In this article we will discuss about:- 1. Introduction to Transmission Lines 2. Conductor Configurations, Spacing’s and Clearances of Transmission Lines 3. Span Lengths 4. Sag and Tension 5. Stringing Chart 6. Sag Template 7. Equivalent Span 8. Vibrations and Dampers.
Contents:
- Introduction to Transmission Lines
- Conductor Configurations, Spacing’s and Clearances of Transmission Lines
- Span Lengths of Transmission Lines
- Sag and Tension of Transmission Lines
- Stringing Chart of Transmission Lines
- Sag Template of Transmission Lines
- Equivalent Span of Transmission Lines
- Vibrations and Dampers in Transmission Lines
1. Introduction to Transmission Lines:
Transmission and distribution lines are vital links between generating stations and consumers as power from generating stations is transmitted at high voltage (such as 132, 220 or 400 kV) over long distances to the major load centres and then the power is distributed to various substations located at various places and localities through distribution lines.
ADVERTISEMENTS:
Because of tremendous industrial growth, requirement of power has increased manifold. Hence it becomes imperative that transmission and distribution of power from the generating stations to the various consumers is carried out with minimum possible loss and disturbance.
This objective can be achieved only if the transmission and distribution system is so designed and constructed that it is an efficient, technically sound and reliable system. The line should have sufficient current carrying capacity so as to transmit the required power over a given distance without an excessive voltage drop and overheating.
The line losses should be small and insulation of the line should be adequate to cope with the system voltage. The line should have sufficient mechanical strength to cope with the worst probable (not worst possible) weather conditions and provide satisfactory service over a long period of time without the necessity of too much maintenance.
2. Conductor Configurations, Spacing’s and Clearances of Transmission Lines:
ADVERTISEMENTS:
Conductor Configurations:
Several conductor configurations are possible, but three configurations are the most common i.e., horizontal configuration (or horizontal disposition of conductors), vertical configuration and triangular configuration.
There is no special advantage in using the symmetrical delta or triangular configuration [Fig. 10.1(a)] and in most cases flat horizontal or vertical configurations are employed from mechanical considerations, particularly when suspension insulators are used. In horizontal configuration, all the conductors are mounted over one cross-arm, as shown in Fig. 10.1(b).
Though such an arrangement of conductors needs supports of smaller height but needs a wider right of way. In certain congested areas where it is not possible to have horizontal arrangement of conductors, the conductors are placed in vertical formation (along the length of pole one below the other). The drawbacks of vertical formations are taller towers and more lightning hazards. There are places where both horizontal and vertical formations are applied.
ADVERTISEMENTS:
In unsymmetrical arrangement of conductors, the conductors are usually transposed at regular intervals in order to balance the electrical characteristics of various phases, and prevent inductive interference with neighbouring communication circuits.
Experience shows that a vertical configuration is the most economical for double circuit lines and horizontal or L-type configuration for single circuit lines.
Conductor Spacings:
ADVERTISEMENTS:
The spacing of conductors is determined by considerations partly electrical and partly mechanical. Larger spacing causes increase in inductance of the line and hence the voltage drop, so that to keep the latter within a reasonable value the conductors should be as close together as is consistent with the prevention of corona.
The basic consideration regarding the minimum spacing between conductors is that the electrical clearances between conductors under the worst condition i.e. maximum temperature and wind pressure shall not be less than the limits for safety, particularly at the mid spans.
Owing to the action of the gusts of wind, conductor has got tendency to move about in an elliptical path, therefore, in case of suspension insulators, the minimum clearance to supporting structures should be calculated with a 45° swing of the suspension string towards the structure.
An empirical formula commonly employed for determination of spacing of conductors for an aluminium conductor line is given below:
ADVERTISEMENTS:
Spacing = √S + (V/150) metres … (10.1)
where S is sag in metres and V is line voltage in kV.
Conductor Clearances:
The minimum vertical clearances between the ground and the conductor.
These values are given below:
3. Span Lengths of Transmission Lines:
Neglecting the deciding influence upon the span length of such local conditions as the necessity for following the contiguity of roads, canals or railways, it is interesting to note that there is one definite value for the span length which will give the minimum overall cost of the line.
As the length of span increases, the number of insulators and supports decreases resulting in decrease in cost but at the same time the height of the support will go up to allow for more sag and also the length of the cross-arms will have to be increased to take up increased spacing, this will cause increase in cost.
