An advanced BEM-based CAE tool for the analysis of earthing systems

Transcription

1 An advanced BEM-based CAE tool for the analysis of earthing systems M. Casteleiro, F. Navarrina, I. Colominas, J. París, X. Nogueira & L. Ramírez Group of Numerical Methods in Engineering (GMNI) - Dept. of Applied Mathematics School of Civil Engineering, University of A Coruña, Spain Abstract In this paper we present TOTBEM: a freeware application for the in-house computer aided design and analysis of grounding grids. The system is based on a BEM formulation that has been presented by the authors in a number of publications. This CAE tool is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over-ground substations with a grounding grid embedded in a multiple-layer stratified soil model. The actual version of the software is available for testing purposes (and also for its technical use) at no cost and can be run on any basic personal computer (as of 2012) with no special requirements. The distribution kit consists of a single ISO bootable image file that can be freely downloaded from the Internet and copied into a DVD or a USB flash memory drive. The application runs on the Ubuntu (Lucid Lynx) LTS release of Linux and can be easily started by just booting the system from the live DVD/USB that contains the downloaded file. This operation does not modify the native operative system nor installs any software in the computer, but the application is fully operational while the live DVD/USB is taking control. The core of the system is the BEM-based analysis code, which includes highly efficient integration and acceleration techniques proposed by the authors for reducing the computational cost and improving the rate of convergence of the series expansions involved in multiple-layer soil computations. The pre- and post-processing engines of the application have been built on top of the open source SALOME platform toolkit. The scope and power of the proposed approach are shown by solving some important application problems in Electrical Engineering, including the analysis of transferred potentials and compact underground substations. 1 Introduction The main objective of an earthing system is to safeguard that persons staying in the surroundings of the installation will not be exposed to dangerous electrical shocks. As a second aim in importance, the system must guarantee the integrity of equipment and the continuity of power supply when a fault condition occurs. In order to achieve these goals, the equivalent resistance of the earthing system is required to be low enough to assure that any eventual fault current dissipation into the ground would take place mainly through the buried electrodes. At

2 the same time, the maximum difference of potential between close points on the earth surface is required not to overpass certain thresholds in accordance to safety regulations [1-3]. The basic equations that govern the process can be written as div( ) =0, = grad( ) in, = 0 in, = GPR in, 0 when, (1) where is the earth, is the soil conductivity tensor, is the earth surface, is the normal exterior unit field to, and denotes the boundary (exterior surface in contact with the soil) of the buried electrodes [4-6]. The complete solution to problem (1) gives the values of current density ( ) and potential ( ) at an arbitrary point within when the earthing system is energized to the so-called Ground Potential Rise (GPR) with respect to remote earth. In these terms, the leakage current density σ( ) at an arbitrary point on, the ground current (total surge current being leaked into the earth) and the equivalent resistance of the earthing system, can be written as ( ) = ( ), = ( ), = GPR, (2) where is the normal exterior unit field to. Obviously, there is not a general analytical solution to statement (1). For this reason, only very crude approximations were available until the 70 s. On the other hand, the numerical solution to many practical problems of this kind can be obtained by means of the Finite Difference Method (FDM) or the Finite Element Method (FEM). Unfortunately, this is not true in our case. In most substation earthing systems, the buried active electrode (i.e. the grounding grid) is formed by interconnected bare cylindrical conductors whose diameter/lenght ratio is very small ( 0.001). Furthermore, E is a half-infinite domain and the electrode is excluded. Thus, the need to discretize the geometry of the problem leads to prohibitive computing requirements in most practical cases, what precludes the use of the above mentioned methods (as a general rule) in earthing analysis. In the absence of mathematically well-founded methods type FDM or FEM, several so-called computer methods [1-3,7] have been proposed through time in an attempt to get and approximate solution to problem (1). Although these techniques are widely used, some important problems have been reported, namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [1,5]. At this point, it should be mentioned that the complete solution to problem (1) is not actually needed in the context of earthing analysis, since all safety parameters that characterize the earthing system depend on the values of potential ( ) for on boundary S and on the values of leakage current ( ) for on boundary as in (2). For this reason, we turn our attention to the Boundary Element Method (BEM). A review on the history of this powerful numerical method can be found in [8]. Internationally relevant and pioneering work in both, development and dissemination of BEM is due to Prof. Enrique Alarcón [9-10]. In the last years, the authors have proposed a BEM-based numerical formulation for grounding analysis [4-6]. This is the core or the herein presented TOTBEM freeware application. Finally, the selection of the appropriate soil model is an essential issue in grounding analysis. The simplest is the so-called uniform soil model, in which earth conductivity tensor is replaced by a constant scalar conductivity. On the other hand, if the soil is significantly stratified (either horizontally or vertically), a layered soil model could be the right choice [1,11,12]. In the following sections we will demonstrate the reliability, flexibility and scope of the proposed approach by solving some important problems of earthing analysis.

