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General
Up to this point, line design had followed deterministic methodology. In the early 1980s, after the major snow/ice incidents of 1981/2, an investigation into alternative methods was started. This resulted in a technical document ENATR 111 that laid down the basic design principles following a semi-probabilistic methodology. In 1988 this concept of probabilistic methodology (in fact a semi-probabilistic methodology in this case) was introduced in the specification ENATS 43-40 which encompassed the work of ENATR 111.
Traditional deterministic overhead line design has involved the calculation of mechanical loads and deflections based on the assumption that lines are statically determinate. Deflections of conductors in wind have been taken as the same as those on a pendulum of equivalent mass and area to the span of conductor, with a length equal to the sag of the conductor. Loads transferred to the support have been thought of as being the vector sum of the weight and wind span of the conductor with the tension along the line of action of the conductor, all under particular loading conditions. These assumptions underpin the mathematical models behind the traditional deterministic design approach.
Probabilistic design is based on the recognition that nothing can be measured with absolute certainty, in particular, neither the strength of a component nor the applied load. In general, the actual strength and applied load will vary about a particular nominal value in accordance with a probability function.
The load-factored approach uses a more or less rigorous probabilistic analysis of applied loads and of anticipated conductor deflections together with a more or less traditional approach to the ultimate strengths of components and a geometric, partial-factored approach to set reliability levels.
Assumptions
There is nothing wrong with or intrinsically superior about either the deterministic or probabilistic approach. Each has limitations and each is based upon certain assump- tions, but the deterministic base appears to align with an externally regulated regime, and the move towards probabilistic seems to align better with self-regulation. In prac- tice, neither the traditional deterministic nor the more modern probabilistic design
as applied to wood pole overhead lines reflects a purist approach. Both have been properly tempered by the practical consideration that is the hallmark of engineering design.
Deterministic design
Under set conditions of mechanical loading (the design loading case) the stress in each component has been limited to a certain proportion of the nominal ultimate capability of the component defined in terms of elastic limit or ultimate tensile strength. The factor by which the permitted stress is below the ultimate capability defined in this way is known as the factor of safety.
Under set conditions of conductor temperature, the clearance is specified between positions where a member of the public may stand (or park a vehicle) and uninsulated, live, conductors. Initially, conductor temperatures were also set or, more precisely, the temperature at which clearances should be maintained were set out, but in the 1970 regulations the term ‘conductor likely operating temperature’ was introduced to reflect the tendency to operate conductors at ever higher temperatures. No criteria were set for clearances at any other temperature, for example at 0◦C with ice loading. Under this situation conductors could meet the regulations at 0◦C with a high ice loading when barely above ground level as long as at a higher specified temperature the specified clearance was provided.
Over time it was found that lines built to these criteria performed well in some parts of the country and poorly in others. As a consequence of this, and as a result of the relative influence of each electricity board as regulations were reviewed, changes were made which were more or less arbitrary. Some electricity boards adopted designs that were much more conservative than the requirements of the regulations and others took advantage of the relaxations that were being made through the regu- lations. The effect of these trends was to cause a drift between the objectives of the deterministic models and their use. Over the years the design criteria had been relaxed to reduce the cost of rural electrification. Unfortunately, major failures due to snow and ice storms occurred every two or three years. The occurrence of two storms in the same year (1981 April and December) caused questions to be asked in parliament and an enquiry was set up. By 1985 the Baldock Enquiry had concluded that the process of relaxation had gone a step too far to be consistent with the requirement to ensure a sufficient supply of electricity. An analysis of nationally reported severe storm dis- ruptions was conducted to show that lines designed to a probabilistic approach would have performed better than lines to the earlier BS 1320 and later derivatives, and, on this basis, withstand and reliability factors were specified for general applica- tion. The enquiry thus recommended that alternative design approaches should be investigated in an attempt to find one that would improve the reliability of overhead line systems.
Probabilistic design
This new approach allowed for additional local knowledge factors to be considered either externally by use of high wind factors or internally by varying reliability factors.
Traditional and probabilistic design standards 47 This reflected the relative importance of the circuit when a local case could be made against the ‘fitness for purpose’ clause of the regulations.
True probabilistic design was just coming into vogue for steel tower work but was ruled out for wood pole OHLs because of the different probability functions that applied to steel and wood in tension and compression. A new form of design termed load-factored design was introduced for the purpose.
