V-String Swing Angle Derivation, Design Considerations

V-String Swing Angle Derivation, Design Considerations, and Structure Design Impacts

D. M. Boddy, P.E., M. ASCE1

ABSTRACT The use of V-string insulator hardware assemblies has been utilized on transmission line structures for their control of conductor position, clearance to supporting structure, and structural advantage. In designing V-strings, a critical design criterion consideration is insulator leg compression. Specifically, the weather (wind) condition that induces V-string insulator compression impacts the V-string interior angle, arm lengths, drop bracket length, pole shaft diameter, and foundation reactions. This paper provides insight into V-string analysis methodology and comparisons of different conductors, wind loadings, wind and weight span ratio limits, and V-string internal angle configurations. Wind loading effects on insulator leg compression are specifically examined for multiple weather cases ranging from 4 to 21 psf. Also examined is the inefficiency of a set parameter design (line angle range, conductor type, wind and weight span, etc.) compared to the potential design envelope, which can be utilized with design software such as Power Line Systems PLS-CADD®. INTRODUCTION Insulator V-string assemblies are often utilized on extra high voltage (EHV) lines from 230 kV to 765 kV. These assemblies restrict the conductor to a set position, which is advantageous to reduce right-of-way width. It has also been shown that V-strings have a structural advantage compared to I-string assemblies (Power Line Systems, Inc. 2003). This structural advantage detailed by Power Line Systems reduces the overturning moment of the pole shaft for a more economical design. V-string design can be complex, as it involves numerous considerations, including wire type, wire angle range, tension, weight span, wind span, weather cases, and internal V-string angles. A change in any of these parameters can significantly change the performance of the V-string system. The parameter that is most discussed and influential is the weather case(s) inducing V-string insulator compression. A change in this weather condition has dramatic design influences not only in the V-string design, but structure configuration (due to the V-string internal angle), cost (drop bracket and longer arms), and structure family design (angle ranges and hardware assembly type). These configuration changes can also increase the structure overturning moment, increasing the pole shaft and foundation size and cost.

1 SAIC, 203 N. LaSalle, Suite 2100, Chicago, IL 60601; PH (312) 965-8470; [email protected]

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(Θw) would equal the primary insulator angle (Θp). At this limit case, the entire load from the wire will be distributed to the primary insulator with the secondary insulator being a zero force member. Θ = Θ = tan (1) = ∗ tan Θ (2) Where: LH: Horizontal wire load component (force, lbs)

LV: Vertical wire load component (force, lbs) ΘP: Primary insulator angle from the vertical axis (degrees) ΘS: Secondary insulator angle from the vertical axis (degrees)

Equations 1 and 2 denote this condition with LV and LH representing the vertical and horizontal load components. The derivation results in Equation 3, which defines the maximum insulator angle for given parameters. For simplicity, Equation 3 has a vertical and horizontal span components represented in Equations 4 and 5.

Θ = tan ∗ ∗ ∗∗ (3)

= + + − ∗ ∗ (4)

= + 2 ∗ ∗ (5) Where: dwire: Wire diameter (length, in)

pwind: Wind pressure (pressure, psf) rice: Radial ice present on wire (length, in) wwire: Wire weight (force/ length, lbs/ft) Swind: Wind span (length, feet) Sweight: Weight span (weight, feet) T: Wire tension (force, lbs) α: Wire angle (degrees) ν: Vertical span component ρ: Ice density (lbs / ft3) τ: Horizontal span component

For a given tension (or ruling span condition), wire type, wind span, weight span, and primary insulator angle, Equation 3 determines the maximum allowable wire angle. The term “wire angle” is utilized since the wire can experience a different angle than the centerline. This can be due to configuration changes such as rolling or horizontal phase spacing changes. Figure 2 below depicts how wire angle and wind direction effect design considerations. The governing case for the primary insulator is when the wind and wire angle are in the same direction.