Moreover the length of the span depends upon the working voltage, higher the working voltage of the system, the greater will be the economical length of span owing to the higher relative cost of insulators to supports. Moreover the insulators constitute the weakest part of transmission line and reduction in number of towers per km with the use of longer span increases the reliability of the line.
Thus it is not possible to give any hard and fast rule as to the best span length to be adopted, and the only way to determine it is to calculate the total cost per km for a number of different span lengths, and plot the results to get the most economical span length.
Many a time it happens that the conductor size determined from electrical calculations comes out rather small, it is possible to reduce the total cost of line by using a thicker and stronger conductor, and increasing the span length. Sometimes it is not feasible to determine the height of the line support and span length on the basis of line cost alone as lightning hazards increase greatly with the increase in height of conductors above the ground.
The usual spans are:
(a) With wooden poles: 40-50 m.
(b) With steel tubular poles: 50-80 m.
(c) With RCC poles: 80-200 m
(d) With steel towers: 200-400 m and above.
For river-crossings, etc. exceptionally long spans up to 800 m or so have been satisfactorily employed.
4. Sag and Tension of Transmission Lines:
Overhead lines are supported on mechanical structures consisting of components like insulators, cross-arms, poles or towers, etc. The strength of these components must be such that there is no mechanical failure of line, even under the worst weather conditions.
The conductor is acted upon by the forces such as weight of the conductor itself, wind pressure and tension. A conductor stretched between two supports will have an ultimate strength at which it will fail and the ultimate strength of a conductor depends upon the type of conductor material used for overhead line.
While stringing overhead lines it is necessary to allow a reasonable factor of safety in respect of the tension to which the conductor is subjected. The tension in the conductor is normally expected to be less than 50% of its ultimate tensile strength even when there is 12.7 mm radial coating of ice and a wind pressure of the order of 380 N/m2.
The tension in a conductor depends on the diameter of the conductor, length of the conductor between supports, material of conductor, sag in conductor, wind pressure and temperature. The relationship between tension and sag is dependent on the loading conditions and temperature variations. For instance, the tension increases when temperature decreases and there is a corresponding decrease in sag. Icing-up of the line and wind loading causes stretching of the conductor by an amount governed by the line tension.
Sag:
A perfectly flexible wire of uniform cross-section, when strung between the two supports at the same level, will form a catenary. However, if the sag is very small compared to the span, its shape approximates a parabola.
The difference in level between the points of supports and the lowest point on the conductor is known as sag.
The factors affecting the sag in an overhead line are given below:
(i) Weight of the Conductor:
This affects the sag directly. Heavier the conductor, greater will be the sag. In locations where ice formation takes place on the conductor, this will also cause increase in the sag.
(ii) Length of the Span:
This also affects the sag. Sag is directly proportional to the square of the span length. Hence other conditions, such as type of conductor, working tension, temperature etc., remaining the same a section with longer span will have much greater sag.
(iii) Working Tensile Strength:
The sag is inversely proportional to the working tensile strength of conductor if other conditions such as temperature, length of span etc. remain the same. Working tensile strength of the conductor is determined by multiplying the ultimate stress and area of x-section and dividing by a factor of safety.
(iv) Temperature:
All metallic bodies expand with the rise in temperature and, therefore, the length of the conductor increases with the rise in temperature, and so does the sag.
The sag plays an important role in the design of overhead line. It is disadvantageous to provide either too high sag or too low sag. In case the sag is too high, more conductor material is required, more weight on the supports is to be supported, higher supports are necessary and there is a chance of greater swing-amplitude due to wind load. On the other hand in the case of too low sag, there is more tension in the conductor and thus the conductor is liable to break if any additional stress is to be taken, such as due to vibration of line or due to fall in temperature.
Normally two conditions should be investigated, when making sag-tension calculations:
(a) At Minimum Temperature:
The lowest sag and maximum tension in conductor-section occurs when the temperature is minimum and wind maximum. Under these conditions, tension on the conductor should not exceed the breaking strength of the conductor divided by a factor of safety of 2.5.
(b) At Maximum Temperature:
On the other hand maximum sag occurs when temperature is maximum and there is no wind pressure.
Approximate formulae for the calculation of sag are given below:
S = wL2/T
where w = weight of conductor in kg per metre length,
L = length of the span in metres, and
T = tension in the conductor in kg.
