Rating Of Electric Power Cables In Unfavorable Thermal Environment

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ISBN: 9780471679097 | 0471679097
Cover: Hardcover
Copyright: 4/15/2005

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Rating of Electric Power Cables in Unfavorable Thermal Environment is the first text to provide you with the computational tools and techniques needed to successfully design and install power cables in areas affected by such factors as outside heat sources, ground moisture, or impediments to heat dissipation. After thoroughly reviewing standard rating models, the author discusses several new techniques designed to improve cable ampacity, as well as new computational techniques for analysis of cyclic loads. To facilitate computational tasks he utilizes six representational model cables throughout the book, including transmission-class, high-voltage, distribution, and bundled types. End-of-chapter summaries, liberal numerical examples, and practical, real world applications make this text a valuable resource for making better design and operation decisions.

Preface

1 Review of Power Cable Standard Rating Methods

(76)

1.1 Introduction

(1)

1.2 Energy Conservation Equations

(5)

1.2.1 Heat Transfer Mechanism in Power Cable Systems

(3)

1.2.1.1 Conduction

(1)

1.2.1.2 Convection

(1)

1.2.1.3 Radiation

(1)

1.2.1.4 Energy Balance Equations

(1)

1.2.2 Heat Transfer Equations

(2)

1.2.2.1 Underground Directly Buried Cables

(1)

1.2.2.2 Cables in Air

(1)

1.2.3 Analytical Versus Numerical Methods of Solving Heat Transfer Equations

(1)

1.3 Thermal Network Analogs

(12)

1.3.1 Thermal Resistance

(2)

1.3.1 Thermal Capacitance

(1)

1.3.3 Construction of a Ladder Network of a Cable

(9)

1.3.3.1 Representation of Capacitances of the Dielectric

(4)

1.3.3.2 Reduction of a Ladder Network to a Two-Loop Circuit

(4)

1.4 Rating Equations Steady-State Conditions

(5)

1.4.1 Buried Cables

(5)

1.4.1.1 Steady-State Rating Equation without Moisture Migration

(2)

1.4.1.2 Steady-State Rating Equation with Moisture Migration

(3)

1.4.2 Cables in Air

(1)

1.5 Rating Equations-Transient Conditions

(12)

1.5.1 Response to a Step Function

(7)

1.5.1.1 Preliminaries

(1)

1.5.1.2 Temperature Rise in the Internal Parts of the Cable

(3)

1.5.1.3 Second Part of the Thermal Circuit Influence of the Soil

(1)

1.5.1.4 Groups of Equally or Unequally Loaded Cables

(1)

1.5.1.5 Total Temperature Rise

(1)

1.5.2 Transient Temperature Rise under Variable Loading

(1)

1.5.3 Conductor Resistance Variations during Transients

(1)

1.5.4 Cyclic Rating Factor

(4)

1.6 Evaluation of Parameters

(36)

1.6.1 List of Symbols

(2)

1.6.1.1 General Data

(1)

1.6.1.2 Cable Parameters

(2)

1.6.1.3 Installation Conditions

(1)

1.6.2 Conductor ac Resistance

(2)

1.6.3 Dielectric Losses

(1)

1.6.4 Sheath Loss Factor

(8)

1.6.4.1 Sheath Bonding Arrangements

(3)

1.6.4.2 Loss Factors for Single-Conductor Cables

(3)

1.6.4.3 Three-Conductor Cables

(1)

1.6.4.4 Pipe-Type Cables

(1)

1.6.5 Armor Loss Factor

(3)

1.6.5.1 Single-Conductor Cables

(1)

1.6.5.2 Three-Conductor Cables Steel Wire Armor

(1)

1.6.5.3 Three-Conductor Cables-Steel Tape Armor or Reinforcement

(1)

1.6.5.4 Pipe-Type Cables in Steel Pipe-Pipe Loss Factor

(1)

1.6.6 Thermal Resistances

(17)

1.6.6.1 Thermal Resistance of the Insulation

(4)

1.6.6.2 Thermal Resistance between Sheath and Armor, T2

(1)

1.6.6.3 Thermal Resistance of Outer Covering (Serving), T3

(1)

1.6.6.4 Pipe-Type Cables

(1)

1.6.6.5 External Thermal Resistance

(9)

