## Modelling of long High Voltage AC Cables in the Transmission System

Research output: Research › Ph.D. thesis

### Abstract

The research documented in this thesis addresses Modelling of long High Voltage AC cables in Transmission Systems. Modelling techniques of HV AC cables has been a subject to researchers as early as in the 1920’ies and research in the field continues steadily as cables become more complicated in design and more popular at higher voltage levels and for longer transmission lengths.

In recent years, the interest towards using underground cables in power transmission has increased considerably. In Denmark, the entire 150 kV and 132 kV transmission network shall be undergrounded during the next 20 years. Even 400 kV transmission lines will be undergrounded gradually as more experience is gathered. Precise modelling of long and many (meshed) underground cable lines is therefore essential and it is important that differences between simulations and measurements are identified, studied and eliminated. A study of the cable model accuracy for transmission line modelling is the topic of the research documented in this thesis. The main part of the work is split in two. Firstly planning, performing and analysing high frequency field measurements for model validation. Secondly improvements to the existing cable models.

Before the two main parts are discussed, transmission cables are described; their physical layout and mathematical representation. Relevant literature study on modelling transmission cables by introducing existing models and explaining how to model in the software used in this thesis, EMTDC/PSCAD is provided.

A typical HV AC underground power cable is formed by 4 main layers, namely; Conductor-Insulation-Screen-Insulation. In addition to these main layers, the cable also has semiconductive screens, swelling tapes and metal foil. For high frequency modelling in EMT-based software, each of these layers must be correctly represented. Description of how to perform such simulations is therefore given in the thesis.

The first main part of the work is the field measurements. The usual practice for validating a cable model has been to compare the simulation results to frequency domain calculations transformed to the time domain by use of Inverse Fast Fourier Transform (IFFT). This however, does not ensure the accuracy of the entry parameters of the modelling procedure, the parameter conversion and the modelling assumptions. Therefore, in order to analyse how cables behave field tests are performed. The purpose of the field measurements is to analyse the cable model, investigate the accuracy of the model, identify origin of disagreement between measurement and simulation results and validate the improved simulations when identified origin of disagreement has been eliminated by more accurate modelling.

Before starting any field tests, the measurement preparation is of great importance. All field measurements are therefore planned with simulations based on manufacturer cable data. Such preparation is performed both in order to plan where and what to measure and more importantly, to have a base for comparison at the measuring site.

Measurements are performed on a 400 kV 7.6 km long cable, which is a part of a hybrid OHL/cable transmission line. The cables are laid in flat formation and have been in operation for several years. For performing the measurements, the cables are disconnected from the OHL, and a single cable is energised with a fast front impulse generator. The field measurements are compared to simulations using the Frequency dependent Phase Model in EMTDC/PSCAD (this is based on the Universal Line Model). From the comparison it is observed how a deviation between field measurements and simulations appears after some time and by modal analysis it is possible to identify the source of deviation. Based on this analysis it is suggested that the existing simulation model, is precise and accurate for short cables or cables with no crossbonding points. In order to verify this, field measurements on a 150 kV 1.78 km long cable are performed. This cable is laid in a tight trefoil configuration and field measurements are performed under construction of the cable line. The suggestion of the existing model being accurate for non-crossbonded cables is verified, by excitation of exclusively the coaxial mode, which will dominate when no crossbondings are present. The identified source of deviation is also validated and suggestions for improvements of the cable model are given.

In order to validate the suggested improvements, after implementation, field measurements on longer parts of the 150 kV cable line are performed. Field measurements on a single major section, containing 2 crossbonding points, are performed as well as on a 55 km long part of the cable, having 33 crossbonding points. Comparison of field measurement and simulation results show deviation appearing after some time. From analysing the modal currents, the source of deviation is identified.