3 2 Grounding analysis for uniform soil models The first example corresponds to the grounding analysis of the Barberá Substation (Barcelona, Spain) by means of a uniform soil model. Figure 1 shows the plan of the grounding grid. Table 1 summarizes the main characteristics of the earthing system, as well as the numerical model (408 linear boundary elements) being used and the numerical results that were obtained. Figure 1: Barberá earthing system. Grid plan. Table 1: Barberá. Input data and output results. Data Number of electrodes: 408 Diameter of electrodes: mm Max./Min Electrode Length: 19m/3 m Depth of the grid: 0.80 m Max. dimensions of grid: x 90 m Total Protected surface: m GPR: 10 kv BEM Numerical Model Type of approach: Galerkin Type of 1D element: Linear Number of elements: 408 Degrees of freedom: 238 One layer soil model Earth resistivity: 50 Ωm Fault Current: ka Equivalent resistance: Ω

4 Figure 2 shows the potential distribution on the earth surface when a fault condition occurs. Figure 3 displays the potential profile along a certain line (what is useful to obtain some characteristic parameters such as the step and the touch voltage). Figure 4 shows a 3D view of the potential distribution on the earth surface. For a detailed discussion see Colominas [4,5]. Figure 2: Barberá. Potential contours (kv) on the ground. Uniform soil model. Figure 3: Barberá. Potential profile along line in figure 2. Uniform soil model. Figure 4: Barberá. 3D View of potential contours on the ground. Uniform soil model.

5 3 Grounding analysis for multiple-layered soil models This second example corresponds to the grounding analysis of the Santiago II Substation (Santiago de Comp., Spain). In this example we compare the results obtained by means of a uniform soil model and a two layer soil model. Figure 5 shows the plan of the grounding grid. Table 2 summarizes the main characteristics of the earthing system, as well as the numerical model (582 linear boundary elements) being used and the numerical results that were obtained. Figure 5: Santiago II earthing system. Grid plan. Table 2: Santiago II. Input data and output results. Data Number of electrodes: 534 Number of ground rods: 24 Diameter of electrodes: mm Diameter of ground rods: Depth of the grid: 0.75 m Length of ground rods: 4 m Max. dimensions of grid: x 195 m GPR: 10 kv BEM Numerical Model Type of approach: Galerkin Type of 1D element: Linear Number of elements: 582 Degrees of freedom: 386 One layer soil model Earth resistivity: 60 Ωm Total Current: 6.73 ka Equivalent resistance: Ω Two layer soil model Upper layer resistivity: 200 Ωm Lower layer resistivity: 60 Ωm Thickness upper layer 1.2 m Total current: 5.61 ka Equivalent resistance: Ω

6 Figure 6: Santiago II. Potential contours ( 10 kv) on the ground. Uniform soil model. Figure 7: Santiago II. Potential contours ( 10 kv) on the ground. Two-layer soil model.