Calculation of Sag and Tension:
A conductor strung between two supports at the same level forms a catenary. For extra high voltage lines, when sag exceeds 10% of the span length, formulae based on catenary should be used,
Consider a portion OP of a curved length l of a wire hanging in still air with O as the lowest point on the wire [Fig. 10.2 (a)]. Let the weight of conductor per metre length be w kg.
If T0 is the tension at point O (lowest point on the wire and where the curve is horizontal) and T the tension at point P (distant I from the lowest point O), the portion OP (length I) is in equilibrium under the action of three forces, namely T0, T and the weight of the wire of length I acting vertically downward through centre of gravity, wl.
The above three forces can be represented by a triangle shown in Fig. 10.2 (b) and from this triangle,
Tan θ = wl/T0 … (10.2)
The horizontal and vertical distances of the length OP of the wire are x and y respectively, since the coordinates of the point P are (x, y).
Now from triangle shown in Fig. 10.2 (c),
Integrating both sides we get,
From initial conditions, i.e. when x = 0, I = 0, we get C = 0 and Eq. (10.7) becomes,
Integrating both sides we get,
Equation (10.13) is the equation of the curve, called the catenary.
The function cosh is the hyperbolic cosine and is such that,
If the fourth and higher order terms are neglected,
From Fig. 10.2(b) the tension T at point P is given by:
If the line is supported between two points A and B at the same level and the length of the span is L, then at the supports x = ± L/2 and
T = T0 cosh wL/2T0 … (10.16)
The sag S is the value of y at A or B and is given by:
Length of line in a half span,
Neglecting terms of order exceeding cube we have,
The maximum tension occurs when x = L/2 so maximum tension is given as:
Tmax = T0 + wS … (10.21)
For very small sags the term wS may be neglected in comparison with T0, and the tension is considered approximately uniform throughout the conductor.
Approximate Formulae:
The sag could also be very simply deduced as follows:
Consider a conductor suspended between two, equal level supports A and B. The conductor is assumed to be flexible and sags below the level AB due to its own weight. Though the exact shape of the conductor is that of a catenary but except for lines with very long span and large sag, it is sufficiently accurate to assume that the shape of the hanging conductor is that of a parabola y = ax2 where a is a constant for a given conductor and O is the origin. The curve at point O, being the lowest one, will be horizontal.
Let the length of span (i.e. horizontal distance between supports) be L metres, weight of conductor per metre length be w kg and tension in the conductor be T kg.
Assuming curvature very small, the length of conductor hanging between two supports may be taken equal to the length of span and maximum sag may be considered at half span length with equi-level supports.
Consider x metre length of conductor between mid-point O and point N.
The two external forces acting on the portion ON of the conductor are:
(i) The tension T acting at point O and
(ii) The weight of the conductor of x metres length i.e. wx acting at x/2 metres from point N.
Equating the moments of the above two forces about point N we get,
Supports at Different Levels:
When transmission lines are run on steep inclines, as in case of hilly areas, the two supports A and B will be at different levels. The shape of the conductor strung between the supports may be assumed to be a part of the parabola. In this case, the lowest point of the conductor will not lie in the middle of the span.
Consider an overhead line conductor AOB, supported over the supports A and B, as illustrated in Fig. 10.4.
Let the difference in levels between the two supports be h and the lowest point O of the conductor be at a distance of x metres from the support at low level.
So, distance of O from higher level support = (L – x) metres
From Eq. (10.24)
S1 = wx2/2T … (10.26)
and S2 = w (L – x)2/2T … (10.27)
Difference in two levels of supports,
From the above Eqs. (10.26), (10.27) and (10.28) location of point O and thus the values of S1 and S2 can be determined.
Effect of Ice:
In areas where it becomes too cold in winter, there is a possibility of formation of an ice coating on the line conductors. The formation of an ice coating on a line conductor has a twofold effect—increase in weight and effective diameter of the conductor.
In this condition the weight of conductor, together with weight of ice acts vertically downwards.
Thus the total vertical weight acting on the conductor per metre length is wc + wi where wc is the weight of conductor in kg per metre length and wi is the weight of ice coating per metre length, wc is known and wi is determined as follows:
Let the diameter of conductor be D metres and radial thickness of ice coating is r metre, as illustrated in Fig. 10.5. The overall diameter of ice covered conductor, as obvious from Fig. 10.5, becomes equal to (D + 2r) metre.
