsive waveshapes, Eq. (3) can be rewritten as:
For the capacitive circuit, the resistance R2 is estimated at the point of the V × I curve where the derivative di is equal to the initial slope. dv The initial slope is given by: 3
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Fig. 2. Schematic diagram of the experimental arrangement. Table 2 Calculated Impulse parameters applying the double exponential model for G1 grounding system configuration. Generator charging voltage (kV)
20 25
Calculated parameters for the current impulse
Calculated parameters for the voltage impulse
I (A)
a (s−1)
b (s−1)
V (V)
c (s−1)
d (s−1)
3872 4437
29720 29630
174900 175200
10202 11210
28580 28360
118400 118200
Table 3 Calculated impulse parameters applying the double exponential model for G2 grounding system configuration. Generator charging voltage (kV)
Fig. 3. Measured voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G1. 20 25
Calculated parameters for the current impulse I (A)
a (s−1)
2949 4220
19190 21280
b (s−1) 86500 77350
Calculated parameters for the voltage impulse V (V)
c (s−1)
d (s−1)
23580 29850
18230 18610
332400 318600
Fig. 4. Measured voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G2.
dv = R1 di
Fig. 5. Adjusted voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G1.
(5)
Besides, for the circuit of Fig. 9a, the voltage across the current source can be expressed as:
v = R1 i + vR2.
dv R2 dt
(6)
= 0. Therefore, at this point the current in the capacitor is zero and:
v (t2) = (R1 + R2 ) i (t2).
Differentiating (6) with respect to time and using (5), it follows that, at time t2, when the slope of the V × I curve is equal to the initial slope,
Thus, the resistance R2 of the capacitive circuit is calculated: 4
(7)
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circuit of Fig. 9b:
i=
v + i2. R1
(9)
By differentiating (9) and, again, using (5), it follows that, at a time t2, di when the slope of the V × I curve is equal to the initial slope, dt2 = 0. Therefore, the voltage v is fully applied on the resistor R2 and, at this instant t2:
1 1⎞ i (t2) = v (t2) ∙ ⎛ + . R2 ⎠ ⎝ R1 ⎜
⎟
(10)
Hence, the resistance R2 of the inductive circuit can be calculated as:
i (t ) 1⎤ R2 = 1/ ⎡ 2 − . ⎢ R1 ⎥ ⎣ v (t2) ⎦ Fig. 6. Adjusted voltage and current curves as a function of time for the 20 kV and 25 kV charging voltages for the grounding system configuration G2.
(11)
4.3. Calculation of the capacitance C The capacitance C can be calculated from the time of peak current, di indicated by t1. This is, when t = t1, dt = 0 ., Thus, by differentiating (6) with respect to time, one obtains:
dvR2 dv (t1) = (t1). dt dt
(12)
Besides, the relationship between the total voltage v and the voltage vR2 in the R2C branch is given by: (13)
vR2 = v − R1 i.
Thus, by replacing (12) and (13) in expression (14) for the current in the branch R2C:
i=
v2 dv + C 2, R2 dt
(14)
the expression (15) for the capacitance C can be obtained:
R v (t1) ⎤ dv C = ⎡ ⎛1 + 1 ⎞ i (t1) − / (t1). ⎢⎝ R2 ⎠ R2 ⎥ ⎣ ⎦ dt
Fig. 7. V × I curves for the 20 kV and 25 kV charging voltages for the G1 grounding system configuration.
⎜
⎟
(15)
4.4. Inductance L calculation The inductance L can be calculated considering different time instants. During a lightning discharge, the overvoltage peak value is usually considered as a critical parameter. Thereby the proposed model considers the voltage peak time t1 for the inductance calculation. When dv t = t1, dt = 0 . By differentiating (9) with respect to time, it follows that:
di2 di (t1) = (t1). dt dt
(16)
Besides, the total current i and the current iR2 in the branch RL are related by:
iR2 = i −
v . R1
(17)
Thus, by replacing (16) and (17) in (18) for the voltage in branch RL: Fig. 8. V × I curves for the 20 kV and 25 kV charging voltages for the G2 grounding system configuration.
