Losses In Xlpe Insulated Cables Engineering Essay
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Power cables, mainly underground power cables form a bulk part of electrical power systems network. Accordingly, when medium voltage XLPE cables were first installed in the late 1960's, cable manufacturers and electric utilities expected them to perform reliably for 20 to 30 years. However, history has shown that these cables had high percentage of life losses whereby the service life of some of these cables was far shorter than expected. Many cables failed after only 10 to 15 years in service. The failure of XLPE cables was happened due to the aging process. Aging of XLPE cables is related to the temperature of the insulation. For XLPE cables, the normal maximum operating temperature is 90 °C. At this maximum value, the consumption rate of anti-oxidant has been calculated to afford a cable life of 30 years. Increasing the XLPE cables operating temperature will increase the rate which the anti-oxidant is used up. Subsequently, it will reduce the service life of XLPE cables. The reaction follows the Arrhenius relationship which is an exponential function. From this, even a small increase in temperature, it will hence give significant impact on the aging process of XLPE cables. Once the anti-oxidant in the cables is used up, the cables will start to oxidize and become easily broken. Then, the cables will be subject to stress cracking and electrical failure at positions of mechanical stress. In addition, the presence of harmonics in power system causes a conductor to overheat. This overheating process makes the cable to increase in term of temperature to its insulation. Therefore, cable will soften and the mechanical performances will reduce which is called as premature aging. Thus, it is important to investigate the presence of harmonic in any electrical equipment. From this we could know the temperature due to the overheating process and evaluate the life losses of any associated cables.
TABLE OF CONTENTS
TABLE OF CONTENTS
1.2 Premature Aging due to Harmonic
1.3 Development of Power Cables
1.3.1 Oil-Impregnated Paper Power Cables
1.3.2 Solid-Dielectric-Extruded Power Cables
220.127.116.11 Technology of XLPE Cables
1.4 Losses in Power Cables
1.5 Objectives of Study
1.6 Scopes of study
2.2. Power System Harmonics
2.2.1. Definition of Harmonics
2.2.2. Source of Harmonics
2.2.3. The Harm of Harmonic
2.2.4. Effects of Harmonics on Power System
18.104.22.168 Motors and Generators
22.214.171.124 Power Cables
2.2.5. Economical Damage due to Harmonic Losses
2.3 Underground Power Cables
2.3.1 Gas-filled Cable
2.3.2 XLPE Cables
EVALUATION OF THE AGING COST DUE TO
HARMONIC LOSSES IN XLPE CABLES
3.2 Calculation of Losses
3.2.1 Resistance of the conductor
3.2.2 Skin Effect
3.2.3 Proximity Effect
3.2.4 Total Power Losses
126.96.36.199 Joule Losses
188.8.131.52 Dielectric losses
3.3 Probabilistic Evaluation of the Economical Damage due to Harmonic Losses
3.3.1 Expected Value of the Aging Cost due
to Harmonic Losses
DATA, MODELLING AND ASSUMPTIONS
RESULTS, ANALYSIS, AND DISCUSSIONS
CONCLUSIONS AND RECOMMENDATIONS
6.1 Expected result
By means of the discovery of electricity in the early 19th Century, all countries in the world nowadays have virtually utilized electricity as a source of light and energy. This has led to the existence of distribution-transmission line system carrying current, even if at different voltages and transporting it over long distances till the end users or customers. For the distribution-transmission line system, engineers had thought critically in finding the suitable power cables for power system.
Mainly, most of the bulk electrical energy generated from the generation centers is being transported to major load centers within a large geographical area by the transmission systems using overhead lines . In the other words, the distribution system delivers the electrical energy from these load centers to customers who are within a smaller geographical area. For safety, reliability and aesthetics, the electric circuits used to transport energy to such customers are usually underground power cables, though this kind of arrangement is expensive but has more advantages than the overhead lines .
Over the years, high demand of reliable electricity power supply has led the electricity markets to be highly competitive. Electric utility companies now have to develop means of maintaining, enhance the safety and reliability of their expensive power system components to operate advantageously and meet the demands of their customers.
One of power system component that constitutes a bulk part of the distribution and transmission line systems in urban areas is the underground power cable. For instance, in the United Kingdom there are about 93000 km of 11 kV cable and more than 13000 km of 33 kV . In Malaysia with rush of development has led to increasing demands of electrical energy. Doing this, underground cable distribution is increasing significantly. It is estimated that there are about 180000 km of underground cables in Malaysia, forming about 80 % of the underground power distribution system. This shows that, the technology of underground power cables has grown up very fast by the time as the world is moving extremely in science and technology.
However, lately the presence of harmonic in electrical energy systems is well known . The harmonics are due to nonlinear loads such as static converter and can damage the system components . In the case of the cables, harmonics can cause relevant additional losses in the conducting and in the insulating materials which cannot be neglected. From the economical point of view, the presence of harmonics can cause economical damage which increasing the operating costs and decreasing the useful life of the system components.
The economical damage due to harmonic losses can be defined as the summation of the operating costs and the aging costs. As stated in , the operating costs are referred to the costs of the incremental energy losses caused by the harmonic flow in the component, where the term 'incremental' means that these losses are superimposed to the ones at the fundamental while the aging costs are referred to the incremental investment costs caused by the premature aging of the components caused by the harmonic pollution.
Premature Aging due to Harmonic
Aging failures have become a major and urgent concern in many utilities since many power system components are approaching the turning point to the end of life. For the case of power cables, the premature aging occurs due to harmonic pollution. The harmonic flow can lead to additional heating in power cables. Subsequently, temperature will rise and premature aging may result.
