This paper describes the implementation of a full frequency-dependent model for transmission lines and cables in a state-space-based solver for electromagnetic transients. This implementation is for real-time simulation of power system switching transients. It is based on the wideband universal line model with modifications being incorporated to meet the computational speed requirements of real-time applications. The real-time performance of the implementation is demonstrated through application examples.

A Wideband Line/Cable Model for Real-Time Simulations of Power System Transients

A transmission grid is normally laid out as an almost pure overhead line (OHL) network. The introduction of transmission voltage level XLPE cables and the increasing interest in the environmental impact of OHL has resulted in an increasing interest in the use of underground cables on transmission level. In Denmark for instance, the entire 150 kV, 132 kV and 220 kV and parts of the 400 kV transmission network will be placed underground before 2030. To reduce the operating losses of a cable-based transmission system, crossbonding schemes are normally used. The use of crossbonding introduces new difficulties for the fault locator systems currently in use and such can therefore not be applied directly. In this thesis, the analysis and development of a fault locator system capable of locating faults with high accuracy on crossbonded cables and hybrid lines is presented. The thesis is divided into five parts; The preliminaries, a part which deals with the use of impedance-based fault location methods on crossbonded cables, a part which deals with travelling wave-based fault location, a part listing the conclusions and contributions of the thesis and an appendix. A state-of-the-art analysis is conducted on the use of both impedanceand travelling wavebased fault location methods, and it is found in both cases that the research field is not covered in detail. Therefore, the use of both fault location methods is examined in detail. It is found that an impedance-based method is difficult to implement in practice due to the electrical behaviour of the crossbonded cable system under fault conditions. The fault loop impedance appears as being discontinuous at the crossbondings. These discontinuities dominate the fault loop impedance for shorter cables and the result is large errors if the reactive part is used directly to determine the distance to fault. The discontinuities make the utilisation of an analytical methods difficult, as fault location methods in general expect a homogenous series impedance matrix for the entire cable run. An analysis of the influencing parameters is carried out and it is found that the fault loop impedance is almost independent on the grounding resistances in the field at the ends of each major section and on the grounding resistance at the substations. This is because little current returns to the source in the ground and the fault loop impedance is therefore mostly dependent on parameters describing the cable itself. The use of an impedance-based method for fault location on hybrid lines is examined. The very different fault impedances of the overhead lines and cable systems make a practical implementation of the fault locator difficult. Small deviations in the parameters of the OHL will result in large errors for fault location in the cable section. Field measurements showing the effect of short circuits on crossbonded systems conducted on parts of the electrical connection to the Anholt offshore wind farm are performed. The purpose is to examine whether neural networks can be trained using data from state-of-theart cable models to predict and estimate the fault location on crossbonded cables. Numerous measurements of different short circuits are carried out and it is concluded that the state-ofthe-art models predict general behaviour of the crossbonded system under fault conditions well, but the accuracy of the calculated impedance is low for fault location purposes. The neural networks can therefore not be trained and no impedance-based fault location method can be used for crossbonded cables or hybrid lines. The use of travelling wave-based methods is examined for crossbonded cables. It is found that the two-terminal method can be used to estimate the location of faults with high accuracy. The single-terminal method cannot be used on longer crossbonded cables due to the numerous reflections created at the crossbonding. Core voltages, core currents and sheath currents can be used as input to the fault locator system where the core and sheath current signals become more advantageous to use as the number of additional lines connected to the same substation as the monitored cable is increased. The fault signals can be analysed directly in the time domain wherefore a transformation method is not a necessity. The parameters influencing the two-terminal travelling wave method are examined and it is found that the method can be used on long cables and that the method is independent of most system parameters as fault inception angle and fault resistance. The travelling wave method can be used to locate faults on hybrid lines of any type. A method designed for DC-lines is re-designed making it applicable for hybrid lines comprised by crossbonded cables and OHLs or cables of different types. Travelling wave-based field measurements are conducted on the Anholt connection to verify the proposed method. Faults, at reduced a voltage are artificially applied in the cable system and the transient response is measured at two terminals at the cable’s ends. The measurements are time-synchronised and it is found that a very accurate estimation of the fault location can be obtained using the method proposed. Methods for measuring the coaxial wave velocity are identified and the coaxial wave velocity on the Anholt cable is determined using these methods. It is verified that a constant coaxial wave velocity (frequency independent) can be used as an input parameter to the fault locator system and the coaxial attenuation predicted by current cable models agrees with results obtained on the Anholt cable. Based on the results of the field measurements, it is concluded that: Fault location using a synchronised two-terminal method is applicable on crossbonded cables with use of the coaxial wave velocity and fault signals analysed directly in the time domain. The use of the Wavelet Transform for fault location on crossbonded cables is examined. With use of the transform’s ability to localise transients in time, very accurate fault location on shorter cable systems can be achieved (approximately less than 20 km which accounts for 75 % of all Danish cable lines). For longer cables, it was proposed to combine the use of the Wavelet Transform with a visual inspection of the time domain signals. This increased in all cases the accuracy of the fault location estimation and reduces the chance of acting on a faulted estimation by the fault locator. A fault locator system capable of locating fault with high accuracy on crossbonded cables is developed and realised in practice. The system consists of two units that must be installed at the ends of the cable the system monitors. A Wavelet based trigger system capable of triggering on all realistic fault signals is developed with the use of a signal pre-condition technique developed especially for crossbonded cables. Core voltage, core currents or sheath currents can freely be chosen as input to the fault locator units where the inputs can be different at each cable end. The fault locator system works for both pure crossbonded cables and hybrid lines. The functionality of the units are verified using both simulated and field data and is found to function as expected.

