, Description:OPTIMAL CONFIGURATION OF POWER CABLES INSIDE A TRENCH

TECHNICAL FIELD
[001] The present disclosure relates to a field of power cables. More specifically, the present disclosure relates to an optimal configuration of power cables with unequal loading inside a trench.

BACKGROUND
[002] Power cables are employed for transmission and distribution of electrical power in rural, suburban and urban areas. These power cables are characterized as low voltage cables, medium voltage cables and high voltage cables. These power cables are installed underground in a trench by open trenching method or trenchless method based on type of location. The power cables are laid underground inside the trench for connecting cities to power generation stations. Also, the layout of power cables depends on the associated de-rating factors. Traditionally, the power cables are installed in single or pair of two cables inside the trench to send maximum current through the power cables without overshooting of continuous conductor temperature. In addition, the power cables are forced to be loaded evenly with current from a single power source as per available power cable circuit laying standards. Further, the placement of the power cables affects the properties of the power cables. In an example, the power cables face an issue of loss of power when placement of the power cables is too close to each other inside the trench. The depth of cable placement inside trench also affects power carrying capacity. In another example, the temperature attained by the power cables overshoots the maximum permissible temperature when placement of the power cables is too close to each other. So, the depth of laying, number of cables, size of trench i.e. length and width of trench, placement of cables inside the trench and combination of all these parameters affects on power loss in cables. In light of the foregoing discussion, there exists a constant need to find an optimal configuration of the power cables with minimum power loss inside the trench. The optimal configuration is found to lay the power cables in a way such that maximum current is passed through the power cables without overshooting the maximum permissible temperature which may cause a deterious effect on life of the cable.

OBJECT OF THE DISCLOSURE
[003] A primary object of the present disclosure is to provide an optimal configuration for laying a plurality of power cables inside a trench.
[004] Another object of the present disclosure is to provide the optimal configuration to increase current carrying capacity of each cable of the plurality of power cables.
[005] Another object of the present disclosure is to provide the optimal configuration to maintain a first temperature through each cable of the plurality of power cables.
[006] Yet another object of the present disclosure is to provide the optimal configuration to increase the current carrying capacity of the plurality of power cables without overshooting the first temperature.
[007] Yet another object of the present disclosure is to provide the optimal configuration for the plurality of power cables during different loading conditions inside the trench.
SUMMARY
[008] In an aspect, the present disclosure provides a maximum current configuration for laying four power cables inside a trench. The maximum current configuration includes a first power cable lying inside the trench substantially parallel to ground surface. The maximum current configuration includes a second power cable lying substantially beneath and substantially parallel to the first power cable inside the trench. The maximum current configuration includes a third power cable lying substantially adjacent and substantially parallel to the first power cable inside the trench. The maximum current configuration includes a fourth power cable lying substantially beneath and substantially parallel to the third power cable inside the trench. The first power cable is loaded with a first load. The second power cable lies at a first distance from the first power cable. The second power cable lies parallel to the first power cable along a first axis perpendicular to the ground surface. The first axis passes through corresponding geometrical centers of the first power cable and the second power cable. The third power cable lies at a second distance from the first power cable. The third power cable lies parallel to the first power cable along a second axis parallel to the ground surface. The second axis passes through corresponding geometrical centers of the first power cable and the third power cable. The third power cable is loaded with the first load. The fourth power cable lies at a third distance from the third power cable. The fourth power cable lies parallel to the third power cable along a third axis perpendicular to the ground surface. The third axis passes through corresponding geometrical centers of the third power cable and the fourth power cable. The fourth power cable lies substantially adjacent and substantially parallel to the second power cable inside the trench. The fourth power cable lies at a fourth distance from the second power cable. The fourth power cable lies parallel to the second power cable along a fourth axis parallel to the ground surface. The fourth axis passes through corresponding geometrical centers of the second power cable and the fourth power cable. The third axis is parallel to the first axis. The fourth axis is parallel to the second axis. The fourth distance is equal to the second distance. The first distance and the third distance is always less than the second distance and the fourth distance. The first power cable, the second power cable, the third power cable and the fourth power cable lie in the trench in a rectangular configuration. The rectangular configuration ensures maximum current carrying capacity without exceeding the first temperature through each cable of the four power cables.

