Forensic analysis of transmission lines is not a new science. Utilities have long sought untapped capacity in existing lines through rerating studies or have attempted to flush out reliability issues by similar means. However, because of recent assessment requirements enacted by the North American Electric Reliability Corp. (NERC), this work is no longer a discretionary activity. At present, analysis of existing transmission line assets across the United States is reaching an unprecedented pace. Equally unprecedented is the computing power at the disposal of today's transmission line engineers. Paired with advanced surveying technology such as light detection and ranging (LiDAR), computer models can mimic line behavior in 3-D space with astounding accuracy.
For some lines now under assessment, this work will mark their first incarnation in a computer model. Many of these transmission assets have been in operation for the better half of a century. During that time, they have been exposed to any number of loading events, maintenance operations and upgrades, each altering the line's performance, sometimes in ways unknown to the owner. Particularly over rough terrain, each of these perturbing elements can become amplified and present a greater challenge to model.
The Salt River Project had the opportunity to evaluate one such line following a conductor upgrade project that yielded some unexpected and undesirable results. The required analysis ventured beyond the normal capabilities of commercially available analysis software and, ultimately, provided valuable insight for evaluating lines with suboptimal survey data or those exhibiting uncommon behavior.
The Line
The subject of investigation was a 230-kV line considered a major component of the Arizona transmission system, which traverses approximately 17 miles (27 km) of mountainous terrain. Originally constructed in the 1970s, this line was upgraded with the addition of a second subconductor in 2008 to increase capacity. Limits on structure loading and ground clearance required a variety of bundle configurations through various sections of the line and negated the potential for a future circuit.
Post-upgrade inspections revealed numerous suspension insulators significantly out of plumb, raising concerns over the line's serviceability and structure loading. The owner initiated a traditional ground survey of 40 spans through the most difficult terrain to assess the extent of the problem. Results indicated nearly half of the insulators were displaced beyond the capabilities of the owner's typical live-line maintenance tooling. In general, new insulators were displaced in the uphill direction, which indicated a problem with the offset clipping application and subjected some structures to torsion loading where existing insulators were displaced in the opposite direction. A field survey confirmed strong deviations from design sag values, raising further concerns about ground clearance and structure loading.
Analysis Methods
The ground survey effort was accomplished over a period of four weeks. When completed, the data represented conductor temperatures that varied by 20°F (11°C). Such disparity in temperature posed a unique challenge to modeling the behavior of the line. The variable temperatures essentially provided mismatched snapshots of the conductor's position from span to span. A sag calibration process — an adaptation of commonly used modeling techniques — was developed using Power Line System's PLS-CADD to overcome these temperature discrepancies.
This approach was highly successful at predicting conductor sag at observed conditions. However, this method did an equally poor job of predicting insulator swing. Thus, interest in potential remediation techniques required a more accurate method to simulate insulator-swing behavior. A secondary insulator-swing calibration technique provided the desired level of accuracy.
Sag Calibration
Commercially available transmission line analysis software does not provide a direct means to evaluate survey data representing multiple temperatures within a continuous section of conductor. Thus, it becomes necessary to normalize data for a common temperature value or reference temperature. This relatively straightforward method provides excellent correlations to measured line sag values, typically producing variance between measured and predicted values within 1 inch (25 mm).
Normalization to a reference temperature begins with a line model derived from an initial assumption of the as-built conductor tension. Barring extreme differences, the design conductor tension is adequate as a starting point for the normalization process. The goal of this step is to approximate span behavior with changes in temperature rather than model precise conductor position.
Selection of a reference temperature is best achieved using an actual temperature value for a span within the section, preferably a temperature near the mean of those represented within the section. Comparison between sag values calculated for each span at the surveyed and reference temperatures reveals the theoretical change in sag had each span been surveyed at the reference temperature.
With this behavior established, the line engineer simply adjusts the elevation of the survey data by dA to create a theoretical survey point for the reference temperature. A finite element conductor model, adjusted to match the simulated survey data, yields a representation of the line at the reference temperature. As a check, observation of the model at each survey temperature should reveal agreement between the model and surveyed sag.
For the Salt River Project's evaluation, the initial assumption of design tensions was quite adequate; however, if it proves inaccurate, a second iteration will likely lead to a better solution.