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The maximum line angle shown in the figures is 10 degrees. This focuses the discussion of designs to tangents and small-angle V-strings. It also allows the wind pressure parameters to be studied, as the conductor tension influence is not the primary horizontal load component in this range. DESIGN CRITERIA IMPACTS As one can see in Equations 3 through 6, the design of the V-string depends on many parameters, including the following:

• Wire type (diameter, dwire, and weight, wweight) • Wire tension (T) • Wind span (Swind) • Weight span (Sweight) • Wire angle (α) • Weather conditions (radial ice, rice, ice density, ρice, and wind pressure ,pwind)

Since transmission line design is typically based on the ruling span concept, the variables were simplified by assuming a design ruling span, tension limit, and wind-to-weight span ratio. These design assumptions are utilized across the industry to simplify the design process and allow a parameter V-string analysis within. The design examples and parameter analysis contained within are based on a hypothetical 345 kV V-string design. The ruling span was assumed to be 900 feet with a tension limit of 36 percent rated tensile strength at National Electrical Safety Code (NESC) 250B Heavy initial loading conditions (0 F; 0.50 in. of ice; 4 psf; initial). The conductor wire properties considered:

• Bundled 1272 kcmil Type 7 aluminum conductor, steel reinforced (ACSR) / trapezoidal wire (TW) Bittern

• T2-1113 kcmil 45/7 ACSR T2-Bluejay • 2156 kcmil 84/19 ACSR Bluebird

Wind Pressure Many different wind conditions are utilized throughout the industry for design criteria. However, a wind criterion for V-string compression is not always included or considered. This omission leaves the criterion open to interpretation or does not consider insulator compression to be a design parameter. To study the effects of wind pressure criteria on V-string design, the following wind pressures at 60 F were examined for a 45 degree primary angle (90 degree internal angle) V-string utilizing Bluebird ACSR with a ruling span of 900 feet in Figure 3: 4 psf, 6 psf, 8 psf, 15 psf, and 21 psf.


Figure 3. Wind pressure effect on the maximum allowable wire angle for Bluebird ACSR conductor; 900-foot ruling span; 900-foot wind span; primary insulator angle of 45 degrees. One of the first things noticed in the Figure 3 comparison is the large impact the wind criteria has on the maximum allowable wire angle. For a wind-to-weight span ratio of 1.6, the maximum wire angle can vary from 5 degrees with no wind to only 1 degree with 8 psf of wind loading. For wind loadings of 15 psf and 21 psf, the V-string is in compression for wind-to-weight span ratios exceeding 1.1 and 0.80, respectively. This means that for a 21 psf design wind criteria, every structure would require a 900-foot wind span and at least a 1125-foot weight span. This is impractical, as not every structure can be on a hilltop resulting in weight spans always exceeding the wind span. Conductor Selection The conductor selection can significantly affect the V-string design and performance as the maximum allowable wire angle depends on the wire weight, diameter, and tension. Each of these parameters influences the swing of the conductor considerably and thereby the performance of the V-string. For the three conductors selected, Figure 4 was created to examine the effect of different conductors. One of the explicit conclusions from Figure 4 is the difference similar voltage conductors have on the performance of the V-string. The bundled Bittern has much less of an allowable wire angle than the TP-Bluejay or Bluebird conductors. This can be attributed to the increase in wind area and tension (higher rated tensile strength, RTS). When comparing TP-Bluejay and Bluebird, the difference in conductor diameters (wind area) can be seen as both of these have similar tensions and weight.

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Wind Span / Weight Span

Bluebird ACSR; 45 Degree Primary Insulator Angle900 ft RS; 900ft Wind Span

60F; No Wind; Bare 60F; 4 PSF; Bare 60F; 6 PSF; Bare60F; 8 PSF; Bare 60F; 15 PSF; Bare 60F; 21 PSF; Bare


Figure 4. Conductor selection effect on the maximum allowable wire angle for a 900-foot ruling span; 900-foot wind span; primary insulator angle of 45 degrees; 6 psf wind. Ruling Span and Span Length Influence Another key factor in the design of a V-string is ruling span and span length. The ruling span often determines the tension via the design limit percentage of the rated tensile strength. The span length also has a large impact as it changes the vertical load component. Figure 5 displays the variation in maximum allowable wire angle for five different ruling spans which can also be used to represent span length.

