If you can't explain it simply, then you don't know it well enough. — Albert Einstein

Sag in transmission lines

Overhead power lines (transmission and distribution lines) are suspended on pole/tower supports. Suspended conductors are subjected to mechanical tension which must be under safe value. Excess mechanical tension may break the conductor. Therefore, a conductor between two supports must not be fully stretched and allowed to have a dip or sag.
The difference in level between the points of support and the lowest point on the conductor is called as sag.
Keeping the desired sag in overhead power lines is an important consideration. If the amount of sag is very low, the conductor is exposed to a higher mechanical tension which may break the conductor. Whereas, if the amount of sag is very high, the conductor may swing at higher amplitudes due to the wind and may contact with alongside conductors. Lower sag means tight conductor and higher tension. Higher sag means loose conductor and lower tension. Therefore, a suitable value of sag is calculated so that the conductor remains in safe tension limit keeping the sag minimum.
  • The tension at any point on the conductor acts tangentially. Therefore, the tension at the lowermost point on the conductor is horizontal.
  • The horizontal component of tension at any point on the conductor is constant.
  • The tension at the support points is nearly equal to the horizontal component of tension at any point on the conductor.

Calculation of sag

The tension on a suspended conductor is governed by the conductor weight, effects of wind, ice loading and temperature variations. Generally, conductor tension is kept less than 50% of its ultimate tensile strength. The value of sag is calculated for two different scenarios - (i) supports are at equal levels and (ii) supports are at unequal levels.

When supports are at equal levels

Consider a conductor suspended at supports of equal heights as shown in the figure below. A and B are the support points and O is the lowest point on the conductor.

sag in power lines when supports are at equal levels


Let,
  • l = length of the conductor span
  • w = weight per unit length of the conductor
  • T = tension in the conductor
Consider a point P on the conductor. Considering the lowest point O as the origin, let the coordinates of point P be x and y. Assume the curvature is so small that the curved length is equal to its horizontal projection (i.e. OP = x). The forces acting on the conductor portion OP are -
  1. the weight w.x acting at a distance x/2 from the point O
  2. the tension T acting at the point O
Equating the moments of the two forces about point O, we get,
T.y = w.x * x/2
or, y = w.x2 / 2T
The maximum sag (dip) is represented by the value of y at either of the support points. At support point A,
x = l/2 and y = S (sag)
therefore, sag S = w(l/2)2 / 2T
therefore, sag S = w.l2/8T

When supports are at unequal levels

We generally encounter supports of unequal heights in hilly areas. The following figure shows a conductor suspended on supports at unequal heights.

sag in power lines when supports are at unequal levels


Let,
  • l = length of the conductor span
  • w = weight per unit length of the conductor
  • T = tension in the conductor
  • h = difference in levels between the two supports
  • x1 = distance of support at lower level (A) from the origin O
  • x2 = distance of support at higher level (B) from the origin O
From the above calculation of sag in the previous point, y = w.x2 / 2T
Now, at support A, x = x1 and y = S1
Therefore, S1 = w.x12 / 2T
sag in power lines equation


Values of S1 and S2 can be easily calculated from x1 and x2.

[Also read: Insulators used in overhead power lines]

Effect of wind and ice loading

The above calculations of sag are only true for still air and normal temperature conditions. However, in actual practice conductors are suspended to wind pressures and often loaded with ice coating in cold areas. The force due to wind is assumed to act horizontally to the conductor. And the force applied by ice loading is vertically downwards. Therefore, the total force on the conductor is the vector sum of vertical and horizontal forces.

In this case, weight of the conductor per unit length will be,
wt = sqrt.[(w + wi)2 + (ww)2]
where,
  • w = weight of the conductor per unit length
  • wi = weight of the loaded ice per unit length
  • ww = wind force per unit length
When a conductor has wind as well as ice loading,
  • The conductor sets itself in a plane at an angle θ to the vertical plane.
    Where, tan θ = ww / (w + wi)
  • In this case, sag is given by S = wt.l2 / 2T. But, here, S represents the slant sag, i.e. sag is in the plane where the conductor has set itself. The vertical sag is equal to S.cosθ
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Signs of electrical hazards and precautions

Electricity is essential for life in the modern world, but it can also pose deadly hazards. Below is some information about the potential hazards of contact with electricity, as well as precautions you can take to avoid electrocution or shock injury.
signs of electrical hazards and precautions

Dangers of electricity

Anybody who comes into contact with electricity can sustain serious burns or shock. In some cases, electrocution can even be fatal. Most electrical injuries occur when people encounter downed power lines, frayed power cords or malfunctioning electrical appliances. People may also be injured if they come into contact with water that is touching a source of electricity.