Insulator-Swing Calibration
To explore remediation techniques short of completely retensioning the line being studied, there was a need to develop a PLS-CADD model capable of predicting insulator swing with high accuracy. While the sag-calibrated model did a good job evaluating conductor sag, it regularly converged on excessive insulator-swing values, occasionally in the wrong direction.
The difficulty achieving an insulator-swing-calibrated model within PLS-CADD is the lack of a direct means to dictate insulator swing outside of plumb. This is typically not an issue, as PLS-CADD SAPS analysis generally converges on an appropriate insulator position. However, the sparse survey data paired with atypical insulator behavior on the study line often yielded incorrect solutions when left to standard modeling techniques.
Ground survey data recovered for the study line includes detailed swing information for each suspension insulator, providing an avenue for better analysis. In a manner similar to the sag-calibration process, insulator swing is normalized to the same reference temperature as in the sag-calibrated model. With insulator-swing data and vertical loads derived by the sag-calibrated model, differential tension acting at each suspension insulator is easily determined. These differential tension values are then used to calculate horizontal tension as it varies along the entire conductor section, with an educated assumption on the starting span's tension obtained from the sag-calibrated model.
Accounting for thermal and elastic expansion, the unstressed conductor length is calculated in a spreadsheet using the horizontal tension calculated for each span. Comparing unstressed conductor lengths calculated by the sag-calibrated model and those derived from the survey data reveals small differences in unstressed lengths. Adjusting unstressed conductor lengths within PLS-CADD to match the new values forces convergence on more accurate insulator-swing values. This method greatly increases the accuracy of insulator-swing calculations for the study line, generally to within 1 inch with minimal loss in sag-calculation accuracy.
The Results
The results of the forensic investigation on the study line demonstrated the as-built condition satisfies all National Electrical Safety Code clearance and structure loading requirements. Prior to development of the analysis techniques, more conventional analysis efforts indicated a need for large-scale retensioning work to satisfy structure loading and ground clearance requirements at an estimated cost of US$2 million to $3 million. The reduced remediation scope resulting from this new methodology was welcomed news for the owner, drastically reducing the scope and cost of mitigation. Isolated spans with tension in excess of the owner's limits for vibration control were mitigated with additional damping.
Although improved analysis techniques prevented unnecessary intervention on the existing condition of the line, the remaining — and perhaps more troublesome — issue was the inability to perform energized maintenance on damaged porcelain insulators because of their mass and constraints imposed by available tooling. Ultimately, the owner concluded that the most economical option was to replace porcelain insulators with polymer equivalents on an as-needed basis during regular maintenance activities. The lighter polymer insulators permit live-line replacement at higher swing angles otherwise impossible with porcelain insulators.
Subsequent analyses and field investigations have shown the primary contributing factor to the issues observed on the study line was the application of offset clipping in the incorrect direction, augmented by deviations from conductor-stringing procedures. At the time this work occurred, the NERC's line assessment initiative had not surfaced, and the efforts presented here seemed (to those involved) a once-in-a-career opportunity. Since then, there have been multiple opportunities to use the methods developed for this study during the ongoing line assessment initiative. NERC has required utilities to take a close look at their transmission line assets. It is probably fair to say some in the utility industry will not relish what they find. However, it is quite clear from this experience and others that a deep forensic analysis toolbox can provide significant cost savings to line owners when uncertainty might otherwise prevail.
Jeff Wruble ([email protected]) is the supervisor of transmission line engineering and design at Salt River Project in Tempe, Arizona. U.S. He holds a BSEE degree, a MBA degree and a master's degree in systems engineering from Arizona State University.
Zack Heim ([email protected]) is the manager of grid development for DGA Consulting, a Tempe, Arizona, U.S., civil engineering firm specializing in the electric utility industry. Prior to the formation of DGA Consulting, he was a senior engineer for Salt River Project, specializing in extra-high-voltage transmission structure and span analysis. He holds a BSCE degree from Arizona State University and is a registered professional engineer in Arizona and Utah.
Companies mentioned:
DGA Consulting | www.dgacon.com
North American Electric Reliability Corp. | www.nerc.com
Power Line Systems | www.powline.com
Salt River Project | www.srpnet.com