1.6.7 Thermal Capacitances

(8)

1.6.7.1 Oil in the Conductor

(2)

1.6.7.2 Conductor

(1)

1.6.7.3 Insulation

(1)

1.6.7.4 Metallic Sheath or Any Other Concentric Layer

(1)

1.6.7.5 Reinforcing Tapes

(1)

1.6.7.6 Armor

(1)

1.6.7.7 Pipe-Type Cables

(1)

1.7 Concluding Remarks

(1)

References

(4)

2 Ampacity Reduction Factors for Cables Crossing Thermally Unfavorable Regions

(44)

2.1 Cables Crossing Thermally Unfavorable Regions

(24)

2.1.1 Introduction

(1)

2.1.2 Ampacity Reduction Modeling

(1)

2.1.3 Temperature Distribution Along the Rated Cable

(6)

2.1.4 Derating Factor

(6)

2.1.5 Cyclic Rating for Cable Crossing Unfavorable Region

(9)

2.1.6 Soil Dryout Caused by Moisture Migration

(2)

2.2 Ventilated Routes

101

(16)

2.2.1 Cable Laid in a Pipe with Air Convection

102

(6)

2.2.1.1 Self-Supporting Air Convection

102

(6)

2.2.1.2 Forced Air Convection

108

(1)

2.2.2 Numerical Example Illustrating the Cooling Pipe Concepts

108

(4)

2.2.3 Reduction of a Magnetic Field

112

(5)

2.3 Concluding Remarks

117

(1)

2.4 Chapter Summary

117

(2)

References

119

(2)

3 Cable Crossings-Derating Considerations

121

(44)

3.1 Introduction

121

(1)

3.2 Utility Practices

122

(2)

3.3 Derating Factor

124

(1)

3.4 Temperature Distribution Along the Rated Cable and the Mutual Thermal Resistance

125

(15)

3.4.1 Single External Heat Source

125

(6)

3.4.2 Heating by a Steam Pipe

131

(3)

3.4.3 Multiple Crossing Heat Sources

134

(6)

3.5 Consideration of a Screen Longitudinal Heat Flow

140

(5)

3.6 Transient Temperature Rise of Cable Crossings

145

(11)

3.6.1 Transient External Thermal Resistance

145

(2)

3.6.2 Cyclic Rating

147

(21)

3.6.2.1 Cyclic Loading of the External Heat Source

147

(2)

3.6.2.2 Rated Cable with Cyclic Load

149

(7)

3.7 Soil Dryout Caused by Moisture Migration

156

(5)

3.8 Concluding Remarks

161

(1)

3.9 Chapter Summary

161

(3)

References

164

(1)

4 Application of Thermal Backfills for Cables Crossing Unfavorable Thermal Environments

165

(46)

4.1 A Brief History of Soil Thermal Resistivity Measurements

166

(2)

4.2 Optimization of Power Cable and Thermal Backfill Configurations

168

(19)

4.2.1 Analysis of the Effect of Parameter Variations

169

(1)

4.2.2 Formulation of the Optimization Problem

170

(8)

4.2.3 Assessment of Sensitivities to Ambient Fluctuations

178

(9)

4.3 Parameter Uncertainty in Rating Analysis of Cables Crossing Unfavorable Thermal Environments

187

(15)

4.3.1 Sample Cable System

188

(2)

4.3.2 Statistical Variations of Cable Circuit Parameters

190

(4)

4.3.2.1 Load Probability Distribution

190

(1)

4.3.2.2 Ambient Temperature Probability Distribution

190

(1)

4.3.2.3 Native Soil and Backfill Probability Distributions

190

(4)

4.3.3 Computation of Temperature Distribution Using Monte Carlo Simulation

194

(3)

4.3.3.1 Steady-State Analysis

194

(2)

4.3.3.2 Transient Analysis

196

(1)

4.3.4 Sample Applications

197

(5)

4.4 Stochastic Optimization

202

(4)

4.5 Concluding Remarks

206

(1)

4.6 Chapter Summary

207

(2)

References

209

(2)

5 Special Considerations for Real-Time Rating Analysis and Deeply Buried Cables

211

(36)

5.1 Introduction

211

(2)

5.2 Prediction of Conductor Temperature from the Conductor Current

213

(9)

5.2.1 Introduction

213

(1)