STATEMENT OF THE DISCLOSURE
[009] The present disclosure provides a maximum current configuration for laying four power cables inside a trench. The maximum current configuration includes a first power cable lying inside the trench substantially parallel to ground surface. The maximum current configuration includes a second power cable lying substantially beneath and substantially parallel to the first power cable inside the trench. The maximum current configuration includes a third power cable lying substantially adjacent and substantially parallel to the first power cable inside the trench. The maximum current configuration includes a fourth power cable lying substantially beneath and substantially parallel to the third power cable inside the trench. The first power cable is loaded with a first load. The second power cable lies at a first distance from the first power cable. The second power cable lies parallel to the first power cable along a first axis perpendicular to the ground surface. The first axis passes through corresponding geometrical centers of the first power cable and the second power cable. The third power cable lies at a second distance from the first power cable. The third power cable lies parallel to the first power cable along a second axis parallel to the ground surface. The second axis passes through corresponding geometrical centers of the first power cable and the third power cable. The third power cable is loaded with the first load. The fourth power cable lies at a third distance from the third power cable. The fourth power cable lies parallel to the third power cable along a third axis perpendicular to the ground surface. The third axis passes through corresponding geometrical centers of the third power cable and the fourth power cable. The fourth power cable lies substantially adjacent and substantially parallel to the second power cable inside the trench. The fourth power cable lies at a fourth distance from the second power cable. The fourth power cable lies parallel to the second power cable along a fourth axis parallel to the ground surface. The fourth axis passes through corresponding geometrical centers of the second power cable and the fourth power cable. The third axis is parallel to the first axis. The fourth axis is parallel to the second axis. The fourth distance is equal to the second distance. The first distance and the third distance is always less than the second distance and the fourth distance. The first power cable, the second power cable, the third power cable and the fourth power cable lie in the trench in a rectangular configuration. The rectangular configuration ensures maximum current carrying capacity without exceeding the first temperature through each cable of the four power cables.

BRIEF DESCRIPTION OF FIGURES
[0010] Having thus described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale and wherein
[0011] FIG. 1 illustrates a cross sectional view of a maximum current configuration of four power cables inside a trench, in accordance with an embodiment of the present disclosure.
[0012] It should be noted that the accompanying figures are intended to present illustrations of exemplary embodiments of the present disclosure. These figures are not intended to limit the scope of the present disclosure. It should also be noted that accompanying figures are not necessarily drawn to scale.

DETAILED DESCRIPTION
[0013] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present technology. It will be apparent, however, to one skilled in the art that the present technology can be practiced without these specific details. In other instances, structures and devices are shown in block diagram form only in order to avoid obscuring the present technology.
[0014] Reference in this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present technology. The appearance of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Moreover, various features are described which may be exhibited by some embodiments and not by others. Similarly, various requirements are described which may be requirements for some embodiments but not other embodiments.Moreover, although the following description contains many specifics for the purposes of illustration, anyone skilled in the art will appreciate that many variations and/or alterations to said details are within the scope of the present technology. Similarly, although many of the features of the present technology are described in terms of each other, or in conjunction with each other, one skilled in the art will appreciate that many of these features can be provided independently of other features. Accordingly, this description of the present technology is set forth without any loss of generality to and without imposing limitations upon, the present technology.
[0015] FIG. 1 illustrates a cross sectional view 100 of a maximum current configuration of four power cables laid inside a trench 102, in accordance with an embodiment of the present disclosure. The cross sectional view 100 includes the trench 102, a first power cable 104, a second power cable 106, a third power cable 108, and a fourth power cable 110. The four power cables include the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 lying inside the trench 102.
[0016] The four power cables denote presence of more than one power cable laid inside the trench 102. In general, a trench is a type of excavation or depression in ground that is generally deeper than it is wide, and narrow compared with its length. In general, excavation is the act or process of digging, especially when something specific is being removed from ground surface. In an example, archaeologists use excavation to find artifacts and fossils. In civil engineering field, trenches are often created to install underground infrastructure or utilities. Also, trenches are later used to access these installations. In an example, the underground infrastructure or utilities include power cables, gas mains, water mains, telephone lines and the like.
[0017] The power cable is an electrical cable, an assembly of one or more electrical conductors that are usually held together with an overall sheath. The conductor is an object or type of material that allows the flow of an electrical current in one or more directions. In general, the conductors are commonly made up of materials made up of metals. The sheath is a protective covering around the power cable. The power cables may be installed as permanent wiring within buildings, buried in the ground surface, run overhead, or exposed. Further, the power cables are employed for transmission and distribution of electrical power to rural areas, urban areas, sub-urban areas and the like. The power cables are characterized as low voltage cables, medium voltage cables and high voltage cables. In general, the low voltage power cables refer to the cables having operable voltage in a range of below 600 V. In an example, the low voltage power cables refer to wiring and cabling infrastructure within homes that supports various digital technologies. In general, the medium voltage power cables refer to the cables having operable voltage in a range of 1900 V to 33000 V. In general, the high voltage power cables refer to the cables having operable voltage in a range of 66000 V and above.