The same phenomena and source for deviation between field measurements and simulation results is identified for a 400 kV flat formation crossbonded 7.6 km cable line, a 150 kV tight trefoil crossbonded 2.5 km cable line and 150 kV tight trefoil crossbonded 55 km cable line. The source of the deviation is validated by explicitly exciting the intersheath mode of a 150 kV tight trefoil formation non crossbonded 1.78 km cable line.

The main conclusions in the first part of the thesis are:

♦ The existing cable model is precise and accurate for short cables or cables with no crossbonding points.

♦ There is deviation between simulation and field measurement results on long cables. The existing cable model is not of acceptable accuracy for crossbonded cable lines.

♦ Inaccurate modelling of the cable screen is the reason for deviation between simulation and field measurement results. This is because of intersheath mode reflecting from the crossbonding points.

The second main part of the work deals with improving the cable model based on the findings from analysis of the field measurements. The existing EMT-based models have the configuration for cables: conductor-insulation (with or without SC layers)-conductor-insulation(-conductor-insulation), whereas a transmission line single core XLPE cable will normally have the configuration: conductor-SC layerinsulation-SC layer-conductor-SC layer-conductor-insulation. Furthermore the existing cable models use analytical equations to calculate the series impedances and shunt admittances of the cable line. These analytical equations include skin effect, whereas they do not include proximity effect.

The cable model is firstly improved in such a way, that the correct physical layout of the screen (wired conductor-SC layer-solid hollow conductor) is implemented in the model. These improvements result in a more correct series impedance and hence a more correct damping of the simulations. Even though

the series impedance is more correct, it does still not include the proximity effect and high frequency oscillations are not correctly damped in the simulations. At higher frequencies the proximity effect will force the current to be more constrained to smaller regions, resulting in a change in the impedance of the conductor. Therefore the cable model is secondly improved in such a way, that the impedance matrix is no longer calculated from the analytical equations but from a finite element method including the proximity effect.

A MATLAB program is constructed in order to calculate the impedance matrix based on the finite element method. Furthermore, this MATLAB program also includes the correct physical layout of the cable screen. The modelling procedure is then changed so that the existing model will no longer use analytical equations, but call the series impedance matrix from the output of the MATLAB program. The shunt admittance matrix is still calculated inside the existing model with analytical equations and calculations of the cable’s terminal conditions is performed as before, where the difference lies in the new series impedance matrix. By including the proximity effect, the impedance matrix will change at higher frequencies, resulting in more correct damping. By combining both the correct physical layout of the screen and the proximity effect, the damping of the simulation results becomes correct and the simulated signals become identical to field measurement results.

The main conclusions in the second part of the thesis are:

♦ By improving the cable model with respect to correct physical layout of the screen, a correct damping will appear in the simulation results.

♦ The correct physical layout of the cable screen does not eliminate high frequency oscillations that appear.

♦ By including the proximity effect in the model, the impedance will change at high frequencies resulting in accurate damping of the high frequency oscillations.

♦ By combining the proximity effect and the correct physical layout of the screen, the simulation results agree with field measurement results within the tolerance of the field measurements. This is the case for a non-crossbonded cable where the intersheath mode is explicitly excited, for a 2.5 km cable with two crossbonding points and for a 55 km long cable line with 33 crossbonding points.

In recent years, the interest towards using underground cables in power transmission has increased considerably. In Denmark, the entire 150 kV and 132 kV transmission network shall be undergrounded during the next 20 years. Even 400 kV transmission lines will be undergrounded gradually as more experience is gathered. Precise modelling of long and many (meshed) underground cable lines is therefore essential and it is important that differences between simulations and measurements are identified, studied and eliminated. A study of the cable model accuracy for transmission line modelling is the topic of the research documented in this thesis. The main part of the work is split in two. Firstly planning, performing and analysing high frequency field measurements for model validation. Secondly improvements to the existing cable models.

Before the two main parts are discussed, transmission cables are described; their physical layout and mathematical representation. Relevant literature study on modelling transmission cables by introducing existing models and explaining how to model in the software used in this thesis, EMTDC/PSCAD is provided.