Figure 5. Ruling span effect on the maximum allowable wire angle for a primary insulator angle of 45 degrees; 6 psf wind.

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45 Degree Primary Insulator Angle900 ft RS; 900ft Wind Span; 60F; 6 PSF

2156 kcmil 84/19 ACSR Bluebird TP-1113 kcmil 45/7 ACSR TP-BluejayBundle 1272 kcmil ACSR/TW Bittern

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Bluebird ACSR; 45 Degree Primary Insulator Angle60F; 6PSF

600 RS 700 RS 800 RS 900 RS 1000 RS


As can be seen in Figure 5, the ruling span effect is less for a tangent angle range (1 degree) and larger for a small angle range (5 degrees). At shorter ruling spans, the allowable wire angle is less, as the wire angle and tension component is a lower percentage of the horizontal load component. In other words, the weight span is less while the transverse load component decreases in a disproportionate amount due to the wire angle and tension (Equations 4 and 5). Design Usage From the derivation of the primary insulator angle and secondary minimum insulator angle, a number of inputs can have significant impact on the design and V-string performance. Figure 6 displays a primary insulator graph where the ruling span (wind span for purposes here) is varied. The data in Figure 6 is typical for the primary insulator angle. One of the most noticeable characteristics in Figure 6 is the variation in allowable wire angle at certain wind-to-weight span ratios which has implications depending on the V-string usage. When designing a V-string, it is normal for a maximum wind-to-weight span ratio and wire angle to be specified (such as 2.8 degrees max wire angle and 1.4 max wind/weight span ratio). This type of definition creates a “design parameter area,” which is depicted in Figure 6. While design parameter limitation makes application easier and more straightforward, it also creates excess conservatism for structures with a wind/weight span ratio less than 1.4 that can support a larger wire angle. It also eliminates structures with no line angle that have a wind/weight span ratio exceeding 1.4. These design limits create considerable “design dead loss areas” that could otherwise be utilized.

Figure 6. Design parameter area and allowable design curve comparison for Bluebird ACSR conductor; 900-foot ruling span; primary insulator angle of 45 degrees; 6 psf wind.

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Bluebird ACSR; 45 Degree Primary Insulator Angle900 ft Ruling Span; 6 PSF

700 ft Wind Span 800 Ft Wind Span 900 ft Wind Span 1000 ft Wind Span 1100 ft Wind Span

DESIGN PARAMETER AREAMAXIMUM WIRE ANGLE RANGE OF 2.8 DEGREES

MINIMUM WEIGHT SPAN = 500 FTMINIMUM WIND SPAN = 700 FT

Design Dead Loss Area

Design Dead Loss Area


Design software such as Power Line Systems, Inc.’s PLS-CADD® can model and analyze V-string insulators along the design curve in Figure 6 (denoted as a two-part insulator in the software). This allows the designer to use the same V-string design for a tangent structure with a small angle range such as 0 to 1 degrees and also a small angle with a range of 1 to 3 degrees. This same system would be employed with different wind span-to-weight span ratio limits. This also allows the V-string design to be employed more efficiently and thereby cost-effectively by reducing the design dead loss areas. DESIGN EXAMPLES The design examples below (Figures 7 through 10) are shown for the three conductors discussed above with the wind condition varying. Only the primary insulator angle is shown, which can either be mirrored in symmetry for a tangent or used for a small angle (running angle). The design examples highlight the design criteria wind condition and its influence on V-string geometry. One of the main takeaways from the design examples is how existing V-string designs perform. The most common V-string utilized for tangents is a 45 degree primary insulator angle (90 degree internal with no tilt). Figure 7 displays this design and the performance for a wind pressure of 6, 8, 15, and 21 psf. For the 21 psf case, the V-string will be in compression, which, for most parts of the United States, is a 90 mph wind with a 50-year return period (American Society of Civil Engineers [ASCE] 2005). If the V-string criterion for compression was the same as NESC 250C extreme wind loading, a 60 degree primary insulator angle (120 degree internal angle with no tilt) would be required as shown in Figure 10 (Institute of Electrical and Electronics Engineers 2012 Edition). This large of a V-string angle has its own considerations, such as drop brackets, longer hardware links and potentially higher strength insulators. Even with a 60 degree primary angle, the design wind-to-weight span is limited from 0.8 to 1.4.


