High Voltage Engineering: Theory, systems, and pratice

Legal Notice
Acknowledgements
Preface
Author’s Note

I Fundamentals of High Voltage

1 Introduction to High Voltage Systems
1.1 Historical Context: TheWar of Currents
1.1.1 The DC Limitation (The Pearl Street Era)
1.1.2 The AC Victory (The Transformer Principle)
1.2 The Economics of Voltage Choice (Kelvin’s Law)
1.2.1 The Two Opposing Cost Functions
1.2.2 Finding the Optimum
1.3 Standardization of Voltage Levels (IEC 60038)
1.4 The Portuguese Grid Structure (RNT & RND)
1.4.1 The 400 kV Backbone (RNT)
1.4.2 The 220 kV and 150 kV Sub-Transmission
1.4.3 The 60 kV Distribution (RND)
1.5 Standard Atmospheric Conditions
1.5.1 The Physics: Mean Free Path and Paschen’s Law
1.5.2 Standard Conditions (IEC 60060-1)
1.5.3 Correction for Altitude (The d Factor)
1.6 Summary
2 Electric Fields and Dielectrics
2.1 The Electric Field and Potential
2.1.1 Governing Equations: Poisson and Laplace
2.2 Field Uniformity and Utilization Factor
2.3 Analytical Methods: The Method of Images
2.4 Numerical Methods: Finite Difference Method (FDM)
2.5 Advanced Numerical Methods
2.5.1 The Charge Simulation Method (CSM)
2.5.2 The Finite Element Method (FEM)
2.6 Field Refraction at Dielectric Boundaries
2.7 Physics of Polarization and tan d
2.7.1 Dielectric Loss
2.7.2 Complex Permittivity and Mechanisms
2.8 Breakdown Mechanisms
2.8.1 Townsend Mechanism
2.8.2 Streamer Mechanism (Raether-Meek)
2.8.3 Paschen’s Law
2.9 Practice Problems
2.10 Summary

II Generation and Measurement
3 Generation of High Voltages and Currents
3.1 High Voltage AC Generation
3.1.1 Cascade Connection of Transformers
3.2 Series Resonant Circuits
3.2.1 Physical Principle
3.2.2 Voltage Amplification (The Q-Factor)
3.3 High Voltage DC Generation
3.3.1 The Cockcroft-Walton Voltage Multiplier
3.3.2 Voltage Drop and Ripple
3.4 Impulse Voltage Generation (The Marx Generator)
3.4.1 Principle of Operation
3.4.2 Transient Analysis: The Laplace Approach
3.4.3 Voltage Efficiency
3.5 Summary
4 High Voltage Measurement Techniques
4.1 Sphere Gaps: The Physics of Calibration
4.1.1 Theoretical Basis: The Streamer Criterion
4.1.2 Atmospheric Correction Factor (Kd)
4.1.3 Statistical Determination: The Up-and-Down Method
4.2 Voltage Dividers: Transient Theory
4.2.1 Resistive Dividers
4.2.2 Damped Capacitive Dividers (The R-C Divider)
4.2.3 The Mixed Divider (Zaengl Type)
4.3 Current Measurement: Rogowski Coils and OCTs
4.3.1 The Rogowski Coil
4.3.2 Optical Current Transformers (OCT)
4.4 Digital Signal Processing in HV Measurements
4.4.1 Sampling Rate (Nyquist Criterion)
4.4.2 Vertical Resolution and ENOB
4.5 Solved Problems
4.6 Summary

