A Recursive Solution for Power-Transmission Loss in DC-Powered Networks

This article presents a recursive solution to the power-transmission loss in DC-powered networks. In such a network, the load cannot be modeled as a fixed equivalent resistance value, since the switching regulator may draw more or less current based on the actual supply voltage to meet the power demand. Although the power-transmission loss itself is simply I2 RL, I, in turn, depends on the load’s supply voltage, which, in turn, depends on I, making it impossible to derive a closed-form solution by classical resistive network analysis in general. The proposed approach is to first derive a closed-form solution to I in the one-node topology using the quadratic formula. Next, we extend our solution to a locally daisy-chained (LDC) network, where the network is readily decomposable into stages, such that the solution combines the closed-form formula for the current stage with the recursive solution for the subsequent stages. We then generalize the LDC topology to trees. In practice, the solution converges quickly after a small number of iterations. It has been validated on real-life networks, such as power over controller area network (PoCAN).