[0018] In an embodiment of the present disclosure, the power cables are laid underground inside the trench 102 for connecting cities to power generation stations. The layout of the power cables inside the trench 102 depends on the associated de-rating factors. In general, the de-rating is operation of any device at less than its rated maximum capability in order to prolong its life. In general, the de-rating factors are factors that can be applied to base ampacities to obtain actual installed current ratings. In general, ampacity is defined as the maximum amount of electric current that can flow through the conductor before sustaining immediate or progressive deterioration. In general, the de-rating factors are defined in IEC60287 standard for evenly loaded cables. In an example, the de-rating refers to operation of the power cables below their maximum power rating, current rating, voltage rating and the like. In general, the power rating is defined as the highest power input allowed to flow through the power cables. In general, the current rating or ampacity is defined as the maximum electric current that the power cable can continuously carry while remaining within its temperature rating. In general, the voltage rating is defined as the highest voltage that may be continuously applied to a cable construction in compliance with relevant cable standard. In general, the IEC 60287 standard is International Standard that defines procedures and equations to be used in determining the current carrying capacity of the power cables. The term evenly loaded cables refer to the four power cables that are powered with same amount of current.
[0019] In an embodiment of the present disclosure, each cable of the four power cables is similar to each other. In an embodiment of the present disclosure, each cable of the four power cables is a three core power cable. In general, the three core power cable corresponds to a power cable with three insulated conductor units inside a core of the power cable. The core of the power cable protects the three insulated conductor units of the power cable. In general, the three core power cable is used for a perfect balanced 3-phase system. In general, the three phase system is a system that has three phases. The term three phases denote that the current passes through three wires and there is a neutral wire to pass fault current to the earth. In an embodiment of the present disclosure, each cable of the four power cables is a 66 kV, three core power cable. In an embodiment of the present disclosure, each cable of the four power cables is a three core insulated XLPE (cross linked polyethylene) cable. In an embodiment of the present disclosure, each cable of the four power cables has a voltage grade of 66 kV (E). In another embodiment of the present disclosure, each cable of the four power cables has a voltage grade of 66 kV (E). In an example, each cable of the four power cables is 66 kV, three core A2XCW2Y power cable. Furthermore, each cable of the four power cables can be any one of simple electrical power cable and hybrid cable. In general, the hybrid cable is a cable having one or more optical fiber cable units along with the electrical conductor units. In an embodiment of the present disclosure, each cable of the four power cables is a simple electrical power cable. In another embodiment of the present disclosure, each cable of the four power cables is a hybrid cable having one or more optical fiber cable units along with the electrical conductor units.
[0020] The optimal configuration of the power cables refer to the maximum current configuration of the power cables. The maximum current configuration is defined as a configuration to place the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 inside the trench 102. The maximum current configuration is defined as the configuration that maintains a first temperature through each cable of the four power cables. In an embodiment of the present disclosure, the four power cables include the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110. Further, the maximum current configuration is defined as the configuration to increase current carrying capacity or ampacity of each cable of the four power cables. The maximum current configuration is defined as the configuration to increase the current carrying capacity of the four power cables during uneven loading of the four power cables. The term uneven loading refers to providing different value of current to the four power cables. In an embodiment of the present disclosure, the maximum current configuration is defined in such a way to maintain the first temperature through each cable of the four power cables. The temperature of each cable of the four power cables must not exceed the first temperature. In an example, the temperature of the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 must not exceed the first temperature. The first temperature is maximum temperature permissible that may be achieved inside each cable of the four power cables due to flow of current through the four power cables. In an embodiment of the present disclosure, the first temperature lies in a range of 90oC to 92oC.In an embodiment of the present disclosure, the four power cables are used to transmit large amount of current. Further, the transmission of larger amount of current generates large amount of heat in the four power cables. Furthermore, the total heat dissipation impacts rated core temperature of the four power cables. Also, the electrical current passing through the four power cables produce a lot of electrical losses. In addition, the electrical losses are the main reason for dissipation of large amount of heat in the four power cables. Further, the dissipation of heat inside the four power cables impact current carrying capacity of the power cables. The impact is caused because more amount of heat generated inside the four power cables deteriorates quality of the four power cables. Therefore, the temperature of each cable of the four power cables must be below the first temperature.
[0021] The trench 102 includes the first power cable 104. The first power cable 104 lies inside the trench 102 substantially parallel to the ground surface. In an embodiment of the present disclosure, the first power cable 104 lies beneath the ground surface at a depth in a range of 1.2 m to 1.5 m. However, the range of the depth is not limited to specified range. Further, the first power cable 104 is loaded with a first load. In an embodiment of the present disclosure, the soil thermal resistivity inside the trench 102 is maintained at 1.5 Km/W. In general, the thermal resistivity is a heat property and a measurement of temperature difference by which an object or material resists heat flow. In an embodiment of the present disclosure, the ground temperature is kept at a constant value of 30oC for calculation purposes. In an embodiment of the present disclosure, the resistance of conductor is maintained at a value of 0.000129 O/ M. However, the above mentioned parameters may have different range of values.
