Electromagnetic Transients in Large HV Cable Networks: Modeling and calculations (Energy Engineering)

Cover
Contents
About the authors
Preface
	Aims and reasons for writing this book
1 Introduction
	1.1 Chapter 2: Series impedance and shunt admittance
	1.2 Chapter 3: Modeling of cables
	1.3 Chapter 4: Wave propagation characteristics of overhead and underground cables
	1.4 Chapter 5: Steady-state and transient characteristics on three-phase cables
	1.5 Chapter 6: Transients in the interconnected EHV cable network in Denmark
	1.6 Chapter 7: Steady-state and transient behavior of hybrid overhead line-underground cable networks in the Netherlands
2 Series impedance and shunt admittance
	2.1 Formulation of series impedance and shunt admittance
	2.2 Review of existing formulas of earth-return impedance and admittance
		2.2.1 Overhead cable (line)
			2.2.1.1 Formulas based on quasi-TEM assumption
			2.2.1.2 Formulas based on complete field solution
		2.2.2 Underground cable
			2.2.2.1 Formulas based on quasi-TEM assumption
			2.2.2.2 Formulas based on complete field solution
	2.3 Accurate and approximate earth-return impedance formulas for overhead cable (line)
		2.3.1 Accurate impedance formulas for stratified earth
		2.3.2 Approximate impedance formulas
			2.3.2.1 Pollaczek
			2.3.2.2 Carson
			2.3.2.3 Sunde
		2.3.3 Further approximation of formulas
		2.3.4 Discussion
	2.4 Accurate and approximate earth-return admittance formulas for overhead cable (line)
		2.4.1 Accurate admittance formulas
		2.4.2 Approximate admittance formulas
	2.5 Accurate and approximate earth-return impedance formulas for underground cable
		2.5.1 Accurate impedance formulas
		2.5.2 Approximate impedance formulas
			2.5.2.1 Pollaczek
			2.5.2.2 Sunde
			2.5.2.3 Papadopoulos
		2.5.3 Further approximation of formulas
			2.5.3.1 Wedepohl
			2.5.3.2 Vance
			2.5.3.3 Bridges
			2.5.3.4 Saad
			2.5.3.5 Petrache
			2.5.3.6 Theethayi
	2.6 Accurate and approximate earth-return admittance formulas for underground cable
		2.6.1 Accurate admittance formulas
			2.6.1.1 Line voltage integral equation referred to infinite depth in the earth
			2.6.1.2 Line voltage integral equation referred to the earth surface
			2.6.1.3 Line voltage integral equation referred to penetration depth in the earth
		2.6.2 Approximate admittance formulas
			2.6.2.1 Papadopoulos
			2.6.2.2 Magalhães
		2.6.3 Further approximation of formulas
		2.6.4 Applicable limit of quasi-TEM-based formulas
		2.6.5 Definition of classical and extended TL approaches
	2.7 Derivation of the modified earth-return Green function for MoM-SO technique
	2.8 Comparison of calculated impedance and admittance by different methods
		2.8.1 Overhead lines
			2.8.1.1 Series impedance
			2.8.1.2 Numerical instability of MoM-SO and solution
			2.8.1.3 Shunt admittance
		2.8.2 Underground cables
			2.8.2.1 Series impedance
			2.8.2.2 Shunt admittance
		2.8.3 Concluding remarks
	2.9 Impedance and admittance at f = 0 for HVDC line [66]
		2.9.1 Impedance in a low-frequency condition
			2.9.1.1 Classical TL approach
			2.9.1.2 Impedance calculated by classical TL approach in a low-frequency condition
		2.9.2 Admittance in a low-frequency condition
		2.9.3 Wave propagation characteristics in a low-frequency condition
			2.9.3.1 Propagation constant
			2.9.3.2 Characteristic impedance
		2.9.4 Investigation of parameters at a frequency approaching zero
			2.9.4.1 Impedance and capacitance
			2.9.4.2 Phase velocity and characteristic impedance
		2.9.5 New approach to determine the parameters at f = 0
			2.9.5.1 Distortion-less line model based on circuit theory
			2.9.5.2 Method-1: Theoretical estimation of G0
			2.9.5.3 Method-2: Estimating G0 at any location x along HVDC line from monitored voltage Vx
			2.9.5.4 Low-frequency responses of wave propagation related parameters
		2.9.6 Concluding remarks
	2.10 Theoretical formulation of external electromagnetic fields generated by overhead lines and underground cables