Volume of ice coating per metre length of conductor = π/4 [(D + 2r)2 – D2]
= π/4 [4Dr + 4r2] = r (D + r) m3
The density of ice is approximately 920 kg per m3, so
The weight of ice coating per metre length, wi = 920 × r (D + r) kg
= 2,890.3 r (D + r) kg/m … (10.29)
Combined Effect of Wind and Ice:
Due to weight of ice deposits on the line, and the wind pressure, the mechanical stress increases in the conductor and, therefore, the line must be designed to withstand these stresses and tensions. Under this condition, the weight of the conductor, together with weight of ice acts vertically downwards while the wind loading ww acts horizontally.
Resultant weight per metre length of conductor including ice coating and wind force,
where ww = Wind force in kg per metre length
= Wind pressure per m of projected area × projected area per metre length
= p × (D + 2r) … (10.31)
∴ Maximum sag = wr L2/8 T … (10.32)
When the ice and wind are acting simultaneously, the lowest point of the conductor does not remain vertically down but away from it at an angle θ given by the expression,
The sag calculated from Eq. (10.32) will not be vertical sag but will be slant sag and vertical sag will be obtained by multiplying the slant sag with cos θ,
5. Stringing Chart of Transmission Lines:
Under statutory conditions, the sag is required to be determined for worst probable conditions and the minimum ground clearance is to be maintained for these conditions. At the time of erection the severe conditions do not prevail, the temperature is usually higher, the designer, therefore, should know the sag to be allowed and the tension in the line to be allowed, so that under no condition there should be any danger to the line.
Stringing chart is helpful in knowing the sag and tension at any temperature. This chart gives the data for sag to be allowed and the tension to be allowed at a particular temperature.
For preparation of stringing or sag chart first of all calculate the sag and tension on the conductor under the worst conditions i.e. maximum wind pressure and minimum temperature, assuming a suitable factor of safety in fixing the maximum working tension for the conductor. Now evaluate the sag and tension for a series of temperatures in steps within the working range of temperatures.
The equation for determining stringing chart of a line is derived as below:
Let w1, f1, l1, S1 and t1 be the load per unit length, the stress, the span length, sag and temperature at the maximum load conditions (with the ice and wind and low temperature usually – 5.5°); w2, f2, l2, S2 and t2 be the values under stringing conditions, a is the area of x-section of the conductor, α is the coefficient of linear expansion and E is the modulus of elasticity.
The span length at maximum load condition is:
The temperature rise from t1 to t2 causes an increase in the span length of l1α (t2 – t1) which is practically equal to l1α (t2 – t1). The fall in stress from f1 to f2 causes a decrease in the length of 
The new length l2 is thus given by:
Equation (10.39) is a cubic equation and can be solved graphically or analytically. From this equation erection tension T1 = f1a can be determined such that tension T2 – f2a under worst probable conditions will not exceed the safe limit of tension.
After determining f2, the corresponding sag can be determined from the equation:
Various values of f2 and S2 are calculated using Eqs. (10.39) and (10.40) repeatedly for different temperatures. Now the graph of tension vs temperature and sag vs temperature can be plotted, as shown in Fig. 10.19. This graph is plotted for a fixed span and is called the stringing chart. The stringing chart is very useful while erecting the transmission line conductors for adjusting the sag and tension properly.
6. Sag Template of Transmission Lines:
In the initial planning stages a survey of the proposed route enables an estimated line profile to be drawn, as illustrated in Fig. 10.11(a). Such a profile is constructed with the horizontal scale much more reduced (say to 1/10) in comparison to vertical scale. This profile should meet the minimum clearance requirements, and the location of the supports should be such that some horizontal adjustment is possible without departing from the standard or tangent tower lengths.
Use is made of sag templates drawn to the same scale as the line profile, to ensure the required clearance. The sag template is usually made on celluloid or tracing cloth. In sag template, shown in Fig. 10.11(b), the upper curve I represent the conductor line. The middle curve (i.e. curve II) is below the upper curve I by a uniform vertical distance equal to the desired minimum vertical clearance to ground.
This clearance to ground is governed by the operating voltage and is given, according to IE rules, in Table 10.2. The lower curve (curve III) is below the upper curve by a uniform vertical distance equal to the height of a standard tower measured to the point of support of the conductor.