[0022] The trench 102 includes the second power cable 106. The second power cable 106 lies substantially beneath the first power cable 104. In addition, the second power cable 106 lies substantially parallel to the first power cable 104 inside the trench 102. Also, the second power cable 106 lies at a first distance D1 from the first power cable 104. The second power cable 106 is separated from the first power cable 104 with the first distance D1 in between. Further, the second power cable 106 lies parallel to the first power cable 104 along a first axis 112. The first axis 112 is perpendicular to the ground surface. The first axis 112 passes through corresponding geometrical centers of the first power cable 104 and the second power cable 106. In general, the first axis 112 is axis whose direction is normal to the ground surface. The term normal refers to object that is perpendicular (makes an angle of 90o) with a given object. The object here refers to any line, vector and the like.
[0023] Further, the first distance D1 is distance between corresponding geometrical centers of the first power cable 104 and the second power cable 106 along the first axis 112. In general, the geometrical center of the power cable is a point in some sense in the middle of the power cable. In an embodiment of the present disclosure, the first distance D1 lies in a range of 300 mm to 310mm for this example. This distance may vary based on the requirements. However, the range of the first distance D1 is not limited to the above mentioned range. Furthermore, the second power cable 106 may or may not be loaded with a second load. In an embodiment of the present disclosure, the second power cable 106 is loaded with the second load. In another embodiment of the present disclosure, the second power cable 106 is not loaded with the second load.
[0024] The trench 102 includes the third power cable 108. The third power cable 108 lies substantially adjacent to the first power cable 104. In addition, the third power cable 108 lies substantially parallel to the first power cable 104 inside the trench 102. Also, the third power cable 108 lies at a second distance D2 from the first power cable 104. The third power cable 108 is separated from the first power cable 104 with the second distance D2 in between. Further, the third power cable 108 lies parallel to the first power cable 104 along a second axis 116. The second axis 116 is parallel to the ground surface. The second axis 116 passes through corresponding geometrical centers of the first power cable 104 and the third power cable 108. The second axis 116 refer to an axis whose direction is tangent to the ground surface. In general, the tangent to any curve at a given point is a straight line that just touches the curve at that point.
[0025] The second distance D2 is distance between corresponding geometrical centers of the first power cable 104 and the third power cable 108 along the second axis 116. In an embodiment of the present disclosure, the second distance D2 lies in a range of 975 mm to 985 mm for this example. This distance may vary based on the requirements. However, the range of the second distance D2 is not limited to the above mentioned range. Furthermore, the third power cable 108 is loaded with the first load. In an embodiment of the present disclosure, the third power cable 108 and the first power cable 104 is loaded with the first load.
[0026] The trench 102 includes the fourth power cable 110. The fourth power 110 cable lies substantially beneath the third power cable 108. The fourth power cable 110 lies parallel to the third power cable 108 inside the trench 102. In addition, the fourth power cable 110 lies at a third distance D3 from the third power cable 108. The fourth power cable 110 is separated from the third power cable 108 with the third distance D3 in between. Further, the fourth power cable 110 lies parallel to the third power cable 108 along a third axis 114. The third axis 114 is perpendicular to the ground surface. The third axis 114 passes through corresponding geometrical centers of the third power cable 108 and the fourth power cable 110.
[0027] In addition, the fourth power cable 110 lies substantially adjacent to the second power cable 106. The fourth power cable 110 lies substantially parallel to the second power cable 106 inside the trench 102. In addition, the fourth power cable 110 lies at a fourth distance D4 from the second power cable 106. The fourth power cable 110 is separated from the second power cable 106 with the fourth distance D4 in between. The fourth power cable 110 lies parallel to the second power cable 106 along a fourth axis 118. The fourth axis 118 is parallel to the ground surface. The fourth axis 118 passes through corresponding geometrical centers of the second power cable 106 and the fourth power cable 110. Furthermore, the fourth power cable 110 may or may not be loaded with a third load. In an embodiment of the present disclosure, the fourth power cable 110 is loaded with the third load. In another embodiment of the present disclosure, the fourth power cable 110 is not loaded with the third load.
[0028] The third distance D3 is distance between corresponding geometrical centers of the third power cable 108 and the fourth power cable 110. In an embodiment of the present disclosure, the third distance D3 is equal to the first distance D1. In addition, the fourth distance D4 is distance between corresponding geometrical centers of the second power cable 106 and the fourth power cable 110. In an embodiment of the present disclosure, the fourth distance D4 is equal to the second distance D2. Also, the first distance D1 is always less than the second distance D2 and the fourth distance D4. Moreover, the third distance D3 is always less than the second distance D2 and the fourth distance D4. The third axis 114 is parallel to the first axis 112 and vice versa. The fourth axis 118 is parallel to the second axis 116 and vice versa.