Development of Power Cables 
Power cable technology had its beginnings in the 1880s when the need for power distribution cables became pressing. With urban growth, it became increasingly necessary to replace some of the overhead lines for power transmission and distribution system with underground cables. The illumination of the larger cities proceeded at such a rapid pace that under some circumstances it was impossible to accommodate the number and size of feeders required for distribution, using the overhead line system approach.
In fact this situation deteriorated so notably in New York City that, in addition to the technical and aesthetic considerations, the overhead line system began to pose a safety hazard to the line workers themselves, the firemen, and the public. As a result, the city passed an ordinance law in 1884 requires removing the overhead line structures and replacing them with underground power cables. Similar laws and public pressure were applied in other cities, with the consequence that by the early 1900s, underground electrification via insulated cables was on its way to becoming a well-established practice .
A practical lead press was invented in 1879 and subsequently employed to manufacture 2kV cables for Vienna in 1885. During the same period, vulcanized rubber was used to produce cables on a commercial scale, although use of guttapercha had already been made as early as 1846. Impregnated-paper power cables were first put on the market in 1894 by Callender Cables of England, using impregnant mixtures of rosin oil, rosin and castor oil and only in 1918 were these replaced by mineral oils. In North America, impregnated-paper cables were first supplied by the Norwich Wire Company. Varnished cambric cables were introduced by the General Electric Company in 1902. The behavior of these cables with hightemperature was subsequently improved the addition of black asphalt.
Some of the more common early solid and liquid insulating employed in various underground cable installations were natural rubber, gutta-percha, oil and wax, rosin and asphalt, jute, hemp, and cotton. In 1890, Ferranti developed the first oil-impregnated-paper power cable. By following their manufacture, his cables were installed in London in 1891 for 10 kV operations. In addition, the cables were made in 20 ft lengths as the total circuit was 30 miles in length about splicing joints were four required. Nevertheless, these cables performed so well that the last cable length was removed from service only in 1933. Cable installation continued to proceed at a rapid pace, so that by the turn of the 20th century many major cities throughout the world had many miles of underground power cables. For example, already by the end of 1909, the Commonwealth Edison Company in Chicago had 400 miles of underground cable operated in the voltage range between 9 to 20 kV. Montreal had some 4500 ft circuits of three-conductor cables installed in ducts under the Lachine canal for 25
kV operations; the same voltage was used for cable traversing the St. Lawrence River in 1906. With some experiences behind them, cable manufacturers were increasingly gaining confidence and during the St. Louis Exposition in 1904 power cables developed for voltages as high as 50 kV were put on display .
Oil-Impregnated Paper Power Cables 
During the period prior to World War I, extensive use was made of oilimpregnated paper cables of the three-conductor belted type for voltages up to 25 kV. Due to non-uniform stress distribution in the cable construction, the belted cable proved to be highly partial discharge susceptible when attempts were made to extend the operating voltage range with larger wall thickness to approximately 35 kV, to meet the increased power demand following World War I . This problem was resolved by shielding the individual conductors, using 3-mil-thick copper tapes. The outside of the shielded conductors was thus maintained at the same ground potential.
Figure 1.3.1 Cross-section of an Oil-impregnated Paper Insulated Cable
In addition, the belt insulation was replaced with a binder consisting of fabric tapes and strands of interwoven copper wire. The purpose of the latter was again to maintain the shields of the three cables at the same potential. Over the years, the conductor shapes of the three-conductor shielded paper insulated cables have evolved into three forms, namely circular, oval, and sectoral.
In many utilities a substantial portion of the present-day distribution load is still carried at 35 kV via three-phase oil-impregnated paper belted cables, with the three conductors individually grounded. There is little inducement to replace these cables with solid extruded dielectric cables, whose outer diameter for an equivalent power rating would exceed that of the ducts accommodating the more compact threephase oil-paper belted cables. Moreover, the oil-paper belted cables have been characterized by remarkably long in-service lifetimes that often exceed 65 years. Belted cables with unshielded conductors are still deployed but only for working voltages equal to or less than 15 kV.
With the individual conductors shielded, it was possible to extend the use of the three-phase belted cables for voltages as high as 69 kV, though on the average their application has been confined to voltages below 35 kV. The main reason for this upper limit has again been associated with the occurrence of partial discharges, which had in numerous instances led to the deterioration and failure of the dielectric at the elevated voltages. The partial discharges were found to take place in voids, which were formed either during the manufacturing process or during the load cycling while in service.
Solid-Dielectric-Extruded Power Cables [1, 14]
With the discovery of the hydrocarbon thermoplastic polyethylene (PE) in England in 1933, polyethylene became rapidly, the insulant of choice for RF coaxial cables. PE was first used as an insulant for power cables in the 1950s. In the mid 1960s, conventional PE became the material of choice for the rapidly expanding URD systems in the United States. It was known to be superior to butyl rubber for moisture resistance, and could be readily extruded. It was used with tape shields, which achieved their semi-conducting properties because of carbon black. By 1968, virtually all of the URD installations consisted of polyethylene-insulated medium voltage cables.
The polyethylene was referred to as HMWPE; this simply meant that the insulation used had a very high "average" molecular weight. The higher the molecular weight, the better the electrical properties. The highest molecular weight PE that could be readily extruded was adopted. Jacketed construction was seldom employed at that time. Extruded thermoplastic shields were introduced between 1965 and 1975 leading both to easier processing and better reliability of the cable .
