In this post, we will make an example calculation for generating a sag template. We will follow the steps defined in the previous post.
Step 1: Gather design data.
Scale and Ruling Span :
In this example, we will assume that the route plan scale is 1 cm: 2 m vertical and 1 cm: 20 m horizontal. The ruling span will be 300 meters.
Voltage Level and Conductor Data :
This line will be 300 meters 69kV line-line with 795MCM ACSR Conductor. The details of the conductor are as follows:
- Codeword: Condor
- Stranding: 54/7 (Aluminum / Steel)
- Rated Tensile Strength (RTS): 12,954.5 kg
- Unit Weight: 1.527 kg/m
- Cross-sectional Area: 0.0004548 m^2
- Outside Diameter: 0.02776 m
- Initial Modulus of Elasticity: 59000000000 Pa
- Final Modulus of Elasticity: 59000000000 Pa (assume no change in Young’s Modulus)
- Coefficient of Thermal Expansion: 0.0000193 / ℃
Conductor Tension Limits :
The purpose of limiting the tension in the conductor is to avoid tensile failure. Another is to avoid conductor fatigue due to aeolian vibration. According to CIGRE brochure WG B2-12, typical values internally accepted, as well as IEC 60826, for tension limits is shown below:
- 50 – 75% of RTS under maximum climatic heavy load conditions.
- 20 – 30% of RTS with no ice or no wind at 15 ℃ when the conductor is initially installed under tension.
- 15 – 25% of RTS with no ices or no wind at 15℃ when the conductor is in final condition. Final condition means that the conductor have already sufferred heavy loading or has been in place for many years.
On the other hand, RUS and NESC 2017 has the following guidelines for tension limits:
The following explained the tension conditions in the table above:
Initial Unloaded Tensions refers to the conductor as it is strung initially before any ice or wind is applied.
Final Unloaded Tension refers to the state of the wire after it has experienced ice and wind loads, long term creep and permanent inelastic deformation.
Standard Loaded Condition refers to the conductor state when it is loaded with simultaneous ice and wind per NESC loading districts.
Extreme Wind Tension is the tension when wind is acting on the conductor under no ice condition.
Extreme Ice Tension is the is the tension when the conductor is loaded with specified amount of radial ice under no wind condition.
Extreme Ice with Concurrent Wind refers to the condition where extreme ice on the wire is accompanied by a moderate amount of wind.
For this example, let us follow the tension limits set by the NESC. The initial conductor tension is 35% of RTS.
Ground Clearances:
Based on the table below, the required minimum ground clearance for 69kV line accessible to traffic is 5.9 meters. For this example, we will use 7.0 meters.
Step 2: Determine the weather conditions that may affect your conductor.
The table below shows the typical load cases that the conductor may be subjected to. For this calculation, we will consider the following climatic conditions:
- Initial Condition
- Temperature = 15 ℃
- Cold Curve:
- Temperature = -20 ℃
- Maximum Sag Curve:
- Extreme Ice:
- Ice thickness = 25 mm
- Temperature = 0 ℃
- k constant = 0 kg/m
- Extreme ice with concurrent wind:
- Ice thickness = 25 mm
- Temperature = -10 ℃
- k constant = 0 kg/m
- Wind pressure = 190 Pa
- Maximum conductor temperature:
- Temperature = 50 ℃ (assumed value, check with your local weather conditions)
- Extreme Wind
- Temperature = 15 ℃
- Wind Pressure = 991 Pa
- Extreme Ice:
Step 3: Calculate the sag and tension of the conductor.
The following is the result using my sag-tension calculator version 2 (See next posts to download). The “extreme ice” weather case controls the maximum sag of the conductor. Hence, this value of sag will be used to graph the “maximum sag or hot curve”.
₱500.00
Step 4: Plotting of the catenary curve
The next step is to derive the equations of the different curves and plot those in a scaled paper. In this case, I will use AUTOCAD to easily generate the sag curves.
Recall the equation of the catenary with the lowest point taken as the origin.
The C constant is a function of the Horizontal Tension and the unit of the conductor which were already calculated. Using the results shown above, the different equations were derived. But for now, we are interested in the vertical sag and not the total sag. Hence, the cosine of blowout angle should be multiplied to the result. However in this example, it will not matter since blowout angle = 0 degrees and cosine 0 = 1.
We are now ready to generate points to be plotted. But take note that we have to extend the curve up to 3x the length of ruling span and use the appropriate scale defined earlier. Using Excel, we arrived at the scaled coordinates below:
In Autocad, use the SPLINE command to generate a curve base on given points. Here are the steps:
- Copy the coordinates from Excel.
- In Autocad, type SPLINE –> Method –>Fit –> Paste the coordinates.
Ground Clearance Curve is just a copy of the Maximum Sag Curve with offset distance equal to minimum ground clearance. In this case, we set the ground clearance to 7 meters or 7/2 = 3.5 units (cm) in Autocad.
Tower Footing Curve is just a copy of the Maximum Sag Curve with offset distance equal to maximum sag. In this case, the maximum vertical sag to 7.18 meters or 7.18/2 = 3.59 units (cm) in Autocad.
Step 5: Transfer the plotted curve to a transparent paper or celluloid.
On the next post, we will described on how to use the sag template in transmission line design.
References:
NS220 Overhead Design Manual
Principles of Mechanical Design in Overhead Transmission Lines
Standard Handbook For Electrical Engineers
UEP Bulletin 1724E 200. Design Manual for High Voltage Transmission Lines
Construction Manual for Transmission Lines
