How Accurate Are Your Line Clearance Calculations?

Line-to-ground clearances dictate maximum line-loading levels, usually post-contingency, in many operating situations. Since measuring them all is not

Line-to-ground clearances dictate maximum line-loading levels, usually post-contingency, in many operating situations. Since measuring them all is not possible in real time, utilities must rely on predictions of this important operation condition. But how good are the predictors?

Conductor clearance above ground is a complex and uncertain function of variables concerning when the conductor and line were built, what mechanical and electrical loadings the line has endured, and even the pre- and post-contingency weather and line loading. Lines that may be loaded to a level that might compromise required ground clearances are critically analyzed to ensure clearance is not an issue. If clearance is an issue, one of several real-time thermal-rating systems can be deployed to manage the phase-to-ground clearance.

Typical overhead line thermalrating systems are based on measurements of tension, sag, temperature or weather and circuit load. In the last instance, the data are used to predict a conductor temperature that tracks changes in sag. These measurements or predictions may not be good enough to address all the relevant uncertainties, especially since some conductor properties change during high-temperature operation. Many utilities and specialty manufacturers of rating systems have lingering concerns about how well any given system actually predicts conductor clearance.

Studies carried out at Kinectrics for a major utility in Ontario, Canada, have resulted in “report cards” that indicate how well the various thermal-rating systems perform. The process developed has shown great value in establishing or re-evaluating the accuracy of predictors of clearance, simultaneously, at several locations.

Conductor Clearance Measurement Hardware

The fundamental requirement in the report card development is a collection of what a scientist might call ground truth. Or, in this case, some truth about where the conductor is with respect to the ground under various operating and meteorological conditions. The requirement was that clearance be explicitly measured so that reality could be compared to various predictions.

Remember the Polariod cameras that were introduced in the 1980s? They used a sonar range finder. Today, you can purchase a device at most hardware stores that uses similar technology to measure distances up to 50 ft (15 m). Industrial versions of this sonar equipment have been on the market for 50 years. Some utilities have been using this equipment to measure ground-to-conductor clearance since 1987. The data from the industrial units are also reliable in rain, snow and high winds because the sonar transducers (like the one in shown) are very powerful and the echo processing benefits from modern electronics and signal processing. Clearance data up to 200 ft (60 m) can be collected and delivered via the Internet for remote processing using telephone, radio or satellite in a variety of secure formats.

The equipment used at monitoring locations is portable and has a low installation cost. This makes it possible to monitor many spans in a verification project and allows the equipment to have a useful life beyond any single application. During a pilot project, clearances were measured at four locations along one circuit and then the equipment was redeployed to measure five adjacent circuits during the following year.

In addition to monitoring clearance, the parameters (ambient temperature, circuit loading, wind speed and wind direction) that influence conductor temperature are also monitored. These parameters were averaged every 10 minutes at locations directly under the lines.

After the completion of survey projects, the equipment left to validate existing Sagometers, CAT-1 tension monitors, or serve as a permanent clearance monitor. Clearance data are especially useful for:

  • Lines that have been reconductored and now have new uncertain sag-tension relations
  • Lines that have been retensioned or treated with a Sagging Line Mitigator (SLiM).
  • Lines with conductor characteristics that have been affected by high-temperature annealing.

Measurement vs. Prediction

Between deadend towers, a transmission line behaves like a set of coupled springs that are affected by the swing of insulators along the line direction. The math to solve this interaction was provided in 1989 and is known as the “SWING” model. This method was endorsed in 1999 by an IEEE task force on “Bare Conductor Sag at High Temperature.” This SWING model is the foundation for using a single measurement of tension, sag or clearance to predict clearances at other locations, 3 to 30 to 300 spans away. The main caveat to using a single measurement to predict accurate clearances of all spans in a stringing section is that tower locations, some conductor parameters and the ground profile are well known.

As an introduction to how predictors of clearance can be graded, the figure above right shows the observed relation between a CAT-1 tension monitor and the tension calculated from a sonar clearance measurement during an 8-hour emergency loading event. The two readings track quite closely.

The Pearson regression coefficient (R2) is a measure of how well one variable can predict another. The value of R2 given in the figure above is 94.26%. If all the data points fell on a straight line, then this R2 value would be 100%. These studies have used the regression coefficient to grade nine possible predictors of clearance from best to worst, as shown in the table.