XLPE was first patented in 1959 for a filled compound and in 1963 for unfilled by Dr. Frank Precopio. It was not widely used because of the tremendous pressure to keep the cost of URD down near the cost of an overhead system. This higher cost was caused by the need for additives (cross linking agents) and the cost of manufacturing based on the need for massive, continuous vulcanizing (CV) tubes. EPR was introduced at about the same time. The significantly higher initial cost of these cables slowed their acceptance for utility purposes until the 1980s. The superior operating and allowable emergency temperatures of XLPE and EPR made them the choice for feeder cables in commercial and industrial applications. These
materials do not melt and flow like HMWPE.
The emergence of power distribution cables insulated with PE have replaced a significant portion of the oil-impregnated-paper insulated power cables used at operating voltages up to 35 kV. But lower voltage PILC cables are still being manufactured, due to their in-service longevity and reliability. In spite the long record of service and reliability of PILC cables, they are being gradually replaced by the less hygroscopic polymeric insulated cables, XLPE. XLPE cables have distinct advantages which are lighter weight, better electrical and thermal properties, less maintenance, and easier terminating and jointing procedure etc. Today, XLPE cables are being extensively used in many countries all over the world. In 1959, Japan and USA commercialized XLPE cables up to medium voltage rating. Since then a fast development of XLPE cables has taken place. Presently, XLPE cable of 500 kV class has been installed in Japan.
The introduction of XLPE has increased the capability of polymeric insulated cables because of their higher temperature ratings. XLPE insulations perform well at elevated temperatures. Their normal operating temperature is about 90 °C and designed to withstand an emergency overload and short circuit ratings of 130 °C and 250 °C, respectively.
Technology of XLPE Cables
XLPE has become the most favored insulant. Germany, USA, Asian and Scandinavian countries have installed gigantic quantities of such cables. Japan has developed XLPE cables up to 500 kV which is the highest voltage rating of XLPE cables manufactured so far. The basic material for XLPE cable is polyethylene (PE). PE has very good electrical properties. However, its mechanical strength decreases significantly above 75 °C restricting its continuous operating temperature to 70 °C only.
The improved thermal characteristics of PE are obtained by establishing a large number of cross-links between its liner molecular chains employing suitable techniques. The introduction of XLPE has increased the capability of polymeric insulated cables because of their higher temperature ratings. The processes for converting PE to XLPE are electron irradiation, chemical cross linking, and organic silane method.
Electron irradiation is a slow process and it is difficult to ensure an even degree of cross linking throughout the thick insulation required for power cables. Therefore this process is usually restricted to thin insulation of 1 to 2 mm thickness only. Chemical cross linking process is the process by which cross-linking of PE is established using organic peroxide such as dicumyl peroxide (DCP) at high temperature in the range 250 to 350 °C and pressure 15-20 kg/cm2. This method is employed in the production of XLPE cables of all voltage range, from LV to EHV. Sioplas technique is a relatively new method of cross linking PE into XLPE. Cross linking is achieved by mixing suitable silane to PE and exposing this to ambient conditions. This method has the distinct advantage of lower capital expenditure as no special arrangements to maintain high pressure and temperature are required. But the process is very slow for thick insulation and hence restricted to low voltage and medium voltage XLPE cables.
The general construction of XLPE cable consists of copper or aluminium conductor, extruded layer of semi conducting material over conductor (for voltage class above 3.3 kV), extruded XLPE insulation, extruded layer of semi-conducting material (for cables of voltage rating above 3.3 kV), copper wire or tape as metallic screen, armour, inner sheath and outer sheath, usually made of PVC etc. Three core XLPE cables are generally used up to maximum 33 kV. Cables of 66 kV and above voltage rating are of single core construction.
Figure 1.3.2 Solid dielectric extruded power cable 
The manufacturing process of XLPE cables consists of mixing of PE with cross-linking agent (DCP) and antioxidants, extrusion of semiconducting layers and insulation over the conductor, crosslinking the PE compound in curing lines at high temperature and pressure and cooling the core to ambient temperature. All these processes are carried out in one step employing catenaries lines for curing and cooling, hence the name continuous catenaries vulcanization. Semiconducting layers and insulation are extruded using triple extrusion technique.
The curing process was initially carried out with steam at high temperature and pressure. This resulted in the formation of microvoids within the insulation and restricted the application of steam curing process up to 33 kV. To achieve reliable HV cables, it was therefore necessary to employ curing in the absence of steam. For this reason, dry curing methods were developed, where PE was crosslinked under nitrogen pressure in silicone oil, in molten salt and also in long dies. The numbers of microvoids were drastically reduced. A new curing process has recently appeared namely silane process which is more economical.
Losses in Power Cables
Losses in power cables include losses in conductor, insulation, sheath, and screens armors. Conductor losses (I2Rac losses) depend upon the rms current I effective AC resistance of the cable conductor. Dielectric losses comprise of losses due to leakage through the cable insulation and caused by dielectric polarization under AC stresses. It includes the net dielectric losses depend upon cable voltage, its frequency as well as the permittivity and loss tangent of the cable dielectric material, as shown by the equation below:
Power loss = Ï‰CoV2Îµr tan Î´  (1)
Generally, tan Î´, which partially controls the dielectric losses, is significantly
higher for oil-paper insulation as compared to XLPE insulation. For most of the dielectric materials used in cables, tan Î´ depends upon temperature, applied stress and supply frequency. For oil-paper insulation tan Î´ is also strongly influenced by moisture content. Therefore, in voltage cables, a moisture level of less than 0.05 % is desirable in order keep dielectric losses within acceptable limits. The presence of voids and microcracks can also influence dielectric losses. These voids are formed in the insulation or at the screens/insulation interfaces during manufacture, installation or operation.