[0029] The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 always lie inside the trench 102 in a rectangular configuration (as mentioned above). The rectangular configuration ensures maximum current carrying capacity through each cable of the four power cables during different loading conditions (even and uneven loading). In addition, the rectangular configuration ensures maximum current carrying capacity without exceeding the first temperature through each cable of the four power cables. The maximum current configuration maintains a first temperature in each cable of the four power cables. The first temperature is maximum temperature permissible through each cable of the four power cables.
[0030] In an embodiment of the present disclosure, the first power cable 104 is loaded with the first load. Also, the third power cable 108 is loaded with the first load. The second power cable 106 is loaded with the second load. The fourth power cable 110 is not loaded with any load. In an embodiment of the present disclosure, the first power cable 104 is loaded with the first load of 300 Amperes. Also, the third power cable 108 is loaded with the first load of 300 Amperes. Further, the second power cable 106 is loaded with the second load of 215 Amperes. Furthermore, the fourth power cable 110 is not loaded with any load. The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 lie in the rectangular configuration inside the trench 102 to achieve optimal performance. The term optimal performance signifies maximum current carrying capacity of each cable of the four power cables without exceeding the first temperature.
[0031] In another embodiment of the present disclosure, the first power cable 104 is loaded with the first load of 279 Amperes. Also, the third power cable 108 is loaded with the first load of 279 Amperes. Further, the second power cable 106 is loaded with the second load of 279 Amperes. Furthermore, the fourth power cable 110 is not loaded with any load. The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 lie in the rectangular configuration inside the trench 102 to achieve optimal performance.
[0032] In an embodiment of the present disclosure, the first power cable 104 is loaded with the first load. In addition, the third power cable 108 is loaded with the first load. Further, the second power cable 106 is loaded with the second load. The fourth power cable 110 is loaded with the third load. In an embodiment of the present disclosure the second load is equal to the third load. In another embodiment of the present disclosure, the second load is not equal to the third load. In an embodiment of the present disclosure, the first power cable 104 is loaded with the first load of 300 Amperes. Also, the third power cable 108 is loaded with the first load of 300 Amperes. The second power cable 106 is loaded with the second load of 180 Amperes. The fourth power cable 110 is loaded with the third load of 180 Amperes. The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 lie in the rectangular configuration inside the trench 102 to achieve optimal performance.
[0033] In another embodiment of the present disclosure, the first power cable 104 is loaded with the first load of 263.9 Amperes. Also, the third power cable 108 is loaded with the first load of 263.9 Amperes. The second power cable 106 is loaded with the second load of 263.9 Amperes. The fourth power cable 110 is loaded with the third load of 263.9 Amperes. The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 lie in the rectangular configuration inside the trench 102 to achieve optimal performance.
[0034] The maximum current configuration for laying the four power cables is found out to be the rectangular configuration by virtue of experimentation. The purpose of the experimentation specifically is to increase ampacity of each cable of the four power cables under a plurality of conditions. The first condition of the plurality of conditions is that temperature attained in and around each cable of the plurality of cables is less than the first temperature. The second condition of the plurality of conditions is that the first power cable 104 and the third power cable 108 are connected to the same first load. The third condition of the plurality of conditions is to find the second load and the third load that is connected with the second power cable 106 and the fourth power cable 110 respectively. The fourth condition of the plurality of conditions is to find the maximum current configuration of the four power cables that fulfil all the above stated conditions.
[0035] Further, the experimentation is conducted to fulfil a plurality of objectives. The first objective of the plurality of objectives is to optimize center to center distance between each cable of the four power cables. The center to center distance refers to the distance between geometrical center of one cable of the four power cables to geometrical center of nearest cable of the four power cables. The second objective of the plurality of objectives is to load the four power cables with unequal load. The third objective of the plurality of objectives is to reduce power loss in each cable of the plurality of cables. The fourth objective of the plurality of objectives is to increase power carrying capacity of each cable of the plurality of cables. The fourth objective of the plurality of objectives is to conduct the experimentation to achieve the maximum current configuration that satisfies above mentioned objectives.
[0036] Initially, the four power cables are placed in an in-line arrangement in a straight line. The four power cables are placed at some distance from each other. The distance between the four power cables is the center to center distance between each cable of the four power cables with its adjacent neighbor. The depth of laying of the four power cables inside the trench 102 is kept at a range of 1.2 m to 1.5 m. In an embodiment of the present disclosure, the depth of the trench 102 lies in a range of 1.075 m to 1.5m. In an embodiment of the present disclosure, the width of the trench 102 lies in a range of 1.1 to 1.5m. However, the depth and the width of the trench 102 are not limited to the above mentioned values. This trench size will vary based on requirement.
