Mathematical model for predicting residential magnetic fields

This paper describes the development and testing of a mathematical model which enabled the value of the average magnetic flux density occurring inside a house to be determined from non-intrusive measurements made outside the house. The contributing sources were power frequency electrical currents in transmission lines, distribution lines, service drops, grounding systems, household wiring and domestic appliances. By combining their individual predicted magnetic flux densities, a mathematical model was derived, whose input variables were the measured value of the net current at the service drop entry to the house, two distances, and the number of adjacent service drops. The output variable was the resultant measured magnetic flux density. A comprehensive companion study was made of an initial cohort of 14 typical Sydney houses in which spot and continuous measurements of magnetic flux density and electrical current were made using both commercially available and specially designed instrumentation. A total of 12,190 measurements of magnetic flux density were made inside houses, and 2,790 were made externally, revealing that contributions from household wiring and domestic appliances were minimal. The maximum measured internal and external magnetic flux densities were 2.814 μT (28.14 mG) and 3.314 μT (33.14 mG) respectively. These values were less than 2% of the ICNIRP public reference level. The maximum measured currents were 27.12 A in a service drop line, and 12.99 A in a ground system. By using non-linear regression analysis, the data accumulated from nine houses were used to evaluate the weighting factors for each of the input variables. In four other houses tested by the model, the correlation coefficient between the predicted and measured sets of data was 0.97, thus validating the model. The correlation coefficient for all 13 houses was 0.98. This coefficient was substantially higher than that that of other investigators, due mainly to the inclusion of the number of adjacent service drops in the model. The reliability of the model was improved by restricting its use to houses in which the magnetic flux density exceeded 0.07 μT (0.7 mG), and by averaging the results of several houses.