R2 =
v (t2) − R1. i (t2)
v = R2 iR2 + L
di2 , dt
(18)
the inductance L can be calculated as: (8)
R di L = ⎡ ⎛1 + 2 ⎞ v (t1) − R2 i (t1)⎤/ (t1). ⎢⎝ ⎥ dt R1 ⎠ ⎣ ⎦ ⎜
For the inductive circuit, (5) also holds true. Then, by analyzing the 5
⎟
(19)
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Fig. 9. Proposed circuit for electric models (a) capacitive and (b) inductive.
Fig. 10. Experimental test circuit and scale model used in [17].
5. Reference model
6. Model evaluation
In [17], the authors proposed a model based on electric circuits capable of representing the transient effects of a grounding system subjected to current impulses. They conducted experimental tests on a scale model grounding system, as shown in Fig. 10. The authors proposed the circuit presented in Fig. 11 in order to represent the grounding system impulse response, as well the methods to calculate the circuit parameters through data obtained from tests. The development of the equations and the definition of the parameters of the proposed circuit are further detailed in [17].
The model evaluation was done using: the two grounding system configurations analyzed, G1 and G2; the grounding system configuration of [17]; the proposed models (inductive and capacitive) and the model presented in [17]. The grounding system configuration of [17] consists of a simple grounding rod reproduced in reduced model. The proposed circuit of Fig. 9 and the circuit presented in [17] were simulated in the PSIM® software. As circuit inputs, the current impulse according to (1) and the calculated parameters for the 20 kV and 25 kV generator charging voltages were considered. The simulations have as output the voltage waveforms over time. In order to evaluate the reliability of the proposed model, the simulated voltage waveform was
Fig. 11. Schematic representation of the proposed circuit of [17]. 6
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compared with the measured voltages through the performance metrics R² and RMSE (root-mean-square error). The coefficient of determination, also called R2, is an adjustment measure of the generalized linear statistical model and it varies between 0 and 1 [28]. The closer to 1 is the R2, the better is the fit between the reference and estimated variables. The RMSE evaluates the fit between an estimator and the observed values [28]. The lower the RMSE value, the better is the fit between the estimated and observed values. The models evaluation resulted in three different cases. Case 1 and Case 2 consisted of modeling the impulsive response of the grounding system configurations G1 and G2 (Fig. 1), respectively. The capacitive and inductive proposed models, presented in Figs. 9a and b, were applied for the Cases 1 and 2, respectively. In order to evaluate the proposed models accuracy, the model presented in [17], shown in Fig. 11, was used as reference for both cases. Finally, the Case 3 consisted of modeling the impulsive response of the grounding system configuration of [17], presented in Fig. 10, using the inductive proposed model and the model presented in [17].
Table 5 Values of the circuit elements calculated using the methodology of [17]. RL (Ω)
RN0(Ω)
RN (mΩ)
LN (μH)
A
α
1.595
24.726
24.726
100
−94.986
0.280
6.1. Case 1: grounding system G1 The proposed capacitive model was chosen after the characterization of the grounding system configuration G1 through its V × I curve shown in Fig. 7. Then, (4), (11) and (15) were applied to determine the values of the elements R1, R2 and C from a computational routine that has as input the voltage and current waveforms shown in Fig. 7. Table 4 shows the values of the calculated circuit elements. The methodology used by [17] was implemented in a computational routine to determine the values of the circuit elements presented in [17], which has as input the voltage and current waveforms shown in Fig. 7. Table 5 shows the values of the calculated circuit elements. In Fig. 12, the voltage waveforms obtained from the simulations are shown in the time domain. In Figs. 13 and 14, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed capacitive circuit and the circuit presented in [17] are shown in Table 6. When comparing the results from Figs. 12, 13 and 14, we verified that the proposed capacitive model was more efficient in representing the response of the grounding system configuration G1. Its application resulted in smaller errors and peak voltage values closer to the measured value. Both models presented better results for the impulse with 25 kV charging voltage. A possible explanation for the higher errors presented by the model developed in [17] can be associated to the model conception, since it was developed focused in grounding systems with inductive response.