In polymeric cables, they are formed during the extrusion process while in paper-insulated cables, during the impregnation cycle. Voids may also form in cables by the differential expansion contraction of cable materials due to cyclic loading or short circuit conditions. These voids have a higher electric stress as compared to the bulk insulation. However, the gas inside a void usually has lower breakdown strength as compared to the main insulation. When the electric stress in void exceeds the breakdown strength of gas within the void, PD occurs.
Any partial discharge in such voids increases the effective tan Î´ value for insulation. Consequently, when the applied voltage is raised above the charge inception threshold, the dielectric losses exhibit a distinct increase. Similarly, impurities in the cable insulation and screening materials also increase dielectric losses.
The AC current flowing along each cable conductor induces emf the metallic sheaths of the cable. Without grounding, such sheaths would operate at a potential above the ground potential and can pose a hazard. Furthermore, it will accelerate degradation of the jacket and materials, thereby affecting the cable's life and reliability. When the sheaths are bonded, circulating current flows in them causing power losses. However, for three-core cables such losses are negligible. In addition to circulating currents, eddy currents are also induced in sheaths of both single and multi-core cables causing additional losses which usually are of small magnitudes.
1.5 Objectives of Study
This project is conducted to evaluate the expected value of aging cost due to harmonic losses in XLPE cables. Therefore, this project is conducted regarding to these objectives:
To investigate the effects of harmonics losses on XLPE cables from
economical point of view.
To evaluate the expected value of the aging cost due to harmonics losses
in XLPE insulated cables.
1.6 Scope of study
This study will focus on XLPE insulated cables
This study will use the characteristics of single core underground cables.
The effect of harmonics losses on XLPE cable will be investigated
A program will be developed to evaluate the expected value of aging cost
due to harmonic losses.
The economical damage due to harmonic losses is quantified by means of the expected values of the operating costs and of the aging costs. For this, it will focus only for the calculation of the expected values of the aging costs.
We design power systems to function at the fundamental frequency . In Malaysia, the fundamental frequency is standardized at 50 Hz. This design is prone to unsatisfactory operation. At the same time, failure will happen when subjected to voltages and currents those contain substantial harmonic frequency elements. Frequently, the electrical equipment may seem operate normally. However, when they operate under a certain combination of conditions it might enhance the impact of harmonics which cause results to damage .
Most people do not realize that harmonics have been around for a long time. Since the first AC generator began to operate more than 100 years ago (Sankaran, C., 1995), electrical power systems have experienced harmonics. When harmonics present in electrical equipment, it can cause the equipment to malfunction and fail to work. In this case proper design and rating are needed to prevent the presence of harmonics.
2.2 Power System Harmonics
The objective of the electric utility is to deliver sinusoidal voltage at fairly constant magnitude throughout their system. In fact, in order to achieve this objective is reasonably complicated because there are loads that exist on the power system that will produce harmonic currents. These currents produced may result in distorted voltages and currents that can give negative impact to the system performance in different ways.
As the number of harmonic producing loads has increased over the years, it has become increasingly necessary to address their influence when making any addition or changes to an installation. We should consider two important concepts that have to bear in mind with regard to power system harmonics. The first concept is the nature of harmonic current producing loads (non linear loads) and the second concept is the way in which harmonic currents flow and how the resulting harmonic voltages develop.
Ideally, voltage and current waveforms are perfect sinusoids. However, because of the increased popularity of electronic and other non-linear loads, these waveforms quite often become distorted. This deviation from a perfect sine wave can be represented by harmonics - sinusoidal components having a frequency that is an integral multiple of the fundamental frequency. Thus, a pure voltage or current sine wave has no distortion and no harmonics, and a non-sinusoidal wave has distortion and harmonics. To quantify the distortion, the term total harmonic distortion (THD) is used. The term expresses the distortion as a percentage of the fundamental (pure sine) of voltage and current waveforms. In addition, current harmonics can distort the voltage waveform and cause voltage harmonics. Voltage distortion affects not only sensitive electronic loads but also electric motors and capacitor banks.
2.2.1 Definition of Harmonic
Harmonics are defined as current and voltages at frequencies that are integer multiples of the fundamental power frequency . For example, if the fundamental frequency is 50 Hz, then the second harmonic is 100 Hz, the third is 150 Hz, and etc . The presence of harmonics in electrical energy systems is well recognized due to nonlinear loads such as static converters and it can damage the system components . These nonlinear loads will draw current in abrupt pulses rather than in a smooth sinusoidal manner. Then, these pulses cause distorted current wave shapes which in turn and cause harmonic currents to flow back into other parts of the power system. In the case of power cables, harmonics can cause relevant additional losses in the conducting and in the insulating materials which cannot be neglected in the cable size .
2.2.2 Source of harmonics
Most harmonics originate from the generation of harmonic current caused by nonlinear load signatures . The major sources of power system harmonics include switching operations, power electronic devices and other nonlinear loads and etc . Electronic devices are nonlinear and thus they create distorted currents even when supplied with a purely sinusoidal voltage. As nonlinear currents flow through a facility's electrical system and the distribution-transmission lines, additional voltage distortions are produced due to the impedance associated with the electrical network. Thus, as electrical power is generated, distributed, and utilized, voltage and current waveform distortions are produced .
As the number and ratings of power electronic devices connected to the power systems increase, the harmonic currents injected into power system and the resulting voltage distortions have become a major problem for power quality. This is the current issues that always be taken into account nowadays. Furthermore, the installation of power factor improving capacitors may lead to resonance conditions that amplify specific harmonic currents flowing into transformers and generators. On the other hand, large industrial ac motors may also provide a path for the harmonic currents. These currents can cause overheating problems for the motors, generators, and transformers. Power grid connected electric devices which can generate harmonic currents in the power system include fluorescent light ballast transformers, induction motors, incandescent light dimmers, overexcited transformers, arc welding equipment, AC/DC rotary converters, battery chargers, computers, and any type of device that utilizes rectified AC power to drive DC equipment .
