During a severe storm, one thing is almost always certain in heavily treed areas: trees will inevitably fall on overhead distribution lines, causing damage and outages. Because it is neither environmentally acceptable nor practical to remove all trees whose falling arc may intersect a distribution line, lines need to be designed so that the component most likely to fail mechanically is also the one that can be repaired with minimum cost and time.

A study conducted to determine the sequence of failure of tangent, angle and deadend pole structures for both single-phase and three-phase distribution lines concluded that existing designs can be improved by altering the mechanical strength and configuration of some line components.

Probability-Based Design Traditionally, safety factors are applied to each component of a structure independent of one another. The purpose of the safety factor is to ensure that the component adequately resists the anticipated weather loading over the service life of the structure. In this case, both the loading and component strength are assumed to be single-valued. However, in reality, load and strength values vary according to probabilistic distributions, and component failures do not necessarily follow the sequence predicted by the deterministic approach.

In 1976, a design approach using the probabilistic principle to assess the risk of mechanical failure of an overhead line was introduced to CIGRE (International Conference on Large High Voltage Electrical Systems). Since then many articles and technical reports have been published on the evaluation of loading and strength of overhead lines using the probabilistic approach. Included are an International Electrotechnical Commission (IEC) technical report in 1991, and a Canadian Electrical Association (CEA) report in 1988. The Canadian Standards Association (CSA) is currently working on a standard that includes probability-based design. The concepts in the 1991 IEC report and the 1988 CEA report were adapted to the mechanical coordination study as shown in Fig. 1.

Study Approach A tree that falls on a conductor usually will increase the conductor tension. The new tension from the additional load is calculated using a method developed in the 1993 report to B.C. Hydro, "Mechanical Coordination of Overhead Distribution Lines" by P.W. International, Inc., Vancouver, British Columbia, Canada. This increase in conductor tension is transferred to other components of the distribution line, including the pole and associated hardware. The new loads for these components are calculated using the basic principles of mechanics and incorporate the effect of pole bending as shown in Fig. 2.

The probabilistic method requires knowledge of the strength dispersion of each component. Here, the component strength is assumed to follow a normal distribution with a standard deviation as indicated below: Pole: Western Red Cedar 19% Lodgepole Pine 13% Crossarm: 19% Conductor: 5% Hardware: 10% Insulator: 15% Tie Wire: 8%

Single-valued loads, Q, are calculated based on a design-code wind speed of 88 km/hr (55 mph) and single-valued estimates of tree weights. In the future, these single-value loads could be expanded easily to a distribution function based on the probability of occurrence of different wind speeds and tree weights. The probability of failure of each component is determined. The shaded area in Fig. 3 and the sequence of failure is obtained by arranging these probabilities in descending order. When a load exceeds a component's mean breaking strength by five standard deviations, the probability of failure is rounded off to 100%. Similarly, when the load is five standard deviations below the component's mean breaking strength, the probability of failure is given as 0%.

The resultant load from the fallen tree is found to be large enough to cause 100% failure on a number of the components. In order to rank these components, the load could have been scaled down so that the load on the weakest component is less than five standard deviations above its mean breaking strength. However, in this study, a secondary indicator was developed to compare those components with a 100% failure probability. This indicator, called the "failure index" is determined by taking the ratio of the load on the component to the mean component strength (Q/Rm in Fig. 3), and is the inverse of the conventional safety factor. The component with a higher failure index will likely fail before the component with a lower value. The sequence of failure is established using both the probability of failure and the failure index.

Sequence of Failure Six single-phase and nine three-phase structures were selected for testing. The sequence of failure for each type of structure was studied using a number of input parameters, such as pole species, pole length, pole class and conductor size. For the single-phase structures, two pole species and three pole lengths were considered. For the three-phase structures, this list was expanded to include two conductor sizes (for feeders and laterals) and two pole classes.

Eight categories based on impact location of falling tree, tree weight, and wind load on the tree were investigated as listed in Table 1. The categories included two impact locations, one at mid-span and the other near pole; four tree weights; and two wind loads on the tree. In each category 432 cases were studied, resulting in a total of 3456 cases. Table 2 shows a sample of the results.

The sequence-of-failure concept assists a distribution designer in evaluating how well a component can withstand a given load relative to other components, and assists in selecting the proper strength requirement for this component in order to minimize damage to the distribution line. In general, only the first few components in the sequence are important for study. A desirable sequence of failure can be achieved by designing a distribution line with one or more easier-to-repair, weaker components in order to minimize restoration cost and time. In other words, when a tree hits a line, it's better to have just the conductor on the ground instead of both the conductor and broken poles on the ground.

The failure sequence for the remaining components must be recalculated each time the previous weakest component in the sequence has been determined. Computer programs have been developed to facilitate the extensive calculations required.

Conclusions For standard B.C. Hydro pole structures, results indicated that the sequence of failure was not affected by the pole species (Western Red Cedar or Lodgepole Pine), the pole lengths (40, 45 or 50 ft), the pole classes (34 for feeders and 45 for laterals), and 45 for falling tree sizes. The failure sequence for trees falling at mid-span and near the pole differed only slightly.

Some general conclusions were drawn for each of the generic structure types (tangents, angles and deadends). For tangent structures, the No. 2 ACSR phase and neutral conductors tended to fail first when a tree fell on either conductor. When the conductor was a 336.4-kcmil ASC feeder, the pole instead of the conductor tended to fail first. For angle structures, the Preformed guy grip for the phase and the tie wire for the neutral usually failed first. For deadend structures, the Preformed guy grip tended to fail first. Accordingly, modifications to the sequence of failure could be achieved by altering the strength of individual pole-structure components and making corrective design changes. For example, in some instances mechanical coordination could be improved by reducing the strength of the tie-wire. Future work will involve the development of special structural links (or mechanical fuses) with predetermined narrow failure ranges. TDW Fred L. Kaempffer is currently the manager of Joint-Use Administration at B.C. Hydro. He has more than 12 years of experience in the development of construction standards for distribution lines.

Paul Wong is a principal engineer with P.W. International, Inc., an engineering consulting firm specializing in transmission and distribution studies and designs, and in scientific investigations of topics related to electric utilities.