		2.10.1 Overhead lines
		2.10.2 Underground cables
			2.10.2.1 Formulation of an excitation current based on a bidirectional propagation with terminating conditions
			2.10.2.2 Formulation of vectors of external electromagnetic field components
	2.11 Conclusions
	Appendix A1 Cable internal impedance and admittance including semiconducting layer [1] A1.1 Formulation of internal impedance ma
		A1.1.1 Single-core coaxial (SC) cable [1]
			A1.1.1.1 SC cable composed of core, sheath, and armor
			A1.1.1.2 SC cable composed of core and sheath
			A1.1.1.3 SC cable composed only of core
			A1.1.1.4 Component impedances of SC cable
		A1.1.2 Pipe-enclosed type (PT) cable [1,83,84]
			A1.1.2.1 Formulation of PT cable impedance matrix
		A1.1.3 Component impedance of PT cable
	A1.2 Formulation of potential coefficient matrix
		A1.2.1 Single-core coaxial (SC) cable
			A1.2.1.1 SC cable composed of core, sheath, and armor
			A1.2.1.2 SC cable composed of core and sheath
			A1.2.1.3 SC cable composed only of core
		A1.2.2 Pipe-enclosed type (PT) cable
	A1.3 Semiconducting layer (two-layered conductor) impedance [85]
		A1.3.1 Derivation of impedance
		A1.3.2 Impedance of two-layered conductor
	A1.4 Investigation of cable internal impedance [90]
		A1.4.1 Accurate formula by Schelkunoff [2]
		A1.4.2 Approximate formula by Wedepohl/Wilcox [49]
		A1.4.3 Conductor outer surface impedance Zo with arbitrary cross-section [91]
		A1.4.4 Discussion on accurate and approximate impedances [90]
			A1.4.4.1 Numerical instability
			A1.4.4.2 Countermeasure of the numerical instability
			A1.4.4.3 Comparison of calculated results by accurate and approximate formulas
	Appendix A2 Derivation of electromagnetic field equations and earth-return parameters for a multiphase underground cable system
	A2.1 Derivation of electromagnetic field formulas
	A2.2 Derivation of modal equation
	A2.3 Derivation of generalized earth-return impedance and admittance formulas
		A2.3.1 Complete field solution
			A2.3.1.1 A single underground cable
			A2.3.1.2 Multiphase underground cable
		A2.3.2 Quasi-TEM solution
			A2.3.2.1 Numerical difficulties for the formulas based on complete electromagnetic field solutions
			A2.3.2.2 Earth-return impedance and admittance formulas based on quasi-TEM assumption
			A2.3.2.3 Line voltage integral equation referred to infinite depth in the earth
			A2.3.2.4 Line voltage integral equation referred to the earth surface
			A2.3.2.5 Line voltage integral equation referred to penetration depth in the earth
	Appendix A3 Derivation of electromagnetic field equations for a multiphase overhead line system
		A3.1 Derivation of electromagnetic field formulas
	References
3 Modeling of cables
	3.1 Transmission line models in EMT-type simulation tools
		3.1.1 Equivalent π-circuit model [4]
		3.1.2 Distributed parameters transmission line model
			3.1.2.1 Basic concept of model
			3.1.2.2 Constant-parameter (CP) line model
		3.1.3 Frequency-dependent line model in modal domain
			3.1.3.1 Frequency-dependent effect
			3.1.3.2 Frequency-dependent line model in modal domain
		3.1.4 Frequency-dependent line model in the phase domain
			3.1.4.1 Curve fitting techniques of ULM
	3.2 Modeling of frequency-dependent soil parameters
		3.2.1 Review of models of frequency-dependent soil parameters
			3.2.1.1 Longmire/Smith (LS) model
			3.2.1.2 Alipio/Visacro (AV) model
			3.2.1.3 Scott (SC) model
		3.2.2 Calculated results of FD soil models
		3.2.3 Comparison with measured data
		3.2.4 Summary
	3.3 Various cable installation
		3.3.1 Cable installed underneath a bridge
		3.3.2 Tower-installed (vertical) cable
			3.3.2.1 Field measurement
			3.3.2.2 Theoretical analysis and modeling for EMTP simulation
			3.3.2.3 EMT simulation results
			3.3.2.4 Voltage difference between tower and cable
			3.3.2.5 Concluding remarks
		3.3.3 Cable installed in a tunnel
			3.3.3.1 Existing model of tunnel-installed cable [69,77]
			3.3.3.2 Accurate tunnel model [79]