2.2.3 The Harm of Harmonics
Harmonics only mean trouble if the power system is not well designed to handle them. High harmonic neutral currents are a problem only if the neutral is not properly sized. Current harmonics are not a problem to a transformer if it is derated appropriately. Even some voltage distortion below 8 % THD at the point of utilization is acceptable as long as sensitive equipment is not affected. However, it is always important to be aware of the presence of harmonics and to try to minimize them by purchasing low distortion electronic ballasts and reactors for PWM ASDs. This will not only keep the harmonics in check and improve the power factor in the facility, but will also save energy by reducing losses on power system components. In addition, any time there is a considerable increase of non-linear loads, it is important to check power system components to prevent problems.
2.2.4 Effects of Harmonics on Power System
Harmonic currents and voltage distortion are becoming the most severe and complex electrical challenge for the electrical industry from day to day. Because reflective harmonic currents operate at frequencies higher than the fundamental, we must be concerned with their effect in the electrical distribution system . The number one hazard with harmonic currents is equipment failure because of current overload that may result in fires. We must study the effect of harmonics on power system components in because it very related to power quality in power system.
184.108.40.206 Motors and Generators
A major effect of harmonic voltages and currents in rotating machinery (induction and synchronous) is increased heating due to iron and copper losses at the harmonic frequencies . The harmonic components thus affect the machine efficiency, and can also affect the torque developed.
Harmonic currents in a motor can give rise to a higher audible noise emission as compared with sinusoidal excitation . The harmonics also produce a resultant flux distribution in the air gap. This can cause or enhance phenomena called cogging (refusal to start smoothly) or crawling (very high slip) in induction motors. Harmonic pairs, such as the fifth and seventh harmonics, have the potential for creating mechanical oscillations in a motor-load system or in a turbine-generator combination.
The mechanical oscillations result when oscillating torques, caused by interaction between harmonic currents and the fundamental frequency magnetic field, excite a mechanical resonant frequency . For instance, the fifth and seventh harmonics can combine to produce a torsional stimulus on a generator rotor at the sixth harmonic frequency. If the frequency of a mechanical resonance exists close to the frequency of electrical stimulus, high-stress mechanical forces can be developed .
With the exception that harmonics applied to transformers may result in increased audible noise, the effects on these components usually are those arising from parasitic heating. The effect of harmonics on transformers is twofold: current harmonics cause an increase in copper losses and stray flux losses, and voltage harmonics cause an increase in iron losses . The overall effect is an increase in the transformer heating, as compared to purely sinusoidal operation at fundamental frequency. It should be noted that the transformer losses caused by both harmonic voltages and harmonic currents are frequency dependent. The losses will increase with the increasing of frequency. Therefore, higher frequency harmonic components can be more significant than lower frequency components in causing transformer heating.
Transformer losses may be segregated into load losses and no load losses. Load loss may be further divided by I2R (winding losses) and stray losses . Stray losses are of special importance when evaluating the added heating due to the effect of a nonsinusoidal current waveform. While stray losses are eddy-current losses due to stray electromagnetic flux in the windings, core, and core clamps, magnetic shields, tank wall, and other structural parts of the transformer. The winding stray loss includes winding conductor strand eddy-current loss and the loss due to circulating currents between strands or parallel winding circuits. This loss will rise in proportion to the square of the load current and the square of frequency. The temperature will also rise in the structural parts because of eddy currents, again approximately as the square of the load current and the square of the frequency.
220.127.116.11 Power Cables
Cables involved in system resonance may be subjected to voltage stress and corona, which can lead to dielectric or insulation failure . Cables that are subjected to ordinary levels of harmonic current are prone to heating. The flow of non-sinusoidal current in a conductor will cause additional heating over and above what would be expected for the rms value of the waveform. This is due to two phenomena known as skin effect and proximity effect, both of which vary as a function of frequency as well as conductor size and spacing.
The subsequent of these two effects is the effective ac resistance raised above the dc resistance especially for larger conductors. When a current waveform that is rich in high frequency harmonics is flowing in a cable, the equivalent Rac for the cable is raised even higher, amplifying the loss which can affect the service life of cable.
A major concern arising from the use of capacitors in a power system is the possibility of system resonance. This effect imposes voltages and currents that are considerably higher than would be the case without resonance. The reactance of a capacitor bank decreases with frequency, and the bank. Therefore, it acts as a sink for higher harmonic currents. This effect increases the heating and dielectric stresses. Frequent switching of nonlinear magnetic components (e.g., iron core), such as transformers and reactors, can produce harmonic currents that will add to the loading of capacitors .
The result of the increased heating and voltage stress brought about by harmonics is a shortened capacitor life. Although the previous discussion is intended to describe effects in power distribution apparatus such as power factor improvement or harmonic filter capacitors, it should be noted that other capacitors can be affected as well. For instance, the capacitors used in capacitor-run single-phase motors, or those used in rectifier snubber circuits, will be subjected to similar thermal and voltage stresses .
2.2.5 Economical Damage Due To Harmonic Losses
Among the effects of voltage and current distortions on the components of industrial energy systems, the generation of additional losses plays a fundamental role: the losses lead to an economical damage for the growing of the operating and investment costs . The economical damage due to harmonic losses is a probabilistic quantity, because the current and voltage harmonics, on which it depends, are probabilistic in nature . Among the effects of voltage and current distortions on the components of industrial energy systems, the general of additional losses plays a fundamental role. These losses lead both to the growing of the operating costs and to an additional heating in the components which in turn reduces their useful life.
