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Transformer help

I'm doing an engineering design project for school in which our group will design a power distribution system for Ontario (a province in Canada).  We need to keep in mind the provincial budget for the task. 
We have figured the most cost-effective method to do this would be to improvise the existing power system.  Our group decided that digging up and replacing transmission lines would be extremely expensive and thus impractical (according to our calculations, it would take billions of dollars).  We have also researched and found that an improvement in one-tenth of the efficiency of one-million transformers in a single year would save 600 000 MW of power...but the average efficiency of transformers now is already 97%. 
We also know that much of the losses (winding and core) in transformers are attributed to hysteresis (part of the wire remains magnetized due to resistance of the metal wire).  To reduce hysteresis, we could either use superconducting wires, change the material of the wires to a metal with less resistance, or increase the gauge of the wire (whcih would make the wire heavier, and more costly) but this all seems either impractical or not innovative enough for a design project.
Does anyone know any other way to reduce hysteresis (esp. reduce it significantly)?  Does anyone have any other recommendations for our design project?  It'll be really helpful...

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