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The paper provides a formulation and solution for the problem of optimizing power flows in polyphase power systems with significant source (line) impedance with the presence of linear and nonlinear loads. An optimal solution considering significant line impedance has been already obtained in recent works. Unfortunately, it relies on network and load parameters that are not easy to determine during operation. We developed an adaptive compensation scheme that relies only on measurements of the load voltage and current so as to allow precise control of the compensated load as well as the real power flowing out of the compensator, while reducing line losses to within a few percent of its theoretical minimum. Properties of the solution are illustrated for a three phase induction motor supplied with unbalanced voltages.