Mathematical programming and resistor transformer diode networks
In this paper, we present results for networks with ideal transformers, conical diodes and resistors which are conical analogues of vector space based fundamental results for networks with ideal transformers and resistors. By a conical diode we mean a device which satisfies VD≤0, iD≥0, where VD, iD represent the voltage and current associated with the device. We show: 1) if we connect ideal transformers and conical diodes resulting in a 'transformer diode multiport' (TD-multiport) the permissible voltage vectors and current vectors at the exposed ports form complementary polar cones; and 2) if we connect across the ports of a TD-multiport a 1 Ω resistor in series with a voltage source Ei for the ith port (for each i), then the voltage vector appearing across the ports of the multiport would be the projection of the voltage source vector E onto the port voltage cone of the multiport.
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