A typical HV AC underground power cable is formed by 4 main layers, namely; Conductor-Insulation-Screen-Insulation. In addition to these main layers, the cable also has semiconductive screens, swelling tapes and metal foil. For high frequency modelling in EMT-based software, each of these layers must be correctly represented. Description of how to perform such simulations is therefore given in the thesis.

The first main part of the work is the field measurements. The usual practice for validating a cable model has been to compare the simulation results to frequency domain calculations transformed to the time domain by use of Inverse Fast Fourier Transform (IFFT). This however, does not ensure the accuracy of the entry parameters of the modelling procedure, the parameter conversion and the modelling assumptions. Therefore, in order to analyse how cables behave field tests are performed. The purpose of the field measurements is to analyse the cable model, investigate the accuracy of the model, identify origin of disagreement between measurement and simulation results and validate the improved simulations when identified origin of disagreement has been eliminated by more accurate modelling.

Before starting any field tests, the measurement preparation is of great importance. All field measurements are therefore planned with simulations based on manufacturer cable data. Such preparation is performed both in order to plan where and what to measure and more importantly, to have a base for comparison at the measuring site.

Measurements are performed on a 400 kV 7.6 km long cable, which is a part of a hybrid OHL/cable transmission line. The cables are laid in flat formation and have been in operation for several years. For performing the measurements, the cables are disconnected from the OHL, and a single cable is energised with a fast front impulse generator. The field measurements are compared to simulations using the Frequency dependent Phase Model in EMTDC/PSCAD (this is based on the Universal Line Model). From the comparison it is observed how a deviation between field measurements and simulations appears after some time and by modal analysis it is possible to identify the source of deviation. Based on this analysis it is suggested that the existing simulation model, is precise and accurate for short cables or cables with no crossbonding points. In order to verify this, field measurements on a 150 kV 1.78 km long cable are performed. This cable is laid in a tight trefoil configuration and field measurements are performed under construction of the cable line. The suggestion of the existing model being accurate for non-crossbonded cables is verified, by excitation of exclusively the coaxial mode, which will dominate when no crossbondings are present. The identified source of deviation is also validated and suggestions for improvements of the cable model are given.

In order to validate the suggested improvements, after implementation, field measurements on longer parts of the 150 kV cable line are performed. Field measurements on a single major section, containing 2 crossbonding points, are performed as well as on a 55 km long part of the cable, having 33 crossbonding points. Comparison of field measurement and simulation results show deviation appearing after some time. From analysing the modal currents, the source of deviation is identified.

The same phenomena and source for deviation between field measurements and simulation results is identified for a 400 kV flat formation crossbonded 7.6 km cable line, a 150 kV tight trefoil crossbonded 2.5 km cable line and 150 kV tight trefoil crossbonded 55 km cable line. The source of the deviation is validated by explicitly exciting the intersheath mode of a 150 kV tight trefoil formation non crossbonded 1.78 km cable line.

The main conclusions in the first part of the thesis are:

♦ The existing cable model is precise and accurate for short cables or cables with no crossbonding points.

♦ There is deviation between simulation and field measurement results on long cables. The existing cable model is not of acceptable accuracy for crossbonded cable lines.

♦ Inaccurate modelling of the cable screen is the reason for deviation between simulation and field measurement results. This is because of intersheath mode reflecting from the crossbonding points.

The second main part of the work deals with improving the cable model based on the findings from analysis of the field measurements. The existing EMT-based models have the configuration for cables: conductor-insulation (with or without SC layers)-conductor-insulation(-conductor-insulation), whereas a transmission line single core XLPE cable will normally have the configuration: conductor-SC layerinsulation-SC layer-conductor-SC layer-conductor-insulation. Furthermore the existing cable models use analytical equations to calculate the series impedances and shunt admittances of the cable line. These analytical equations include skin effect, whereas they do not include proximity effect.