Identifying potential hazards

To keep yourself safe from electrical injuries, look for the following signs of electrical hazards:
  • Appliances located near any source of water, including bathtubs, sinks and spills. Water is a conductor of electricity and its presence raises the risk of an electrical injury.
  • Power cords and electrical wires close to any source of water.
  • Power cords and wires close to sources of heat. Heat may damage cords and wires, making injury more likely.
  • Downed electrical lines, especially after inclement weather. If you see something that looks like a downed power line, call the power company to report the incident immediately.
  • Worn electrical wires or power cords. A worn wire or cord doesn't provide proper insulation and can raise the risk of injuries or fires.
If you notice any of these potential electrical hazards, avoid contact with the area until the risk has been mitigated.

[Also read: Safety tips while using portable generators.]

Keeping children safe

Because of their age and/or lack of experience with electricity, children face a greater risk of sustaining electrical injuries than adults. To keep your children safe, teach them about the dangers of electricity. Make sure they know the basics of staying safe around electrical appliances, power cords and power lines. Children should also be taught to avoid contact with cords and electrical appliances any time they are wet or touching water.
Instruct your children to report any damaged electrical lines or cords to you immediately. If your children are very young, install protective covers over your electrical outlets and keep cords and other electrical dangers out of reach. If an incident involving electricity does occur, seek medical attention immediately.
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Corona rings and Grading rings

Corona rings are toroidal shaped metallic rings which are fixed at the end of bushings and insulator strings. They are also called as anti-corona rings. Corona rings are used to prevent corona discharge that occurs in high-voltage power lines. Corona discharge or corona loss is a significant issue with very high voltage power lines which causes power loss. One way to reduce corona discharge is using corona rings.

How corona rings work?

Corona discharge occurs when the electric field (potential gradient) at the surface of conductors exceed a critical value, called as critical disruptive voltage. The value of critical disruptive voltage varies with atmospheric condition. Its value is roughly 30 kV/cm. The electric field greatest where the curvature is sharpest. Therefore, corona discharge occurs first at the points where the curvature is greatest - i.e. at suspension points, corners and edges. Corona rings are installed at these points to prevent corona formation.

corona discharge on a corona ring
Corona discharge on a corona ring
Image source: Wikimedia commons

A corona ring is electrically connected to the conductor, encircling the points where corona discharge may occur. Therefore, the corona ring distributes the electric field (or charge) across a wider area, because of its smooth round shape. Hence, it reduces the potential gradient below the critical disruptive value.
Manufacturers usually recommend aluminum corona rings to be installed at the conductor end of the string insulators for lines above 230 kV and on both ends of the insulator for 500 kV.

What are grading rings?

Grading rings are very similar to corona rings. In fact, one can say, grading ring and corona ring are two different names for the same device. The difference is due to their main purpose of use and their placement. Grading rings encircle insulators rather than conductors. Their main purpose is to reduce the potential gradient along the insulator. Grading rings help in equalizing the potential distribution over a string of suspension insulator. Hence, grading rings improve the string efficiency and prevent insulation breakdown. Grading rings also serve the purpose of corona rings to some extent.
corona rings and grading rings
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Testing of overhead line insulators

Proper operation of a transmission or distribution line is highly dependent upon the proper working of insulators. A good insulator should have a good mechanical strength to withstand the mechanical load and stresses. It should have a high dielectric strength to withstand operating and flashover voltages. Also, an insulator must be free from pores or voids, which may damage it. Therefore, to ensure desired performance of insulators, each insulator has to undergo various tests.

testing of overhead line insulators

Testing of insulators

Following are the different types of tests that are carried out on overhead line insulators.
  1. Flashover tests
  2. Performance tests
  3. Routine tests

Flashover tests of insulators

Three types of flashover tests are conducted before the insulator is said to have passed the flashover test.
  1. Power frequency dry flashover test
  2. Power frequency wet flashover test
  3. Impulse frequency flashover test

Power frequency dry flashover test

The insulator to be tested is mounted in the same manner in which it is to be used. Then, a variable voltage source of power frequency is connected between the electrodes of the insulator. The voltage is gradually increased up to the specified voltage. This specified voltage is less than the minimum flashover voltage. The voltage at which surrounding air of the insulator breaks down and become conductive is known as flashover voltage. The insulator must be capable of withstanding the specified voltage for one minute without flashover.

