In this article we will discuss about:- 1. Introduction to Insulated Cables 2. Insulated Cable Conductors 3. Insulating Materials 4. Capacitance of Three-Core Belted Type Cables 5. Heating 6. Operating Problems.
Contents:
- Introduction to Insulated Cables
- Insulated Cable Conductors
- Insulating Materials for Cables
- Capacitance of Three-Core Belted Type Cables
- Heating of Insulated Cables
- Operating Problems Associated with Underground Insulated Cables
1. Introduction to Insulated Cables:
The merits and demerits of transmission and distribution of electric power by underground cables in comparison with that by overhead system, the initial heavy cost is the only factor which discouraged the use of underground cables for the purpose of transmission and distribution of electric power inspite of its numerous advantages. Underground cables are used for transmission and distribution of power where it becomes impracticable to make use of overhead construction.
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Such location may be congested urban area where right-of-way cost would be excessive or local ordinances prohibit overhead lines for reasons of safety, or around plants and substations; or crossings of wide bodies of water which for various reasons would not permit the overhead crossings. The type of cable used will depend upon the voltage and service requirements. Recent improvements in design and manufacture have led to the development of cables suitable for use at the highest voltages associated with modern transmission systems.
An electric cable may be defined as a single conductor insulated through its full length; or two or more conductors each provided with its own insulation and laid up together under one outer protective covering.
2. Insulated
Cable Conductors:
For all cables the conductor was, at one time, almost universally stranded copper but because of scarcity of copper, only aluminium is allowed to be used in power cables in India. Copper conductors are only used for cables used in control circuits.
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The stranding is necessary to provide flexibility to cables and the conductor numbers are 3, 7, 19, 37, and so on, all numbers except 3 having a centrally disposed conductor with all the others around it. Thus a 7-strand has a central conductor with 6 around it. The various conductors are spiralled round the central conductor, and when there is more than one layer alternate layers are spiralled in opposite directions. This is to prevent ‘bird-caging’ when the conductor is bent.
The spiralling of the conductors obviously causes the increase in resistance, since the length of each spiralled conductor is greater than the central strand, and the flow of current is along the various conductors. It is therefore necessary to be particular in the designation of the cross-section.
Requirements of Insulated Cable:
(i) The conductor (usually annealed copper with about 99% purity or aluminium) used in cables should be stranded one in order to provide flexibility to the cables and should be of such x-sectional area that it may carry the desired load current without overheating and causing excessive voltage drop.
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(ii) The insulation provided should be of such thickness that it may give high degree of safety and reliability at the working voltage for which it is designed.
(iii) The cables should be provided with a mechanical protection so that it may withstand the rough usage in laying it.
(iv) Materials used in manufacture of cables should be such as to give complete chemical and physical stability throughout.
3. Insulating Materials for Cables:
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The satisfactory operation of a cable depends to a great extent upon the characteristics of insulation employed. So the proper choice of insulating material for cables is considerably important.
The main requirements of the insulating materials used for cables are:
1. High insulation resistance to avoid leakage current.
2. High dielectric strength to avoid electrical breakdown of the cable.
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3. Good mechanical properties i.e. tenacity and elasticity. Good tenacity is required in the material to withstand the mechanical handling of cables.
4. Immune to attacks by acids and alkalies, over a range of temperature of about – 18°C to 94°C.
5. Non-hygroscopic because the dielectric strength of any material goes very much down with moisture content. In case the insulating material is hygroscopic, it must be enclosed in a water tight covering like lead sheath etc.
6. Non-inflammable.
7. Low coefficient of thermal expansion.
8. Low permittivity.
9. Capability of withstanding high rupturing voltages.
The last point but not the least is that a dielectric should not be expensive and it should be possible to handle it from the point of view of the manufacturer.
No one insulating material possesses all the above mentioned qualities, so the type of insulating material used in a cable depends upon the service for which the cable is required. The various insulating materials used in manufacture of cables are rubber, VIR, paper, polyvinyl chloride, varnished cambric, polyethylene, vulcanized bitumen, gutta-percha, silk, cotton, enamel etc.
4. Capacitance of Three-Core Belted Type Cables:
The capacitance of a cable system is of much greater importance than that of an overhead line of the same length firstly due to the narrow spacing between the conductors themselves and between the conductors and earthed sheath and secondly due to their separation by a dielectric medium of higher permittivity as compared to air.
Since there is a potential difference between pairs of conductors and between each conductor and sheath there will be a system of electrostatic fields in the cross-section of the cable somewhat as shown in Fig. 11.17. Consequently the three-core cable has capacitance between the cores and each core has capacitance with sheath, as shown in Fig. 11.18.
Let the capacitance between cores be CC and capacitance between cores and sheath be CS.
The delta-connected capacitances can be converted into equivalent star-connected capacitances, as shown in Fig. 11.18.
