A simple equivalent circuit to represent the thermal heat flow equations for power transformers is presented. Key features are the use of a current source analogy to represent heat input due to losses, and a nonlinear resistor analogy to represent the effect of air or oil cooling convection currents. An interesting historical note concerns the fact that the foregoing effect was first quantified in 1817. It is shown that the idea of "exponential response" is not the best way to think of the dynamics of the situation. It is also shown that one can consider ambient temperature to be a variable input to the system, and that it is properly represented as an ideal voltage source. Physical experimental verification, on an in-service 250 MVA transformer, is described in a companion paper.

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The downed-wires problem, known as high impedance faults, is described. A high voltage laboratory setup was devised to investigate the phenomenon. The laboratory model results agreed with field test results, and previous research efforts. The arcing fault model was justified. The setup was used ~ as a source of fault current signal.A simple approach was taken to design an arcing fault detector. The algorithm utilizes the random behauior of the fault current. It compares the positive and negative current peaks in one cycle to those in the next cycle to measure the flicker in the current signal. The asymmetry of the current is calculated by comparing the positive peak to the negative peak, for each cycle: the moving window length is half a cycle. Both values are used as a signature of arcing. The result is filtered and compared with a suitable detection threshold.The algorithm was tested by traces of normal load, and no-load current disturbed by currents of faults on dry and wet soil, arc welders, computers, and fluorescent light loads, as well as short circuit currents. The algorithm performed well under the test conditions, except for the arc welder load. This load is also a source of insecurity for other algorithms. The detection criterion will be integrated with another detection method to improve the security during arcing load events.On-line testing is required to demonstrate algorithm dependability.

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