In many cases the probability function will take the form of a normal distribu- tion and most familiar probabilistic design is associated with normal distributions. However, the principles of probabilistic design apply equally well to all other prob- ability functions. Underpinning such design there is the expectation that a reasonable estimate can be made of the probability function that applies.
In practice, failure is likely when the applied load exceeds the actual capability of a particular component to withstand the load applied. There is a distinction between failure in practice and failure to meet the design. The layman may anticipate that the design will ensure no failure in practice, but this is not realistic. There may well be circumstances that arise in which the device fails in practice while meeting the design requirements. This can occur, for example, if practical loads exceed those catered for by the design or if the actual strength of a particular component falls outside the range catered for in the design.
Probabilistic design accepts that at the limit there will be an overlap between the probability distribution of applied load and the line capability, yet if this overlap is kept small enough then the risk of failure is small. Of course, the effect of diminishing the overlap is to increase the margin between the centre of the two distributions, and this is generally associated with increased cost and less practical design.
One of the major problems with probabilistic design in the context of overhead lines supported on wood poles is the wide variation of performance of components – especially of poles and foundations. The situation is greatly confounded by the wide variability with time of applied loads. This situation is not nearly so acute in the case of overhead lines supported on steel towers where both the materials and the structures are more predictable. Nonetheless, it is important to recognise that with probabilistic design it is much more difficult in the event of a particular failure to determine if this is a failure to meet the design or one of the failures that the design accepted would occur.
A particular probabilistic design may accept a risk of failure of, say, 5 per cent of supports every 50 years. This may be based on the mechanical loads that may occur during likely weather conditions and the probability distribution of the strength of wood poles erected in situ.
It is clearly highly unlikely that following a particular event it would be possible to determine if a support which had failed had met or had not met the design requirements for the following reasons:
1 Such a support could have been a support that had strength at the lowest end of the representative probability function. We could not know this, however, since it would not have been possible to measure this in situ prior to the failure. Even if we were able to assess this after the event this would give us no more certainty,
not least because the pole will be broken at its weakest point and the foundations will have been modified by the failure.
2 Such a support may have had lower strength than was anticipated by the prob- ability function. We cannot, however, know this with certainty since we would need to know the strength of all of the other poles as, at the limit, all probability functions allow for units of very low strength with decreasing likelihood. If it is found after the event that the pole exhibits rot it may be taken that it was weaker than it could have been. This is true but irrelevant in the assessment of the adequacy of the design since it may still have had strength remaining as described by the probability function.
3 The weather experienced may have been more extreme than had been catered for by the design.
4 The manner in which the mechanical loads accrued in light of the weather may have been more extreme than was catered for by the design.
Consequently, to assess the relevance of particularly a probabilistic design to practical considerations it is necessary to take a wide view of a series of failures over a period of time. These can be obtained from the National Fault Information Recording Service (NAFIRS). All utilities are required to report faults to this service. Principally, the design uses more traditional calculations based on sets of values that use a probabilistic base to reflect the likely variation of loadings to be expected across the UK. In other words, the UK is now accepted as having several different areas that suffer different wind and ice loads, i.e. they therefore have different probabilities of suffering high stresses due to the weather. Some line components are the same across the country. A piece of steel is as strong in Shetland as in London, and so can be specifically defined. However, the weather has a higher probability of being more severe in Shetland than in London and so this is allowed for.
Considerable simplification is accepted as being necessary to yield a manageable analysis, particularly in terms of drag factors, densities of wet snow accretion, types of accretion etc. when applied to the variable length, multi-span sections of an overhead line. Wherever possible, the simplification process uses factors already in use by overhead line designers with adjustments made in the analysis of overall withstand and reliability factors. In other words, there is a trade-off between a risk of failure and the ability of a line to withstand particular loads.
The load-factored approach
General
The load-factored approach combines a probabilistic analysis of applied loads together with a traditional approach to the ultimate strengths of components. Load-factored design
Load-factored design is generated by consideration of the following components: • modelling of weather conditions during wet snow storms
Traditional and probabilistic design standards 49 • modelling of loadings on lines
• modelling of how conductors clash in the wind.
Traditional methods of calculating capability in ultimate terms are used. Factors are calculated which allow scaling of the site-specific site loadings such that failure can be predicted where it has occurred in recent extreme storms, i.e. the models are calibrated with historical event data.
The use of this load-factored design with very traditional structural design enabled the preparation of ENATS 43-40 to set a standard that could be shown by modelling to: • perform better in the exposed areas which had suffered damage in the recent high
profile storms
• allow for more economical design in those areas which had had good service from earlier designs.
