2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Transient Responses due to Various Burial Depths on a Single Long Horizontal Ground Conductor W. F., Wan Ahmad*, D. W. P., Thomas**, C., Christopoulos**, K. A., Mohd Sharim*, J., Jasni*, M. Z. A., Ab Kadir* and H., Hizam* *Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia. Email:
[email protected] **School of Electrical and Electronic Engineering, the University of Nottingham, University Park, NG7 2RD Nottingham, United Kingdom. Email:
[email protected]
occurrence of voltage sags [3]. Moreover, transmission lines also need such protection as they are the lightning prone and could cause voltage sag [4]. Lightning is a discharge of static electricity and usually occurs in thunderclouds [1]. A typical lightning is an electrical discharge between either cloud or the earth (cloud-toground flash), or within the cloud (intra-cloud flash), or different clouds (inter-cloud flash), or between a cloud and its surrounding air [1]. Ground conductor is typically used to dissipate transient currents effectively into its surrounding soil, preventing damage to the electrical power system [2]. Thus, the performance of such systems is influenced by proper functioning of a ground conductor itself where a proper ground will create a simpler and straighter path for the transient currents to follow to the earth’s or by-pass the site’s equipment [3]. This will ensure the safety of the system, equipment and personnel who connected to it [1].
Abstract—The purpose for this paper is to determine the effective burial depth for a single long horizontal ground conductor which is part of a lightning protection system. In this study, transient responses behaviours of the ground conductor towards various burial depths with lightning excitation are presented. The simulation is done in the time domain using TLM which is found to be the ideally suited numerical method due to its many advantages. The excitation voltage is injected at one end of the ground conductor, represented by a derivative Gaussian pure injection voltage source. Results are presented regarding various burial depths at each node of the ground conductor and a good agreement with an IEEE standard is shown. Keywords— BEM, derivative Gaussian, FDTD, FEM, MoM, grounding conductor, TDIE, Transient response, TLM, voltage sag
I.
INTRODUCTION
According to National Electric Code (NEC) the word “ground” is defined as a conducting connection, whether intentional or accidental between an electric circuit or equipment and the earth, or to some conducting body that serves in a place of the earth. Theoretically, there are two different types of common grounding, i.e. the earth and equipment groundings [1]. Earth grounding is an intentional connection from a circuit conductor usually the neutral to a ground electrode placed in the earth [1], [2]. While the equipment grounding is needed to ensure the operating equipment within a structure is properly grounded [1], [2]. Also, a grounding system’s main purpose is to provide a safe path for the transient currents to be dissipated into the earth. Examples of transient currents are resulted from lightning strikes, static discharges, electromagnetic interference (EMI) and radio frequency interferences (RFI) [2]. A good grounding system is not only for the personnel safety but also to provide the protection for power plants and its equipment [1]. Also a good grounding system will improve the reliability of an equipment and reduce the likelihood damage resulted from the transient currents [3]. This is important as an electric utility is unable to deliver a high efficient power supply to the consumers after a lightning strike due to the
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II. NUMERICAL METHODS Transient and steady-state characteristics of a ground conductor have been investigated experimentally and numerically in the literatures. Such examples of numerical methods applied are MoM, FDTD and TLM. Numerical electromagnetic analysis can be performed by assuming a well-profiled condition where values of both conductivity and permeability of the ground are known or set arbitrary [4]. Such results from these analyses are useful in understanding the phenomena as well as in confirming the measured results. Numerical modelling is a way of representing a physical system using specific quantities. For an electromagnetic system, it is generally required to obtain the electric and magnetic fields within a volume of space and subject to appropriate boundary conditions [5]. Analytical methods for the solution of electromagnetic problems involve propagation of electromagnetic waves and their interaction with materials and structures, and it can only be applied in a few simple cases with a lot of assumptions and approximations [5]. In studying situation encountered in this study, it is necessary to develop a numerical method which could model Maxwell’s equations computationally. Most electromagnetic problems involve either differential or
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