5.2.2 Mathematical Model

213

(9)

5.3 Practical Application of the Temperature Prediction Equation

222

(1)

5.4 Field Verification of the Temperature Calculations

223

(1)

5.5 Loss Factor Calculations in Rating Standards

224

(13)

5.5.1 Daily Load Cycle

224

(6)

5.5.2 Consideration of Weekly Load Variations

230

(7)

5.5.2.1 Characteristic Diameter

233

(4)

5.6 Deeply Buried Cables

237

(5)

5.6.1 Characteristic Diameter

238

(4)

5.6.2 Temperature Changes for Deeply Buried Cables

242

(1)

5.7 Concluding Remarks

242

(1)

5.8 Chapter Summary

243

(2)

References

245

(2)

6 Installations Involving Multiple Cables in Air

247

(32)

6.1 Introduction

247

(1)

6.2 Current Rating of Multicore Cables

247

(19)

6.2.1 Introduction

248

(1)

6.2.2 Background

249

(5)

6.2.2.1 Evaluation of the Jacket Thermal Resistance

249

(1)

6.2.2.2 Rating Equations

250

(1)

6.2.2.3 Evaluation of the External Thermal Resistance

251

(3)

6.2.3 Heat Conduction Inside the Cable Bundle

254

(12)

6.2.3.1 Uniform Loss Density

254

(8)

6.2.3.2 Unequally Loaded Bundle

262

(4)

6.3 Examples of Derating Factors

266

(4)

6.3.1 Rating Factors

267

(6)

6.3.1.1 Laying in a Single Layer on Wall, Floors, or in Cable Trays

267

(1)

6.3.1.2 Laying in a Single Layer under Ceilings

268

(1)

6.3.1.3 Laying in a Single Layer on Ventilated Cable Trays

268

(1)

6.3.1.4 Laying in a Single Layer on Cable Ladders, Brackets, or Wire Mesh

269

(1)

6.3.1.5 Laying in Several Layers

270

(1)

6.3.1.6 Several Cables Connected in Parallel

270

(1)

6.4 Concluding Remarks

270

(3)

6.5 Chapter Summary

273

(3)

6.5.1 Cables in Free Air

273

(1)

6.5.2 Cables in Moving Air

274

(1)

6.5.3 Unequally Loaded Bundle

275

(8)

6.5.3.1 Central Part Loaded

275

(1)

6.5.3.2 Outer Part Loaded

275

(1)

References

276

(3)

7 Rating of Pipe-Type Cables with Slow Circulation of Dielectric Fluid

279

(24)

7.1 Nomenclature

279

(1)

7.2 Introduction

280

(3)

7.3 Thermal Effects of Dielectric Fluid Circulation

283

(16)

7.3.1 Background Information

284

(1)

7.3.1.1 Calculation of Coolant Parameters

284

(1)

7.3.1.2 Thermal Calculations

285

(1)

7.3.2 Buller's Model

285

(6)

7.3.2.1 Effective Cooling Distance

287

(4)

7.3.3 Model for Real-Time Rating Computations

291

(8)

7.3.3.1 Oil Velocity Profile

292

(1)

7.3.3.2 Oil Temperature Distribution

293

(1)

7.3.3.3 Thermal Resistances of the Oil Film

294

(5)

7.4 Concluding Remarks

299

(1)

7.5 Chapter Summary

300

(2)

References

302

(1)

Appendix A: Model Cables

303

(10)

Model Cable No. 1

303

(1)

Model Cable No. 2

303

(2)

Model Cable No. 3

305

(1)

Model Cable No. 4

305

(1)

Model Cable No. 5

305

(3)

Model Cable No. 6

308

(4)

References

312

(1)

Appendix B: Computations of the Mean Moisture Content in Media Surrounding Underground Power Cables

313

(4)

Introduction

313

(1)

Soil-Water Balance

314

(1)

Determination of Potential Evapotranspiration

315

(1)

Weekly Soil-Water Balance Calculations

315

(1)

References

315

(2)

Appendix C: Estimation of Backfill Thermal Resistivity

317

(4)

Reference

319

(2)

Appendix D: Equations for Dielectric Fluid Parameters

321

(2)

Index

323

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Rating Of Electric Power Cables In Unfavorable Thermal Environment

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