The cable model is firstly improved in such a way, that the correct physical layout of the screen (wired conductor-SC layer-solid hollow conductor) is implemented in the model. These improvements result in a more correct series impedance and hence a more correct damping of the simulations. Even though

the series impedance is more correct, it does still not include the proximity effect and high frequency oscillations are not correctly damped in the simulations. At higher frequencies the proximity effect will force the current to be more constrained to smaller regions, resulting in a change in the impedance of the conductor. Therefore the cable model is secondly improved in such a way, that the impedance matrix is no longer calculated from the analytical equations but from a finite element method including the proximity effect.

A MATLAB program is constructed in order to calculate the impedance matrix based on the finite element method. Furthermore, this MATLAB program also includes the correct physical layout of the cable screen. The modelling procedure is then changed so that the existing model will no longer use analytical equations, but call the series impedance matrix from the output of the MATLAB program. The shunt admittance matrix is still calculated inside the existing model with analytical equations and calculations of the cable’s terminal conditions is performed as before, where the difference lies in the new series impedance matrix. By including the proximity effect, the impedance matrix will change at higher frequencies, resulting in more correct damping. By combining both the correct physical layout of the screen and the proximity effect, the damping of the simulation results becomes correct and the simulated signals become identical to field measurement results.

The main conclusions in the second part of the thesis are:

♦ By improving the cable model with respect to correct physical layout of the screen, a correct damping will appear in the simulation results.

♦ The correct physical layout of the cable screen does not eliminate high frequency oscillations that appear.

♦ By including the proximity effect in the model, the impedance will change at high frequencies resulting in accurate damping of the high frequency oscillations.

♦ By combining the proximity effect and the correct physical layout of the screen, the simulation results agree with field measurement results within the tolerance of the field measurements. This is the case for a non-crossbonded cable where the intersheath mode is explicitly excited, for a 2.5 km cable with two crossbonding points and for a 55 km long cable line with 33 crossbonding points.

### Details

The research documented in this thesis addresses Modelling of long High Voltage AC cables in Transmission Systems. Modelling techniques of HV AC cables has been a subject to researchers as early as in the 1920’ies and research in the field continues steadily as cables become more complicated in design and more popular at higher voltage levels and for longer transmission lengths.

In recent years, the interest towards using underground cables in power transmission has increased considerably. In Denmark, the entire 150 kV and 132 kV transmission network shall be undergrounded during the next 20 years. Even 400 kV transmission lines will be undergrounded gradually as more experience is gathered. Precise modelling of long and many (meshed) underground cable lines is therefore essential and it is important that differences between simulations and measurements are identified, studied and eliminated. A study of the cable model accuracy for transmission line modelling is the topic of the research documented in this thesis. The main part of the work is split in two. Firstly planning, performing and analysing high frequency field measurements for model validation. Secondly improvements to the existing cable models.

Before the two main parts are discussed, transmission cables are described; their physical layout and mathematical representation. Relevant literature study on modelling transmission cables by introducing existing models and explaining how to model in the software used in this thesis, EMTDC/PSCAD is provided.

A typical HV AC underground power cable is formed by 4 main layers, namely; Conductor-Insulation-Screen-Insulation. In addition to these main layers, the cable also has semiconductive screens, swelling tapes and metal foil. For high frequency modelling in EMT-based software, each of these layers must be correctly represented. Description of how to perform such simulations is therefore given in the thesis.

The first main part of the work is the field measurements. The usual practice for validating a cable model has been to compare the simulation results to frequency domain calculations transformed to the time domain by use of Inverse Fast Fourier Transform (IFFT). This however, does not ensure the accuracy of the entry parameters of the modelling procedure, the parameter conversion and the modelling assumptions. Therefore, in order to analyse how cables behave field tests are performed. The purpose of the field measurements is to analyse the cable model, investigate the accuracy of the model, identify origin of disagreement between measurement and simulation results and validate the improved simulations when identified origin of disagreement has been eliminated by more accurate modelling.