III Transmission
5 High Voltage Insulators and Outdoor Insulation
5.1 Insulator Technologies and Materials
5.1.1 Toughened Glass (Cap and Pin)
5.1.2 Porcelain (Ceramic)
5.1.3 Composite (Polymeric) Insulators
5.2 The Physics of Hydrophobicity
5.2.1 Hydrophobicity Transfer (The LMW Effect)
5.3 The Pollution Flashover Mechanism
5.3.1 The Physical Process (Step-by-Step)
5.3.2 Mathematical Model: The Obenaus Theory
5.4 Design: Selecting Leakage Distance (IEC 60815)
5.4.1 Pollution Classes (SPS)
5.4.2 Dimensioning Equation
5.5 Voltage Distribution and String Efficiency
5.5.1 The Capacitance Model
5.5.2 Mathematical Derivation
5.5.3 String Efficiency (?)
5.5.4 Methods to Improve Efficiency
5.6 Insulator Testing Standards (IEC 60383)
5.6.1 Type Tests
5.6.2 Sample Tests
5.6.3 Routine Tests
5.7 Solved Problems
5.8 Summary6 Overhead Transmission Lines: Physics and Mechanics
6.1 The Physics of Conductors
6.1.1 ACSR Conductors
6.1.2 Skin Effect and Resistance
6.2 Line Parameters: Matrix Derivation
6.2.1 Flux Linkage and Inductance
6.2.2 Bundled Conductors
6.3 Corona Phenomenon
6.3.1 Critical Disruptive Voltage (Peek’s Law)
6.3.2 Corona Loss
6.4 Mechanical Design: The Catenary
6.4.1 The Parabolic Approximation
6.5 Change of State Equation
6.6 Conductor Dynamics: Aeolian Vibrations
6.6.1 Aeolian Vibration (High Frequency)
6.6.2 Galloping (Low Frequency)
6.7 Solved Problems
6.8 Summary
7 High Voltage Cables: Design and Application
7.1 Cable Construction and Materials
7.1.1 1. The Conductor
7.1.2 2. Semiconductor Screens
7.1.3 3. Insulation (XLPE)
7.1.4 4. Metallic Sheath
7.2 Electrostatic Design
7.2.1 Electric Field Distribution (AC)
7.2.2 The "Field Inversion" Phenomenon (HVDC)
7.3 Electrical Parameters
7.3.1 Capacitance and Charging Current
7.3.2 Inductance
7.4 Thermal Rating (IEC 60287)
7.4.1 The Neher-McGrath Equation
7.4.2 Thermal Resistances
7.5 Cable Accessories: The Weak Points
7.5.1 Terminations and Stress Cones
7.6 Sheath Bonding Systems
7.6.1 Cross-Bonding
7.7 Solved Problems

IV Substations and Equipment
8 Power Transformers: Design and Physics
8.1 Electromagnetic Design
8.1.1 Core Physics: Hysteresis and Eddy Currents
8.1.2 Flux Density Limits and Saturation
8.2 Transient Phenomena: Inrush Current
8.3 Short-Circuit Forces: The Mechanical Challenge
8.3.1 Radial Forces (Hoop Stress)
8.3.2 Axial Forces (Telescoping)
8.4 The Autotransformer in Transmission Grids
8.4.1 Principle of Operation
8.4.2 The Power Advantage (Co-Ratio)
8.5 Winding Configurations and Vector Groups
8.5.1 Why the Tertiary Delta?
8.6 On-Load Tap Changers (OLTC)
8.7 Dielectric Design (Oil-Paper System)
8.7.1 Field Distribution Mechanism
8.8 Thermal Aging and Life Expectancy
8.8.1 Arrhenius Law and Montsinger’s Rule
8.9 Solved Problems
8.10 Summary
9 Switchgear Technology and Arc Physics
9.1 Physics of the Electric Arc
9.1.1 Thermal Ionization
9.1.2 Arc Models for Simulation
9.2 The Interruption Process: Grid Interaction
9.2.1 1. Dielectric Recovery (Ud)
9.2.2 2. Transient Recovery Voltage (TRV)
9.3 Standard TRV Classes (IEC 62271-100)
9.3.1 Terminal Fault (T10, T30, T60, T100)
9.3.2 The Short-Line Fault (SLF)
9.4 Interruption Technologies: Why SF6?
9.4.1 Key Properties
9.4.2 Arc Quenching Mechanisms
9.5 Operating Mechanisms
9.5.1 Spring Drive
9.5.2 Hydraulic Drive
9.6 The Future: HVDC Circuit Breakers
9.6.1 The Hybrid DC Breaker
9.7 Solved Problems
9.8 Summary
10 Grounding Systems in High Voltage Substations
10.1 Physiological Effects of Current
10.1.1 Current Thresholds (IEC 60479-1)
10.1.2 Dalziel’s Energy Criteria
10.2 The Physics of Potential Rise (GPR)
10.2.1 Shock Scenarios
10.3 Soil Physics and Modeling
10.3.1 Measurement: TheWenner 4-Pin Method
10.3.2 Two-Layer Soil Model
10.4 Grounding Grid Design (IEEE 80)
10.4.1 Step 1: Tolerable Limits
10.4.2 Step 2: Grid Resistance (Rg)
10.4.3 Step 3: Maximum Mesh Voltage (Em)
10.5 Materials and Corrosion
10.6 Solved Problems
10.7 SummaryV Protection and Automation
11 High Voltage System Protection and Digital Substations
11.1 Mathematical Basis: Symmetrical Components
11.1.1 The Transformation Matrix
11.1.2 Sequence Networks for Fault Analysis
11.2 Instrument Transformers: The Eyes of the System
11.2.1 Current Transformers (CT) and Saturation
11.2.2 Capacitive Voltage Transformers (CVT)
11.3 Distance Protection (Relay 21)
11.3.1 Principle of Operation
11.3.2 Digital Algorithm (DFT)
11.3.3 The Quadrilateral Characteristic
11.4 Differential Protection (Relay 87)
11.4.1 The Percentage Restraint Characteristic
11.5 The Digital Substation: IEC 61850
11.5.1 Architecture and Data Model
11.5.2 Real-Time Traffic: GOOSE and SV
11.6 Solved Problems
11.7 Summary