The Ceq = 3CC … (11.15)
The star point may be assumed to be at zero potential and if the sheath is also at zero potential, the capacitance of each core to neutral.
CN = Ceq + CS = 3CC + CS … (11.16)
If VP is the phase voltage, then the charging current is given,
IC = 2πfVPCN amperes … (11.17)
The values of capacitances CC and CS may be determined by measurement as follows:
1. Capacitance is measured between the three cores bunched together and the earthed sheath. (Fig. 11.20 a). This gives 3CS because three capacitances CC are eliminated leaving the three capacitances CS in parallel
i.e. C1 = 3 CS
or CS = C1/3 … (11.18)
2. Capacitance between the two cores or lines is measured with the third core being either insulated or connected to sheath (Fig. 11.20 b). This eliminates one of the capacitors CS and measured value C2 gives CN/2 directly.
C2 = CC + CC/2 + CS/2
or C2 = 1/2 (3 CC + CS) = 1/2 CN … (11.19)
3. The capacitance is measured between the two cores shorted with the sheath and the third core (Fig. 11.20 c). This gives 2 CC + CS
i.e. C3 = 2 CC + CS … (11.20)
From the above equations values of CC and CS can be determined.
It is very difficult to determine the capacitance CN of the cable from the geometry of the figure. However the empirical formulae given below may be used for determining the value of CN.
where d = diameter of conductor,
t = thickness of belt insulation and
T = thickness of conductor insulation.
The value of CN is usually determined by experiments, as described above, not by the empirical formula.
5. Heating of Insulated Cables:
The temperature rise of a body depends upon the rate of generation and dissipation of heat by the body. The temperature goes on rising until the rate of heat generation becomes equal to that of heat dissipation.
The temperature rise of a cable under operating conditions depends upon the following factors:
(a) Total heat produced within the cable i.e. up to its periphery.
(b) The conveyance of heat up to the periphery of the cable.
(c) The conveyance of heat through the medium, and thus away from the cable.
(d) The current carrying capacity of the cable, or cables, singly and collectively, where installed under the varying conditions encountered in practice.
(e) The nature of the load—continuous, intermittent or possibility of short-circuits etc.
(a) Heat Generation in Cables:
Within the cables the sources of heat generation are:
(i) I2R losses in the conductor.
(ii) Dielectric losses in the cable insulation,
(iii) Losses in the metallic sheath and armourings.
(i) Copper Losses in the Conductors:
Resistance of conductor at an operating temperature of 65°C (assumed) is determined from the resistance given in standard tables (usually at 15.6°C) from the following relation.
Rh = Ra [1 + αa (65 – 15.6)]
where Rh, Ra and αa are the hot resistance (resistance at 65° C), resistance at ambient temperature of 15.6° C and the temperature coefficient of resistance at ambient temperature of 15.6° C.
To allow for stranding, the resistance of a single-core cable is multiplied by the factor 1.02. In case of multicore cables the resistance is further multiplied by the factor 1.02 in order to allow for the lay of the whole conductor.
(ii) Dielectric Losses:
The energy losses occurring in the dielectric of cables are due to leakage and so called dielectric hysteresis. The former loss, is due to passing of current by conduction through the resistance of dielectric, and is independent of supply frequency and, therefore, it occurs both with d c and a c. The leakage current is proportional to the applied voltage and, therefore, the loss is proportional to the square of the applied voltage.
With alternating voltages there is a further loss of energy, usually known as hysteresis loss, and this loss under usually operating conditions is very much higher than the leakage loss. Apparently some energy is consumed in reversing the stresses in solid dielectrics, and this appears as heat, causing increase in temperature of the dielectric. At normal operating stresses the dielectric hysteresis loss is proportional to the square of the electrostatic stresses that is to the square of the applied voltage.
In order to take into account the above losses, the charging current of a cable I is assumed to have two components – One being true capacitance current which is equal to ω C V and leads the applied voltage by 90° and the other being the energy component which is in phase with the applied voltage and represents the dielectric loss component of current.
The equivalent circuit for this system is represented by a parallel combination of leakage resistance R, representing dielectric power loss, and a capacitance C, as shown in Fig. 11.22 (a). The phasor diagram is shown in Fig. 11.22 (b).
If V is the applied voltage C is the capacitance of cable, ɸ is the phase angle between voltage and current called the power factor angle of the cable and δ is the loss angle of the dielectric,
Sine, δ is normally very small, so tan δ can be taken equal to δ (in radians) and dielectric loss per phase is given by the expression
P = V2 ω C δ watts … (11.22)
This shows that the dielectric losses are proportional to the square of the voltage, with the result that, although these are of little importance in low-voltage cables, these are of very great importance in high voltage (say over 22,000 V) cables.