7 Figure 6 shows the potential distribution on the earth surface for the uniform soil model. Figure 7 shows the potential distribution on the earth surface for the two-layer soil model. Figure 8 compares both potential distributions by means of a 3D visualization. It seems quite obvious that the results obtained by using a multiple-layer soil model are significantly different from those obtained by using a uniform soil model. Since security is our main concern, we conclude -as a general rule- that the use of multi-layer soil formulations is essential to obtain good results, in spite of their higher computational effort. Figure 8: Santiago II grounding system. 3D views of the potential distribution on the ground for the uniform (left), and for the two-layer (right) soil models. We also note that the analysis corresponding to the two-layer soil model in this example is particularly difficult, since part of the grid is buried in the upper layer while the other part is buried in the lower layer (notice that the ground rods are larger than the thickness of the upper layer). A comprehensive discussion of this case can be found in Colominas [12]. 4 Analysis of transferred earth potentials The transferred earth potentials phenomenon occurs when a grounding grid is energized due to a fault condition, while a significant fraction of the GPR voltage is transported to a remote site by buried or half-buried passive conductors (communication or signal circuits, neutral wires, metal pipes, rails, metallic fences, etc.) that are not connected to the active earthing electrodes [13]. When this happens, a non-protected area could experience a sharp and unexpected ground potential rise in spite of being located quite far from the substation [2]. The danger that this possibility represents for the security of humans and for the integrity of equipment is evident. However, only very crude approximations were available for the computation of these effects until the authors proposed an extension of their BEM formulation to solve this kind of problems for both, uniform soil models [14] and multiple-layer models [15]. To demonstrate the importance of this issue, a new analysis of the Barberá Substation is presented. In this occasion, we will introduce a fictitious nearby railroad track. Figure 9 shows the plan of the grounding grid and the situation of the railroad track. The presence of this kind of passive conductors is not rare in real cases, since they may be necessary to move high-power transformers and other heavy devices. Table 3 summarizes the main characteristics of the earthing system, as well as the numerical model (408 linear boundary elements) being used and the numerical results that were obtained. Figure 10 shows the potential distribution on the earth surface when a fault condition occurs. Figure 11 shows a 3D view of the potential distribution on the earth surface. The effect of the transferred earth potentials phenomenon in the potential distribution on the earth surface is evident if we compare these results with those presented in section 2. For a detailed discussion on these issues see Colominas [14,15].

8 Figure 9: Barberá grounding system with a railroad track. Grid plan and track situation. Table 3: Barberá with a railroad track. Input data and output results. Data Number of electrodes: 408 Diameter of electrodes: mm Depth of the grid: 0.80 m Max. dimensions of grid: 140 x 90 Total Protected surface: 6500 m 2 GPR: 10 kv Railway Tracks: Characteristics Number of tracks: 2 Length of the tracks: 130 m Distance between the tracks: 1668 mm Diameter of the tracks: 94 mm Depth: 0.10 m BEM Numerical Model Type of approach: Galerkin Type of 1D element: Linear Number of elements: 408 Degrees of freedom: 260 One layer soil model Earth resistivity: 50 Ωm Fault Current: ka Equivalent resistance: Ω Ratio of Transferred Potentials : 42.33% 2 m

9 Figure 10: Barberá with a railroad track. Potential contours ( 10 kv) on the ground. Figure 11: Barberá with a railroad track. 3D view of potential distribution on the ground.