integral equation methods [1], [6], [7]. Examples of the differential equation methods are Transmission-Line Modelling (TLM), Finite-Difference Time-Domain (FDTD) and Finite Element Method (FEM). While, the integral equation methods are Moment of Method (MoM), Boundary Element method (BEM) and Time-Domain Integral Equation (TDIE). Differential equation methods require simpler mathematical equations to be generated compared to the integral equation methods. In this study, the ground conductor is assumed to be straight and its surrounding soil is considered to be a homogenous medium. Thus, the nonlinearities and inhomogeneous criteria are not considered. Therefore, FEM is eliminated due to it requires larger space in the computer memory and it maps the triangular meshing. Main difference between the TLM and FDTD techniques is in the mappings of the unit cell and the time stepping process [1], [2], [8], [9]. In FDTD, the electric and magnetic fields are separated in space and time by half a space step and half a time step, respectively [1]. On the other hand, all fields are solved at the same point in space (i.e. at the centre of the cell and simultaneously in time) in TLM meshes [1], [9]-[11]. Hence, this study is adopting TLM method which is classified as a differential time-domain method and ideally suited for electromagnetic compatibility problems. Another reasons is due to TLM is expressed in terms of circuit concepts which are more familiar and easier to be understood with a single calculation will give information over a wide range of frequencies [1], [9], [12]. This is important as this study is involved with high frequency transients i.e. lightning. Also, an increased resolution can be applied where it is required in TLM method [1], [9], [12]. And, both the internal and external environments can be modelled simultaneously [1], [9], [12]. Typically, a TLM algorithm contains electric circuit distributed elements and the transmission-line segment length l. Each segment is then described by lumping together its capacitance and inductance [1], [12]. First, the initial conditions and the input data are determined. This includes the propagation delay t, the total iteration kmax the transmission-line segment length l and the total segmentation N of the transmission-line model. Then,
calculations of the line parameters per unit length, i.e. resistance Rd, inductance Ld, conductance Gd and capacitance Cd, are obtained. After finding the values of these parameters, the transient node current kIn and transient incident node voltage kVni are obtained at kts. Later, the scattering impulses, i.e. the transient reflected node voltages kVnr are calculated. These reflected impulses then propagate to the neighbouring nodes where they get scattered at the next time step. The new transient node current k+1In and the new transient incident node voltages k+1Vni are both determined with respect to the new increased time (k+1) ts. These are known as the connection impulses which will link two adjacent transmission-line segments. This scattering and connecting algorithm is then repeated for as long as the output is desired. The TLM algorithm which is implemented in this study is following [1], [12]. III. A 1-D TRANSMISSION-LINE MODEL In this work, the ground conductor is represented as a single long horizontal ground conductor (SLHGC) with the simulation is done in the time-domain and certain parameters are fixed. The excitation voltage is injected at one end of the ground conductor, represented by a derivative Gaussian pure injection voltage source modeling the lightning return stroke. This excitation source is chosen for its computation efficiency reason following [1], [13]-[15]. The physical model of an SLHGC is illustrated in Fig. 1. The model is constructed under the assumption of its surrounding soil is homogenous and the ground conductor is symmetrical. This study investigated the transient responses of the ground conductor through five segments. Fig. 2 shows the SLHGC as a lossy transmission line terminated with an RC load as the RC load represents an open circuit termination in the TLM [1], [12]. The Thevenin equivalent circuits are shown in Fig. 3. The radius and the burial depth of SLHGC are a and h, respectively of the ground conductor. Rd, Ld, Gd, and Cd are the series resistance, series inductance, shunt admittance and shunt capacitance, respectively per segmentation of l, with l is the length of SLHGC and N is its total segmentation. RC and CL are the load resistance and capacitance, respectively in the circuit.
Figure 1. Physical Model of a fully buried Single Long Horizontal Ground Conductor [1]
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Figure 2. A Lossy Transmission Line with an RC Load Circuit [1], [12]
Figure 3. 1-D Transmission-Line Model for a Lossy Transmission Line with an Open Circuit Termination [1], [12]
IV.
peak value, k is the time step number, Δt is the time step, t 0 = 5 ×10 −6 s is the time delay, r = 0.001 V is the truncation of the wave and h = 5 ×10 −6 s is the time span to half width of the wave as described in [1], [13]-[15].
CHOICE OF PARAMETERS
In order to relate the effect of burial depth h, Sunde equations are used to determine the per unit parameters of the ground conductor, i.e. Rd, Ld, Gd, and Cd constants using (1) to (4) as defined in [1], [12]. Note that π = 3.142 , μ0 = 4π × 10−7 H/m, ε o = 10 −9 36π F/m and these electrical parameters are calculated based on the soil properties and the geometry of the SLHGC.
Rd = ρ c πa 2 /m
[( (
)) ]
Ld = [μ o 2π ] ln 2A 2ha − 1 H/m 2π S/m Gd = ρ s ln 2A 2ha − 1 2πε 0ε s F/m Cd = ln 2A 2ha − 1
[( (
( (
)) ]
))
[
]
½ − V0 ⋅ − 2 ln (r ) ⋅ [exp(0.5)] ⋅ °° V °° Vs (kΔt ) = ®ª kΔt − t º ª § ln (r )(kΔt − t )2 ·º ¾ 0 0 ¨ ¸» ° °« » ⋅ «exp¨ ¸ h2 ¹¼» ¿° ¯°¬ h ¼ ¬« ©
(1) (2) (3) (4)
The first ground conductor model is taken to be fully buried 0.5m in the homogenous soil, with length A = 110 m, total segmentation N=25, radius a = 6 mm, relative soil permeability r = 9.0 and soil resistivity = 103 m, and the SLHGC is considered as copper with its resistivity c=1.7241x10-8m. Note that all of these parameters are following [1], [13], [14]. The excitation voltage derivative Gaussian is as shown in Fig. 4 and calculated using (5) with Vo = 100kV is the
Figure 4. Typical Vs (t ) Profile with Derivative Gaussian Wave [1], [13]-[15]
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(5)
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
V.