If the location of the left tower has been decided, the location of the right hand tower can be determined by adjusting the sag template so that the conductor line passes through the point of support on the left hand tower and the clearance line is tangent to ground at one or more points.
In the above particular case, illustrated the points of conductor support are upon the same horizontal level, but the same process applies when the route is a steeply sloping one. However, the shape and position of the conductor will always be represented by curve I, as shown in Fig. 10.11(b).
Sag template is very a convenient method for allocating the positions and height of the towers/supports correctly on the profile.
7. Equivalent Span of Transmission Lines:
It may not be possible to have a section of transmission line consisting of successive spans of equal lengths because the location of the towers depends upon the profile of land along which the transmission line is to be laid. Sometimes also, the towers are forced to be located to give spans of different lengths so that minimum interference is caused with the use of land. When the successive spans are of unequal lengths changes in tension in load or temperature will cause unequal changes in tension in the different spans.
It is very tedious to make calculations of sag and tension for each and every span individually and then to make adjustment while erecting the transmission line. In the erection of a transmission line the conductors are run out through snatch blocks attached to the support arms equally tensioned at each end of a section of five or six blocks. When the conductors are clamped to suspension insulator strings, the equal tension is maintained by insulator swing. When the conductors are bound to pin-type insulators, the flexibility of the supports ensures equal tension.
It is often convenient to make sag and tension calculations in terms of a hypothetical equivalent span, this tension being applied to each span within the section of overhead line between the tensioning points. If there are n spans of length L1, L2, L3, etc. which are to be given an equivalent span Le, then the strung length of the equivalent line must be the same as that of the individual spans.
This may be expressed as:
If the line tension T0 is determined for the equivalent span, the sag for the individual spans may be calculated from Eqs. (10.17) using the approximate value of span.
It is to be noted that the method of sag template for locating the towers should not be used for long spans as well as where the slope of the profile is very steep. In such cases, actual calculations for sag and tension should be made.
8. Vibrations and Dampers in Transmission Lines:
The overhead transmission line experiences vibrations in the vertical plane and there are two types of such vibrations, in addition to normal swinging in wind, called the aeoline vibrations or resonant vibrations or high frequency oscillations and galloping or dancing or low frequency vibrations.
Simple swinging of conductors is harmless provided the clearance is sufficiently large so that the conductors do not approach within the sparking distance of each other.
Aeoline vibrations are high frequency (5-100 Hz) and low amplitude (20 mm to 50 mm) vibrations. They are caused by vortex phenomenon in light winds (5-20 km/hour). The line conductor vibrates in a number of loops.
The length of the loop (half-wave length) depends on tension T and weight of conductor w per metre length and is given by
. The loop length varies from 1 to 10 metres depending upon T, w and f. These vibrations are common to all conductors and are more or less always present. The harmful effects of such vibrations take place at clamps or supports where the conductor suffers fatigue and breaks eventually.
Low frequency vibrations (about one Hz) occur during sleet storms with a strong wind. The amplitude is very large, about 6 metres or more, and the conductors are said to ‘dance’. Operation is almost impossible for the conductors touch one another, since the ‘dancing’ takes place horizontally and vertically.
It is considered that the phenomenon takes place due to the fact that the line conductor receives an irregular coating of sleet. If the cross-section of the coating is considered to be an ellipse, the line will experience a drag; furthermore, if the major axis of an ellipse makes an angle of 45° to the wind, there will be a considerable aerodynamic lift (or downward thrust) such as is experienced by an aerofoil.
The conductor will thus dance horizontally and vertically with large amplitude and in an irregular manner owing to the irregular deposition of sleet. The stranding of conductors also contributes to these vibrations. The travel of conductor follows the path of an ellipse. There is no method for prevention of these (low-frequency) vibrations. However, danger due to such vibrations can be reduced if horizontal conductor configuration is used.
The conductors are protected by dampers which prevent the resonant vibrations from reaching the conductors at the clamps or supports.
The stock bridge damper, consists of two weights attached to a piece of stranded cable 0.3 or 0.5 m long, which is clamped to the line conductor. The energy of vibration is absorbed by the stranded cable, and the vibration is rapidly damped out.
Another successful damper consists of a box containing a weight resting on a spring. In this case the spring absorbs the energy of vibration. The fatigue may be reduced by reinforcing the conductor for a few metres on either side of the clamp by binding metal rods or a length of the same conductor to the main conductor outside the clamp.