Power transmitting towers are usually 10m to 40m high and the separation between two consecutive towers is about 200m to 400m. Finite Element Method (FEM) is not suitable for simulation in these applications. BEM is useful on very large domains where a FEM approximation would have too many elements to be practical. Integrated Engineering Software’s COULOMB’s BEM solver is best suited to simulate this problem. It is based on boundary integral equation, which allows the unbounded problem to be entirely defined at its boundary, and therefore reduces the number of variables required to solve it. This methodology can be used to find the potential gradients not only over the surface of the conductors, but also anywhere of interest in space.
For W as the width of the ground plane and H as the height of the tower, following cases were considered.
W=H, for analyzing electric field on the ground and 1 metre above the ground.
W=3H, for analyzing field in the space between the power lines and 1 metre above the ground.
It should be noted that number of 2D triangular elements on ground will increase as size of ground plane increases and solver will take a longer time. This time can be reduced if lower (1/100) triangular element density (number of triangular elements per unit area) is taken as compared to the element density on the insulator strings and metallic hardware. Electric field analysis for W=H and W=3H (see figure 2a and 2b) showed that there is not much difference between E-field variations for both the cases. So, W=H case is considered as a good case to analyze the problem as it could reduce problem complexity and produce highly accurate results.
Figure 3 shows power line setup with 200-400m separation between two towers. If power line is considered as a thin long cylinder with radius 1cm to 3 cm, then it would require vast number of 2D triangular discretization elements, and the model would not be easy to solve. To simplify this, power lines could be assumed as linear segments, which would need 1D discretizing elements.
For comparison, both cases (linear segments and thin cylinder power lines) were analyzed. Figure 4 shows the plot of E-Field along the Line AB for both cases. It shows that results for linear segments overlaps the plot for thin cylindrical power line showing less than 1% difference between both results. Hence, simulation of power lines as linear segments is recommended to reduce the number of elements and faster solution.
Keeping the desired sag in overhead power lines is an important consideration, hence while calculating the fields at the communication cable, sagging in the cable should also be simulated. If the amount of sag is very low, the conductor is exposed to a higher mechanical tension which may break the conductor. Whereas, if the amount of sag is very high, the conductor may swing at higher amplitudes due to the wind and may contact alongside conductors. For equal heights of the towers, maximum sag S = u *L*L/(8T), where u is the weight per unit length of the power line, L is the span length, T is the optimum mechanical tension applied to the line. The shape of the sagged line is very close to a parabola. Usually, the parameters u and T are not readily available, but the maxim sag S is. Figure 5 shows the E-field plot along the communication line. It is seen that the field near the points A&B is significantly higher than that in the middle point C.
It can take a lot of time to simulate a transmission tower due to complexity of the model. Hence, it is better to model only the part of the tower where the insulation strings are connected to the power lines, with approximating the rest of the tower as a solid structure. Both cases were simulated to see the difference. Figure 6 show electric field plots for actual tower geometry and for part of the geometry with communication lines only. It is seen that plots of both cases overlapped and hence simulating the part of tower could produce accurate results while saving lot of time.
The evaluation of electric field from Insulator and the connected metallic hardware along the communication lines is also an important aspect in this simulation study (see figure 7). E field is large only in and around the few sheds (say 5 or 6) on either end of the insulator. Note that the tower is at ground potential (0V). If the E field on these first sheds on either side of the insulator string is less than the breakdown filed, the E field on the other sheds will be much less than the critical E field. Therefore, modeling of only the first few sheds on either side of the insulator is important and the rest of the model can be treated like a cylindrical insulator.
Symmetry and periodicity conditions in COULOMB were utilized to reduce the size of the model and therefore the time and hard disk space required to obtain a solution. The primary requirement for using a symmetry condition in a design is that the geometry and materials have mirror symmetry about one or more of the principal planes. COULOMB allows to define symmetry about any of the three principal Cartesian planes: X = 0 (YZ plane), Y = 0 (ZX plane), and Z = 0 (XY plane).
Insulators and some of its connected metallic hardware are axi-symmetric objects. For the simulation, these can be modeled as two 180° sections or four 90° sections. This will simplify the model and electric field can be conveniently calculated at the side of interest.
Figure 8 show the plot of electric field along first 7 sheds of insulator looking from four sides. The results obtained shows than axisymmetric modeling can be a good alternative to 3D modeling to compute electric field accurately.
Dr. Prasad obtained his Ph.D. in 1983 and is currently one of the members of INTEGRATED’S Technical Support Team. He has been involved in developing INTEGRATED Engineering Software programs for the last 28 years. The focus of his work has been the simulation of the real-world electromagnetic field models. Dr. Prasad has considerable expertise in the minimization of the complexity of the real-world models without losing its electromagnetic functionality. With almost three decades of experience in the simulation of electric, magnetic, thermal, and high frequency electromagnetic problems, Dr. Prasad considers himself a true quick trouble shooter.
