Rating of Electric Power Cables in Unfavorable Thermal Environment

RATING OF ELECTRIC POWER CABLES IN UNFAVORABLE THERMAL ENVIRONMENT
 IEEE Press Editorial Board
 Front Matter
 Table of Contents
 Preface
1. Review of Power Cable Standard Rating Methods
 1.1 Introduction
 1.2 Energy Conservation Equations
  1.2.1 Heat Transfer Mechanism in Power Cable Systems
   1.2.1.1 Conduction
   1.2.1.2 Convection
   1.2.1.3 Radiation
   1.2.1.4 Energy Balance Equations
  1.2.2 Heat Transfer Equations
   1.2.2.1 Underground, Directly Buried Cables
   1.2.2.2 Cables in Air
  1.2.3 Analytical versus Numerical Methods of Solving Heat Transfer Equations
 1.3 Thermal Network Analogs
  1.3.1 Thermal Resistance
  1.3.2 Thermal Capacitance
  1.3.3 Construction of a Ladder Network of a Cable
   1.3.3.1 Representation of Capacitances of the Dielectric
   1.3.3.2 Reduction of a Ladder Network to a Two-Loop Circuit
 1.4 Rating Equations - Steady-State Conditions
  1.4.1 Buried Cables
   1.4.1.1 Steady-State Rating Equation without Moisture Migration
   1.4.1.2 Steady-State Rating Equation with Moisture Migration
  1.4.2 Cables in Air
 1.5 Rating Equations - Transient Conditions
  1.5.1 Response to a Step Function
   1.5.1.1 Preliminaries
   1.5.1.2 Temperature Rise in the Internal Parts of the Cable
   1.5.1.3 Second Part of the Thermal Circuit - Influence of the Soil
   1.5.1.4 Groups of Equally or Unequally Loaded Cables
   1.5.1.5 Total Temperature Rise
  1.5.2 Transient Temperature Rise under Variable Loading
  1.5.3 Conductor Resistance Variations during Transients
  1.5.4 Cyclic Rating Factor
 1.6 Evaluation of Parameters
  1.6.1 List of Symbols
   1.6.1.1 General Data
   1.6.1.2 Cable Parameters
   1.6.1.3 Installation Conditions
  1.6.2 Conductor ac Resistance
  1.6.3 Dielectric Losses
  1.6.4 Sheath Loss Factor
   1.6.4.1 Sheath Bonding Arrangements
   1.6.4.2 Loss Factors for Single-Conductor Cables
   1.6.4.3 Three-Conductor Cables
   1.6.4.4 Pipe-Type Cables
  1.6.5 Armor Loss Factor
   1.6.5.1 Single-Conductor Cables
   1.6.5.2 Three-Conductor Cables - Steel Wire Armor
   1.6.5.3 Three-Conductor Cables - Steel Tape Armor or Reinforcement
   1.6.5.4 Pipe-Type Cables in Steel Pipe - Pipe Loss Factor
  1.6.6 Thermal Resistances
   1.6.6.1 Thermal Resistance of the Insulation
   1.6.6.2 Thermal Resistance between Sheath and Armor, T_2
   1.6.6.3 Thermal Resistance of Outer Covering (Serving), T_3
   1.6.6.4 Pipe-Type Cables
   1.6.6.5 External Thermal Resistance
  1.6.7 Thermal Capacitances
   1.6.7.1 Oil in the Conductor
   1.6.7.2 Conductor
   1.6.7.3 Insulation
   1.6.7.4 Metallic Sheath or Any other Concentric Layer
   1.6.7.5 Reinforcing Tapes
   1.6.7.6 Armor
   1.6.7.7 Pipe-Type Cables
 1.7 Concluding Remarks
 References
2. Ampacity Reduction Factors for Cables Crossing Thermally Unfavorable Regions
 2.1 Cables Crossing Thermally Unfavorable Regions
  2.1.1 Introduction
  2.1.2 Ampacity Reduction Modeling
  2.1.3 Temperature Distribution along the Rated Cable
  2.1.4 Derating Factor
  2.1.5 Cyclic Rating for Cable Crossing an Unfavorable Region
  2.1.6 Soil Dryout Caused by Moisture Migration
 2.2 Ventilated Routes
  2.2.1 Cable Laid in a Pipe with Air Convection
   2.2.1.1 Self-Supporting Air Convection
   2.2.1.2 Forced Air Convection
  2.2.2 Numerical Example Illustrating the Cooling-Pipe Concepts
  2.2.3 Reduction of a Magnetic Field
 2.3 Concluding Remarks
 2.4 Chapter Summary
 References
3. Cable Crossings - Derating Considerations
 3.1 Introduction
 3.2 Utility Practices
 3.3 Derating Factor
 3.4 Temperature Distribution along the Rated Cable and the Mutual Thermal Resistance
  3.4.1 Single External Heat Source
  3.4.2 Heating by a Steam Pipe
  3.4.3 Multiple Crossing Heat Sources
 3.5 Consideration of a Screen Longitudinal Heat Flow
 3.6 Transient Temperature Rise of Cable Crossings
  3.6.1 Transient External Thermal Resistance
  3.6.2 Cyclic Rating
   3.6.2.1 Cyclic Loading of the External Heat Source
