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Limitations imposed on free-running parallel inverters by the interdependence of critical characteristics of the networks, transformers, and switching elements of these inverters are identified. The transformer's role within these networks with abruptly changing circuit configurations is related to the network's functional mechanism. Special attention is devoted to forms of "volatile" returnable energy stored within the intended paths of magnetic flux and to magnetic saturation effects in pertinent transformer cores that cause harmful current spikes at the termination of individual cycles of operation. Returnable magnetic energies stored in representative "square loop" iron and ferrite transformer cores per unit of volume, and in related air gaps are calculated and tabulated for comparison and reference. A method for mitigation of storage of unwanted magnetic energy and for the prevention of magnetic saturation in inverter transformer cores is presented; it is reinforced with quantitative relations and a report on experimental work.