The economical damage due to harmonic losses can be defined as the sum of operating costs and of the aging costs, both due to harmonic losses . As defined in , the operating costs are referred to the costs of the incremental energy losses caused by the harmonic flow in the components, where the term "incremental" means that these losses are superimposed to the ones at the fundamental and the aging costs are referred to the incremental investment costs caused by the premature aging of the components caused by the harmonic pollution.
2.3 Underground Power Cables
Power cable technology had its beginning in the 1880s when the need for power distribution cables became imperative . However, the high costs of underground power
cables hamper their use to areas where overhead lines are not practicable and aesthetically adequate. Although overhead lines preferred to underground power systems for years, underground power cables attaining to the rivalry level by means of the development at their producing technology, installation techniques and increasing usage at urban areas .
An underground cable is designed to last 40 years, but will probably last significantly longer, making a considerable difference to the life cycle economics of the cable compared with overhead line solutions . For example, there are 60,000 circuit miles of paper-insulated, lead-cover cable (PILC) in service in underground urban systems. Some of these cables are as much as 40-50 years old. As much as 25 % of today's infrastructure will need to be replaced or upgraded in the next 10 years.
2.3.1 Gas-filled Cable
A gas-filled cable having low heat emission and low power loss and is being used for the transmission of high-voltage electric current. The cable includes one or more conductors which are axially spaced in position relative to each other by means of supporting insulators inside an enclosing conduit which is filled with an insulating gaseous medium. In such a cable the conduit comprises on one hand a cylindrical metal sheath of plain or low-alloy merchant steel having a carbon content of less than 0.6% and on the other hand a metal shield of non-magnetic material fixed inside the sheath and having a low specific electrical resistivity. The metal shield has a plurality of openings there through spaced along its length for forming particle traps.
The present invention concerns a gas-filled cable intended for the transmission of high-voltage electric current and consisting of one or more conductors, these being held axially in position by means of supporting insulators inside an enclosing conduit filled with an insulating gaseous medium.
According to known practice, gas-filled cables may be used for both underground and surface transmission of electric current up to about 1,000 kV. By comparison with overhead power-lines carrying the same voltage, gas-filled surface cables have proved to have a greater current-carrying capacity and at the same time to be less liable to operational disturbances. However, a major disadvantage of such cables has, until now, been the high cost of manufacture, the chief contributor to this being the outer conduit of the cable itself which must be so constructed as to keep power losses at a reasonable level. Laboratory tests have previously indicated that carbon steel is an unsuitable material for cable conduits, one reason for this being that its use is associated with large losses of power.
In cables buried underground a further difficulty is met with in the heat emitted from the cable, which must be carried off through the ground. This causes the ground in the vicinity of the cable to dry out, leading in turn to reduce thermal dissipation capacity in the ground itself and a possible deterioration of the natural environment in which the cable is buried-plant-life, for instance, may be harmed.
In order to avoid the ground drying-out and the side-effects which this may involve, the temperature of the conduit of a gas-filled cable should not rise above approximately to 40 °C; and in view of the danger of thermal collapse of the insulating medium present within the cable itself, the maximum operational temperature inside the ducts should not be in excess of 105 °C. It is therefore essential that the heat developed in the cable be kept as low as possible and that the conditions in the vicinity of the cable be kept constantly favourable to thermal conduction. In previous types of gas-filled cables using carbon steel in the conduit, induced currents in the conduit cause heat releases greater than in cables having a conduit of e.g. aluminium, copper or other nonmagnetic material.
A method known previously in connection with cooling systems for superconducting cryogenic cables uses a cable conduit comprising an outer sheath of high-alloy steel consisting of an iron/nickel alloy containing 30-45 % nickel, and an inner lining or shield of e.g. aluminium. By this means, losses in the outer conduit can be kept down, while the conduit itself functions as a transport system for a cooling medium which may be liquid helium, He, or nitrogen gas, N2.
The main objective of the invention is to reduce heat emission from gas-filled cables at the same time as power losses are kept low and the total manufacturing costs are such that the cable type will be able to compete on the market. In gas-filled cables of the type described in the introductory paragraph this is rendered possible in that the conduit comprises a cylindrical metal sheath of magnetic material enclosing a metal shield of non-magnetic material having low resistivity. Here it has proved feasible to construct an outer metal sheath of plain or low-alloy merchant steel with a carbon content of less than 0.6 %, preferably approx 0.2 %. Like the sheath, the shield may also be cylindrical; a suitable thickness for this has been found to be approximately 8-30 % of the total thickness of the conduit, although 12-20 % is to be preferred.
Another objective of the invention is to achieve a cable of the type under discussion in which the insulation between the conduit and the conductors running inside the conduit is maintained at a constant high level of efficiency throughout the life of the cable, for it has been found that in gas-filled cables of the conventional type small particles, of e.g. metal, often remain inside the cable after it has been brought into service.
These particles may be concentrated to certain places and in some cases cause deterioration of the insulation and result in a short-circuit between the conductors and the conduit. However, by providing the cable with so-called particle traps by the method indicated in the following description and claims, it becomes possible to confine these particles to spaces in the cable where they are unable to disturb its functioning. An arrangement of this type is particularly simple and offers many advantages if based on the construction principles of this invention.
2.3.2 XLPE Cables
Polyethylene has been used as electrical insulation material in underground
distribution and transmission class cables, for almost three decades . The polyethylene in a power cable is a special grade, which has cross-linked molecules to allow it to deal with extremely high temperatures without melting or flowing under load which means that it cannot be remelted once it has been stripped from a cable . This makes XLPE sheathing similar to rubber vehicle tyres, which are made from a crosslinked polymer.