   3.6.2.2 Rated Cable with Cyclic Load
 3.7 Soil Dryout Caused by Moisture Migration
 3.8 Concluding Remarks
 3.9 Chapter Summary
 References
4. Application of Thermal Backfills for Cables Crossing Unfavorable Thermal Environments
 4.1 A Brief History of Soil Thermal Resistivity Measurements
 4.2 Optimization of Power Cable and Thermal Backfill Configurations
  4.2.1 Analysis of the Effect of Parameter Variations
  4.2.2 Formulation of the Optimization Problem
  4.2.3 Assessment of Sensitivities to Ambient Fluctuations
 4.3 Parameter Uncertainty in Rating Analysis of Cables Crossing Unfavorable Thermal Environments
  4.3.1 Sample Cable System
  4.3.2 Statistical Variations of Cable Circuit Parameters
   4.3.2.1 Load Probability Distribution
   4.3.2.2 Ambient Temperature Probability Distribution
   4.3.2.3 Native Soil and Backfill Probability Distributions
  4.3.3 Computation of Temperature Distribution Using Monte Carlo Simulation
   4.3.3.1 Steady-State Analysis
   4.3.3.2 Transient Analysis
  4.3.4 Sample Applications
 4.4 Stochastic Optimization
 4.5 Concluding Remarks
 4.6 Chapter Summary
 References
5. Special Considerations for Real-Time Rating Analysis and Deeply Buried Cables
 5.1 Introduction
 5.2 Prediction of Conductor Temperature from the Conductor Current
  5.2.1 Introduction
  5.2.2 Mathematical Model
 5.3 Practical Application of the Temperature Prediction Equation
 5.4 Field Verification of the Temperature Calculations
 5.5 Loss Factor Calculations in Rating Standards
  5.5.1 Daily Load Cycle
  5.5.2 Consideration of Weekly Load Variations
   5.5.2.1 Characteristic Diameter
 5.6 Deeply Buried Cables
  5.6.1 Characteristic Diameter
  5.6.2 Temperature Changes for Deeply Buried Cables
 5.7 Concluding Remarks
 5.8 Chapter Summary
 References
6. Installations Involving Multiple Cables in Air
 6.1 Introduction
 6.2 Current Rating of Multicore Cables
  6.2.1 Introduction
  6.2.2 Background
   6.2.2.1 Evaluation of the Jacket Thermal Resistance
   6.2.2.2 Rating Equations
   6.2.2.3 Evaluation of the External Thermal Resistance
  6.2.3 Heat Conduction inside the Cable Bundle
   6.2.3.1 Uniform Loss Density
   6.2.3.2 Unequally Loaded Bundle
 6.3 Examples of Derating Factors
  6.3.1 Rating Factors
   6.3.1.1 Laying in a Single Layer on Walls, Floors, or in Cable Trays
   6.3.1.2 Laying in a Single Layer under Ceilings
   6.3.1.3 Laying in a Single Layer on Ventilated Cable Trays
   6.3.1.4 Laying in a Single Layer on Cable Ladders, Brackets, or Wire Mesh
   6.3.1.5 Laying in Several Layers
   6.3.1.6 Several Cables Connected in Parallel
 6.4 Concluding Remarks
 6.5 Chapter Summary
  6.5.1 Cables in Free Air
  6.5.2 Cables in Moving Air
  6.5.3 Unequally Loaded Bundle
   6.5.3.1 Central Part Loaded
   6.5.3.2 Outer Part Loaded
 References
7. Rating of Pipe-Type Cables with Slow Oil Circulation of Dielectric Fluid
 7.1 Nomenclature
 7.2 Introduction
 7.3 Thermal Effects of Dielectric Fluid Circulation
  7.3.1 Background Information
   7.3.1.1 Calculation of Coolant Parameters
   7.3.1.2 Thermal Calculations
  7.3.2 Buller\'s Model
   7.3.2.1 Effective Cooling Distance
  7.3.3 Model for Real-Time Rating Computations
   7.3.3.1 Oil Velocity Profile
   7.3.3.2 Oil Temperature Distribution
   7.3.3.3 Thermal Resistances of the Oil Film
 7.4 Concluding Remarks
 7.5 Chapter Summary
 References
Appendices
 Appendix A: Model Cables
  A.1 Model Cable No. 1
  A.2 Model Cable No. 2
  A.3 Model Cable No. 3
  A.4 Model Cable No. 4
  A.5 Model Cable No. 5
  A.6 Cable Model No. 6
  References
 Appendix B: Computations of the Mean Moisture Contents in Media Surrounding Underground Power Cables
  B.1 Introduction
  B.2 Soil-Water Balance
  B.3 Determination of Potential Evapotranspiration
  B.4 Weekly Soil-Water Balance Calculations
  References
 Appendix C: Estimation of Backfill Thermal Resistivity
  Reference
 Appendix D: Equations for Dielectric Fluid Parameters