Fig. 12. Simulated voltage by applying the methods for the grounding system configuration G1.
Fig. 13. Coefficient of determination R² over time for the simulations of the grounding system configuration G1.
6.2. Case 2: grounding system G2 The choice of the proposed inductive model was similar to Case 1 using the V × I curve shown in Fig. 8. Then, (4), (11) and (19) were applied to determine the values of the elements R1, R2 and L from a computational routine that has as input the voltage and current waveforms shown in Fig. 8. Tables 7 and 8 show the values of the calculated circuit elements by the proposed model and the model presented in [17], respectively. In Fig. 15, the voltage waveforms obtained from the simulations are
shown in the time domain. In Figs. 16 and 17, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed inductive circuit and the circuit presented in [17] are shown in Table 9. When comparing the results from Figs. 15, 16 and 17, it has been shown that both models presented relatively small errors. The literature model [17] error is smaller when the total impulse time is considered. However, the proposed model presents minor errors during the rise time and for the peak voltage. The best performance of the model presented in [17] for case 2 when compared to Case 1 was expected due to the inductive essence of the model.
Table 4 Values of the circuit elements calculated for grounding system configuration G1. R1 (Ω)
R2 (Ω)
C (μF)
1.595
0.824
11.058
7
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Fig. 15. Simulated voltage by applying the methods for the grounding system configuration G2.
Fig. 14. RMSE calculated for the simulated response of the grounding system configuration G1. Table 6 Error metrics calculated for the case 1.
Capacitive circuit Circuit presented in Ref. [17]
Generator charging voltage (kV)
R²
Maximum RMSE (%)
Peak voltage error (%)
20 25 20 25
0.94 0.95 0.67 0.91
5.6 4.3 11.8 8.6
3.5 1.5 11.6 3.7
Table 7 Values of the circuit elements calculated for grounding system configuration G2. R1 (Ω)
R2 (Ω)
L (μH)
37.58
13.41
153.0
Fig. 16. Coefficient of determination R² over time for the simulations of the grounding system configuration G2.
Table 8 Values of the circuit elements calculated using the methodology of [17] and V × I curve presented in Fig. 8 as input. RL (Ω)
RN0(Ω)
RN (mΩ)
LN (μH)
A
α
37.49
8.631
8.631
100.0
0.0329
1.0842
6.3. Case 3: reference grounding system As circuit inputs, the current impulses measured in the experimental tests for two different charge levels of generator called (a) and (b), as described in [17], were considered. The determination of the values of the proposed inductive circuit elements and of the circuit presented in [17] was done analogously to Case 2 and are presented in Tables 10 and 11, respectively. In Fig. 18, the voltage waveforms obtained from the simulations are shown in the time domain. In Figs. 19 and 20, the values calculated over time of R² and RMSE regarding the measured and simulated voltages values are presented, respectively. The performance metrics obtained for the evaluation of the proposed inductive circuit and the circuit presented in [17] are shown in Table 12. When comparing the results from Figs. 18, 19 and 20, it has been shown that both models presented relatively small errors and
Fig. 17. RMSE calculated for the simulated response of the grounding system configuration G2.
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Table 9 Error metrics calculated for the Case 2.
Inductive circuit Circuit presented in Ref. [17]
Generator charging voltage (kV)
R²
Maximum RMSE (%)
Peak voltage error (%)
20 25 20 25
0.999 0.996 1.000 0.999
1.2 1.9 1.2 1.4
0.4 0.9 0.6 1.9
Table 10 Values of the circuit elements calculated for grounding system configuration of [17] using the proposed inductive circuit. R1 (Ω)
R2 (Ω)
L (μH)
385.6
455.1
697.3
Fig. 19. Coefficient of determination R² over time of the grounding system configuration of [17].
Table 11 Values of the circuit elements calculated using the methodology of [17]. RL (Ω) 385
RN0(Ω) 39.2
RN (mΩ) 39.2
LN (μH) 100
α
A 6.08 × 10
−8
2.06
Fig. 20. RMSE of the grounding system configuration of [17]. Table 12 Error metrics calculated for the Case 3. Fig. 18. Simulated voltage by applying the methods for the grounding system configuration of [17]. Inductive circuit
coefficient R² values greater than or equal to 0.97. In addition, for the higher voltages tested, the proposed model generally presented smaller errors when compared to the reference model. This fact may indicate a conservative characteristic of the proposed model, representing an attractive feature for the application in transient analysis programs.
