This presentation discusses the estimation of Thevenin equivalents based on current and voltage measurements. These measurements are taken as outputs of an unknown system and are used to estimate a Thevenin equivalent. We illustrate with a small DC system and the measurements used. The requirements on these measurements to avoid computational problems are given. We test the robustness of each estimation technique against very noisy measurements and the impacts of small changes in the measurements. The errors in the values estimated for the parameters are calculated. The extension of parameter estimation using PMU measurements across a transmission line is explored and the principal challenges are discussed.