MultiScale Domain Decomposition Method For Complex Geoelectric Current Field

High voltage direct current(HVDC)and geomagnetic storms will generate current field in the earth.It is very important to accurately calculate the distribution of telluric field for evaluating the influence of telluric current on AC network,buried metal oil and gas pipeline and rail transit power supply system.However,the current study on the HVDC grounding electrode current field,is difficult to take into account both the specific sizes of the grounding electrode and the earth model,in solving the geomagnetic storms induction current field,the existing size of the earth model is of small span,and can not meet the demand of current research on the impact of geomagnetic storms on large grid.In view of the above problems,the main contents and achievements of this dissertation are as follows:According to multiscale constant current field,the domain decomposition method based on finite element method is adopted,the iterative process of domain decomposition iteration by Generalized Minimal Residual Method(GMRES)is derived without directly solving coefficient matrix,and the correctness of the algorithm is verified by an example.In engineering applications,in order to more accurately solve the HVDC grounding electrode current field,domain decomposition method is adopted to solve the multiscale model including the ground electrode,the calculation results are compared with the existing literature in the domain near the electrode,it shows that taking the specific size of the grounding electrode into account will have a certain impact on the result,and more accureate results can be obtained from multiscale model.Through this example GMRES iteration is proved to be more efficient than the relaxation iteration.Domain decomposition method based on GMRES iteration is extended to the solution of multiscale time-harmonic current field.Because the magnitude of the induced current of geomagnetic storms is directly proportional to the change rate of the geomagnetic field,therefore,the time harmonic equivalent of the time-varying geomagnetic field can be carried out,with the emphasis on the interval of serious change of geomagnetic field.Domain decomposition based on Edge-based FEM is proposed.On the premise of ensuring the same distribution of the current density,the multivalue of potential function of the edge element is discussed in accordance with the uniqueness theorem of time-varying electromagnetic field.It is found that potential coupling is the cause of the multivalue.Therefore,when the potential coupling is changed to a fixed value,the potential multivalue vanishes.In view of the current research on the influence of geomagnetic storms on the AC power grid,the field-circuit combined method is generally adopted.In this dissertation,unified model of single return AC transmission line,grounding bodies and earth is built to calculate the GIC in the transmission line.By comparison,it is found that it is applicable in the general frequency range of 0.000 1 Hz-0.1 Hz of the geomagnetic storm for field-circuit combined method.On the basis of magnetotelluric interpretation results,multiscale model of North China,East China,Middle China is established.The surface electric field distribution is calculated.It shows that:because of the great difference between the resistivity of the sea water and the soil,the electric field intensity in the coastal area is generally larger than that in the inland area,the influence of geomagnetic storms on the AC power grid in coastal areas is more serious than that in inland areas.Due to the complex distribution of terrestrial resistivity,the intensity distribution of the surface electric field is also very complex.Therefore,using uniform surface electric field will produce errors in engineering.The surface electric field intensity is closely related to the resistivity of surface layer,the higher the resistivity in inland areas,the greater the electric field intensity.The correctness of the proposed method is verified by comparison with the existing literature,that provides a new algorithm for the calculation of multiscale harmonic current field.