Figure 7. V-string primary insulator 45 degrees design examples for 900-foot ruling span, 900-foot wind span; 6, 8, 15, and 21 psf wind.


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CONCLUSION The design of a V-string is influenced by many factors. Often, the standard industry practice is to designate a V-string by usage, such as tangent, small angle, or by the angle range (0-3 degrees). This, however, is only one of the many parameters that need to be considered. If a parameter design area is going to be defined, it should include the following:

• Conductor type • Maximum wire angle • Minimum wire angle • Maximum wind-to-weight span ratio • Minimum wind span • Maximum tension condition • Maximum wind pressure

Employing programs such as PLS-CADD allows designers to utilize the full range of the V-string design, reducing the design dead loss area. This reduces structure height increases due to swing limit conditions (more weight span required to reduce swing angles). A higher wind pressure criterion for insulator leg compression will lead to a flatter V-string (larger internal angle). This small criteria change impacts the entire structural system for V-string internal angle, drop brackets, arm lengths, custom hardware links, larger pole shafts, and larger foundations. One of the primary objectives of V-strings is to contain the insulator swing and conductor displacement within a right-of-way. As the line angle is increased, the tension component dominates the wind component of the transverse load. The resultant load tends to restrain the insulator motion and thus negates the V-string advantage of conductor restraint. Furthermore, as the line angle increases the primary insulator angle keeps increasing such that an I-string assembly could be a more economical choice. From the V-string design examples and wind pressures studied, one can conclude that V-string insulator compression is not a matter of if, but when it will happen. This can be controlled by determining a reasonable wind-return period for insulator compression and setting strict design usage parameters for the V-string assembly. NOMENCLATURE dwire: Wire diameter (length, in) pwind: Wind pressure (pressure, psf) rice: Radial ice present on wire (length, in) wwire: Wire weight (force/ length, lbs/ft) LH: Horizontal wire load component (force, lbs) LV: Vertical wire load component (force, lbs)


Swind: Wind span (length, feet) Sweight: Weight span (weight, feet) T: Wire tension (force, lbs) α: Wire angle (degrees) ν: Vertical span component ρ: Ice density (lbs / ft3) τ: Horizontal span component ΘP: Primary insulator angle from the vertical axis (degrees) ΘS: Secondary insulator angle from the vertical axis (degrees) ΘW: Wire angle, swing angle, from the vertical axis (degrees) DEDICATION The author would like to dedicate this paper to the memory of Robert J. Camillone, M.ASCE. He was not only an uncle and close friend, but also a professional mentor. His encouragement to participate in industry events and passion for giving back to the engineering community served as an inspiration for this paper. ACKNOWLEDGEMENT The author would like to acknowledge the following people for review of the paper and technical content: Scott Hartley of Power Engineers, Robert Kluge of American Transmission Line Company, Joe Hallman of Rocky Mountain Power, Ron Randle of EDM International, and Jerry Wong of FPL. REFERENCES ASCE, Structural Engineering Institue of. Minimum Design Loads for Builds and Other

Structures (ASCE/SEI 7-05). United States of America: American Society of Civil Engineering, 2005.

Institue of Electrical and Electronics Engineers, Inc. National Electric Safety Code (C2-2012). New York, 2012 Edition.

Power Line Systems, Inc. STRUCTURAL ADVANTAGE OF USING V-STRINGS. 2003. http://www.powerlinesystems.com/products/vstring.pdf (accessed 1 1, 2012).


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V-String Swing Angle Derivation, Design Considerations