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Modeling E-Field on Transmission Lines

Modeling E-Field on Transmission Lines

December 22, 2018 • ARTICLE ARCHIVE, Camera, e-field, Transmission Lines
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Ofil Systems

When designing transmission lines, the overriding criterion has typically been mechanical performance since, if a design does not perform mechanically, electrical design becomes irrelevant. These days, however, mechanical design of transmission lines is robust due to improved structures, conductors, hardware and insulators. As such, line designers must focus rather on optimizing electrical performance. This requires better understanding how hardware, insulators and geometry can impact a transmission assembly. E-field modeling helps in this regard for many applications. This edited contribution to INMR by Jonathan Whitmore of MacLean Power Systems focuses on its value in regard to high voltage transmission assemblies.


E-field modeling is accomplished using computer aided engineering (CAE) software capable of calculating electric field intensity of given objects. An appropriately configured computer with the necessary power is also necessary. Many versions of software can be used, each with strengths and preferred uses, including Coulomb, Maxwell 3D, Comsol and Flux 3D. MacLean Power Systems (MPS) uses Integrated Engineering Software’s (IES) Coulomb software package for modeling based on the Boundary Element Method (BEM) to solve models. BEM – a tool for analyzing boundary value problems for partial differential equations – denotes any method for approximate numerical solution of boundary integral equations. The approximate solution obtained by BEM has the distinguishing feature that it is an exact solution of the differential equation in the domain by means of a finite set of parameters residing on the boundary. Models used for BEM calculations have the advantage of only 2D surface elements that are the interface regions of different materials or surfaces with boundary conditions. This greatly simplifies modeling and results are more accurate due to the smoothness of the integral operator. Moreover, analysis of unbounded structures can be solved by BEM with minimal effort since exterior field is calculated the same way as interior field. This software is a powerful tool for verifying electrical performance as it pertains to corona and corona inception as well as voltage stress on an insulator surface.  

transmission line Modeling E-Field on Transmission Lines inmr 14

Fig. 1
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Assembly models are first designed using SolidWorks software based on customer specifications. An E-field modeling worksheet, completed by the customer, consolidates information from drawings, specifications and acceptance criteria into one document. After all this information is attained, the model can be created, making sure to keep complex details to a minimum and instead focusing on high stress areas that increase simulation solve time. Next, the model is imported to the Coulomb simulation software and boundary conditions are assigned. Insulation medium is defined on insulator volumes (glass, polymer or porcelain). Voltages are assigned to hardware, e.g. single-phase voltage (VSP) is used most often. Hardware in contact with the conductor is assigned the VSP while the tower and ground are assigned 0V. Conductive components not directly in contact with either conductor or tower are assigned a floating voltage that is calculated during simulation. To confirm assembly design, the simulated voltage is 15% higher than nominal service voltage. After all components are assigned a voltage or boundary condition, the software generates a mesh such that he finer the mesh elements, i.e. triangles, the more detailed the output (see Fig. 1). Then, the simulation is started and temporary file size determined. The mesh and temporary file are both used for internal calculations. Temporary file size is relatively large (MB–GB range). The larger the file size, the longer the simulation runtime; solution runtime can range from as little as 10 min to over 24 h.

Once the simulation is complete, an E-field plot is made for the entire model and stress points are identified through visual inspection. The most common is the contour plot (see Fig. 2) but isosurfaces and equipotential plots (as in Fig. 3) are also used for more complex assemblies. For multiphase assemblies, streamlines allow seeing how electric fields move between phases. Additional E-field plots are then created in the areas where higher electrical stresses are observed. All E-field plots are examined to confirm validity and not just a singularity of the simulation. Resulting E-field plots are reviewed and compared with acceptable criteria provided by the customer. A summary of results is provided that includes description of the simulation procedure and list of input data and assumptions.

transmission line Modeling E-Field on Transmission Lines Contour plot

Fig. 2: Contour plot.
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transmission line Modeling E-Field on Transmission Lines Equipotential plot

Fig. 3: Equipotential plot.
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E-field modeling can determine corona inception values on transmission assemblies. Corona causes RIV and electromagnetic interference that results in line losses and can also lead to premature degradation of polymeric insulators exposed to excessive voltage stress (e.g. the EPRI guideline is 0.42kV/mm ->10mm). These types of insulators can lose hydrophobicity and be more susceptible to premature ageing with shortened life expectancy. Newer compact line designs utilizing polymeric insulators allow designers greater flexibility but also can create more concentrated field stresses on insulators that need to be understood. Given that use of polymeric insulators has grown and transmission right of ways have meant more compact lines, corona has become a growing concern. Excessive electrical field stress on ceramic strings also needs to be considered. For example, disks located at the line end of the string are more likely to require replacement. Pin corrosion, radial cracking and ageing at the cement interface all shorten service life and impact life-cycle cost of a line.

The accepted practice for determining corona concerns used to mean testing in a high voltage laboratory but now there is a method that does not require this to verify corona levels. Laboratory testing was once the only way to determine corona inception or RIV levels and IEC 61284, NEMA Std. 107-92 and IEEE 1829 all provide standardized testing parameters for RIV and corona inception of string assemblies used in transmission. These standards do not dictate corona extinction values or minimum acceptable RIV levels but rather are used to define test methodology, equipment and procedures. Typically, an elevated test voltage of 110% to 135% of the rated line to ground voltage is applied. Testing requires a full-size assembly of a single phase to be constructed. The number of HV laboratories of suitable size and with the necessary measuring equipment are limited and there is also a time element to get materials from multiple locations and to schedule laboratory and witnessing. This takes time to manufacture and to secure availability of an appropriately sized facility – both of which are often in short supply and have great expense. Depending on assembly size and complexity, a single test can take up to two days. If the design does not meet acceptable criteria for corona inception or RIV level, the assembly has to be modified and re-tested.

Standards recognizing limitations of testing EHV assemblies with shortened ground clearance have added procedures for use of the calibration method. Here, applied test voltage and distance to ground plane are selected so that localized electric fields of the laboratory set are energized to a voltage stress equivalent to the service condition. Usually, E-field voltage is based on surface gradient of a sub-conductor mid-span at maximum operating voltage. Calibration methods are detailed in IEC 61284 and CSA C411.4-98. Test voltage is set using a calibrating bead on the AL tube used as conductor in the laboratory. 2D or 3D calculations can also be used to match surface gradient on test conductor to a pre-determined service condition.

Exploring the electrical performance of alternate designs requires testing each variation in the laboratory, which means additional time, material and expense. Moreover, will a single-phase model accurately reflect performance of a three-phase assembly in the field? Recent studies by the Bonneville Power Administration in northwest U.S., for example, determined that a laboratory environment does not always replicate field stresses of a three-phase assembly by using a single-phase source voltage. This work showed that adding a factor on the applied phase-to-ground exceeded actual field stresses by as much as 14%. This could lead to false positives of corona inception causing the addition of supplementary grading protection (e.g. larger shields, sphere nuts, etc.) that can increase installation time and make future energized maintenance more difficult.

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