		3.3.4 Cable installed in an HDPE tube
			3.3.4.1 COMSOL and cable constants calculations of impedance and capacitance
			3.3.4.2 Equivalent model for eccentric cable insulators
			3.3.4.3 Transient simulation in comparison with the field test result
			3.3.3.4 Effect of HDPE tube
			3.3.3.4 Concluding remarks
		3.3.5 Submarine cable
	3.4 Cable bonding
		3.4.1 Bonding methods
		3.4.2 Various bonding methods
			3.4.2.1 Definition of modal components
	3.5 Numerical electromagnetic analysis [113,114]
		3.5.1 Method of moments (MoM) in time and frequency domains
			3.5.1.1 MoM in the time domain
			3.5.1.2 MoM in the frequency domain
		3.5.2 Finite-difference time-domain (FDTD) method
		3.5.3 Finite element method (FEM)
			3.5.3.1 Basic theory of FEM
			3.5.3.2 COMSOL multiphysics
	3.6 Conclusions
	Appendix A3.1 Maxwell’s equations
	References
4 Wave propagation characteristics of overhead and underground cables
	4.1 Evaluation of propagation constant for overhead and underground cables
	4.2 Overhead cables
		4.2.1 Overhead line
			4.2.1.1 Attenuation constant
			4.2.1.2 Calculated results of electromagnetic field components
		4.2.2 Overhead cable
			4.2.2.1 Attenuation constant
			4.2.2.2 Propagation function
			4.2.2.3 Transition frequency
	4.3 Underground cables
		4.3.1 Propagation constant
		4.3.2 External electromagnetic field components
			4.3.2.1 Uni-directional wave propagation
			4.3.2.2 Bidirectional wave propagation
	4.4 Input impedance of cross-bonded cable
		4.4.1 Bonding methods for cross-bonded cable
		4.4.2 Model circuit
		4.4.3 Input impedance
		4.4.4 Resonant frequency
		4.4.5 Attenuation characteristics
		4.4.6 Time responses
		4.4.7 Application of frequency responses for calculating the propagation constants of cross-bonded cables
		4.4.8 Modeling methods of complete cross-bonded cable systems
	4.5 Conclusions
	References
5 Steady-state and transient characteristics on three-phase cables
	5.1 Cable discharge
		5.1.1 Introduction
		5.1.2 Basic formulas and parameters for charging and discharging phenomena
			5.1.2.1 Charging
			5.1.2.2 Discharging
			5.1.2.3 Parameters related to charging and discharging
		5.1.3 Test results
			5.1.3.1 Field test on a 275 kV POF cable in Japan (Test-A)
			5.1.3.2 Laboratory test (Test-B)
			5.1.3.3 Field test on a 275 kV POF Cable in UK (Test-C)
		5.1.4 Theoretical analysis
			5.1.4.1 Test-A
			5.1.4.2 Test-B
			5.1.4.3 Test-C
		5.1.5 Survey of leakage resistance and time constant for cable discharge
			5.1.5.1 Cable parameters
			5.1.5.2 Insulator parameters and leakage current
			5.1.5.3 Formula and typical values discharge time constant
			5.1.5.4 Correction factor for humidity
		5.1.6 EMT simulation
			5.1.6.1 POF cable in Japan
			5.1.6.2 275 kV POF cable in the UK
		5.1.7 Summary
	5.2 Field measurement of cable transients and EMT simulations
		5.2.1 Field measurement
			5.2.1.1 Equipment and instruments required for field measurement
			5.2.1.2 Conditions of test site
			5.2.1.3 Time schedule [22,23]
		5.2.2 Measured results of switching surges on a homogenous cable system (one minor section)
			5.2.2.1 RTE 225 kV cable and field measurement
			5.2.2.2 Validation of cable parameters
			5.2.2.3 EMT simulation of field tests on a minor section
		5.2.3 Measured results of switching surges on the major section of the RET cable system
			5.2.3.1 Coaxial mode
			5.2.3.2 Inter-sheath mode
			5.2.3.3 Earth-return mode (sheaths grounded)
		5.2.4 Summary
	5.3 Switching surges on underground cables using extended and classical TL approaches
		5.3.1 Energization of propagation modes
			5.3.1.1 Coaxial mode
			5.3.1.2 Inter-sheath mode
			5.3.1.3 Earth-return mode
		5.3.2 Energization of a cross-bonded cable
			5.3.2.1 Sheath bonding methods
			5.3.2.2 Energization of a major section
			5.3.2.3 Energization of three cascaded major sections
		5.3.3 Summary
	5.4 Very fast transient (VFT) in gas-insulated substation (GIS, overhead cable)
		5.4.1 Very-fast transient (VFT)