VI Insulation Coordination and Transients
12 Overvoltages and Protection Methods
12.1 Introduction
12.2 Physics of TravelingWaves
12.2.1 Derivation of the Telegrapher’s Equations
12.2.2 d’Alembert’s Solution and Surge Impedance
12.3 Reflection and Refraction of Waves
12.3.1 Bewley Lattice Diagrams
12.4 Lightning Phenomenon and Modeling
12.4.1 Mathematical Model: The Heidler Function
12.4.2 The Electro-Geometric Model (EGM)
12.5 Switching Transients
12.5.1 Transient Recovery Voltage (TRV)
12.5.2 Current Chopping
12.5.3 The Ferranti Effect
12.6 Insulation Coordination
12.6.1 Standard Insulation Levels (REN Context)
12.6.2 Surge Arresters (MOVs)
13 Surge Arresters: Theory, Technology, and Sizing
13.1 Historical Evolution and Technology
13.1.1 The Spark Gap Era (Gapped Arresters)
13.1.2 Silicon Carbide (SiC) with Series Gaps
13.1.3 Metal Oxide Varistors (MOV/ZnO)
13.2 Physics of the Metal Oxide Varistor
13.2.1 Microstructure
13.2.2 Band Theory and Conduction Mechanism
13.3 Electrical Characteristics and Modeling
13.3.1 The V-I Characteristic
13.3.2 Equivalent Circuit Model
13.4 Sizing and Selection Procedure
13.4.1 Step 1: Continuous Operating Voltage (Uc)
13.4.2 Step 2: Temporary Overvoltage (TOV) Capability
13.4.3 Step 3: Energy Class and Line Discharge
13.4.4 Step 4: Insulation Coordination Margins
13.5 The Separation Distance Effect
13.6 Installation Mechanics: Lead Length
14 Insulation Coordination: Statistical Methods
14.1 Principles of Probabilistic Coordination
14.1.1 The Stress-Strength Interference Model
14.2 Statistical Definitions of Variables
14.2.1 The Stress Distribution (Overvoltage)
14.2.2 The Strength Distribution (Insulation)
14.3 Calculation of the Risk of Failure
14.3.1 The IEC Simplified Method
14.4 From Voltage to Geometry: The Gap Factor
14.5 Atmospheric Corrections (IEC 60060-1)
14.5.1 Relative Air Density (d)
14.5.2 Exponent m
14.6 Summary

VII Future and Maintenance
15 HVDC Transmission: Technology and Physics
15.1 The Physics and Economics of DC Transmission
15.1.1 The Capacitive Current Limit (AC)
15.1.2 Economic Break-even Distance
15.2 Line Commutated Converters (LCC)
15.2.1 The Graetz Bridge Analysis
15.2.2 Commutation Overlap and Harmonics
15.3 Voltage Source Converters (VSC)
15.3.1 Vector Control (P - Q Decoupling)
15.3.2 Modular Multilevel Converter (MMC)
15.4 Insulation Physics: The Challenge of DC Cables
15.4.1 Conductivity and Stress Inversion
15.5 HVDC Configurations
15.6 Summary
16 Testing, Diagnostics, and Asset Management
16.1 High Voltage Testing Techniques (IEC 60060-1)
16.1.1 Lightning Impulse Voltage (LI)
16.1.2 Switching Impulse Voltage (SI)
16.2 Dielectric Loss Measurement (tan d)
16.2.1 The Schering Bridge Principle
16.3 Partial Discharge (PD) Diagnostics
16.3.1 The "abc" Capacitive Model
16.3.2 Phase-Resolved PD (PRPD) Analysis
16.4 Dissolved Gas Analysis (DGA)
16.4.1 The Duval Triangle
16.5 Sweep Frequency Response Analysis (SFRA)
16.6 Summary
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Filipe Azevedo is a Professor at ISEP (Polytechnic of Porto) and a Senior Researcher at INESC TEC—Institute for Systems and Computer Engineering, Technology and Science. He holds undergraduate and master’s degrees in Electrical and Computer Engineering from the University of Porto, and received a Ph.D. in Electrical and Computer Engineering, with distinction and honors.
He began his professional career at EFACEC Energia before moving into higher education and research. Since 2000, he has taught at ISEP in the fields of electric power systems, power system economics, and artificial intelligence, and is responsible for courses in high-voltage protection, power systems, and electric power distribution. His research focuses on artificial intelligence, smart grids, renewable energy integration, electricity markets, and decision-support methods for planning and operation.
With more than two decades of academic and scientific experience, he combines rigorous scholarship with practical engineering insight in power-system applications where safety, reliability, and operational performance are critical.