G.J. Anders

Power cable thermal analysis with consideration of heat and moisture transfer in the soil

A method of numerically modeling coupled heat and moisture flow around power cables in steady-state and transient conditions that is based on the Philip and DeVries model for flow in soils is presented. The method has been implemented in a computer program for an IBM or compatible personal computer that utilizes the Galerkin finite-element method. The program uses sparsity-based algorithms that can handle large finite-element grid structures and calculate accurately the steady-state and transient temperatures, moisture distributions, and isothermal contours for power cables buried in media containing complex configurations of soil, boundaries, heat sources and sinks. The program has been validated by data from field tests, which show good agreement between predicted and measured results. >

Parameters affecting economic selection of cable sizes

The evaluation of power cable costs considers the present worth of funds required for a new cable installation. Two components make up this cost, first the initial investment cost, and second, the cost of losses ever the life of the cable. Generally, for a given voltage class, the capital investment component increases as the conductor size increases. Conversely the losses decrease as conductor size increases. Selection of cable size is currently based on ampacity considerations; that is, a cable with a minimum acceptable cross-sectional area is usually selected without consideration of the cost of the losses that will occur during the life of the cable. Since the cost of losses over the lifetime of the cable may require substantial selection of a larger conductor size than required, ampacity consideration will often result in smaller value of losses and, hence, may lead to a lower overall cost. A number of examples which demonstrate sensitivity of the conductor cross-section and overall cost to variations in key parameters of the model are presented in the paper. >

Transient ratings of buried power cables. I. Historical perspective and mathematical model

The authors report the results of a recently completed major project on power cable transient calculations. It used a fundamental analytical method using a lumped parameter model for computation of transient ratings of buried power cables. An account is given for past work in the field of thermal transients in buried cables. A full description of the mathematical model is given. A summary of the state-of-the-art is provided. Developments relevant to the analysis of groups of unequally loaded and/or dissimilar cables and cables located in ductbanks or thermal backfills are presented. >

Calculation of the internal thermal resistance and ampacity of 3-core unscreened cables with fillers

All 3-core cables require fillers to fill the space between insulated cores and the belt insulation or a sheath. The equations given in IEC 287 and in the Neher-McGrath paper (1957) for the internal thermal resistance of 3-core cables were developed for paper insulated cables. For such cables, it was assumed that the insulation and filler materials have the same thermal resistivities. In reality, in 3-core cables a variety of materials are used as fillers. The majority of these will have a higher thermal resistivity than the insulation. In the previous paper, a new formula was developed to compute the value of the internal thermal resistance of belted cables taking into account the thermal resistivity of the filler. In this paper, screened cables are considered and a new formula for the computation of the internal thermal resistance of such cables is presented. The effect of filler resistivity on cable ampacity is also discussed.

Cable crossings-derating considerations. I. Derivation of derating equations

Dangerously high interference temperatures can occur at points where cables cross external heat sources even when the crossing occurs at 90/spl deg/. For perpendicular and oblique crossings, these interference temperatures are usually ignored for distribution circuits, whereas for transmission cables, corrective actions in physical installation condition are sometimes taken. Analytical solutions are almost never used to determine the effect of external heat source on the ampacity of the rated cable. The main reason no computations are performed is an absence of either derating formulas or derating tables (curves) and not the lack of a need. To fill this gap, an analytical solution for the computation of the derating factors has been developed and is presented in this paper. The solution is simple and accurate enough to be suitable for standardization purposes. A numerical example involving the intersection of a pipe-type cable by a distribution circuit is presented to show the effect of perpendicular and oblique crossings on the ampacity of both circuits. In this practical example, the ampacity of the pipe-type cable is significantly affected for a range of crossing angles. A conservative practice, used by many utilities in cases like this, would be to assume that the cables are parallel. However, in our example for a 90/spl deg/ crossing, such an approach would unnecessarily decreases the ampacity of the pipe-type cable by almost 20%.

Reliability considerations in accelerated life testing of electrical insulation with generalized life distribution function

The authors introduced a new approach to estimate life distributions at nominal conditions from the results of accelerated life testing of electrical insulating materials. A very general family of probability distributions is introduced, and a best fit member of this family is used to represent life data at each stress level. Nonlinear optimization techniques are applied in conjunction with linear regression analysis. In any accelerated life testing study important questions pertain to the minimal and maximal stress levels to be applied. A method of determination of the minimal stress level as well as the suitable number of tests based on reliability considerations is presented. A numerical example based on test data and a user-friendly computer program are presented. >

Cable crossings-derating considerations. II. Example of derivation of derating curves

For pt.I see ibid., vol.14, no.3, p.705-14 (1999). Cables crossing other heat sources either perpendicularly or at oblique angles will experience a rise in conductor temperature which should result in ampacity derating. In the first part of the paper a mathematical model for calculation of derating factors was presented. In this paper, a practical numerical example is considered with a 138 kV pipe-type cable crossing a 10 kV distribution circuit. The numerical analysis presented confirms experimental findings reported in the literature that the cable crossing may elevate conductor temperature by as much as 20/spl deg/C.

Rating of cables on riser poles, in trays, in tunnels and shafts-a review

This paper reviews rating of cables installed in air. The following cable installations are investigated: (1) cables on riser poles, (2) cables in open and closed trays, (3) cables wrapped in fire protection covers, (4) cables in horizontal tunnels, and (5) cables in vertical shafts. The rating of cables in these installations is computed by solving energy balance equations for the unknown surface temperature with a given conductor current. In ampacity computations the conductor current is adjusted iteratively until permissible cable conductor and surface temperatures are achieved. It is shown in the paper how the same energy balance equations can be used to compute the ratings of all the above cable installations.

Cable environment analysis and the probabilistic approach to cable rating

The steps undertaken to determine the ratings of four 32 yr-old, 115 kV, LPOF (low-pressure oil-filled) cable circuits supplying downtown Toronto, Canada are described. The refurbishment of the circuits involved extensive condition surveys and development of mathematical models employing probabilistic methods and finite-element techniques to obtain accurate predictions of cable ampacities. It is found that the condition of a cable and that of the environment in which it is buried are sensitive to several time-dependent factors with complex relationships. These factors cannot be detected by any kind of theoretical analysis and, therefore, before any life extension or current uprating of an aging cable circuit can be attempted, an adequate condition survey of the cable and of the cable route is essential. The probabilistic method used for thermal analysis of loaded cables combined with the information gained from the cable condition survey has the advantage over deterministic methods of quantifying the benefit/risk trade-offs and therefore allowing for more informed decision making. >

The effect of magnetic field on optimal design of a rigid-bus substation

Substation rigid-bus design involves electrical, mechanical, and structural considerations. In order to integrate these considerations into one document, IEEE in cooperation with ANSI has issued a comprehensive guide for design of substation rigid-bus systems. The design process based on this guide involves substantial manual effort to integrate all types of calculations. This is particularly evident when the computations have to be repeated several times in order to arrive at a more economic design. In an earlier paper the authors presented a mathematical model and computer program which automates the design process. There has been concern expressed about the possible biological effects of low level magnetic fields. In view of this, a new design constraint taking into account the limits imposed on the magnitude of the magnetic field can be added to the design guidelines. In this paper the authors introduce such a constraint and show how the magnitude of allowable magnetic field at a specified distance from the station buses affects the optimal design of a rigid bus substation. >