		5.4.2 Numerical instability of EMT simulation of VFT
			5.4.2.1 Model circuit
			5.4.2.2 Propagation function and step response
			5.4.2.3 Simulation results
		5.4.3 EMT simulation of VFTs in a 500 kV GIS
			5.4.3.1 Model circuit of 500 kV GIS
			5.4.3.2 EMT simulation results and discussions
			5.4.3.3 Theoretical analysis
		5.4.4 Summary
	5.5 EMT simulation in comparison with experimental and FDTD computed results
		5.5.1 Modeling of GIS elements/components in EMT simulation
		5.5.2 Proto-type GIS
			5.5.2.1 Test circuit
			5.5.2.2 Experimental result in the test circuit
			5.5.2.3 EMT simulation result
		5.5.3 Ultra-high voltage GIS
		5.5.4 FDTD computation
			5.5.4.1 Case-A: 500 kV GIB
			5.5.4.2 Case-B: Partial discharge pulse propagation along GIB with elbow part
			5.5.4.3 Case-C: Two-conductor system involving a nonuniform line [117]
		5.5.5 Summary
	5.6 Conclusions
	Appendix A5.1 Basic formulation for theoretical analysis
		A5.1.1 Charging a cable
		A5.1.2 Discharging a cable
		A5.1.3 Leakage resistance R for cable discharge
	Appendix A5.2 Impulse generator (pulse generator)
	References
6 Transients in interconnected EHV cable network in Denmark
	6.1 Background of EHV cable network in Denmark
	6.2 Model setup
		6.2.1 Modeled area
		6.2.2 Underground cable
			6.2.2.1 Physical and electrical information
			6.2.2.2 Cable layout
			6.2.2.3 Cable route
			6.2.2.4 Modeling of auxiliary components [7]
			6.2.2.5 Effects of cable models
			6.2.2.6 Effects of cross-bonding
			6.2.2.7 Effects of span length
			6.2.2.8 Effects of armor
		6.2.3 Overhead line
			6.2.3.1 Conductor and tower configuration
			6.2.3.2 Phase configuration
			6.2.3.3 Comparison between PSCAD and ATP-EMTP [7]
		6.2.4 Models representing apparatuses in the network
			6.2.4.1 Transformers
			6.2.4.2 Shunt reactors
			6.2.4.3 Surge arresters
			6.2.4.4 Generators
			6.2.4.5 Loads
	6.3 Temporary overvoltage
		6.3.1 Series resonance overvoltage
			6.3.1.1 Most severe scenario
			6.3.1.2 Dominant frequency in energization overvoltage
			6.3.1.3 Natural frequency of series resonance circuit
			6.3.1.4 Simulation results of series resonance overvoltage
		6.3.2 Parallel resonance overvoltage
			6.3.2.1 Most severe scenario
			6.3.2.2 Natural frequency of parallel resonance circuit
			6.3.2.3 Simulation results of parallel resonance overvoltage
		6.3.3 Overvoltage caused by system islanding
			6.3.3.1 Study conditions
			6.3.3.2 Simulation results of overvoltage caused by system islanding 6.3.3.3 ASV 400 kV bus fault
			6.3.3.4 KYV 400 kV bus fault
			6.3.3.5 TOR 400 kV bus fault
	6.4 Ground fault and fault clearing over-voltages
		6.4.1.1 Study conditions and parameters
		6.4.1.2 Results of the analysis
		6.4.1.3 Results with the sequential switching
	6.5 Conclusions
	References
7 Steady-state and transient behavior of hybrid overhead line-underground cable networks in the Netherlands
	7.1 Background of EHV hybrid OHL-cable networks in the Netherlands
	7.2 Approach and modeling
		7.2.1 Spaak project
			7.2.1.1 Mixed-line configuration
			7.2.1.2 Shunt reactors location
			7.2.1.3 Alternative mixed-line configurations
			7.2.1.4 Cable scenarios
		7.2.2 Grid modeling
			7.2.2.1 Grid model for steady-state studies
			7.2.2.2 Grid model for transient studies
	7.3 Shunt compensation allocation in hybrid OHL-cable systems
		7.3.1 Cable capacitive behavior
		7.3.2 Negative effects of cable reactive power
		7.3.3 Reactive power compensation
		7.3.4 Simulation results
			7.3.4.1 Sizing criteria
			7.3.4.2 Load-flow scenarios
			7.3.4.3 Global compensation
			7.3.4.4 Most decisive sizing criterion
			7.3.4.5 Distributed compensation
			7.3.4.6 Impact of mixed-line configuration
		7.3.5 Cable overloading
	7.4 Resonance behavior of hybrid OHL-cable systems
		7.4.1 Resonance in electrical circuits
		7.4.2 Typical grid topologies leading to resonance in cable systems
			7.4.2.1 Series resonance topologies
			7.4.2.2 Parallel resonance topologies