[0037] The experimentation is first validated with help of finite element analysis (FEM) technique (Numerical technique) or method for single cable placed in the trench 102. In addition, the numerical simulation is conducted for thermal analysis to determine the maximum current configuration for laying the four power cables inside the trench 102 post validation of single power cable. In an embodiment of the present disclosure, the diameter of each cable of the four power cables is 125 mm. However, the diameter of the four power cables is not limited to the above mentioned diameter. In an embodiment of the present disclosure, the thermal resistivity of the soil is kept at 1.5 Km/W. Also, the ambient temperature of air and soil is considered to be at a temperature of 30oC. The depth of laying of the four power cables is considered to be at 1.3m. In addition, the rated current, the de-rating factor and conductor resistance are considered to be at their actual operating temperature. However, the above stated parameters are not limited to their stated values. In general, the conductor resistance is defined as opposition to the flow of electrical current through the conductor. In general, the term rated current means the maximum value of current beyond which an equipment or machine will not be operating according to its desired operation.
[0038] Initially, steady-state behavior of a single cable of the four power cables is calculated. Further, the finite element analysis technique is used to calculate resistive losses in terms of change in temperature in the single cable of the four power cables. Furthermore, the results obtained by using FEM are compared with results obtained by using IEC standard. Also, the results obtained by using FEM are analyzed with results obtained by using IEC standard for standard configuration. Further, the analyzed results are used to determine the maximum current configuration for placement of the four power cables inside the trench 102.
[0039] The de-rating factors for a plurality of equally loaded circuits are available in IEC standard. Further, the thermal analysis or heat simulation is done to calculate the maximum current that may be passed through the second power cable 106 and the fourth power cable 110. In addition, the first power cable 104 and the third power cable 108 are connected with the first load. The four power cables is placed at the distance inside the trench 102. The distance is maintained so that insulation material properties of the four power cables are not affected during heat dissipation. The heat is dissipated through the four power cables due to flow of electric current passing through the four power cables. In general, the permissible current ratings of the four power cables are affected when the circuit is unequally loaded. Further, the affect in the permissible current ratings affect total heat dissipation of the circuit.
[0040] Further, the current carrying capacity of the single power cable of the four power cables is validated using IEC calculation. In addition, the current carrying capacity of the four power cables placed in the in-line arrangement is examined based on IEC calculation. Further, the numerical analysis of maximum permissible current carrying capacity of the plurality of the four power cables is conducted. The numerical analysis is conducted to find the maximum current configuration to lay the four power cables inside the trench 102. Further, a two-dimensional thermal model of the four power cables is developed. The thermal model is developed in two-dimensional co-ordinate system to get radial distribution of temperature inside each cable of the four power cables and surroundings. The geometry of the four power cables is designed in FEA simulation software. In an embodiment of the present disclosure, the geometry of the four power cables is designed in Design Modeller software of Ansys. In another embodiment of the present disclosure, the geometry of the four power cables is designed in any other simulation software possible.
[0041] The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 are to be placed inside the trench 102. In an embodiment of the present disclosure, the four power cables is identical in construction. In another embodiment of the present disclosure, the four power cables is not identical in construction. In an embodiment of the present disclosure, a plurality of parameters of the four power cables is kept constant. The plurality of parameters includes thermal resistivity, moisture of soil, number of circuits, ambient temperature of medium and the like. In general, the ambient temperature is the air temperature of an environment or object. In addition, the value of current or temperature of cable depends upon the laying depth and the laying structure of the four power cables inside the trench 102.
[0042] Initially, the four power cables is laid inside the trench 102 in the in-line arrangement. The four power cables are laid at a distance of 300 mm from its adjacent neighbor. The geometrical parameters, material properties and physical descriptions related to the four power cables are defined inside the simulation software. The temperature on bottom and two side boundaries of region covered by the four power cables is assumed to be pre-defined and constant. In addition, the top boundary of region covered by the four power cables is set as a convective heat transfer surface for air flow. In general, the convective heat transfer is often referred to the transfer of heat from one place to another by movement of fluids. Further, heat loss boundary conditions are applied on conductors. Furthermore, convection boundary conditions are applied at soil and air interface. The simulation of the single cable of the four power cables is conducted based on defined geometry. The results of simulation matched with results obtained from empirical calculations.