It has been found that, over the working temperature range, the dielectric losses in most cables fall to a minimum at about 40°C and then rise again. The variation when plotted gives rise to what is known as the ‘V’ curve of the dielectric losses and the minimum temperature point corresponds very closely to the temperature of liquefaction of the resinous impregnating compound.
Since the variation of capacitance current with temperature is small, the dielectric power factor-temperature curve is of the same general shape as the dielectric loss-temperature curve. In this connection, it seems preferable to exhibit dielectric — loss data in terms of dielectric power factor rather than in power loss per km of cable in order to facilitate comparison between different types and sizes of cables.
The actual shape of ‘V’ curve depends on several factors and may be deliberately changed by using different papers, impregnating compounds, and methods of manufacture.
The operating temperature of a paper-insulated cable is about 65°C which is to the right of the lowest point on the ‘V’ curve. So around the operating temperature, if the temperature further increases, due to overload or any other reason, dielectric losses will increase causing further increase in heat generation and so rise in temperature.
The increase in temperature will also cause increase in temperature gradient between the cable and the atmosphere that will result in greater heat dissipation. In case the rate of heat dissipation is less in comparison to that of heat generation, the temperature will go on increasing until the dielectric overheats and fails electrically. This is referred to as thermal instability.
Fortunately, action taken to reduce dielectric losses makes the dielectric loss-temperature curve flat and reduces the tendency towards thermal instability.
(iii) Sheath and Armouring Losses:
In case of power transmission by single-core cables, the presence of lead sheath around each conductor influences the electrical characteristics of the circuit. In 3-core cables the effect is negligible but for single core cables the effect is of great importance. The electromagnetic fields produced by the currents flowing through the conductors induce emfs in the sheaths, and under certain conditions heavy currents are set up therein.
The actual current flowing along the sheath depends, amongst other things, on the magnitude and frequency of the current in the conductor, the arrangement and spacing of the cables, the sheath resistance and upon the conditions that the sheath is bounded (two different cables having sheath electrically connected at both ends) or unbounded (cables having one end or no end electrically short-circuited).
The induced sheath currents are of two types:
(i) The currents, which have both outward and inward directions, called the sheath eddies.
(ii) The currents, which have outward and inward current paths in separate sheaths, as shown in Fig. 11.24, called the sheath-circuit eddies.
Thus for unbounded cables sheath eddies will be there, but for bounded cables both sheath eddies and sheath circuit eddies will be there.
The approximate formulae for eddy loss for unbounded cables given by Arnold are as follows:
where, I is the current per conductor, r is the mean radius of the sheath, d is the inter- axial spacing of conductors, and Rs is the sheath resistance in ohms.
If f = 50 Hz, then 78 ω2 × 10-9 = 78 (2 × 50)2 × 10-9 = 0.0077
Conductor loss = I2R
where R is the resistance of conductor,
The sheath loss in open-circuited sheath is about 2% of the total loss and can be neglected.
The voltage induced in the sheath = I × ω M = I Xm
where M is the mutual inductance between conductor and sheath.
The value of M between the conductor and sheath can be determined in a similar manner to that of self-inductance of the two conductors.
For two sheaths with respect to the core conductors (Fig. 11.24) the mutual inductance is given as:
M = 4 loge d/r × 10-7 H/m
Large voltages are induced in the sheaths if they are open-circuited, and it is very probable that arcing will occur between them. It is, therefore, standard practice to bond the sheaths at both ends so that high voltages are avoided. The impedance of the sheath current path is due to the sheath resistance Rs and the sheath-self-inductance, which is equal to M.
Thus if the sheaths are bonded the sheath current is given by the expression:
The magnitude of the sheath current is independent of the distance between the bonds, since Xm and Rs both, are proportional to the length.
where R is the resistance of the conductors.
With large conductors and close spacing Xm is very small in comparison with Rs and therefore, the ratio of sheath losses to copper losses
6. Operating Problems Associated with Underground Insulated Cables:
A cable, because of narrow spacing between the conductors themselves and between the conductors and earthed sheath and due to their separation by a dielectric medium of higher permittivity, has large capacitance resulting in high charging current and reactive power (capacitive).
The charging current and reactive power drawn by the cable of capacity C farads from 3-phase supply of V volts and frequency f Hz are given by the following expressions:
Flow of charging current causes heating of cable. This reduces the load current capability of the cable. Sometimes current carrying capability of the cable is also reduced due to dielectric losses resulting in increase in temperature rise. The use of cable, in practice, is reduced to a length of less than 50 km because of these factors.
Because of capacitive current/capacitive reactive power drawn from the system, an increase in receiving-end voltage may occur under no-load conditions (Ferranti effect). Thus the receiving-end voltage may vary considerably from full-load to no-load conditions.
Generation of capacitive reactive power may hamper the stability conditions of large generators as large size generators have high synchronous reactance (about 1.5 pu) and their leading MVAR capacity is low.
The interruption of cable capacitive currents may give rise to over-voltage.