10 5 TOTBEM: An open-source CAD-CAE system for grounding analysis The proposed BEM-based numerical formulation for uniform and multiple-layer soil models has been implemented in a freeware application for the in-house computer aided design and analysis of grounding grids [16]. The actual version of the software (TOTBEM) is available for testing purposes (and for its technical use) at no cost and can be run on any basic personal computer (as of 2012) with no special requirements. The package provides fully operational pre-processing, analysis and post processing tools. The distribution kit consists of a single ISO bootable image file that can be freely downloaded from the Internet and copied into a DVD or a USB flash memory drive. The application runs on the Ubuntu (Lucid Lynx) LTS release of Linux and can be easily started by just booting the system from the live DVD/USB that contains the downloaded file. This operation does not modify the native operative system nor installs any software in the computer, but the application is still fully operational while the live DVD/USB is taking control. The kernel of the system is the BEM-based analysis code, which includes highly efficient acceleration techniques proposed by the authors [17] for improving the rate of convergence of the series expansions that are involved in multiple-layer soil computations. The pre- and postprocessing engines of the application have been built on top of the open source SALOME platform toolkit [16]. Figure 12: TOTBEM pre-processor. Input data toolbox.

11 Figure 13: TOTBEM post-processor. 3D view of potential distribution on the ground. Figure 12 shows the input data toolbox of the TOTBEM pre-processor in action. Figure 13 shows the TOTBEM post-processor displaying a 3D visualization of the potential distribution on the ground for the earthing analysis being executed. 6 Analysis of compact underground substations The research presented in the previous sections is restricted to the case in which the soil can be considered either uniform or stratified in multiple layers, being its resistivity an order of magnitude higher than the resistivity of the grounding electrode itself. Assuming that the soil is normally regularized before installing the earthing grid, and that the ground surface is leveled right after (prior to assembling the equipment and bringing it into service), the proposed approach is suitable for computing the equivalent resistance and the step and touch voltage in most large electrical over-ground facilities. This important category includes all step-up and step-down transmission substations, as well as a number of distribution substations indeed. Nevertheless, the current trend in Electric Power Engineering moves in another direction, due to the growing preference for smaller underground substations. This pushes the need for developing new earthing analysis techniques that could be applied to facilities of this kind. Compact underground substations are very common at present in urban environments where the space is limited. In this case, the substation is located inside a monoblock concrete

12 structure (containing the transformers, the switches and the rest of the equipment). The whole set is buried under the pavement. Figure 14 shows the scheme of one of these substations (with dimensions l w h = m 3 ). The main grounding electrode is a quadrilateral ring located at 0.8 m of the concrete block itself, buried to 0.5 m depth and supplemented by a 4 m long vertical rod at each vertex. The diameter of the electrodes in the ring is mm and the diameter of each vertical rod is mm. The resistivity of the soil is 50 Ω m and the GPR is 10 kv in the case being considered. On the other hand, the steel framework within the reinforced concrete structure will act as an active electrode of the earthing system, if it is grounded. Otherwise, it will act as a passive electrode (see Section 4). Figure 14: Compact underground substation. Monoblock structure and grounding electrode. It seems obvious that neither the uniform nor the multiple-layer soil concepts fit well to this case, since there are finite regions with different resistivities embedded into the soil (i.e., the concrete structure and the working space inside). Similar considerations can be made when a chemical treatment has been applied to part of the soil, when there are concrete foundations in the site or swimming pools, soil depressions, lakes, hydroelectric dams, etc. in the vicinity. In spite of the interest for using this kind of soil models, the corresponding BEM formulation is much more complicated [18,19] and the technology is not yet ready to be used for solving practical problems. The authors are working at present in an approximate formulation that takes into account the specifics of this type of compact underground substations. Figure 15 shows the potential distribution on the earth surface obtained by means of this new approach. More details will be given in forthcoming papers.

13 Figure 15: Compact underground substation. Potential contours ( 10 kv) on the ground. 7 Conclusions In this paper we have presented TOTBEM: a freeware, user-friendly, CAE simulation tool for the earthing analysis of large electrical over-ground facilities. The kernel of the application is a powerful and efficient grounding analysis module. This module implements a complete and well founded BEM numerical approach that has been previously proposed by the authors. The pre- and post-processing engines of the application have been built on top of the open source SALOME platform toolkit. The scope, flexibility and power of the proposed approach have been demonstrated by solving some important application problems in Electrical Engineering. 8 Acknowledgements This work has been partially supported by the Ministerio de Educación y Ciencia of the Spanish Government (grants #DPI C02-01 and #DPI ), and by R&D projects of the Xunta de Galicia (grants #CN2011/002, #PGDIT09MDS00718PR and #PGDIT09REM005118PR). This research has also been cofinanced with FEDER funds.

