Electromagnetic Transient Modelling of Grounding Structures
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- Institutt for elkraftteknikk 
Grounding is traditionally modelled as a pure resistance. This is a good approximation at low frequencies, but as the frequency gets higher, inductance starts to play an important role. To acquire accurate transient response of the system it is desirable to consider this fact. Special computer programs like CDEGS are required to analyze grounding structures, but this is not directly compatible with other programs for analysis of over-voltages and transients. The main objective of this project is to create a database containing frequency response for some common electrode types with different parameter combinations. This frequency response can be further used to create an equivalent time - domain grounding impedance that can be exported to EMTP programs.Three types of ground electrodes were analyzed in this project; earthing rod, counterpoise grounding with four radials, and horizontal ring electrode. A uniform soil model with variable values of resistivity and relative permittivity was used in all simulations. Geometrical dimensions of the electrodes were varied as well. All conductors were modelled as bare copper conductors. Parameters were determined based on the results of simulations in CDEGS and general recommendations for grounding of transmission towers given by Statnett.Unit current at different frequencies was injected into ground electrodes through a 0.1 meter long copper conductor. Ground potential rise of this conductor, which is equal to impedance to earth of the ground electrode, was extracted from HIFREQ in text format. Frequency resolution in the simulations is 10 points per decade between 0 and 0.1 MHz, 40 points between 0.1 and 1 MHz, and 80 points between 1 and 10 MHz. As a result of the project a database containing impedance and admittance as function of frequency for three types of electrodes has been created. Total number of responses stored in the database is 2268.Vector Fitting is used to convert frequency domain responses to time domain state - space models or RLC - networks. Vector fitting is a method to approximate measured or calculated frequency domain responses with a sum of rational functions. A Matlab routine interfit.m was developed to extract response of an electrode with given parameters. For parameters between the points in the database, linear interpolation is used. As a second step the function calls vector fitting that creates a time ? domain model from the frequency response of the defined ground electrode. Order of approximation in vector fitting should be adjusted for each case, starting with a low value and gradually increasing it till a sufficient approximation after passivity enforcement is achieved. Time ? domain simulations in CDEGS and ATPDraw gave similar results when order of approximation in vector fitting was chosen correctly. Negligible deviation was observed between the responses in time range between 0 and 5 µs in some cases. The results indicate that frequency - dependent models created by this method can be used in EMTP programs.