Power frequency wet flashover test (Rain test)

In this test also, the insulator to be tested is mounted in the same manner in which it is to be used. Similar to the above test, a variable voltage source of power frequency is connected between the electrodes. Additionally, in this test, the insulator is sprayed with water at an angle of 45° in such a manner that its precipitation should not be more than 5.08 mm/min. The voltage is then gradually increased up to the specified voltage. The voltage is maintained at the specified value for 30 seconds or one minute and the insulator is observed for puncture or breakdown. If the voltage is maintained for one minute, this test is also called as one-minute rain test.

Impulse frequency flashover test

This test is to ensure that the insulator is capable of sustaining high voltage surges caused by lightning. The insulator under test is mounted in the same manner as in above tests. An impulse voltage generator which generates a very high voltage at a frequency of several hundred kilohertz is connected to the insulator. This voltage is applied to the insulator and spark-over voltage is noted. The ratio of impulse spark-over voltage to spark-over voltage at power frequency is called as the impulse ratio. This ratio should be approximately 1.4 for pin type insulators and 1.3 for suspension type insulators.
[Also read: String efficiency of suspension insulators]

Performance tests of insulators

  1. Temperature cycle test
  2. Puncture voltage test
  3. Mechanical strength test
  4. Electro-mechanical test
  5. Porosity test

Temperature cycle test

In this test, the insulator under test is first heated in water at 70° for one hour. Then the insulator is immediately cooled at 7° for another hour. This cycle is repeated three times. Then the insulator is dried and its glazing is thoroughly observed for any damages or deterioration.

Puncture voltage test

The purpose of this test is to determine the puncture voltage. The insulator to be tested is suspended in insulating oil. A voltage is applied and increased gradually until the puncture takes place. The voltage at which insulator starts to puncture is called as puncture voltage. This voltage is usually 30% higher than that of the dry flash-over voltage for a suspension type insulators.

Mechanical strength test

In this test, the insulator under test is applied by 250% of the maximum working load for one minute. This test is conducted to determine the ultimate mechanical strength of the insulator.

Electro-mechanical test

This test is conducted only for suspension type insulators. In this test, a tensile stress of 250% of maximum working tensile stress is applied to the insulator. After this, the insulator is tested for 75% of dry spark-over voltage.

Porosity test

In this test, a freshly manufactured insulator sample is broken into pieces. These pieces are then immersed into a 0.5% to 1% alcohol solution fuchsine dye under pressure of 150 kg/cm2 for several hours (say 24 hours). After that, the pieces are removed from the solution and examined for the penetration of the dye into it. This test indicates the degree of porosity.

Routine tests of insulators

  1. High voltage test
  2. Proof load test
  3. Corrosion test

High voltage test

This test is usually carried out for pin insulators. In this test, the insulator is inverted and placed into the water up to the neck. The spindle hole is also filled with water and a high voltage is applied for 5 minutes. The insulator should remain undamaged after this test.

Proof load test

In this test, each insulator is applied with 20% in excess of working mechanical load (say tensile load) for one minute. The insulator should remain undamaged after this test.

Corrosion test

In this test, the insulator with its metal fitting is suspended into a copper sulfate solution for one minute. Then the insulator is removed from the solution and wiped and cleaned. This procedure is repeated for four times. Then the insulator is examined for any metal deposits on it. There should be zero metal deposits on the insulator.
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String efficiency of suspension insulators and methods of improving it

A suspension type string insulator consists of a number of porcelain discs connected in series through metallic links. Suspension insulators or string insulators are very widely used in electrical overhead transmission system. However, there is a significant thing to be considered in case of these string insulators, known as string efficiency.