ENATS 43-40 represents the first stage in developing national acceptance of site-specific overhead line designs for use in the UK. All lines regardless of site had been required to meet nationally determined design criteria and use of these criteria was observed to have produced lines in some areas which provided high levels of reliability and in others frequent failure. The new approach of 43-40 was developed to address this issue. ENATS 43-40 was developed to demonstrate that these designs were achievable nationally at similar costs to those covered by the current ENATS 43-10 and 43-20 (light and heavy construction for 11 and 33 kV lines). The approach
The approach was to:
1 assess the most aggressive weather-related parameters at each location and height in the UK from the perspective of wood pole lines
2 model the mechanism by which these weather parameters cause mechanical loads on overhead lines
3 compare the theoretical capability of lines based on these considerations with real historical events and thereby develop withstand and capability factors associated with line design for susceptible areas.
The weather maps of the UK produced by this method relate to the statistical probability of wet snow accretion calibrated on historical experience of lines having spans less than 150 m and conductor diameters below 20 mm. This is important. The work all relates to wet snow accretion and not to rime ice as wet snow blizzards were considered to be the cause of most major failures. An example is shown in Figure 4.1. Note that a separate map is available for each 100 m increase in altitude.
Recent European standards introduced in the UK have implemented weather maps from BS 8100 rather than ENATS 43-40. This subject will be discussed in detail later in this chapter.
Loads and deflections
Storm information was made available from the Meteorological Office from 240 weather stations as half hourly data in many cases for a 14-year period. These data
increasing severity ice co-ordinates wind co-ordinates A B C D E 1 2 3 4 5 4D 4D 4D 4D 4D 4E 4E 4E 4D 4E 4E 4E 4E 3D 3C 3D 2C 3C 2C 2C 2B 2B 2B 2B 2B 2B 2D 2C 2B 3D 2D 2D 3E 3E 1B 1C 1C 1C 2B 2C 2D 3D 2C 1C 1C 1B1B 1B 3D 3D 3D
Figure 4.1 ENATS weather map for land 200–300 m (courtesy ENA)
were processed to estimate six-minutely data at each site and at each of six equivalent heights both above and, if appropriate, below the level of the site.
The data were again processed to estimate mean wet snow accretion during each period when accretion was likely at these 240 equivalent weather stations. These data were then analysed to estimate the worst build up of wet snow and of wind pressure likely with a 50-year return period during episodes when wet snow was likely at the height of a wood pole overhead line in a rural environment of reasonably rolling countryside.
Traditional and probabilistic design standards 51 A new model was created (based on the above data) for conductor motion and clashing. In such conditions this model was demonstrated to give practical results and to account for failures in previous storms that had not been accounted for until that time.
A new model was created and approved by the Meteorological Office for the mapping of these extreme data and assessing the likely extreme weather-related loads at positions other than those from which data had been gathered. Once again this model appeared to be robust in that exclusion of any data in turn had little effect on the whole spectrum of data representing the country. If the exclusion of some data had affected the model then it would have been too sensitive for general application. It should be noted, however, that no amount of inspection could assess the absolute validity of the model only the relative apparent validity.
Component capability
Earlier approaches had developed an effective database of accepted component cap- ability. Much of this had been the subject of more or less rigorous testing at some stage, yet the statistical data needed for a fully probabilistic approach were not available.
For example, it was known that pole tests had been undertaken to confirm the techniques and assumptions used in the assessment of pole strengths. It was not, however, clear if sufficient tests had been done across a sufficiently representative range of poles to be statistically reliable.
There was a further factor that influenced the decision to accept ultimate failure loads as previously assessed. This was that the new approach had to be acceptable and comprehensible to overhead line engineers of the time who over the years had come to empathise with these methods.
However, this led to certain problems, e.g. in the context of ENATS 43-40 in particular insulator pin capabilities used manufacturers’ certified minimum failing loads to represent capability, but it seems this load did not take account of the deflec- tion (under load) of the pin at these and lower loads. Unfortunately, such pins used at heavy pin angle positions deflected alarmingly in normal service and revisions of ENATS 43-40 had to down rate the ultimate failing load of these components accordingly.
Load factors
We are now armed with the weather-related loads, the component capability, tra- ditional conversion from one to the other, methods of mapping and national storm damage reports. It is possible to assess the factors needed to ensure that the con- sequences of previous storms would be less severe in the future if the new design approach were adopted.