Sag Calculation of Overhead Transmission Line | Practical Approach

Introduction

In this article you learn sag calculation of overhead transmission lines. Explore the factors affecting sag and how it impacts power transmission and Discover how wind conditions affect sag in transmission lines and the engineering considerations for managing this factor. Also learn what are the Temperature’s Influence on Transmission Line Sag

What Is Sag

Sag in overhead transmission lines refers to the vertical distance between the lowest point of a conductor (the wire carrying the electrical current) and the highest point of the supporting structures, such as poles or towers (as shown in figure below). It is a natural and unavoidable phenomenon that occurs due to the weight of the conductor and the tension applied during installation.

Sag is a critical consideration in the design and operation of overhead transmission lines. Excessive sag can lead to several issues, such as decreased clearance between the conductor and the ground, potential contact with nearby objects or vegetation, and reduced electrical clearance. Moreover, severe sag can compromise the structural integrity of the transmission line, leading to safety hazards and service disruptions.

What is The Importance of sag

The importance of sag in overhead transmission lines cannot be overstated as it plays a vital role in ensuring the safe and efficient operation of the power grid. Here are some of the main reasons why greens are so important:

1. Safety: Maintaining the appropriate amount of sag is essential for safety. Proper sag ensures that the conductors remain at a safe distance from the ground and any surrounding objects, such as buildings, trees, and roads. This minimizes the risk of electrical hazards and potential accidents, protecting both the public and utility personnel.
2. Electrical Clearance: Sag helps to maintain adequate electrical clearance between conductors and other structures, such as the supporting towers or poles. Sufficient clearance prevents electrical arcing or contact between conductors, reducing the risk of power outages and equipment damage.
3. Conductor Integrity: By allowing the conductor to sag, the tension in the line is reduced. This helps to minimize the stress on the conductor, ensuring its structural integrity over time. A well-maintained conductor is less likely to experience fatigue or mechanical failure, contributing to the overall reliability of the transmission line.
4. Temperature Compensation: Sag in transmission lines is influenced by temperature changes. As the temperature rises, the conductor expands, leading to increased sag. Conversely, colder temperatures cause the conductor to contract, reducing sag. Understanding the relationship between temperature and sag is essential for maintaining the optimal clearance and preventing excessive tension in the line.
5. Wind Effects: Wind can exert significant force on transmission lines, causing them to sway and inducing additional sag. Engineers consider wind factors when calculating sag to ensure the line can withstand various weather conditions and remain stable during storms.
6. Line Efficiency: Maintaining the correct amount of sag helps to optimize the efficiency of power transmission. Proper sag reduces unnecessary tension in the line, minimizing energy losses due to excessive conductor resistance.
7. System Stability: Sag impacts the overall stability of the power system. An excessive sag can lead to unwanted interactions between conductors, potentially causing short circuits or other faults. Proper sag calculation helps maintain a stable power grid and reduces the risk of disruptions.
8. Longevity of Equipment: By managing sag effectively, the strain on insulators, supporting structures, and other components is reduced. This prolongs the life of the equipment and reduces maintenance costs.

What are Factors Affecting Sag

Several factors influence the sag in overhead transmission lines. Understanding and accounting for these factors are essential to calculate and maintain the appropriate sag for safe and efficient power transmission. The key factors affecting sag include:

1. Conductor Tension: The tension applied to the conductor during installation or maintenance directly impacts sag. Higher tension results in reduced sag, while lower tension leads to increased sag.
2. Conductor Material: The type of material used for the conductor affects its weight and flexibility, which in turn influences sag. Different conductor materials have varying thermal expansion coefficients, impacting sag under different temperature conditions.
3. Temperature: Temperature changes cause the conductor to expand or contract, altering the sag. High temperatures lead to increased sag, while colder temperatures reduce sag.
4. Electrical Load: The amount of current flowing through the conductor affects its temperature, leading to changes in sag. Higher electrical load results in increased sag due to elevated conductor temperature.
5. Span Length: The distance between supporting structures (poles or towers) is known as the span length. Longer spans result in greater sag, while shorter spans lead to reduced sag.
6. Weather Conditions: Wind and ice can exert additional forces on the conductor, causing temporary variations in sag. Severe weather events can have a significant impact on sag levels.
7. Conductor Diameter: The diameter of the conductor influences its weight, and thus, its sag. Thicker conductors tend to have lower sag compared to thinner ones.
8. Sag Tension at Installation: The tension applied during the initial installation of the conductor affects its long-term sag behavior. Proper tensioning during installation is crucial for maintaining desired sag levels.
9. Supporting Structure Height: The height of the supporting structures plays a role in determining the final sag. Taller structures may result in higher clearance and reduced sag.
10. Conductor Type: Different types of conductors, such as bundled conductors or single conductors, exhibit varying sag characteristics.
11. Environmental Conditions: Environmental factors, such as humidity and altitude, can also influence sag behavior.
12. Line Configuration: The arrangement of conductors, such as single-circuit or double-circuit configurations, can affect sag and electrical clearances.

How to Calculate Sag of Overhead Transmission Line

The optimization of conductor sag is crucial for minimizing the required conductor material and avoiding the need for additional pole support height to maintain adequate clearance above ground level. Simultaneously, it is essential to ensure low tension in the conductor to prevent mechanical failures and enable the use of less robust poles. However, there exists a trade-off between low tension (resulting in high sag) and high tension (resulting in low sag) when designing the transmission lines. Engineers must maintain a balance between these factors to achieve an optimal and efficient design.

Mathematically sag, \;\;\; S= \frac{Wl^{2}}{8T}\\\;\\Where l = Span length (in Meter) \;\;\\\textrm{W = weight of conductor (in kg/m)}\\\textrm{T = Tension in the conductor (kg/m)}\\\;\\For standard practices conductor tension is less than 50% of its ultimate tensile strength.

Example: Suppose we have a transmission line of Rabbit conductor of span 25 meters. calculate the sag of the transmission line ?

Sag calculation when surfaces are even

1. Span length is 25 Meters
2. Conductor Tension = 0.35 x 1860 = 651kg/m
3. Tensile strength of Rabbit Conductor as IS 398-1961 is 1860 kg/m
4. Weight of conductor, Wc= 0.213kg/m (Ref. IS : 398 – 1961)
5. Wind pressure (Wp) is 75 kg/m^{2}
6. Diameter of conductor is 10.05mm as per IS : 398 – 1961
7. Wind Load, \textrm{Ww} = 0.667 \times \textrm{Dia of Conductor}\times Wp = 0.667 \times\frac{10.05}{1000}\times 75 =0.502kg/m
8. Ice thickness(t) (As per actual) here we have taken 12mm.
9. Ice Load Wi = 0.0028x(D+t)xt = 0.0028 x (10.05+12)X12 = 0.741 kg/m
10. Resultant Weight, W = \sqrt{(W_c +w_i)^2+(Ww)^2} = \sqrt{(0.213+0.741)^2+(0.502)^2}=1.078 kg/m

Sag, S = \frac{Wl^2}{2T} = \frac{1.078\times25^2}{2\times 651}=0.52 meters

Vertical Sag = Scos(tan^{-1}(\frac{W_w}{W_c+W_i})) = 0.46meters

Horizontal sag = S sin (tan^{-1}(\frac{W_w}{W_c+W_i}))=0.24meters

Sag Calculation When Surfaces are Unequal

consider the unequal has shown in figure below \\\;\\\;\;\;\;\;

Let \\l = Span length\\h = Difference in levels between two supports\\x₁ = Distance of support at lower level (i.e., A) from O\\x₂ = Distance of support at higher level (i.e. B) from O\\T = Tension in the conductor.

x_{1}= \frac{l}{2}-\frac{Th}{wl}\\\;\\x_{2}=\frac{l}{2}+\frac{Th}{wl}\\\;\\S_{1}=\frac{WX_{1}^{2}}{2T}\\\;\\S_{2}=\frac{WX_{2}^{2}}{2T}

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