Potential distribution over a suspension insulator string

The figure below shows a 3-disc string of suspension insulator. As each porcelain disc lies in between two metal links, it forms a capacitor. This capacitance is known as self-capacitance or mutual capacitance. Moreover, air capacitance is also present between metal links and the earthed tower. This is known as shunt capacitance. The figure below illustrates the equivalent circuit of a 3-disc suspension insulator (assuming that shunt capacitance is some fraction of self-capacitance i.e shunt capacitance = k * self-capacitance).

string efficiency


If there were only mutual capacitances, then the charging current would have been the same through all the discs. In this case, the voltage would have been uniformly distributed across the string, i.e. voltage across each disc would have been the same. But, due to the shut capacitances, charging current is not the same through all the discs.

From the above equivalent circuit, applying Kirchoff's current law to node A,
I2 = I1 + i1
V2ωC = V1ωC + V1ωkC
V2 = V1 + V1k
V2 = (1 + k)V1              ...... eq.(i)

applying Kirchoff's current law to node B,
I3 = I2 + i2
V3ωC = V2ωC + (V2 + V1)ωkC
V3 = V2 + (V1 + V2)k
V3 = kV1 + (1 + k) V2
V3 = kV1 + (1 + k)2 V1       ...... from eq.(i)
V3 = V1 [k + (1 + k)2]
V3 = V1 [k + 1 + 2k + k2]
V3 = V1 (1 + 3k + k2)              ...... eq.(ii)

Now, voltage between the conductor and the earther tower is,
V = V1 + V2 + V3
V = V1 + (1 + k)V1 + V1 (1 + 3k + k2)
V = V1 (3 + 4k + k2)               ...... eq.(iii)

from the above equations (i), (ii) & (iii), it is clear that the voltage across the top disc is minimum while voltage across the disc nearest to the conductor is maximum, i.e. V3 = V1 (1 + 3k + k2). As we move towards the cross arm, voltage across the disc goes on decreasing. Due to this non-uniform voltage distribution across the string, the unit nearest to the conductor is under maximum electrical stress and is likely to be punctured.

String efficiency

As explained above, voltage is not uniformly distributed over a suspension insulator string. The disc nearest to the conductor has maximum voltage across it and, hence, it will be under maximum electrical stress. Due to this, the disc nearest to the conductor is likely to be punctured and subsequently, other discs may puncture successively. Therefore, this unequal voltage distribution is undesirable and usually expressed in terms of string efficiency.
The ratio of voltage across the whole string to the product of number of discs and the voltage across the disc nearest to the conductor is called as string efficiency
String efficiency = Voltage across the string / (number of discs X voltage across the disc nearest to the conductor).
Greater the string efficiency, more uniform is the voltage distribution. String efficiency becomes 100% if the voltage across each disc is exactly the same, but this is an ideal case and impossible in practical scenario. However, for DC voltages, insulator capacitances are ineffective and voltage across each unit would be the same. This is why string efficiency for DC system is 100%.
Inequality in voltage distribution increases with the increase in the number of discs in a string. Therefore, shorter strings are more efficient than longer string insulators.

Methods of improving string efficiency

(i) Using longer cross arms

It is clear from the above mathematical expression of string efficiency that the value of string efficiency depends upon the value of k. Lesser the value of k, the greater is the string efficiency. As the value of k approaches to zero, the string efficiency approaches to 100%. The value of k can be decreased by reducing the shunt capacitance. In order to decrease the shunt capacitance, the distance between the insulator string and the tower should be increased, i.e. longer cross-arms should be used. However, there is a limit in increasing the length of cross-arms due to economic considerations.

(ii) Grading of insulator discs

In this method, voltage across each disc can be equailized by using discs with different capacitances. For equalizing the voltage distribution, the top unit of the string must have minimum capacitance, while the disc nearest to the conductor must have maximum capacitance. The insulator discs of different dimensions are so chosen that the each disc has a different capacitance. They are arranged in such a way that the capacitance increases progressively towards the bottom. As voltage is inversely proportional to capacitance, this method tends to equalize the voltage distribution across each disc.

(iii) By using a guard or grading ring

A guard ring or grading ring is basically a metal ring which is electrically connected to the conductor surrounding the bottom unit of the string insulator. The guard ring introduces capacitance between metal links and the line conductor which tends to cancel out the shunt capacitances. As a result, nearly same charging current flows through each disc and, hence, improving the string efficiecy. Grading rings are sometimes similar to corona rings, but they encircle insulators rather than conductors.
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