[0043] Further, the simulation is carried out for two, three and four cables of the four power cables in the in-line arrangement. The temperature attained in and around the four power cables came out to be more than temperature obtained from empirical calculations. In addition, the temperature attained in and around the four power cables came out to be more than the first temperature. The first condition of the plurality of conditions is to find the maximum current configuration such that the temperature attained in and around the four power cables is less than the first temperature. In general, the increase in temperature above the first temperature decreases the current carrying capacity of the four power cables. Further, the simulation is continued with different configurations of the four power cables. In an embodiment of the present disclosure, the main objective of the experimentation becomes to find out the maximum current configuration that fulfils all the mentioned objectives and conditions (as mentioned above). The objective of the experimentation is to find the maximum current configuration of the four power cables such that the temperature attained is less than the first temperature. In addition, the objective is to find the maximum current that is allowed to pass through each cable of the four power cables without exceeding the first temperature. Further, the first power cable 104 and the third power cable 108 are always loaded with the first load. The objective is to find the maximum current that is allowed to pass through the second power cable 106 and the fourth power cable 110 without exceeding the first temperature.
[0044] The first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 are simulated in a plurality of different configurations possible. In an example, the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 are arranged in hash or Z-configuration. In another example, the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110 are arranged in rhombus configuration, square configuration, rectangular configuration and the like. The maximum current configuration that satisfies all required objectives comes out to be the rectangular configuration after simulation of all possible configurations.
[0045] The maximum current configuration is the rectangular configuration of the first power cable 104, the second power cable 106, the third power cable 108 and the fourth power cable 110. The values of the first load, the second load and the third load are derived for the maximum current carrying capacity of the four power cables (as mentioned above). The values of the first load, the second load and the third load are derived such that the temperature attained in and around the four power cables is less than the first temperature.
[0046] In an embodiment of the present disclosure, the current passing through the first power cable 104 is of 279 Amperes. The current passing through the third power cable 108 is of 279 Amperes. In addition, the current passing through the second power cable 106 is of 279 Amperes. The current passing through the fourth power cable 110 is of 0 Amperes. Therefore, the total current passing through the four power cables is of 837 Amperes. The total current of 837 Amperes is the maximum current that can be passed through the four power cables without overshooting the first temperature. The first temperature achieved based on the above configuration comes out to be of 90.2oC. The rectangular configuration stated above provides the maximum amount of current that may be passed through the four power cables meeting all the objectives and conditions (as mentioned above).
[0047] In an embodiment of the present disclosure, the current passing through the first power cable 104 is of 300 Amperes. The current passing through the third power cable 108 is of 300 Amperes. In addition, the current passing through the second power cable 106 is of 180 Amperes. The current passing through the fourth power cable 110 is of 180 Amperes. Therefore, the total current passing through the four power cables is of 960 Amperes. The total current of 960 Amperes is the maximum current that can be passed through the four power cables without overshooting the first temperature. The first temperature achieved based on the above configuration comes out to be of 90.1oC. The rectangular configuration stated above provides the maximum amount of current that may be passed through the four power cables meeting all the objectives and conditions (as mentioned above).
[0048] In an embodiment of the present disclosure, the current passing through the first power cable 104 is of 300 Amperes. The current passing through the third power cable 108 is of 300 Amperes. In addition, the current passing through the second power cable 106 is of 215 Amperes. The current passing through the fourth power cable 110 is of 0 Amperes. Therefore, the total current passing through the four power cables is of 815 Amperes. The total current of 815 Amperes is the maximum current that can be passed through the four power cables without overshooting the first temperature. The first temperature achieved based on the above configuration comes out to be of 90oC. The rectangular configuration stated above provides the maximum amount of current that may be passed through the four power cables meeting all the objectives and conditions (as mentioned above).
[0049] In an embodiment of the present disclosure, the current passing through the first power cable 104 is of 263.9 Amperes. The current passing through the third power cable 108 is of 263.9 Amperes. In addition, the current passing through the second power cable 106 is of 263.9 Amperes. The current passing through the fourth power cable 110 is of 263.9 Amperes. Therefore, the total current passing through the four power cables is of 1055.6 Amperes. The total current of 1055.6 Amperes is the maximum current that can be passed through the four power cables without overshooting the first temperature. The first temperature achieved based on the above configuration comes out to be of 90oC. The rectangular configuration stated above provides the maximum amount of current that may be passed through the four power cables meeting all the objectives and conditions (as mentioned above).
[0050] In an embodiment of the present disclosure, the finite element analysis is done for the above mentioned center to center distance between the four power cables. In addition, the finite element analysis is done for the four power cables with the above mentioned parameters. The center to center distance between the four power cables may vary as per site conditions. In addition, the above mentioned parameters may vary for the four power cables for a plurality of trenches. In an embodiment of the present disclosure, the current carrying capacity of the four power cables will increase with increase in the center to center distance between the four power cables. In another embodiment of the present disclosure, the current carrying capacity of the four power cables will increase with increase in width of the trench 102. In yet another embodiment of the present disclosure, the de-rating of the four power cables will increase if the center to center distance between the power cables is lowered. In an embodiment of the present disclosure, there will be a plurality of case to case analysis for the plurality of the center to center distance between the power cables. In another embodiment of the present disclosure, there will be the plurality of case to case analysis for the plurality of parameters between the power cables.