		7.4.3 Resonance behavior of the Dutch 380 kV grid with the Spaak connection
			7.4.3.1 Parameter selection
			7.4.3.2 Evaluation criteria
			7.4.3.3 Impact of the Spaak connection
			7.4.3.4 Impact of shunt compensation
			7.4.3.5 Impact of shunt compensation location
			7.4.3.6 Impact of mixed-line configuration
	7.5 Energization overvoltages in hybrid OHL-cable systems
		7.5.1 Simulation considerations
		7.5.2 Energization overvoltages
		7.5.3 Statistical analysis of overvoltages
			7.5.3.1 Statistical behavior of circuit breaker
			7.5.3.2 Statistical simulation approach
			7.5.3.3 Simulation results and analysis
		7.5.4 Discussions
	7.6 De-energization transients of hybrid OHL-cable systems
		7.6.1 Capacitive current interruption
		7.6.2 De-energization transients of the Spaak connection
			7.6.2.1 Switching off both the circuit and shunt reactors
			7.6.2.2 Switching-off the circuit
	7.7 Zero-missing phenomenon in cable systems
		7.7.1 Zero-missing phenomenon
		7.7.2 Operation criteria
		7.7.3 Countermeasures
		7.7.4 Simulation results
			7.7.4.1 Simultaneous cable and reactors energization at the voltage peak
			7.7.4.2 Energization in sequence
			7.7.4.3 Sequential switching
			7.7.4.4 Opening faulty phase(s)
			7.7.4.5 Increasing DC-offset damping
		7.7.5 Discussions
	7.8 Conclusions
	References
8 Conclusions
	8.1 Chapter 2: Series impedance and shunt admittance
		8.1.1 Section 2.1: Formulation of series impedance and shunt admittance
		8.1.2 Section 2.2: Review of existing formulas of earthreturn impedance and admittance
		8.1.3 Section 2.3: Accurate and approximate earth-return impedance formulas for overhead cable (line) and Section 2.4: Accurate
		8.1.4 Section 2.5: Accurate and approximate earth-return
impedance formulas for underground cable and
Section 2.6: Accurate and approximate earth-return
admittance formulas for underground cable
		8.1.5 Section 2.7: Derivation of the modified earth-return Green function for MoM-SO technique
		8.1.6 Section 2.8: Comparison of calculated impedance and admittance by different methods
		8.1.7 Section 2.9: Impedance and admittance at f = 0 for HVDC line
	8.2 Chapter 3: Modeling of cables
		8.2.1 Section 3.1: Transmission line models in EMT-type simulation tools
		8.2.2 Section 3.2: Modeling of frequency-dependent soil parameters
		8.2.3 Section 3.3: Various cable installation
		8.2.4 Section 3.4: Cable bonding
		8.2.5 Section 3.5: Numerical electromagnetic analysis
	8.3 Chapter 4: Wave propagation characteristics of overhead and underground cables
	8.4 Chapter 5: Steady-state and transient characteristics on three-phase cables
		8.4.1 Section 5.1: Cable discharge
		8.4.2 Section 5.2: Field measurement of cable transients and EMT simulation
		8.4.3 Section 5.3: Switching surges on underground cables using extended and classical TL approaches
		8.4.4 Section 5.4: Very fast transient (VFT) in gas-insulated substation (GIS, overhead cable)
		8.4.5 Section 5.5: EMT simulation in comparison with experimental and FDTD computed results
	8.5 Chapter 6: Transients in the interconnected EHV cable network in Denmark
		8.5.1 Section 6.1: Background of EHV cable network in Denmark
		8.5.2 Section 6.2: Model setup
		8.5.3 Section 6.3: Temporary overvoltage
		8.5.4 Section 6.4: Ground fault and fault clearing over-voltages
	8.6 Chapter 7: Steady-state and transient behavior of hybrid overhead line-underground cable networks in the Netherlands
		8.6.1 Section 7.1: Background of EHV hybrid OHL-cable networks in the Netherlands
		8.6.2 Section 7.2: Grid modeling
		8.6.3 Section 7.3: Shunt compensation allocation in Hybrid OHL-cable systems
		8.6.4 Section 7.4: Resonance behavior of hybrid OHL-cable systems
		8.6.5 Section 7.5: Energization overvoltages in hybrid OHL-cable systems
		8.6.6 Section 7.6: De-energization transients of hybrid OHL-cable systems
		8.6.7 Section 7.7: Zero-missing phenomenon in cable systems
Index
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