Measurements and finite element modelling of transformer flux with dc and power frequency current

Doctoral Thesis


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Geomagnetically induced currents (GIC’s) caused by solar storms or other sources of dc excitation in the presence of ac energization can disturb the normal operation of power transformers. If large enough, they cause half-cycle saturation of a power transformer’s core which could lead to overheating due to excessive stray flux. Finite element matrix (FEM) modelling software is of considerable use in transformer engineering as it is able to solve electromagnetic fields in transformers. For many problems, typically involving only specific parts of a transformer, fairly accurate solutions can be reached quickly. Modelling the effects of GIC or leakage currents from dc systems, however, is more complex because dc components are superimposed on ac in transformers with nonlinear electrical core steel parameters. At the beginning of the investigation, FEM models of different bench-scale laboratory transformers and a 40 MVA three-phase three limb power transformer were investigated, but the results did not sufficiently represent the measurement data due to the application of widely used modelling assumptions regarding the transformer joints. Following the preliminary analyses, practical measurements and FEM simulations were carried out using three industrially made model single-phase four limb transformers (1p4L) without tanks. These test transformers resemble a real power transformer because they have high-quality grain oriented electrical core steel and parallel winding assemblies. Practical laboratory measurements recorded during ac testing were used to calibrate 2D FEM models by adding “equivalent air gaps” at the joints. The implementation of this joint detail helped to overcome the shortcomings of the preliminary FEM simulation. Analyses of the electrical and magnetic responses of the FEM models using simultaneous ac and dc then followed. A refined 3D FEM simulation with more detailed modelling of the core joints of 1p4L model transformers agreed more closely with the practical measurements of ac only no-load conditions. Further, the depiction of stray flux leaving the transformer’s saturated core under simultaneous ac and dc excitation showed an improvement in the approach as measured in the physical model. Saturation inductance (Lsat) is an important parameter for input into mid- to low-frequency lumped parameter transformer models that are used in electromagnetic transients software such as PSCAD/EMTDC, but it is not easily measured and is seldom provided by manufacturers. Some Lsat measurements on the 1p4L test transformers are presented in this thesis, along with some 3D FEM analyses. The measurements and FEM analyses investigated “air core inductance” which represents a transformer without a core, and “terminal saturation inductance” which represents deep saturation due to dc excitation. An important finding in this thesis is that “terminal saturation inductance” is the more useful of the two for topological transformer models investigating realistic GIC excitation. Further to this, a new composite depiction of half-cycle saturation with a multi-parametric relationships supported by measurement and simulation is presented. The main contribution of this thesis is that it gives more accurately the electrical response and distribution of the leakage flux under conditions such as those caused by GIC or other sources of leakage dc excitation, as well as including of joint details in the FEM models through calibration with physical models. This calibration can aid transformer modelling and design in industry for mitigation of the effects of GICs, contributing to improved transformer survival during significant geomagnetic disturbances.