RESULTS AND DISCUSSIONS
node currents into the homogenous soil. It may due to the deeper burial depth, the humid the soil is. Hence, an effective burial depth is needed to provide safety and accurately enable a SLHGC to act as a grounding system against high transient such as lightning return strike.
Fig. 5 shows the time variation of transient node voltages and currents of an SLHGC. The work carried out is to examine how long is the time required to dissipate the transient currents effectively through the ground conductor into its surrounding soil. According to Fig. 4 the transient node voltages and transient node currents which are simulated along the ground conductor are reduced to almost 75% and 100%, respectively, at the other end of the ground conductor. This shows that this first model presented follow the Ohm’s law of having an open circuit termination. An open circuit termination relates to there is no metal contact connected at that particular end, for example pipeline or fences. For an open circuit termination, the voltages are to be found having non-zero value, while termination node current to be found a zero value. Fig. 6 shows the transient node voltages with various burial depths that are 0.3m, 0.5m, 1m, 1.5m, 2.5m and 10m. In Fig. 7, the transient node currents are presented with various burial depths that are 0.3m, 0.5m, 1m, 1.5m, 2.5m and 10m. Note that only the burial depth parameter is varied, while other parameters of the SLHGC are remain the same. It is found that only transient node currents vary when different burial depth parameters applied to the ground conductor models. On the other hand, the transient node voltages demonstrate the similar waveforms with peak positive and negative values remain the same with various burial depths. Generally, the higher the burial depth, the higher the transient node currents simulated along the ground conductor. In other word, the deeper the ground conductor located in the earth, the lesser the transient node currents to be dissipated into its surrounding soil. Hence, the purpose of a ground conductor being part of a grounding system is more difficult to be achieved with a high value of the burial depth. Also, a deeper burial depth means a higher maintenance cost for the grounding system! According to the IEEE standard 142-2007 [16] the characteristic impedance Z0 will be 5% decreased with every 0.5m increment of burial depth. With the transient node voltages remain the same, and the transient node currents decreasing, it is shown that the ground conductor models presented in this study are in a good agreement with the IEEE standard. A 5.27% decrement of the characteristic impedance was found when comparing between the 0.5m and 1.0m burial depth ground conductor models. VI.
Figure 5a. Time variations of transient voltages along SLHGC, h = 0.5m
Figure 5b. Time variations of transient currents along SLHGC, h = 0.5m
Figure 6a. Time variation of transient voltage for node 1, for various burial depths
CONCLUSIONS
In this paper, the behaviour of the transient node currents and transient node voltages along a fully buried SLHGC are presented in the time domain using TLM method. The lightning strike is modelled as a derivative Gaussian voltage source and injected at one end of the ground conductor. It is found that the burial depth will only affect the behaviour of the transient node currents. The higher the burial depth, the lower the dispersion rate of the transient
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Figure 7a. Time variation of transient current for node 1for various burial depths
Figure 6b. Time variation of transient voltage for node 7 for various burial depths
Figure 7b. Time variation of transient current node 7 for various burial depths
Figure 6c. Time variation of transient voltage for node 13 for various burial depths
Figure 7c. Time variation of transient current for node 13 for various burial depths Figure 6d. Time variation of transient voltage for node 19 for various burial depths
Figure 7d. Time variation of transient current node 19 for various burial depths
Figure 6e. Time variation of transient voltage for node 25 for various burial depths
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
[7]
[8] [9]
[10]
[11]
Figure 7e. Time variation of transient current for node 25 for various burial depths
[12]
[13]
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W. F. Wan Ahmad, PhD Thesis: Modelling of Lightning Strike on an Earth Ground Conductor, the University of Nottingham, Nottingham, 2007. Y. Baba, N. Nagaoka and A. Ametani, “Modelling of Thin Wires in a Lossy Medium for FDTD Simulations”, IEEE Transaction on EMC, Vol. 47, No.1, 2005. IEEE Recommended Practice for Emergency and Standby Power System For Industrial and Commercial Application, ANSI/IEEE Std 446-1987, pp. 20-36, Nov, 1986. B. Sawir, M. R. Ghani, A. A. Zin, A. H. Yatim, H. Shaibon and K. L. Lo, “Voltage Sag : Malaysian’s Experience”, IEEE 0-78034754-4/98, 1998. J. L. Herring, PhD Thesis: Developments in the TransmissionLine Modelling Method for Electromagnetic Compatibility Studies, the University of Nottingham, Nottingham, 1993. M. N. O. Sadiku, Elements of Electromagnetic, 3rd edition, Oxford University Press, 2001.
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