Circuit presented in Ref. [17]
Experimental tests of Ref. [17]
R²
Maximum RMSE (%)
Peak voltage error (%)
(a) (b) (a) (b)
0.98 0.97 0.99 0.97
5.3 4.7 2.2 8.3
6.0 4.9 1.8 5.1
of the grounding systems applied in its evaluation with values of total RMSE lower than 5%, of peak voltage error lower than 6% and of R² higher than 0.94 in all analyzed cases. Despite its simplicity, the proposed model presented total errors with equivalent values regarding the literature model and, in some cases, even smaller. The proposed model has advantages such as greater ease of parameter calculation and circuit implementation, which presents only linear elements, differently from the circuits found in the literature that use non-linear elements, reducing the model complexity. In addition, smaller errors were observed for higher test voltages, which may indicate a conservative characteristic of the model when applied to studies of transient analysis and insulation coordination. Finally, the model proposed in this work is capable of representing the inductive or capacitive behaviors of grounding systems. In their
7. Conclusions In this work, two electrical models of grounding systems capable of representing capacitive and inductive responses were proposed as well expressions for estimating its parameters from curves V-I obtained from measurements with current impulse generator. For the elaboration and evaluation of the models, experimental tests were carried out in two different grounding systems of real size dimensions that simulate real configurations applied in the electric system. The results of the proposed model were compared, through calculated statistics over time (R2 and RMSE), with the results of the experimental tests and also with results obtained from the literature. The proposed models were able to represent the impulsive response 9
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evaluation, we considered effects of the frequency components and different current impulse intensities. However, the method has a practical limitation, since it depends of the obtaining of preliminary waveform information (current and voltage) about the prevailing grounding system behavior (inductive or capacitive). Due to the presentation of a simple and reliable configuration, the proposed circuits can be coupled, with greater ease and flexibility, to electromagnetic transient analysis programs and in insulation coordination studies.
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Funding This research received no external funding. Conflicts of interest The authors declare no conflict of interest. CRediT authorship contribution statement M.F.B.R. Gonçalves: Methodology. E.G. da Costa: Methodology, Writing - review & editing, Conceptualization. A.F. Andrade: Methodology. V.S. Brito: . G.R.S. Lira: Supervision. G.V.R. Xavier: Writing - review & editing. Acknowledgments The authors want to acknowledge the Postgraduate Program in Electrical Engineering (PPgEE) of the Federal University of Campina Grande (UFCG), the Coordination for the Improvement of Higher Level Education Personnel (CAPES), the National Council for Technological and Scientific Development (CNPq) and the Light Energia S.A. References [1] G. Kindermann, J.M. Campagnolo, Electrical Grounding (in Portuguese), 3rd ed., Sagra-DC Luzzatto, Porto Alegre, Brazil, 1995. [2] S. Visacro, Grounding and Earthing: Basic Concepts, Measurements and Instrumentation, Grounding Strategies (in Portuguese), 2nd ed., ArtLiber Edit., São Paulo, Brazil, 2002. [3] Protection against lightning — Part 1: general principles, Int. Stand. IEC (2010) 62305–62311. [4] R. Rüdenberg, Grounding principles and practice I — fundamental considerations on ground currents, Electr. Eng. 64 (1) (1945) 1–13. [5] S. Visacro, G. Rosado, Response of grounding electrodes to impulsive currents: an experimental evaluation, IEEE Trans. Electromagn. Compat. 51 (1) (2009) 161–164. [6] N. Harid, H. Griffiths, S. Mousa, D. Clark, S. Robson, A. Haddad, On the analysis of impulse test results on grounding systems, IEEE Trans. Ind. Appl. 51 (6) (2015) 5324–5334. [7] J.J. Pantoja, F. Roman, F. Amortegui, C. Rivera, Lightning grounding system of a
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