Online Location of Faults on AC Cables in Underground Transmission Systems

The universal line model is among the most accurate frequency-dependent transmission-line model available in Electromagnetic Transients Program-type simulation tools. One major drawback of this line model is that it sometimes gives unstable simulation results. The instability is related to the occurrence of close poles in the rational model of the propagation function which leads to large residue-pole ratios. In time-domain simulation, these large ratios give a magnification of the error associated with the interpolation of the reflected current wave which acts as the stimulus of the propagation function. An approach is described for avoiding the instability problem by introducing a two-segment interpolation scheme for the extraction of the current wave. The approach gives zero interpolation error when used together with the integration scheme known as recursive convolution and so error magnification becomes inconsequential. The new approach is demonstrated for pertinent examples, including one case with residue-pole ratios exceeding one million.

Avoiding Numerical Instabilities in the Universal Line Model by a Two-Segment Interpolation Scheme

This paper reviews the classical multiconductor transmission line (MTL) equations and proposes additional constraints on these equations. A fundamental physical constraint is that the voltage and current waves must be collocated and travel together with the same propagation function. Based on this condition, the Revised Multiconductor Transmission Line (RMTL) equations are proposed. As opposed to the classical MTL equations that require complex frequency-dependent transformation matrices for their diagonalization, the RMTL equations can be diagonalized very accurately using a single real constant transformation matrix. A new Frequency-Dependent Line Model (FDLM) is proposed based on the RMTL equations. FDLM is compared with the two most accepted frequency-dependent line models in the Electromagnetic Transients Program (EMTP): The JMARTI model (fdLine) that uses a constant transformation matrix as an approximation, and the phase-coordinates Universal Line Model (ULM) that fits the frequency dependence of the transformation matrices. These time-domain models are compared with a reference frequency-domain solution for a double-circuit vertical line.

/pdf/frequency-dependent-multiconductor-transmission-line-model-21bjyhxcc0.pdf

Frequency-Dependent Multiconductor Transmission Line Model With Collocated Voltage and Current Propagation

The universal line model (ULM) has been implemented in several EMT programs for simulation of electromagnetic transients. In some cases, instability problems have been encountered. This paper shows that the current approach for rational function approximation adopted in ULM can lead to large out-of-band passivity violations, thereby causing an unstable simulation. An approach is introduced which prevents the occurrence of large passivity violations. Low-frequency violations are avoided by adding an artificial shunt conductance to the diagonal elements of the shunt admittance matrix while high-frequency violations are avoided by introducing artificial attenuation using a low-pass filter. In addition, high-frequency asymptotic passivity is enforced for the characteristic admittance. Any remaining violations are removed by adding a second-order correction term to the model ports. The approach is shown to mitigate instabilities from a cable system transient simulation, without impairing the quality of the model.

Passivity Enforcement for Transmission Line Models Based on the Method of Characteristics

The universal line model (ULM) is a frequency dependent transmission-line model based on the method of characteristics in the phase domain. Although the ULM is known to produce highly accurate models for both overhead lines and underground cables, situations have been encountered where the pole identification for the propagation function fails. In this paper, we overcome the problem by basing the pole identification on trace fitting rather than mode fitting. This is achieved by introducing delayed basis functions in the vector fitting algorithm, followed by time-delay refinement and model-order reduction. In situations where the modes can be fitted without difficulty, the existing approach using modes obtained by a frequency-dependent transformation matrix remains the most accurate.

J. Nordstrom

Papers

Pole Identification for The Universal Line Model Based on Trace Fitting