[0051] The foregoing descriptions of specific embodiments of the present technology have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the present technology to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the present technology and its practical application, to thereby enable others skilled in the art to best utilize the present technology and various embodiments with various modifications as are suited to the particular use contemplated. It is understood that various omissions and substitutions of equivalents are contemplated as circumstance may suggest or render expedient, but such are intended to cover the application or implementation without departing from the spirit or scope of the claims of the present technology.
[0052] While several possible embodiments of the invention have been described above and illustrated in some cases, it should be interpreted and understood as to have been presented only by way of illustration and example, but not by limitation. Thus, the breadth and scope of a preferred embodiment should not be limited by any of the above-described exemplary embodiments.

Claims:What is claimed is:
1. A maximum current configuration for laying four power cables in a trench (102), the maximum current configuration comprising:
a first power cable (104) lying inside the trench (102) substantially parallel to ground surface, wherein the first power cable (104) is loaded with a first load;
a second power cable (106) lying substantially beneath and substantially parallel to the first power cable (104) inside the trench (102), wherein the second power cable (106) lies at a first distance (D1) from the first power cable (104), wherein the second power cable (106) lies parallel to the first power cable (104) along a first axis (112) perpendicular to the ground surface, wherein the first axis (112) passes through corresponding geometrical centers of the first power cable (104) and the second power cable (106);
a third power cable (108) lying substantially adjacent and substantially parallel to the first power cable (104) inside the trench (102), wherein the third power cable (108) lies at a second distance (D2) from the first power cable (104), wherein the third power cable (108) lies parallel to the first power cable (104) along a second axis (116) parallel to the ground surface, wherein the second axis (116) passes through corresponding geometrical centers of the first power cable (104) and the third power cable (108), wherein the third power cable (108) is loaded with the first load; and
a fourth power cable (110) lying substantially beneath and substantially parallel to the third power cable (108) inside the trench (102), wherein the fourth power cable (110) lies at a third distance (D3) from the third power cable (108), wherein the fourth power cable (110) lies parallel to the third power cable (108) along a third axis (114) perpendicular to the ground surface, wherein the third axis (114) passes through corresponding geometrical centers of the third power cable (108) and the fourth power cable (110), wherein the fourth power cable (110) lies substantially adjacent and substantially parallel to the second power cable (106) inside the trench (102), wherein the fourth power cable (110) lies at a fourth distance (D4) from the second power cable (106), wherein the fourth power cable (110) lies parallel to the second power cable (106) along a fourth axis (118) parallel to the ground surface, wherein the fourth axis (118) passes through corresponding geometrical centers of the second power cable (106) and the fourth power cable (110), wherein the third axis (114) is parallel to the first axis (112), wherein the fourth axis (118) is parallel to the second axis (116), wherein the fourth distance (D4) is equal to the second distance (D2), wherein the first distance (D1) and the third distance (D3) is always less than the second distance (D2) and the fourth distance (D4),
wherein the first power cable (104), the second power cable (106), the third power cable (108) and the fourth power cable (110) lie in the trench (102) in a rectangular configuration, wherein the rectangular configuration ensures maximum current carrying capacity without exceeding the first temperature through each cable of the four power cables.
2. The maximum current configuration as recited in claim 1, wherein the maximum current configuration maintains a first temperature in each cable of the four power cables, wherein the first temperature is maximum temperature permissible through each cable of the four power cables.
3. The maximum current configuration as recited in claim 1, wherein the first power cable (104) and the third power cable (108) is loaded with the first load, wherein the second power cable (106) is loaded with the second load, and wherein the fourth power cable (110) is not loaded with any load.
4. The maximum current configuration as recited in claim 1, wherein the first power cable (104) and the third power cable (108) is loaded with the first load, wherein the second power cable (106) is loaded with the second load, wherein the fourth power cable (110) is loaded with the third load, and wherein the second load is equal to the third load.
5. The maximum current configuration as recited in claim 1, wherein the first power cable (104) and the third power cable (108) lies beneath the ground surface at depth in a range of 1.2 m to 1.5 m.
6. The maximum current configuration as recited in claim 1, wherein the first distance (D1) is in a range of 300 mm to 310mm.
7. The maximum current configuration as recited in claim 1, wherein the second distance (D2) is in a range of 975 mm to 985 mm.
8. The maximum current configuration as recited in claim 1, wherein the third distance (D3) is equal to the first distance (D1).
9. The maximum current configuration as recited in claim 1, wherein depth of the trench (102) lies in a range of 1.075 m to 1.5m, and wherein width of the trench (102) lies in a range of 1.1 to 1.5m.
10. The maximum current configuration as recited in claim 1, wherein the first temperature lies in a range of 90oC to 92oC.
Dated this 4th day of August, 2018