14 9 References [1] IEEE Std. 80, IEEE Guide for safety in AC substation grounding, New York, [2] IEEE Std. 142, IEEE Recommended practice for grounding of industrial and commercial power systems, New York, [3] Sverak, J. G., Progress in step and touch voltage equations of ANSI/IEEE Std 80. Historical perspective, IEEE Trans. Power Del., 13, (3), pp , July [4] Colominas, I., Navarrina, F. and Casteleiro, M., A boundary element formulation for the substation grounding design, Advances in Engineering Software, 30, pp , [5] Colominas, I., Navarrina, F. and Casteleiro, M., A boundary element numerical approach for grounding grid computation, Comput. Meth. Appl. Mech. Eng., 174, pp , [6] Navarrina, F., Colominas, I., and Casteleiro, M., Why do computer methods for grounding analysis produce anomalous results?, IEEE Trans. Power Del., 18, (4), pp , Oct [7] Garrett, D. L. and Pruitt, J. G., Problems encountered with the average potential method of analyzing substation grounding systems, IEEE Trans. Power App. Syst., 104, (12), pp , Dec [8] Cheng, A.H.-D. and Cheng, D.T., Heritage and early history of the Boundary Element Method, Engineering Analysis with Boundary Elements, 29, pp , [9] Alarcón, E., Brebbia, C. and Domínguez, J., The Boundary Element Method in Elasticity, Int. J. Mech. Sci., March [10] Alarcón, E., París, F. and Martin, A., Boundary Elements in Potential and Elasticity Theory, Computer & Structures, 10, pp , [11] Colominas, I., Gómez-Calviño, J., Navarrina, F. and Casteleiro, M, Computer analysis of earthing systems in horizontally and vertically layered soils, Elect. Power Syst. Res., 59, pp , [12] Colominas, I., Navarrina, F. and Casteleiro, M., A numerical formulation for grounding analysis in stratified soils, IEEE Trans. Power Del., 17, (2), pp , Apr [13] Nichols N., Shipp D.D., Designing to avoid hazardous transferred earth potentials, IEEE Trans. Ind. Appl., 1A-18, pp , July [14] Colominas, I., Navarrina, F. and Casteleiro, M., Analysis of transferred earth potentials in grounding systems: A BEM numerical approach, IEEE Trans. Power Del., 20, (1), pp , Jan [15] Colominas, I., Navarrina, F. and Casteleiro, M., Numerical Simulation of Transferred Potentials in Earthing Grids Considering Layered Soil Models, IEEE Trans. Power Del., 22, (3), pp , July [16] París, J., Colominas, I., Nogueira, X., Navarrina, F. and Casteleiro, M., Numerical simulation of multilayer grounding grids in a user-friendly open-source CAD interface, Proceedings of the ICETCE 2012, IEEE Pub., New York, [17] Colominas, I., París, J., Navarrina, F., and Casteleiro, M., Improvement of the computer methods for grounding analysis in layered soils by using high-efficient convergence acceleration techniques, Adv. Engrg. Soft., 44, pp , [18] J. Ma and F.P. Dawalibi, Analysis of grounding systems in soils with finite volumes of different resistivities, IEEE Trans. Power Del., 17, pp , Apr [19] Colominas, I., París, J., Nogueira, X., Navarrina, F. and Casteleiro, M., Grounding Analysis in Heterogeneous Soil Models: Application to Underground Substations, Proceedings of the ICETCE 2012, IEEE Pub., New York, 2012.