Before starting any field tests, the measurement preparation is of great importance. All field measurements are therefore planned with simulations based on manufacturer cable data. Such preparation is performed both in order to plan where and what to measure and more importantly, to have a base for comparison at the measuring site.

Measurements are performed on a 400 kV 7.6 km long cable, which is a part of a hybrid OHL/cable transmission line. The cables are laid in flat formation and have been in operation for several years. For performing the measurements, the cables are disconnected from the OHL, and a single cable is energised with a fast front impulse generator. The field measurements are compared to simulations using the Frequency dependent Phase Model in EMTDC/PSCAD (this is based on the Universal Line Model). From the comparison it is observed how a deviation between field measurements and simulations appears after some time and by modal analysis it is possible to identify the source of deviation. Based on this analysis it is suggested that the existing simulation model, is precise and accurate for short cables or cables with no crossbonding points. In order to verify this, field measurements on a 150 kV 1.78 km long cable are performed. This cable is laid in a tight trefoil configuration and field measurements are performed under construction of the cable line. The suggestion of the existing model being accurate for non-crossbonded cables is verified, by excitation of exclusively the coaxial mode, which will dominate when no crossbondings are present. The identified source of deviation is also validated and suggestions for improvements of the cable model are given.

In order to validate the suggested improvements, after implementation, field measurements on longer parts of the 150 kV cable line are performed. Field measurements on a single major section, containing 2 crossbonding points, are performed as well as on a 55 km long part of the cable, having 33 crossbonding points. Comparison of field measurement and simulation results show deviation appearing after some time. From analysing the modal currents, the source of deviation is identified.

The same phenomena and source for deviation between field measurements and simulation results is identified for a 400 kV flat formation crossbonded 7.6 km cable line, a 150 kV tight trefoil crossbonded 2.5 km cable line and 150 kV tight trefoil crossbonded 55 km cable line. The source of the deviation is validated by explicitly exciting the intersheath mode of a 150 kV tight trefoil formation non crossbonded 1.78 km cable line.

The main conclusions in the first part of the thesis are:

♦ The existing cable model is precise and accurate for short cables or cables with no crossbonding points.

♦ There is deviation between simulation and field measurement results on long cables. The existing cable model is not of acceptable accuracy for crossbonded cable lines.

♦ Inaccurate modelling of the cable screen is the reason for deviation between simulation and field measurement results. This is because of intersheath mode reflecting from the crossbonding points.

The second main part of the work deals with improving the cable model based on the findings from analysis of the field measurements. The existing EMT-based models have the configuration for cables: conductor-insulation (with or without SC layers)-conductor-insulation(-conductor-insulation), whereas a transmission line single core XLPE cable will normally have the configuration: conductor-SC layerinsulation-SC layer-conductor-SC layer-conductor-insulation. Furthermore the existing cable models use analytical equations to calculate the series impedances and shunt admittances of the cable line. These analytical equations include skin effect, whereas they do not include proximity effect.

The cable model is firstly improved in such a way, that the correct physical layout of the screen (wired conductor-SC layer-solid hollow conductor) is implemented in the model. These improvements result in a more correct series impedance and hence a more correct damping of the simulations. Even though

the series impedance is more correct, it does still not include the proximity effect and high frequency oscillations are not correctly damped in the simulations. At higher frequencies the proximity effect will force the current to be more constrained to smaller regions, resulting in a change in the impedance of the conductor. Therefore the cable model is secondly improved in such a way, that the impedance matrix is no longer calculated from the analytical equations but from a finite element method including the proximity effect.

A MATLAB program is constructed in order to calculate the impedance matrix based on the finite element method. Furthermore, this MATLAB program also includes the correct physical layout of the cable screen. The modelling procedure is then changed so that the existing model will no longer use analytical equations, but call the series impedance matrix from the output of the MATLAB program. The shunt admittance matrix is still calculated inside the existing model with analytical equations and calculations of the cable’s terminal conditions is performed as before, where the difference lies in the new series impedance matrix. By including the proximity effect, the impedance matrix will change at higher frequencies, resulting in more correct damping. By combining both the correct physical layout of the screen and the proximity effect, the damping of the simulation results becomes correct and the simulated signals become identical to field measurement results.