Depending on the final application and voltage range, different crosslinking technologies such as silane, irradiation and peroxide crosslinking are employed. Stabilization against thermal degradation has to be adapted to these technologies in order to reduce the negative influence on processing .
Since about 1970 the cross-linked polyethylene (XLPE) insulated power cables have been used in Germany. The XLPE-insulation possesses very good electrical, mechanical and thermal characteristics in medium voltage networks. This type of insulation is excellent chemical resistant and also resistant to cold. Due to various advantages, the XLPE-insulated type has vastly displaced the traditional classical paperinsulated types in many sectors.
In order to prevent the penetration of moisture and also to extend the duration of life, the XLPE insulated medium voltage cables are designed with longitudinally waterproof screen including an additional swell tape and a PE outer sheath. The manufacture of this sheath is based on high density polyethylene (HDPE), in which additive organic peroxide is mixed. Due to the heating and pressure the molecule chains are joined each other, assuring the transion from thermoplastic to elastic condition.
In comparison to PVC and paper-insulated cables, the advantages of XLPE insulated medium voltage power cables are possessing a low dielectric factor, such as it is 100 times smaller than of PVC-insulated cables. Moreover, a better dielectric constant value has an effect on the low mutual capacitance, the short circuit to ground and the charging current of XLPE insulated cables. The good properties of XLPEinsulated cables remain constant at a long temperature range.
In order to avoid any damage, the XLPE-insulated medium voltage cables should carefully laid and installed. It must be ensured that the cables should not be pulled over the hard or sharp edges. The cable ends must be water-tight-sealed. After cutting the length both ends must be sealed immediately. A laying depth of 60 to 80 cm is recommended. Single conductor cables are normally arranged in a trefoil touching or triangular shape. For laying in conduits, especially the influence of thermal insulation of air space between the cable and the inner wall of conduit should be considered. The inner diameter of the conduit should be at least 1.5 times that of the diameter of the cable.
EVALUATION OF THE AGING COST DUE TO HARMONIC LOSSES IN
This study is about the calculation of the expected value of the aging costs due to harmonic losses in XLPE insulated cables. In general, the methods that were used to develop this project are as follows:
Use published method for the dependency of aging with respect to
Use the characteristics of XLPE insulated cables.
Develop a program to implement the calculations by using Microsoft
Office Excel Workbook.
Skin effect, proximity effect, AC resistance at n-the harmonic
Power losses due to harmonic with different loads
Loss of life of cables, expected value of the aging cost
Figure 3.1.1: Flowchart for the study of the aging costs.
3.2 Calculation of Losses
There are two mechanisms in which harmonic currents can cause heating in conductors that is greater than expected for the rms value of the current. The first mechanism is due to current redistribution within the conductor and includes the skin effect and the proximity effect.
The skin effect is due to the shielding of the inner portion of the conductor by the outer layer. Since the current is concentrated in the outer layer, the effective resistance of the conductor is increased. Skin effect increases with frequency and conductor diameter.
The proximity effect is due to the magnetic field of conductors distorting the current distribution in adjacent conductors. In round wires, proximity effect is much less pronounced than skin effect . Metal sheaths and conduit also contribute to the proximity effect.
3.2.1 Resistance of the conductor
The value of alternate current of the conductor at its maximum operating
temperature, Î¸ is calculated for a unit of length by using the equation as below :
and is calculated as
( Î¸ - 20 ) (3)
where is the AC resistance of the conductor at maximum operating temperature for
a unit length, is the DC resistance of the conductor at maximum operating temperature for a unit length, is the skin effect factor, is the proximity effect factor, is the dc resistance of the conductor at 20 °C for a unit length, is the temperature coefficient of resistance at 20 °C, Î¸ is the maximum operating temperature.
The value of is calculated as
where is the nominal cross-sectional area of the conductor taking into account the effect of stranding, and Ï is the resistivity of the conductor material in ohm-meters at 20 °C. Values for table Ï and are given in Table 3.2.1  below.
Table 3.1: Electrical Resistivities & Temperature Coefficients of Metal at 20 °C.
Lead or lead alloy
3.2.2 Skin Effect
The most used computation is given in IEC 287-1-11  for the calculation of the skin effect factor.
and f is the supply frequency in hertz. Values for are given in Chapter 4.
3.2.3 Proximity Effect
The following equation is the calculation of the proximity effect factors . This is referred to  for most three-phase applications.
and is the diameter of the conductor, s is the distance between conductor axes. Values for are given in chapter 4.
Proximity effect is important in closely spaced large single-conductor cables and in three-phase cables with large conductors; its effect may be reduced the same way as skin effect. By increasing the spacing between cables, the proximity effect could be further reduced. On the other hand circulating currents in the sheaths and screens or shields increase with spacing leading to increased losses there, unless special measures are taken to eliminate or reduce the sheath currents.
3.2.4 Total Power Losses
The losses in cables that are taken into account for this study are joule losses and dielectric losses. Thus, for total power losses in this study, it will sum up both losses.
18.104.22.168 Joule Losses
The losses of cable are given with:
Where is the rms value of the harmonic.
22.214.171.124 Dielectric losses
Dielectric loss is voltage dependent but variations are small, taking into account the changes of voltage normally occurring in power systems. It is therefore taken as being constant when calculating current-carrying capacities.
The magnitude of dielectric loss, d W for a unit length of cable (watts per meter) is given by
= 2Ï€fCtan Î´ (8a)
where C is the capacitance of one phase per unit length in farads per meter (F/m), is the maximum system voltage to ground in volts. Table 126.96.36.199 below indicates the value for for different cable type .