The best marks were given to the clearances measured two or nine spans away, in the same stringing section between deadend insulators. The figure on page 31 shows how precise this relation is. The fitted lines do not have the same slope because each span length is slightly different. There is also between 0 ft and 13 ft (4 m) ground profile variation under the lines that gives a fixed offset between readings at any two locations.

The good grade for nearby spans was expected; giving grades of more than 99% is not surprising. However, the correlation grade for the site, located 98 spans (about 20 miles [32 km]) away, is a complete surprise. This span is in a completely different stringing section and has a bearing angle of about 10 degrees relative to the reference line section. The 69% to 73% grade for correlations on the same line 98 spans apart may be cause either for concern or for celebration, depending on the situation.

It was determined that, if conductor temperature was directly measured at on spot on the line, the predicted clearance in that span or three spans away was graded at 77% to 78%. The reason that this grade is not higher is that the “average” temperature along the span, which will dictate sag and thus clearance, will likely be different from the spot temperature measurement. This is connected to why the tension measurement gets a 94% grade. Monitoring tension is implicitly averaging the conductor temperature in the stringing section.

The preceding is a partial explanation that using the IEEE 738 ampacity calculation method based on all the weather data collected directly under the line and circuit loadings had a grade of 65% to 78%. This correlation has a much wider variability grade than the spot temperature measurement approach. One would expect that calculating conductor temperature would not be as accurate as actually measuring it. However, this 65% to 78% grade for the IEEE 738 approach is strikingly similar to the 69% to 73% grade for the 98-spans-away prediction.

Thus, if we used letter grading for this report card, the scores above 90% would be in the A class, and the scores below 80% are likely two grades lower. However, it is not necessary that the most accurate solution be deployed to solve all problems. There are situations where nothing less than a 95%-grade solution will do. And, there are other situations where a less expensive and less accurate solution is adequate. The sonar-based monitor is quite inexpensive and portable as well as accurate.

Future Directions

Projects to develop report cards at other utilities could be carried out for the variables above for Sagometer data or for other prediction methods such as the CIGRÉ method. By doing this work, utilities with good thermal-rating-management processes would gain firsthand experience on the installation and operation of multiple sets of clearance monitoring on operating transmission lines. A utility could locate and install ground-based sets of portable clearance monitoring that can easily be checked for calibration by turning the head sideways and bouncing the sound off a nearby target. They would then have sources of easily understood data that would assure regulators and the local community that they are providing the highest safe thermal ratings under all conditions. Industrywide coordination of results could be provided through such groups as EPRI and IEEE. The projects also could be set up to answer next-step implementation questions such as:

  • Does my existing thermal-rating process give results that I could now explain to a regulator?
  • Is the sonar equipment as accurate and stable over time as specified?
  • Does the strong relationship among clearances in a stringing section or along a line persist at high operating temperatures?
  • Does the relationship of line clearance to conductor temperature hold any more surprises?
  • Are clearance values operator friendly?

It is critically important that utilities continue to investigate the parameters that affect conductor sag and line clearances, particularly as lines are increasingly heavily loaded.

William A. (Bill) Chisholm is a senior research project manger at Kinectrics, the former Ontario Hydro Research Division. He has an undergraduate degree in engineering science, a master's of engineering and a PhD in electrical engineering. He has been involved in thermal rating of overhead transmission systems since 1985 and has other interests in “unusual weather effects” on transmission line reliability, such as lightning and icing flashovers on insulators. He chaired the IEEE Lightning and Insulator Subcommittee for many years and recently coauthored the chapter on lightning and grounding in the forthcoming EPRI Transmission Line Reference Book, 200 kV and above. [email protected]

Report Card for Predictors of Clearance
PredictorGrade (R2)
Clearance, two or nine spans away within the same stringing section 99.3% to 99.5%
Tension in the same stringing section 94%
Clearance in an adjacent line on the same right-of-way 94% to 99%
Clearance in a parallel line, different conductor, same line angle 85% to 90%
Measured conductor surface temperature in the same span or three spans away 77% to 78%
Clearance in the same line, 98 spans away, different section and line angle 69% to 73%
Conductor temperature calculated from IEEE 738, a heat-balance model using weather and line current 65% to 78%
Ambient temperature 53% to 69%
Line current 38% to 53%
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