The main conclusions in the second part of the thesis are:

♦ By improving the cable model with respect to correct physical layout of the screen, a correct damping will appear in the simulation results.

♦ The correct physical layout of the cable screen does not eliminate high frequency oscillations that appear.

♦ By including the proximity effect in the model, the impedance will change at high frequencies resulting in accurate damping of the high frequency oscillations.

♦ By combining the proximity effect and the correct physical layout of the screen, the simulation results agree with field measurement results within the tolerance of the field measurements. This is the case for a non-crossbonded cable where the intersheath mode is explicitly excited, for a 2.5 km cable with two crossbonding points and for a 55 km long cable line with 33 crossbonding points.

In recent years, the interest towards using underground cables in power transmission has increased considerably. In Denmark, the entire 150 kV and 132 kV transmission network shall be undergrounded during the next 20 years. Even 400 kV transmission lines will be undergrounded gradually as more experience is gathered. Precise modelling of long and many (meshed) underground cable lines is therefore essential and it is important that differences between simulations and measurements are identified, studied and eliminated. A study of the cable model accuracy for transmission line modelling is the topic of the research documented in this thesis. The main part of the work is split in two. Firstly planning, performing and analysing high frequency field measurements for model validation. Secondly improvements to the existing cable models.

Before the two main parts are discussed, transmission cables are described; their physical layout and mathematical representation. Relevant literature study on modelling transmission cables by introducing existing models and explaining how to model in the software used in this thesis, EMTDC/PSCAD is provided.

A typical HV AC underground power cable is formed by 4 main layers, namely; Conductor-Insulation-Screen-Insulation. In addition to these main layers, the cable also has semiconductive screens, swelling tapes and metal foil. For high frequency modelling in EMT-based software, each of these layers must be correctly represented. Description of how to perform such simulations is therefore given in the thesis.

The first main part of the work is the field measurements. The usual practice for validating a cable model has been to compare the simulation results to frequency domain calculations transformed to the time domain by use of Inverse Fast Fourier Transform (IFFT). This however, does not ensure the accuracy of the entry parameters of the modelling procedure, the parameter conversion and the modelling assumptions. Therefore, in order to analyse how cables behave field tests are performed. The purpose of the field measurements is to analyse the cable model, investigate the accuracy of the model, identify origin of disagreement between measurement and simulation results and validate the improved simulations when identified origin of disagreement has been eliminated by more accurate modelling.

Before starting any field tests, the measurement preparation is of great importance. All field measurements are therefore planned with simulations based on manufacturer cable data. Such preparation is performed both in order to plan where and what to measure and more importantly, to have a base for comparison at the measuring site.

Measurements are performed on a 400 kV 7.6 km long cable, which is a part of a hybrid OHL/cable transmission line. The cables are laid in flat formation and have been in operation for several years. For performing the measurements, the cables are disconnected from the OHL, and a single cable is energised with a fast front impulse generator. The field measurements are compared to simulations using the Frequency dependent Phase Model in EMTDC/PSCAD (this is based on the Universal Line Model). From the comparison it is observed how a deviation between field measurements and simulations appears after some time and by modal analysis it is possible to identify the source of deviation. Based on this analysis it is suggested that the existing simulation model, is precise and accurate for short cables or cables with no crossbonding points. In order to verify this, field measurements on a 150 kV 1.78 km long cable are performed. This cable is laid in a tight trefoil configuration and field measurements are performed under construction of the cable line. The suggestion of the existing model being accurate for non-crossbonded cables is verified, by excitation of exclusively the coaxial mode, which will dominate when no crossbondings are present. The identified source of deviation is also validated and suggestions for improvements of the cable model are given.