Table 3.2: Lowest Phase to Ground Voltage Where Dielectric Losses Have To Be
Taken into Account
Cables insulated with impregnated
Oil-filled and gas pressure
Cables with other types of insulation
PE (HD and LD)
Under consideration by IEC.
The capacitance of the cable is calculated by
C = (8b)
where is the relative permittivity of the insulation, is the external diameter in millimeters of the insulation inside the screen or shield, and is the outside diameter of the conductor, measured over the conductor screen if any, in millimeters.
Hence, the total power losses of cable can be calculated as
3.3 Probabilistic Evaluation of the Economical Damage due to Harmonic Losses
The economical damage due to harmonic losses is quantified by means of the expected values of the operating costs and of the aging costs. However, in this study, it focuses only the calculation of the expected values of the aging costs due to harmonic losses.
3.3.1 Expected Value of the Aging Cost due to Harmonic Losses
The harmonic flow can lead to additional heating in any component. Subsequently, temperature will rise and premature aging may result. This premature aging cause by the harmonic pollution involves incremental investment cost which is also defined as the aging costs Da due to harmonic losses. Initially, refer to the case of a single component, which is:
Da €½€ € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € € €¨€¹€©
and are the total investment costs for buying the component during the system life in sinusoidal and non-sinusoidal operating conditions respectively. The residual economical values of the component at the end of the useful life are not considered.
is given by:
where , is the present worth value of the cost for the i-the purchase of the component
during the system life and is the number of times the component has to be bought in
sinusoidal operating conditions. The value of can be obtained analogously as:
where is the number of times the component has to be bought in non-sinusoidal
operating conditions and with trivial meaning of .
The value of is linked to , the useful life of the component in sinusoidal operating conditions. Once the value of is estimated, both the number of times the component has to be bought in the system life and the years in which the purchases have to be done are fully estimated.
It is possible to define the expected value of the aging costs due to harmonic losses for the component as:
E(Da) = E( - E() (10)
The expected value of the useful life of an insulated electrical apparatus can be estimated by summing the expected values of the thermal losses of which come in
succession until reaching the unity.
where € is the pdf of the temperature of the component in study during the period
of and Î›€ is obtained from Arrhenius model as:
A and being constant for the insulating material.
For the case of underground cables, the calculation for total thermal losses of life and the aging costs can be simplified using the following method. The lifetime of cables is calculated based on the Arrhenius model as
where is the lifetime of cable insulation at the operating temperature, , and are
Arrhenius constant. The value for equal to -11.627 and equal to 6127.
The value of € € due to harmonic is calculated as below
where is the ambient temperature, 20 °C and is total thermal losses of life which can
be calculated by using the following equation.
where is the thermal resistance of the insulation and is the thermal resistance of the
conduction shield. The value for both thermal resistance can be calculated using the
following equation. The value for Ï , and is indicated in Chapter 4, Table 4.1a.
The value for cable thermal losses is in per unit. The actual useful life of cables during sinusoidal operating conditions is estimated to 30 years. Thus, we multiply the value of thermal loss in per unit with useful life of cable to get the actual value or the estimated lifetime of the cable during the non-sinusoidal operating conditions in year.
The expected of the aging costs of cable is determined by using equation (10). The expected useful life of cable, E  is equal to 30 years. The first purchase, is equal to $50. Since the cable is never substituted during the system life it result E  equal to $50. The value for E  is determined by equation (13). However, the values need to be multiplied with 30 in order to get the actual value. The expected value of E can be determined by the following order.
where is the present worth discount rate for cable taken by 0.083, is the value, and the expected value of the purchase cost to substitute the cable at year is determined by equation (16a). The value that must be taken into account is the variation rate of cable unit cost, which equals to 0.073.
In conclusion, to evaluate the economical damage due to harmonic losses, it is necessary to know the complete knowledge of several pdf's (the pdf's of the current or voltage harmonics applied to each component and the pdf's of the temperature of each insulated electrical apparatus), and moreover, the computation of many integrals.
A simplified approach based on closed form relations also can be proposed to easily evaluate the expected value of the operating costs and aging costs. The approaches require the knowledge of only the mean value, the standard deviation and the covariances of the random variables on which the expected values depend.
DATA, MODELLING, AND ASSUMPTIONS
The cables parameters that were used is given in Table 4.1a .
Table 4.1a: Cable parameters for XLPE insulated cables - copper conductor.
Operating voltage (line-line)
current of insulated cable
Size of conductor
ext. diameter of conductor
diameter of conductor
max. permissible temp. of cond.
thickness of insulation
thermal resistivity of insulation
thickness of serving
burial depth of cable
thermal conductivity of soil
The harmonics data are given in Table 4.1b
Table 4.1b: Harmonics data
The harmonic data were given by the author of reference  via email.
For this study, the useful life of XLPE cables during sinusoidal operating conditions are estimated as 30 years in order to evaluate the actual value of the useful life of XLPE cables during non-sinusoidal conditions. The cables are also assumed that they are never substituted during the system life.
RESULTS, ANALYSIS, AND DISCUSSIONS
Table 5.1a shows the total power losses against the value of its THD for current rated at 650 A. When the value of THD is getting higher, the power losses will increase. Table 5.1b shows the useful life of cable with the different value of THD. Analytically, when the values of THD increase, the useful life of XLPE cables will decrease.
Table 5.1a: The total power losses value for different THD
Total power losses
Table 5.1b: The useful life of cable during non-sinusoidal operating conditions for
Useful life (p.u)
Useful life (years)
Figure 5.1a: Graph for total power losses versus THD
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