In order to validate the suggested improvements, after implementation, field measurements on longer parts of the 150 kV cable line are performed. Field measurements on a single major section, containing 2 crossbonding points, are performed as well as on a 55 km long part of the cable, having 33 crossbonding points. Comparison of field measurement and simulation results show deviation appearing after some time. From analysing the modal currents, the source of deviation is identified.

The same phenomena and source for deviation between field measurements and simulation results is identified for a 400 kV flat formation crossbonded 7.6 km cable line, a 150 kV tight trefoil crossbonded 2.5 km cable line and 150 kV tight trefoil crossbonded 55 km cable line. The source of the deviation is validated by explicitly exciting the intersheath mode of a 150 kV tight trefoil formation non crossbonded 1.78 km cable line.

The main conclusions in the first part of the thesis are:

♦ The existing cable model is precise and accurate for short cables or cables with no crossbonding points.

♦ There is deviation between simulation and field measurement results on long cables. The existing cable model is not of acceptable accuracy for crossbonded cable lines.

♦ Inaccurate modelling of the cable screen is the reason for deviation between simulation and field measurement results. This is because of intersheath mode reflecting from the crossbonding points.

The second main part of the work deals with improving the cable model based on the findings from analysis of the field measurements. The existing EMT-based models have the configuration for cables: conductor-insulation (with or without SC layers)-conductor-insulation(-conductor-insulation), whereas a transmission line single core XLPE cable will normally have the configuration: conductor-SC layerinsulation-SC layer-conductor-SC layer-conductor-insulation. Furthermore the existing cable models use analytical equations to calculate the series impedances and shunt admittances of the cable line. These analytical equations include skin effect, whereas they do not include proximity effect.

The cable model is firstly improved in such a way, that the correct physical layout of the screen (wired conductor-SC layer-solid hollow conductor) is implemented in the model. These improvements result in a more correct series impedance and hence a more correct damping of the simulations. Even though

the series impedance is more correct, it does still not include the proximity effect and high frequency oscillations are not correctly damped in the simulations. At higher frequencies the proximity effect will force the current to be more constrained to smaller regions, resulting in a change in the impedance of the conductor. Therefore the cable model is secondly improved in such a way, that the impedance matrix is no longer calculated from the analytical equations but from a finite element method including the proximity effect.

A MATLAB program is constructed in order to calculate the impedance matrix based on the finite element method. Furthermore, this MATLAB program also includes the correct physical layout of the cable screen. The modelling procedure is then changed so that the existing model will no longer use analytical equations, but call the series impedance matrix from the output of the MATLAB program. The shunt admittance matrix is still calculated inside the existing model with analytical equations and calculations of the cable’s terminal conditions is performed as before, where the difference lies in the new series impedance matrix. By including the proximity effect, the impedance matrix will change at higher frequencies, resulting in more correct damping. By combining both the correct physical layout of the screen and the proximity effect, the damping of the simulation results becomes correct and the simulated signals become identical to field measurement results.

The main conclusions in the second part of the thesis are:

♦ By improving the cable model with respect to correct physical layout of the screen, a correct damping will appear in the simulation results.

♦ The correct physical layout of the cable screen does not eliminate high frequency oscillations that appear.

♦ By including the proximity effect in the model, the impedance will change at high frequencies resulting in accurate damping of the high frequency oscillations.

♦ By combining the proximity effect and the correct physical layout of the screen, the simulation results agree with field measurement results within the tolerance of the field measurements. This is the case for a non-crossbonded cable where the intersheath mode is explicitly excited, for a 2.5 km cable with two crossbonding points and for a 55 km long cable line with 33 crossbonding points.

Original language | English |
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Publisher | Department of Energy Technology, Aalborg University |
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Number of pages | 206 |

ISBN (Print) | 978-87-90707-73-6 |

State | Published - May 2010 |

Publication category | Research |

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